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In [[ballistics]], the '''ballistic coefficient''' ('''BC''') of a body is a measure of its ability to overcome air resistance in flight.<ref>[http://arxiv.org/ftp/arxiv/papers/0705/0705.0389.pdf The Truth About Ballistic Coefficients]</ref>  It is [[inversely proportional]] to the negative acceleration &mdash; a high number indicates a low negative acceleration. This is roughly the same as saying that the projectile in question possesses low drag, although some meaning is lost in the generalization. BC is a function of mass, diameter, and [[drag coefficient]].
{{More footnotes|date=September 2008}}
[[File:Spectral lines en.PNG|thumb|Emission lines and absorption lines compared to a continuous spectrum.]]
In [[physics]], one thinks of '''atomic spectral line'''s from two viewpoints.


==Formulae==
* An '''emission line''' is formed when an electron makes a transition from a particular discrete [[energy level]] {{math|''E''<sub>2</sub>}} of an atom, to a lower energy level {{math|''E''<sub>1</sub>}}, emitting a photon of a particular energy and wavelength. A spectrum of many such photons will show an emission spike at the wavelength associated with these photons.
* An '''absorption line''' is formed when an electron makes a transition from a lower, {{math|''E''<sub>1</sub>}}, to a higher discrete energy state, {{math|''E''<sub>2</sub>}}, with a photon being absorbed in the process. These absorbed photons generally come from background continuum radiation and a spectrum will show a drop in the continuum radiation at the wavelength associated with the absorbed photons.


===General===
The two states must be [[bound state]]s in which the electron is bound to the atom, so the transition is sometimes referred to as a "bound–bound" transition, as opposed to a transition in which the electron is ejected out of the atom completely ("bound–free" transition) into a [[continuous spectrum|continuum]] state, leaving an [[ionization|ionized]] atom, and generating continuum radiation.
:<math>BC_{Physics} = \frac{M}{C_d \cdot A} = \frac{\rho \cdot l}{C_d}</math>


Where:
A [[photon]] with an energy equal to the difference {{math|''E''<sub>2</sub> - ''E''<sub>1</sub>}} between the energy levels is released or absorbed in the process. The frequency {{math|''ν''}} at which the spectral line occurs is related to the photon energy by Bohr's frequency condition <math>E_2-E_1=h\nu</math> where  {{math|''h''}} denotes [[Planck's constant]].<ref name="Bohr 1913">{{harvnb|Bohr|1913}}</ref><ref name="Einstein 1916">{{harvnb|Einstein|1916}}</ref><ref name="Sommerfeld 1923 43">{{harvnb|Sommerfeld|1923|p=43}}</ref><ref name ="Heisenberg 1925 108">{{harvnb|Heisenberg|1925|p=108}}</ref><ref name="Brillouin 1970 31">{{harvnb|Brillouin|1970|p=31}}</ref><ref name="Jammer 1989 113 115">{{harvnb|Jammer|1989|pages=113, 115}}</ref>
*''BC<sub>Physics</sub>'' = ballistic coefficient as used in physics and engineering
*''M'' = mass
*''A'' = cross-sectional area
*''C<sub>d</sub>'' = [[drag coefficient]]
*''<math>\rho</math> (rho)'' = average [[density]]
*''l'' = body length


===Ballistics===
== Emission and absorption coefficients ==
The formula for calculating the ballistic coefficient for small and large arms projectiles ''only'' is as follows:
An atomic spectral line refers to emission and absorption events in a gas in which <math>n_2</math> is the density of atoms in the upper energy state for the line, and <math>n_1</math> is the density of atoms in the lower energy state for the line.
:<math>BC_{Projectile} = \frac{m}{ d^2 \cdot i}</math> <ref>{{cite book | last = Moss, Leeming and Farrar| title = Brassey's Land Warfare Series: Military Ballistics | publisher = Royal Military College of Science, Shrivenham, UK | year = 1995 |page=86 | isbn = 978-1857530841 }}</ref>


Whereas:
The emission of atomic line radiation at frequency {{math|''ν''}} may be described by an [[emission coefficient]] <math>\epsilon</math> with units of energy/time/volume/solid angle. ''ε dt dV dΩ'' is then the energy emitted by a volume element <math>dV</math> in time <math>dt</math> into solid angle <math>d\Omega</math>. For atomic line radiation:
*''BC<sub>Projectile</sub>'' = ballistic coefficient as used in point mass trajectory from the Siacci method (less than 20 degrees).<ref>{{cite book | last = Cline | first = Donna | title = Exterior Ballistics Explained, Trajectories, Part 3 "Atmosphere" | publisher = Lattie Stone Ballistics | year = 2002 | page=39 }}</ref>
*''m'' = mass of bullet in '''kg''' or '''lb'''
*''d'' = measured cross section (diameter) of projectile in '''m''' or '''in'''
*''i'' = Coefficient of form


The Coefficient of form (''i'') can be derived by 6 methods and applied differently depending on the  trajectory models used: G Model, Bugless/Coxe; 3 Sky Screen; 4 Sky Screen; Target Zeroing; Doppler radar.<ref>{{cite book | last = Cline | first = Donna | title = Exterior Ballistics Explained, Trajectories, Part 3 "Atmosphere" | publisher = Lattie Stone Ballistics | year = 2002 | pages=43–48 }}</ref><ref>{{cite book | last = Rinker | first = Robert A.  | title = Understanding Firearm Ballistics; 3rd Edition | publisher = Mulberry House Publishing | year = 1999 |page=176 | isbn = 978-0964559844}}</ref>
:<math>\epsilon = \frac{h\nu}{4\pi}n_2 A_{21}\,</math>


Here are several methods to compute '''''i''''' or '''C<sub>d</sub>''':
where <math>A_{21}</math> is the '''Einstein coefficient''' for spontaneous emission, which is fixed by the intrinsic properties of the relevant atom for the two relevant energy levels.
:<math>i=\frac{2}{n} \cdot \sqrt{\frac{4n-1}{n}}</math> <ref>{{cite book | last = Cline | first = Donna | title = Exterior Ballistics Explained, Trajectories, Part 3 "Atmosphere" | publisher = Lattie Stone Ballistics | year = 2002 | page=44 }}</ref><ref>{{cite book | last = Rinker | first = Robert A.  | title = Understanding Firearm Ballistics; 3rd Edition | publisher = Mulberry House Publishing | year = 1999 |page=176 | isbn = 978-0964559844}}</ref><ref>''Textbook of Small Arms 1909'' (1909). Great Britain. War Office H.M. Stationery Office. ISBN 978-1847914217</ref>


Whereas:
The absorption of atomic line radiation may be described by an [[absorption coefficient]] <math>\kappa</math> with units of 1/length. The expression ''κ' dx'' gives the fraction of intensity absorbed for a light beam at frequency ''ν'' while traveling distance ''dx''. The absorption coefficient is given by:
*''i'' = Coefficient of form.
*''n'' = number of calibers of the projectile's ogive.


:Where ''n''  is unknown:
:<math>\kappa' = \frac{h\nu}{4\pi}~(n_1 B_{12}-n_2 B_{21}) \,</math>


::<math>n = \frac{(4 \cdot l^2 + 1)}{4}</math> <ref>{{cite book | last = Cline | first = Donna | title = Exterior Ballistics Explained, Trajectories, Part 3 "Atmosphere" | publisher = Lattie Stone Ballistics | year = 2002 | page=44 }}</ref>
where <math>B_{12}</math> and <math>B_{21}</math> are the Einstein coefficients for photo absorption and induced emission respectively. Like the coefficient <math>A_{21}</math>, these are also fixed by the intrinsic properties of the relevant atom for the two relevant energy levels. For thermodynamics and for the application of Kirchhoff's law, it is necessary that the total absorption be expressed as the algebraic sum of two components, described respectively by <math>B_{12}</math> and <math>B_{21}</math>, which may be regarded as positive and negative absorption, which are, respectively, the direct photon absorption, and what is commonly called stimulated or induced emission.<ref>Weinstein, M.A. (1960). On the validity of Kirchhoff's law for a freely radiating body, ''American Journal of Physics'', '''28''': 123-25.</ref><ref>Burkhard, D.G., Lochhead, J.V.S., Penchina, C.M. (1972). On the validity of Kirchhoff's law in a nonequilibrium environment, ''American Journal of Physics'', '''40''': 1794-1798.</ref><ref>Baltes, H.P. (1976). On the validity of Kirchhoff's law of heat radiation for a body in a nonequilibrium environment, Chapter 1, pages 1-25 of ''Progress in Optics XIII'', edited by E. Wolf, North-Holland, ISSN 00796638.</ref>


::Whereas:
The above equations have ignored the influence of the spectral line shape. To be accurate, the above equations need to be multiplied by the (normalized) spectral line shape, in which case the units will change to include a 1/Hz term.
:*''n'' = number of calibers of the projectile's ogive.
:*''l'' = length of the head (ogive) in number of calibers.


'''or'''
For conditions of thermodynamic equilibrium, together the number densities <math>n_2</math> and <math>n_1</math>, the Einstein coefficients, and the spectral energy density provide sufficient information to determine the absorption and emission rates.


A drag coefficient can also be calculated mathematically:
===Equilibrium conditions===
:<math> C_{d}= \frac{8}{ \rho \cdot v^2 \cdot \pi \cdot d^2}</math> <ref>{{cite book | last = Moss | first = Leeming and Farrar| title = Brassey's Land Warfare Series: Military Ballistics | publisher = Royal Military College of Science, Shrivenham, UK | location = Reading | year = 1995 |page=79 | isbn = 978-1857530841 }}</ref>


Whereas:
The number densities <math>n_2</math> and <math>n_1</math> are set by the physical state of the gas in which the spectral line occurs, including the local [[spectral radiance]] (or, in some presentations, the local spectral radiant energy density). When that state is either one of strict [[thermodynamic equilibrium]], or one of so-called 'local thermodynamic equilibrium',<ref>Milne, E.A. (1928). The effect of collisions on monochromatic radiative equilibrium, ''Monthly Notices of the Royal Astronomical Society'', '''88''': 493-502. [http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1928MNRAS..88..493M&db_key=AST&link_type=ABSTRACT&high=4c3363690619220]</ref><ref>[[Subrahmanyan Chandrasekhar|Chandrasekhar, S.]] (1950), p. 7.</ref><ref name="Mihalas Mihalas 1984">[http://www.filestube.com/9c5b2744807c2c3d03e9/details.html Mihalas, D., Weibel-Mihalas, B. (1984). ''Foundations of Radiation Hydrodynamics'', Oxford University Press, New York, ISBN 0-19-503437-6.]</ref> then the distribution of atomic states of excitation (which includes <math>n_2</math> and <math>n_1</math>) determines the rates of atomic emissions and absorptions to be such that [[Kirchhoff's law of thermal radiation|Kirchhoff's law of equality of radiative absorptivity and emissivity]] holds. In strict thermodynamic equilibrium, the radiation field is said to be [[black body|black-body]] radiation, and is described by [[Planck's law]]. For local thermodynamic equilibrium, the radiation field does not have to be a black-body field, but the rate of interatomic collisions must vastly exceed the rates of absorption and emission of quanta of light, so that the interatomic collisions entirely dominate the distribution of states of atomic excitation. Circumstances occur in which local thermodynamic equilibrium does not prevail, because the strong radiative effects overwhelm the tendency to the Maxwell-Boltzmann distribution of molecular velocities. For example, in the atmosphere of the sun, the great strength of the radiation dominates. In the upper atmosphere of the earth, at altitudes over 100 km, the rarity of intermolecular collisions is decisive.
*''C<sub>d</sub>'' = drag coefficient.
*''<math>\rho</math> (rho)'' = density of the projectile.
*''v'' = projectile velocity at range.
* ''[[π]] (pi) ≈ 3.14159
*''d'' = measured cross section (diameter) of projectile in '''m''' or '''in'''


'''or'''
In the cases of [[thermodynamic equilibrium]] and of [[local thermodynamic equilibrium]], the number densities of the atoms, both excited and unexcited, may be calculated from the [[Maxwell–Boltzmann distribution]], but for other cases, (e.g. [[laser]]s) the calculation is more complicated.


From standard physics as applied to “G” models:
== Einstein coefficients ==<!-- This section is linked from [[Stimulated emission]] -->
:<math>i = \frac{C_{G}}{C_{p}}</math> <ref>[http://www.exteriorballistics.com/ebexplained/4th/30.cfm Historical Summary]</ref>
In 1916, [[Albert Einstein]] proposed that there are three processes occurring in the formation of an atomic spectral line. The three processes are referred to as '''spontaneous emission''', '''stimulated emission''', and '''absorption'''. With each is associated an '''Einstein coefficient''' which is  a measure of the probability of that particular process occurring. Einstein considered the case of isotropic radiation of frequency {{math|''ν''}}, and spectral energy density {{math|''ρ'' (''ν'')}}.<ref name="Einstein 1916"/><ref>Loudon, R. (2000), Section 1.5, pp. 16–19.</ref> Note that in some treatments, the black-body spectral radiance is used rather than the spectral radiation energy density.<ref>[[Subrahmanyan Chandrasekhar|Chandrasekhar, S.]] (1950), p. 354.</ref><ref name="Mihalas Mihalas 1984"/>


Whereas:
===Spontaneous emission===
*''i'' = Coefficient of form.
{{main|Spontaneous emission}}
*''C<sub>G</sub>'' =  drag coefficient of 1.00 from any “G” model, reference drawing, projectile.<ref>''Reference Notes for Use in the Course in Gunnery and Ammunition'' (1917). Coast Artillery School U.S. Army, p12. ASIN B00E0UERI2</ref>
[[File:AtomicLineSpEm.png|thumb|180px|Schematic diagram of atomic spontaneous emission]]
*''C<sub>p</sub>'' = drag coefficient of the actual test projectile at range.
Spontaneous emission is the process by which an electron "spontaneously" (i.e. without any outside influence) decays from a higher energy level to a lower one.  The process is described by the Einstein coefficient ''A''<sub>21</sub> (''s''<sup>&minus;1</sup>) which gives the probability per unit time that an electron in state 2 with energy <math>E_2</math> will decay spontaneously to state 1 with energy <math>E_1</math>, emitting a photon with an energy {{math|''E''<sub>2</sub> − ''E''<sub>1</sub> {{=}} ''hν''}}. Due to the [[Uncertainty Principle#Energy-time uncertainty principle|energy-time uncertainty principle]], the transition actually produces photons within a narrow range of frequencies called the [[spectral linewidth]]. If <math>n_i</math> is the number density of atoms in state ''i''&nbsp; then the change in the number density of atoms in state 2 per unit time due to spontaneous emission will be:


===Commercial Use===
:<math>\left(\frac{dn_2}{dt}\right)_{\mathrm{spontaneous}}=-A_{21}n_2\,.</math>
This is formula for calculating the ballistic coefficient within smalls arms shooting community, but redundant to '''''BC<sub>Projectile</sub>''''':
:<math>BC_{Smallarms} = \frac{SD}{i}</math> <ref>''Berger Bullets Reloading Manual 1st Edition'' (2012), Berger Bullets LLC, p814</ref>


Whereas:
The same process results in increasing of the population of the state 1:
*''BC<sub>Smallarms</sub>'' = Ballistic coefficient 
*''SD'' = [[Sectional density]]
*''i'' = Coefficient of form (form factor <ref>''Hornady Handbook of Cartridge Reloading:Rifle,Pistol Vol. II'' (1973)| Hornady Manufacturing Company, Fourth Printing July 1978, p505</ref>)


==Historical Precedents of Ballistic Coefficient, Methods and the Standard Model Projectile “G”==
:<math>\left(\frac{dn_1}{dt}\right)_{\mathrm{spontaneous}}=A_{21}n_2\,.</math>
*Within this section, some of the mathematical terms and denotations are from historical references and not within Wikipedia standards. When needed, these terms and denotations shall be followed in bold font  to denote the accepted Wikipedia standard. All Ordnance size and velocities are nominal or averaged as is historically and mathematically customary.


===Background===
=== Stimulated emission ===
In 1537,  [[Niccolò Tartaglia]] did some test firing to determine the maximum angle and range for a [[Projectile|shot]]. His conclusion was near 45 degrees. He noted that the shot [[trajectory]] was continuously [[Parabola|curved]].<ref>[http://www.exteriorballistics.com/ebexplained/4th/30.cfm Historical Summary]</ref>
{{main|Stimulated emission}}
[[File:AtomicLineInEm.png|thumb|180px|Schematic diagram of atomic stimulated emission]]
[[Stimulated emission]] (also known as induced emission) is the process by which an electron is induced to jump from a higher energy level to a lower one by the presence of electromagnetic radiation at (or near) the frequency of the transition. From the thermodynamic viewpoint, this process must be regarded as negative absorption. The process is described by the Einstein coefficient <math>B_{21}</math> (J<sup>&minus;1</sup> m<sup>3</sup> s<sup>&minus;1</sup>), which gives the probability per unit time per unit spectral energy density of the radiation field that an electron in state 2 with energy <math>E_2</math> will decay to state 1 with energy <math>E_1</math>, emitting a photon with an energy {{math|''E''<sub>2</sub> − ''E''<sub>1</sub> {{=}} ''hν''}}. The change in the number density of atoms in state 1 per unit time due to induced emission will be:


In 1636, [[Galileo Galilei]] published results in "Dialogues Concerning Two New Sciences". He found that a falling body had a constant [[acceleration]]. This allowed Galileo to show that a bullet's trajectory was a curve.<ref>Galileo, Galilei, ''Dialogues Concerning Two New Science'' , 2010; pg Fourth Day , THE MOTION OF PROJECTILES, Digireads.com ISBN 978-1420938159</ref><ref>[http://www.exteriorballistics.com/ebexplained/4th/30.cfm Historical Summary]</ref>
:<math>\left(\frac{dn_1}{dt}\right)_{\mathrm{neg}\,\mathrm{absorb}}=B_{21}n_2 \rho(\nu)</math>


Circa 1665, [[Sir Isaac Newton]] derived the [[Drag|law of air resistance]] and stated it was [[Inverse-square law|inversely]] proportional to the air resistance. Newton's experiments on drag were through air and fluids. He showed that drag on shot increases proportionately with the density of the air (or the fluid), cross sectional area and weight of the shot. Newton’s experiments were only at low velocities to about {{convert|260|m/s|ft/s|0|abbr=on}}.<ref>Bashforth, Francis, ''A revised account of the experiments made with the Bashforth chronograph...'', 1890; pg 1, Cambridge at the University Press</ref><ref>William and Robert Cambers; ''CHAMBERS'S ENCYCLOPAEDIA Vol. VIII'', 1891; pg 438, J.B. Lippincott, USA</ref><ref>Pejsa, Arthur, ''New Exact Small Arms Ballistics: The Source Book for Riflemen'', 2008; pg29,  Kenwood Publishing ISBN 978-0974990262</ref>
<br style="clear:both;" />
where <math>\rho(\nu)</math> denotes the spectral energy density of the isotropic radiation field at the frequency of the transition (see [[Planck's law]]).


In 1718, [[John Keill]] challenged the Continental Mathematica, ''“To find the curve that a projectile may describes in the air, on behalf of the simplest assumption of [[Gravity of Earth|gravity]], and the [[density]] of the medium uniform, on the other hand, in the duplicate ratio of the [[velocity]] of the resistance”'' This challenge supposes that air resistance is increases exponentially to the velocity of a projectile. Keill gave no solution for his challenge. [[Johann Bernoulli]] took up this challenge and soon thereafter solved the problem and air resistance varied as “any power” of velocity; known as the [[Bernoulli differential equation|Bernoulli equation]]. This is the precursor to the concept of the “standard projectile”.<ref>Bashforth, Francis, ''A revised account of the experiments made with the Bashforth chronograph...'', 1890; pg 1, Cambridge at the University Press</ref>
Stimulated emission is one of the fundamental processes that led to the development of the [[laser]]. Laser radiation is, however, very far from the present case of isotropic radiation.


In 1742, [[Benjamin Robins]] invented the [[ballistic pendulum]]. This was  a simple mechanical device that could measure a projectiles velocity. Robins reported muzzle velocities ranging from {{convert|1400|ft/s|m/s|0|abbr=on}} to {{convert|1700|ft/s|m/s|0|abbr=on}}. In his book published that same year “New Principles of Gunnery”, he uses numerical integration from [[Euler method|Euler's method]] and found that air resistance “varies as the square of the velocity, but insists it changes at the [[speed of sound]].” <ref>Bashforth, Francis, ''A revised account of the experiments made with the Bashforth chronograph...'', 1890; pg 4, 6, Cambridge at the University Press</ref><ref>[http://www.exteriorballistics.com/ebexplained/4th/30.cfm Historical Summary]</ref><ref>Pejsa, Arthur, ''Modern Practical Ballistics 2nd Edition'', 1991; pg6,  Kenwood Publishing ISBN 978-0961277635</ref>
=== Photo absorption ===
{{main|Absorption (optics)}}
[[File:AtomicLineAb.png|thumb|180px|Schematic diagram of atomic absorption]]
Absorption is the process by which a photon is absorbed by the atom, causing an electron to jump from a lower energy level to a higher one. The process is described by the Einstein coefficient <math>B_{12}</math> (J<sup>&minus;1</sup> m<sup>3</sup> s<sup>&minus;1</sup>), which gives the probability per unit time per unit spectral energy density of the radiation field that an electron in state 1 with energy <math>E_1</math> will absorb a photon with an energy {{math|''E''<sub>2</sub> − ''E''<sub>1</sub> {{=}} ''hν''}} and jump to state 2 with energy <math>E_2</math>. The change in the number density of atoms in state 1 per unit time due to absorption will be:


In 1753, [[Leonhard Euler]]  showed how a theoretical trajectories might be calculated using his method as applied to the Bernoulli equation, but only for resistance varying as the square of the velocity.<ref>Bashforth, Francis, ''A revised account of the experiments made with the Bashforth chronograph...'', 1890; pg 6, Cambridge at the University Press</ref>
:<math>\left(\frac{dn_1}{dt}\right)_{\mathrm{pos}\,\mathrm{absorb}}=-B_{12}n_1 \rho(\nu)</math>
<br style="clear:both;" />


In 1844, the [[Gun chronograph|Electro-ballistic chronograph]] was invented and by 1867 the electro-ballistic chronograph was accurate to with in one ten millionth of a second.<ref>Bashforth, Francis, ''A revised account of the experiments made with the Bashforth chronograph...'', 1890; pg 13, Cambridge at the University Press</ref>
== Detailed balancing ==
The Einstein coefficients are fixed probabilities associated with each atom, and do not depend on the state of the gas of which the atoms are a part. Therefore, any relationship that we can derive between the coefficients at, say, thermodynamic equilibrium will be valid universally.


===Test Firing===
At thermodynamic equilibrium, we will have a simple balancing, in which the net change in the number of any excited atoms is zero, being balanced by loss and gain due to all processes. With respect to bound-bound transitions, we will have [[detailed balance|detailed balancing]] as well, which states that the net exchange between any two levels will be balanced. This is because the probabilities of transition cannot be affected by the presence or absence of other excited atoms. Detailed balance (valid only at equilibrium) requires that the change in time of the number of atoms in level 1 due to the above three processes be zero:
Many countries and their militaries carried out test firings from the mid eighteenth century on using large [[ordnance ammunition|ordnance]] to determine the [[drag]] characteristics of each individual projectile. These individual test firings were logged and reported in extensive ballistics tables.<ref>Bashforth, Francis, ''A revised account of the experiments made with the Bashforth chronograph...'', 1890; pg 5-11, Cambridge at the University Press</ref><ref>Cline, Donna, ''Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient'', 2002; pg 39, Lattie Stone Ballistics</ref>


Of the test firing, most notably were: Francis Bashforth at Woolwich Marshes & Shoeburyness, England  (1864-1889) with velocities to {{convert|2800|ft/s|m/s|0|abbr=on}} and M. Krupp (1865-1880) of [[Krupp|Friedrich Krupp AG]] at Meppen, Germany, Friedrich Krupp AG continued these test firings to 1930; to a lesser extent General Nikolai V. Mayevski, then a Colonel (1868-1869) at St. Petersburg, Russia; the Commission d'Experience de Gâvre (1873 to 1889)  at Le Gâvre, France with velocities to {{convert|1830|m/s|ft/s|0|abbr=on}} and the The [[Royal Artillery|British Royal Artillery]] (1904-1906).<ref>Bashforth, Francis; ''Reports on experiments made with the Bashforth chronograph...'', 1878-1879; pg Protest, 1, H.M Stationary Office, Harrison & Sons, London</ref><ref>Bashforth, Francis, ''A revised account of the experiments made with the Bashforth chronograph...'', 1890; pg 13, 135, Cambridge at the University Press</ref><ref>Ingalls, James M., ''Exterior Ballistics in the Plan Fire'', 1886; pg18,19, D. Van Nostrand Publisher</ref><ref>[http://www.exteriorballistics.com/ebexplained/4th/30.cfm Historical Summary]</ref><ref>Cline, Donna, ''Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient'', 2002; pg 39-40, Lattie Stone Ballistics</ref>
:<math>0=A_{21}n_2+B_{21}n_2\rho(\nu)-B_{12}n_1 \rho(\nu)\,</math>


The test projectiles (shot) used, vary from [[spherical]], [[spheroidal]], [[Ogive|ogival]]; being hollow, solid and cored in design with the elongated ogival-headed projectiles having 1, 1½, 2 and 3 [[caliber]] [[Radius|radii]]. These projectiles varied in size from, {{convert|75|mm|in|1|abbr=on}} at {{convert|3|kg|lbs|1|abbr=on}} to {{convert|254|mm|in|1|abbr=on}} at {{convert|187|kg|lbs|1|abbr=on}} <ref>Bashforth, Francis; ''Reports on experiments made with the Bashforth chronograph...'', 1878-1879; pg 3-4, H.M Stationary Office, Harrison & Sons, London</ref><ref>Bashforth, Francis, ''A revised account of the experiments made with the Bashforth chronograph...'', 1890; pg 36, 135, Cambridge at the University Press</ref><ref>Ingalls, James M., ''Exterior Ballistics in the Plan Fire'', 1886; pg19, D. Van Nostrand Publisher</ref>
Along with detailed balancing, at temperature {{math|''T''}} we may use our knowledge of the equilibrium energy distribution of the atoms, as stated in the [[Maxwell–Boltzmann distribution]], and the equilibrium distribution of the photons, as stated in [[Planck's law of black body radiation]] to derive universal relationships between the Einstein coefficients.


===Methods and the Standard Projectile===
From the Maxwell–Boltzmann distribution we have for the number of excited atomic species ''i'':
Many military's up until the 1860s had to used [[calculus]] to compute a bullet trajectory. The numerical computations necessary to calculate just a single trajectory was lengthy, tedious and done by hand. So, an investigation  to develop a theoretical drag model began. This competition did lead to a major simplification in the experimental treatment of drag. This was the concept of a “standard projectile”. The ballistic tables are made up for a [[Artificiality|factitious]] projectile being defined as: "a factitious weight and with a specific shape and specific dimensions in a ratio of calibers." This simplifies calculation for the ballistic coefficient of a standard model projectile, which could mathematically move through the [[Atmosphere|standard atmosphere]] with the same ability as any actual projectile could move through the actual atmosphere.<ref>Ingalls, James M., ''Exterior Ballistics in the Plan Fire'', 1886; pg8, D. Van Nostrand Publisher</ref><ref>Coast Artillery School Press, ''Reference Notes for Use in the Course in Gunnery and Ammunition'', 1917; pg 12, Coast Artillery School, ASIN:B00E0UERI2</ref><ref>[http://www.exteriorballistics.com/ebexplained/4th/30.cfm Historical Summary]</ref>


====The Bashforth Method====
:<math>\frac{n_i}{n}= \frac{g_i e^{-E_i/kT}}{Z}</math>
In 1870, Bashforth publishes a report containing his ballistic tables. Bashforth found that the drag of his test projectiles varied with the square of  velocity (v<sup>2</sup>) from {{convert|830|ft/s|m/s|0|abbr=on}} to {{convert|430|ft/s|m/s|0|abbr=on}} and with the cube of velocity (v<sup>3</sup>) from {{convert|1000|ft/s|m/s|0|abbr=on}} to {{convert|830|ft/s|m/s|0|abbr=on}}. As of his 1880 report, he found that drag varied by v<sup>6</sup>  from {{convert|1100|ft/s|m/s|0|abbr=on}} to {{convert|1040|ft/s|m/s|0|abbr=on}}. Bashforth used [[Rifling|rifled]] guns of {{convert|3|in|mm|0|abbr=on}}, {{convert|5|in|mm|0|abbr=on}}, {{convert|7|in|mm|0|abbr=on}} and {{convert|9|in|mm|0|abbr=on}};  smooth-bore guns of similar caliber for firing spherical shot and howitzers propelled elongated projectiles having an ogival-head of 1½ caliber radius.<ref>Bashforth, Francis; ''Reports on experiments made with the Bashforth chronograph...'', 1878-1879; pg 4, H.M Stationary Office, Harrison & Sons, London</ref><ref>Bashforth, Francis, ''A revised account of the experiments made with the Bashforth chronograph...'', 1890; pg 135-136, Cambridge at the University Press</ref><ref>Ingalls, James M., ''Exterior Ballistics in the Plan Fire'', 1886; pg19, D. Van Nostrand Publisher</ref>


Bashforth uses ''b'' as the variable for ballistic coefficient.  When ''b'' is equal to or less than v<sup>2</sup>, then ''b'' is equal to ''P'' for the drag of a projectile. It would be found that air does not deflect off the front of a projectile in the same direction, when there are of differing shapes. This prompted the introduction of a second factor to ''b'', the coefficient of form (''i''). This is particularly true at high velocities, greater than {{convert|830|ft/s|m/s|0|abbr=on}}. Hence, Bashforth introrduced the “undetermined multiplier” of any power called the <math>k</math> [[Factor graph|factor]] that compensate for this unknown effects of drag above {{convert|830|ft/s|m/s|0|abbr=on}}; <math>k > i </math>.  Bashforth then integrated <math>k</math> and <math>i</math> as <math>K_v</math>.<ref>Bashforth, Francis; ''Reports on experiments made with the Bashforth chronograph...'', 1878-1879; pg 3,5-6, H.M Stationary Office, Harrison & Sons, London</ref><ref>Bashforth, Francis, ''A revised account of the experiments made with the Bashforth chronograph...'', 1890; pg 1, Cambridge at the University Press</ref><ref>Ingalls, James M., ''Exterior Ballistics in the Plan Fire'', 1886; pg7-8, 31, 136, D. Van Nostrand Publisher</ref><ref>[http://mrpogson.com/homepage/ballistics.html]</ref>
where ''n'' is the total number density of the atomic species, excited and unexcited, ''k'' is [[Boltzmann's constant]], ''T'' is the [[temperature]], <math>g_i</math> is the degeneracy (also called the multiplicity) of state ''i'', and ''Z'' is the [[partition function (statistical mechanics)|partition function]]. From Planck's law of black-body radiation at temperature {{math|''T''}} we have for the spectral energy density at frequency {{math|''ν''}}


Although Bashforth did not conceive the “restricted zone”, he showed mathematically there were 5 restricted zones. Bashforth did not propose a standard projectile, but was well aware of the concept.<ref>Bashforth, Francis; ''Reports on experiments made with the Bashforth chronograph...'', 1878-1879; pg 5-6, H.M Stationary Office, Harrison & Sons, London</ref>
:<math>\rho_\nu(\nu,T)=F(\nu)\frac{1}{e^{h\nu/kT}-1}</math>


====The Mayevski/Siacci Method====
where:
In 1872, General Mayevski published his report ''Trité Balistique Extérieure'', which included the Mayevski model. Using his ballistic tables along with Bashforth's tables from the 1870 report, Mayevski created an analytical math formula that calculated the air resistances of a projectile in terms of [[Logarithm|log A]] and the [[Variable (mathematics)|value]] ''n''. Although Mayevski's math used a differing approach than Bashforth, the resulting calculations of air resistance was the same. Mayevski proposed the restricted zone concept and found there to be 6 restricted zones for projectiles .<ref>Bashforth, Francis, ''A revised account of the experiments made with the Bashforth chronograph...'', 1890; pg pgvii, Cambridge at the University Press</ref><ref>Ingalls, James M., ''Exterior Ballistics in the Plan Fire'', 1886; pg14,18-31, D. Van Nostrand Publisher</ref><ref>Mayevski, Nikolai V, ''Trité Balistique Extérieure'' , 1872; pg58, 133 of the Schedules, Gauthier-Villars, Printer Bookseller office longitudes of the Polytechnic School, (Translated from French )</ref><ref>[http://www.exteriorballistics.com/ebexplained/4th/30.cfm Historical Summary]</ref><ref>Cline, Donna, ''Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient'', 2002; pg 40, Lattie Stone Ballistics</ref>


Circa 1886, General Mayevski published the results from a discussion of experiments made by M. Krupp (1880). Though the ogival-headed projectiles used varied greatly in caliber, they were essential of the same as the standard projectile, being mostly 3 caliber in length, with an ogive of 2 calibers radius. Giving the standard projectile dimensionally as {{convert|10|cm|in|1|abbr=on}} and {{convert|1|kg|lbs|1|abbr=on}}.<ref>Ingalls, James M., ''Exterior Ballistics in the Plan Fire'', 1886; pg19, D. Van Nostrand Publisher</ref><ref>Mayevski, Nikolai V, ''Trité Balistique Extérieure'' , 1872; pg58, Gauthier-Villars, Printer Bookseller office longitudes of the Polytechnic School, (Translated from French )</ref><ref>Siacci, Francesco,''Balistica; Second edition entirely recast'' , 1888; pg7, Torino F.Casanova, Publisher bookseller Via Academy of Sciences, (Translated from Italian and Latin)</ref>
:<math>F(\nu)=\frac{8\pi h\nu^3}{c^3}</math>


In 1880, Colonel [[Francesco Siacci]] published his work “Balistica”. Siacci found as did those who came before him that the resistance and density of the air becomes greater and greater as a projectile displaced the air at higher and higher velocities.<ref>Siacci, Francesco,''Balistica; Second edition entirely recast'' , 1888; pg3, Torino F.Casanova, Publisher bookseller Via Academy of Sciences, (Translated from Italian and Latin)</ref>
where <math>c</math> is the [[speed of light]] and <math>h</math> is [[Planck's constant]].


Siacci's method was for flat-fire trajectories with angles of departure of less than 20 degrees. He found that the angle of departure is sufficiently small to allow for air density to remain the same and was able to reduce the ballistics tables to easily tabulated quadrants giving distance, time, inclination and altitude of the projectile. Using Bashforth's ''k'' and Mayevski's tables, Siacci created a 4 zone model. Siacci used Mayevski's standard projectile. From this method and standard projectile, Siacci formulated a short cut.<ref>Siacci, Francesco, ''Balistica; Second edition entirely recast'' , 1888; pg5,8, Torino F.Casanova, Publisher bookseller Via Academy of Sciences, (Translated from Italian and Latin)</ref><ref>[http://www.exteriorballistics.com/ebexplained/4th/30.cfm Historical Summary]</ref><ref>Cline, Donna, ''Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient'', 2002; pg 39, Lattie Stone Ballistics</ref>
Substituting these expressions into the equation of detailed balancing and remembering that {{math|''E''<sub>2</sub> − ''E''<sub>1</sub> {{=}} ''hν''}} yields:


Siacci found that within a low velocity restricted zone, projectiles of similar shape, and velocity in the same air density behave similar; <math>\tfrac{\delta w}{d^2}</math> or <math>\tfrac{\delta}{C}</math>. Siacci used the variable <math>C</math> for ballistic coefficient.  Meaning, air density is the generally the same for flat-fire trajectories, thus sectional density is equal to the ballistic coefficient and air density can be dropped. Then as the velocity rises to Bashforth's <math>k</math> for high velocity when <math>C</math> requires the introduction of <math>i</math>. Following within today's currently used ballistic trajectory tables for an average ballistic coeficient: <math>\tfrac{m}{d^2} \cdot \tfrac{p_0}{p}</math> would equal <math>\tfrac{m}{d^2 i}</math> equals <math>\tfrac{SD}{i}</math> as <math>BC</math>.<ref>Siacci, Francesco,''Balistica; Second edition entirely recast'' , 1888; pg4, Torino F.Casanova, Publisher bookseller Via Academy of Sciences, (Translated from Italian and Latin)</ref><ref>Cline, Donna, ''Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient'', 2002; pg 42, Lattie Stone Ballistics</ref>
:<math>A_{21}g_2e^{-h\nu/kT}+B_{21}g_2e^{-h\nu/kT}\frac{F(\nu)}{e^{h\nu/kT}-1}=
B_{12}g_1\frac{F(\nu)}{e^{h\nu/kT}-1}</math>


Siacci wrote that within any restricted zone, ''C'' being the same for two or more projectiles, the trajectories differences will be minor. Therefore ''C'' agrees with an average curve, and this average curve applies for all projectiles. Therefore, a single trajectory can be computed for the standard projectile without having to resort to tedious calculus methods, and then a trajectory for any actual bullet with known ''C'' can be  computed from the standard trajectory with just simple [[algebra]].<ref>Siacci, Francesco,''Balistica; Second edition entirely recast'' , 1888; pg5, Torino F.Casanova, Publisher bookseller Via Academy of Sciences, (Translated from Italian and Latin)</ref><ref>[http://www.exteriorballistics.com/ebexplained/4th/30.cfm Historical Summary]</ref>
separating to:


==== The Ballistic Tables====
:<math>A_{21}g_2(e^{h\nu/kT}-1)+ B_{21}g_2F(\nu)= B_{12}g_1e^{h\nu/kT}F(\nu)\,</math>
The aforementioned ballistics tables are generally: functions, air density, projectile time at range, range, degree of projectile departure,  weight  and diameter to facilitate the calculation of ballistic [[formula]]e. These formulae produce the projectile velocity at range, drag and trajectories. The modern day commercially published ballistic tables or software computed ballistics tables for small arms, sporting ammunition are [[External ballistics|exterior ballistic]], trajectory tables.<ref>Bashforth, Francis; ''Reports on experiments made with the Bashforth chronograph...'', 1878-1879; H.M Stationary Office, Harrison & Sons, London</ref><ref>Bashforth, Francis, ''A revised account of the experiments made with the Bashforth chronograph...'', 1890; Cambridge at the University Press</ref><ref>Mayevski, Nikolai V, ''Trité Balistique Extérieure'' , 1872; pg i of the Schedules, Gauthier-Villars, Printer Bookseller office longitudes of the Polytechnic School, (Translated from French )</ref>


The 1870 Bashforth tables were to {{convert|2800|ft/s|m/s|0|abbr=on}}. Mayevski, using his tables, supplemented by the Bashforth tables (to 6 restricted zones) and the Krupp tables. Mayevski conceived a 7th restricted  zone and extended the Bashforth tables to {{convert|1100|m/s|ft/s|0|abbr=on}}.  Mayevski converted Bashforth's data from [[Imperial units|Imperial units of measure]] to [[Metric system|metric units of measure]] (now in [[International System of Units|SI units of measure]]). In 1884, [[James Monroe Ingalls|James Ingalls]] published his tables in the U.S. Army Artillery Circular M using the Mayevski tables. Ingalls extended Mayevski's ballistics tables to {{convert|5000|ft/s|m/s|0|abbr=on}} within an 8th restricted zone, but still with the same ''n'' value (1.55) as Mayevski's 7th restricted  zone. Ingalls, converted Mayevski's results back to Imperial units. The British [[Royal Artillery]] results were very similar to those of Mayevski's and extended their tables to {{convert|5000|ft/s|m/s|0|abbr=on}} within the 8th restricted zone changing the ''n'' value from 1.55 to 1.67. These ballistic tables were published in 1909 and almost identical to those of those of Ingalls. In 1971 the Sierra Bullet company calculated their ballistic tables to 9 restricted zones but only within {{convert|4400|ft/s|m/s|0|abbr=on}}.<ref>Ingalls, James M., ''Exterior Ballistics in the Plan Fire'', 1886; pg19, D. Van Nostrand Publisher</ref><ref>[http://www.exteriorballistics.com/ebexplained/4th/30.cfm Historical Summary]</ref><ref>Cline, Donna, ''Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient'', 2002; pg 40, Lattie Stone Ballistics</ref>
The above equation must hold at any temperature, so


====The G Model====
:<math>A_{21}g_2 = B_{12}g_1F(\nu)\,</math>
In 1881, the Commission d'Experience de Gâvre did a comprehensive survey of data available from their tests as well as other countries. After adopting a standard atmospheric condition for the drag data the Gavre drag function was adopted. This drag function was known as the Gavre function and the standard projectile adopted was the Type 1 projectile. Thereafter, the Type 1 standard projectile was renamed by Ballistics Section of [[Aberdeen Proving Grounds]] in Maryland, USA as G<sub>1</sub> after the Commission d'Experience de Gâvre. For practical purposes the subscript 1 in G<sub>1</sub> is generally written in normal font size as G1.<ref>[http://www.exteriorballistics.com/ebexplained/4th/30.cfm Historical Summary]</ref><ref>Cline, Donna, ''Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient'', 2002; pg 40, Lattie Stone Ballistics</ref>


The general form for the calculations of trajectory adopted for the G model is the Siacci method. The standard model projectile is a "fictitious projectile"  used as mathematical basis for the calculation of actual projectile's trajectory when an initial velocity is known. The G1 model projectile adopted is in dimensionless measures of  2 caliber radius ogival-head and 3.28 caliber in length. By calculation this leaves the body length 1.96 caliber and head, 1.32 caliber long.<ref>Coast Artillery School Press, ''Reference Notes for Use in the Course in Gunnery and Ammunition'', 1917; pg 12, Coast Artillery School, ASIN:B00E0UERI2</ref><ref>[http://www.exteriorballistics.com/ebexplained/4th/30.cfm Historical Summary]</ref>
:<math>- A_{21}g_2 + B_{21}g_2F(\nu) = 0\,</math>


Over the years there has been some confusion{{cn|date=November 2014}} as to adopted size, weight and radius ogival-head of the G1 standard projectile. This misconception may be explained by Colonel Ingalls in the 1886 publication,  Exterior Ballistics in the Plan Fire; page 15, ''In the following tables the first and second columns give the velocities and corresponding resistance, in [[Pound (mass)|pounds]], to an elongated one inch in diameter and having an ogival head of one and a half calibers. They were deduced from Bashforth's experiments by Professor  A. G. Greenhill, and are taken from his papers published in the Proceedings of the Royal Artillery Institution, No 2, Vol. XIII.'' Further it is discussed that said projectile's [[weight]] was one pound.<ref>Ingalls, James M., ''Exterior Ballistics in the Plan Fire'', 1886; pg15, D. Van Nostrand Publisher</ref>
Therefore the three Einstein coefficients are interrelated by:


For the purposes of mathematical convenience for any standard projectile (G) the ''BC'' is 1.00. Where as the projectiles [[sectional density]] (SD) is dimensionless with a mass of 1 divided by the square of the diameter of 1 caliber equaling an SD of 1. Then the standard projectile is assigned a coefficient of form of 1. Following that <math>BC = \tfrac{SD}{i} = \tfrac{1}{1} = 1.00</math>.  ''BC'', as a general rule, within flat-fire trajectory, is carried out to 2 decimal points. ''BC'' is commonly found within commercial publications to be carried out to 3 decimal points as few sporting, small arms projectiles rise to the level of 1.00 for a ballistic coefficient.<ref>Coast Artillery School Press, ''Reference Notes for Use in the Course in Gunnery and Ammunition'', 1917; pg 12, Coast Artillery School, ASIN:B00E0UERI2</ref>
:<math>\frac{A_{21}}{B_{21}}=F(\nu)</math>


When using the Siacci method for diffing G models, the formula used to compute the trajectories is the same. What differs is retardation factors found through testing of actual projectiles that are similar in shape to the standard project reference. This creates slightly different set of retardation factors between differing G models. When the correct G model retardation factors are applied within the Siacci mathematical formula for the same G model ''BC'', a corrected trajectory can be calculated for any G model.
and


Another method of determining trajectory and ballistic coefficient was developed and published by Wallace H. Coxe and Edgar Beugless of DuPont in 1936. This method is by shape comparison an logarithmic scale as drawn on 10 charts. The method estimates the ballistic coefficient related to the drag model of the Ingalls tables. When matching an actual projectile against the drawn caliber radii of Chart No. 1, it will provide ''i'' and by using Chart No. 2, ''C ''can be quickly calculated. Coxe and Beugless used the variabale ''C'' for ballistic coefficient.<ref>Coxe, Wallace H. and Bugless, Edgar, ''Exterior Balistics Charts'', 1936; pg Charts 1, 2 , Ballistic Engineers of the Burnside Laboratory, of E.I. Du Pont De Nemours & Company Inc., Wilmington, Delaware</ref><ref>[http://www.exteriorballistics.com/ebexplained/4th/30.cfm Historical Summary]</ref>
:<math>\frac{B_{21}}{B_{12}}=\frac{g_1}{g_2}</math>


The Siacci method was abandoned by the end of the [[World War I]] for artillery fire. But the [[Ordnance Corps (United States Army)|U.S. Army Ordnance Corps]] continued using the Siacci method into the middle of the 20th century for [[Direct fire|direct (flat-fire)]] tank gunnery. The development of the [[Analog computer|electromechanical analog computer]] contributed to the calculation of aerial bombing trajectories during [[World War II]]. After World War II the advent of the [[Computer|silicon semiconductor based digital computer]] made it possible to create trajectories for the guided missiles/bombs, intercontinental ballistic missiles and space vehicles.<ref>[http://www.exteriorballistics.com/ebexplained/4th/30.cfm Historical Summary]</ref><ref>Cline, Donna, ''Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient'', 2002; pg 39, Lattie Stone Ballistics</ref>
When this relation is inserted into the original equation, one can also find a relation between <math>A_{21}</math> and <math>B_{12}</math>, involving [[Planck's law]].


Between World War I and II the U.S. Army Ballistics research laboratories at Aberdeen Proving Grounds, Maryland, USA developed the standard models for G2, G5, G6. In 1965, [[Olin Corporation|Winchester Western]] published a set of ballistics tables for G1, G5, G6 and GL. In 1971 [[Sierra Bullets|Sierra Bullet Company]] retested all their bullets and concluded that the G5 model was not the best model for their boat tail bullets and started using the G1 model. This was fortunate, as the entire commercial sporting and firearms industries had based their calculations on the G1 model. The G1 model and Mayevski/Siacci Method continue to be the industry standard today. This benefit allows for comparison of all ballistic tables for trajectory within the commercial sporting and firearms industry.<ref>[http://www.exteriorballistics.com/ebexplained/4th/30.cfm Historical Summary]</ref><ref>Cline, Donna, ''Exterior Ballistics Explained, Trajectories, Part 3 “Atmosphere" The “Point-Mass Trajectory: The Siacci Method Ballistic Coefficient'', 2002; pg 42, Lattie Stone Ballistics</ref>
== Oscillator strengths ==
The oscillator strength <math>f_{12}</math> is defined by the following relation to the cross section <math>a_{12}</math> for absorption:


In recent years there have been vast advancements in the calculation of flat-fire trajectories with the advent of [[Doppler radar]] and the personal computer and handheld comuting devices.  Also, the newer [[External_ballistics#Pejsa_model|methodology]] proposed by Dr. Arthur Pejsa and the use of the G7 model used by Mr. Brian Litz, ballistic engineer for Berger Bullets, LLC for calculating boat tailed spitzer rifle bullet trajectories have improved the prediction of flat-fire trajectories.<ref>[http://www.exteriorballistics.com/ebexplained/4th/30.cfm Historical Summary]</ref><ref>Pejsa, Arthur, ''Modern Practical Ballistics 2nd Edition'', 1991;  Kenwood Publishing ISBN 978-0961277635</ref><ref>''Berger Bullets Reloading Manual 1st Edition'' 2012; Berger Bullets LLC; p161, ISBN 978-0-615-63762-4</ref>
:<math>a_{12}=\frac{\pi e^2}{m_e c}\,f_{12}</math>


==Differing mathematical models and bullet ballistic coefficients==
where <math>e</math> is the electron charge and <math>m_e</math> is the electron mass. This allows all three Einstein coefficients to be expressed in terms of the single oscillator strength associated with the particular atomic spectral line:
[[File:G1 Shape Standard Projectile Measurements in Calibers.png|thumb| G1 shape standard projectile. All measurements in calibers/diameters.]]
[[File:G7 Shape Standard Projectile Measurements in Calibers.png|thumb| G7 shape standard projectile. All measurements in calibers/diameters.]]


[[File:Effect of BC on Wind Drift.jpg|thumb| Wind drift calculations for rifle bullets of differing G1 BCs fired with a muzzle velocity of {{convert|2950|ft/s|abbr=on}} in a {{convert|10|mph|abbr=on}} crosswind.<ref>[http://www.jbmballistics.com/cgi-bin/jbmtraj-5.1.cgi JBM Ballistics online trajectory calculator]</ref>]]
:<math>B_{12}=\frac{4\pi^2 e^2}{m_e h\nu c}\,f_{12}</math>
[[File:Effect of BC on Energy Retained.jpg|thumb|Energy calculations for {{convert|140|gr|disp=flip}} rifle bullets of differing G1 BCs fired with a muzzle velocity of {{convert|2950|ft/s}}.<ref>[http://www.jbmballistics.com/cgi-bin/jbmtraj-5.1.cgi JBM ballistics online trajectory calculator]</ref>]]


Most ballistic mathematical models and hence tables or software take for granted that one specific drag function correctly describes the drag and hence the flight characteristics of a bullet related to its ballistic coefficient. Those models do not differentiate between [[wadcutter]], flat-based, [[spitzer bullet|spitzer]], boat-tail, [[very-low-drag bullet|very-low-drag]], etc. bullet types or shapes. They assume one invariable drag function as indicated by the published BC. Several different drag curve models optimized for several standard projectile shapes are available, however.<br>
:<math>B_{21}=\frac{4\pi^2 e^2}{m_e h\nu c}~\frac{g_1}{g_2}~f_{12}</math>
The resulting drag curve models for several standard projectile shapes or types are referred to as:
* G1 or Ingalls (flatbase with 2 caliber (blunt) nose ogive - by far the most popular)<ref>[http://www.shootingsoftware.com/coefficients.htm Exterior Ballistics and Ballistic Coefficients]</ref>
* G2 (Aberdeen J projectile)
* G5 (short 7.5° boat-tail, 6.19 calibers long [[Nose cone design#Tangent ogive|tangent ogive]])
* G6 (flatbase, 6 calibers long [[Nose cone design#Secant ogive|secant ogive]])
* G7 (long 7.5° boat-tail, 10 calibers tangent ogive, preferred by some manufacturers for very-low-drag bullets<ref>[http://02b0516.netsolhost.com/blog1/?p=62 A Better Ballistic Coefficient by Bryan Litz, Ballistician Berger Bullets]</ref>)
* G8 (flatbase, 10 calibers long secant ogive)
* GL (blunt lead nose)


Since these standard projectile shapes differ significantly the G''x'' BC will also differ significantly from the G''y'' BC for an identical bullet.<ref>[http://www.shootersforum.com/ballistics-internal-external/61432-ballistic-coefficient-basics.html Ballistic Coefficient Basics]</ref>  To illustrate this the bullet manufacturer [[berger bullets|Berger]] has published the G1 and G7 BCs for most of their target, tactical, varmint and hunting bullets.<ref>[http://www.bergerbullets.com/products/all-bullets/ Berger Bullets Technical Specifications]</ref> Other manufacturers like Lapua and Nosler also started to publish the G1 and G7 BCs for most of their target bullets.<ref>[http://www.lapua.com/en/products/reloading Lapua bullets technical information]</ref><ref>[http://www.nosler.com/Bullets/AccuBond_LongRange.aspx Nosler AccuBond Longe Range technical information]</ref> How much a projectile deviates from the applied reference projectile is mathematically expressed by the form factor (''i''). The applied reference projectile shape always has a form factor (''i'') of exactly 1. When a particular projectile has a sub 1 form factor (''i'') this indicates that the particular projectile exhibits higher drag than the applied reference projectile shape. A form factor (''i'') greater than 1 indicates the particular projectile exhibits lower drag than the applied reference projectile shape.<ref>[http://www.bergerbullets.com/form-factors-a-useful-analysis-tool/ Form Factors: A Useful Analysis Tool by Bryan Litz, Chief Ballistician Berger Bullets]</ref> In general the G1 model yields comparatively high BC values and is often used by the sporting ammunition industry.
:<math>A_{21}=\frac{8\nu^2 \pi^2 e^2}{m_e c}~\frac{g_1}{g_2}~f_{12}</math>


===The transient nature of bullet ballistic coefficients===
== See also ==
Variations in BC claims for exactly the same projectiles can be explained by differences in the ambient [[air density]] used to compute specific values or differing range-speed measurements on which the stated G1 BC averages are based. Also, the BC changes during a projectile's flight, and stated BCs are always averages for particular range-speed regimes. Further explanation about the variable nature of a projectile's G1 BC during flight can be found at the [[external ballistics]] article. The external ballistics article implies that knowing how a BC was determined is almost as important as knowing the stated BC value itself.
* [[Transition dipole moment]]
* [[Oscillator strength]]
* [[Breit–Wigner distribution]]
* [[Electronic configuration]]
* [[Fano resonance]]
* [[Siegbahn notation]]
* [[Atomic spectroscopy]]
* [[Molecular radiation]], continuous spectra emitted by molecules


For the precise establishment of BCs (or perhaps the scientifically better expressed [[drag coefficient]]s), [[Doppler radar]]-measurements are required. The normal shooting or aerodynamics enthusiast, however, has no access to such expensive professional measurement devices. Weibel 1000e or Infinition BR-1001 [[Doppler radar]]s are used by governments, professional ballisticians, defense forces, and a few ammunition manufacturers to obtain exact real world data on the flight behavior of projectiles of interest.
== References ==
{{reflist}}


Doppler radar measurement results for a lathe turned monolithic solid .50 BMG [[very-low-drag bullet]] (Lost River J40 {{convert|0.510|in|disp=flip}}, {{convert|773|gr|disp=flip}} monolithic solid bullet / twist rate 1:{{convert|15|in|disp=flip}}) look like this:
=== Cited bibliography ===
{{refbegin}}
*{{cite journal
|last1=Bohr |first1=N.
|author1-link=Niels Bohr
|year=1913
|title=On the constitution of atoms and molecules
|url=http://www.ffn.ub.es/luisnavarro/nuevo_maletin/Bohr_1913.pdf
| doi = 10.1080/14786441308634993
|journal=[[Philosophical Magazine]]
|volume=26 |pages=1–25
|ref=harv
}}
*{{cite book
|last1=Brillouin |first1=L.
|author1-link=Léon Brillouin
|year=1970
|title=Relativity Reexamined
|publisher=[[Academic Press]]
|isbn=978-0-12-134945-5
|ref=harv
}}
*[[Subrahmanyan Chandrasekhar|Chandrasekhar, S.]] (1950). ''Radiative Transfer'', Oxford University Press, Oxford.
*{{cite journal | author=Einstein, A.  |author1-link=Albert Einstein| title=Strahlungs-Emission und -Absorption nach der Quantentheorie |journal=Verhandlungen der Deutschen Physikalischen Gesellschaft |volume= 18|pages= 318–323  | year=1916|bibcode = 1916DPhyG..18..318E }} Also {{cite journal
|last1=Einstein |first1=A.
|author1-link=Albert Einstein
|year=1916
|title=Zur Quantentheorie der Strahlung
|journal=[[Mitteilungen der Physikalischen Gessellschaft Zürich]]
|volume=18 |pages=47–62
|ref=harv
}} And a version nearly identical to the latter at {{cite journal
|last1=Einstein |first1=A.
|author1-link=Albert Einstein
|year=1917
|title=Zur Quantentheorie der Strahlung
|journal=[[Physikalische Zeitschrift]]
|volume=18 |pages=121–128
|bibcode=1917PhyZ...18..121E
|ref=harv
}} Translated in {{cite book
|last1=ter Haar |first1=D.
|author-link=Dirk ter Haar
|year=1967
|pages=167–183
|title=The Old Quantum Theory
|publisher=[[Pergamon]]
|lccn=66029628
|ref=harv
}} Also in [http://astro1.panet.utoledo.edu/~ljc/einstein_ab.pdf Boorse, H.A., Motz, L. (1966). ''The world of the atom'', edited with commentaries, Basic Books, Inc., New York, pp. 888–901.]
*{{cite journal
|last1=Heisenberg |first1=W.
|author1-link=Werner Heisenberg
|year=1925
|title=Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen
|journal=[[Zeitschrift für Physik]]
|volume=33
|pages=879–893
|ref=harv
|bibcode = 1925ZPhy...33..879H |doi = 10.1007/BF01328377 }} Translated as "Quantum-theoretical Re-interpretation of kinematic and mechanical relations" in {{cite book
|last1=van der Waerden |first1=B.L.
|author1-link=Bartel Leendert van der Waerden
|year=1967
|title=Sources of Quantum Mechanics
|pages=261–276
|publisher=[[North-Holland Publishing]]
|ref=harv
}}
*{{Cite book
|last1=Jammer |first1=M.
|author1-link=Max Jammer
|year=1989
|title=The Conceptual Development of Quantum Mechanics
|edition=second
|publisher=[[Tomash Publishers]] [[American Institute of Physics]]
|isbn=0-88318-617-9
|ref=harv
}}
*Loudon, R. (1973/2000). ''The Quantum Theory of Light'', (first edition 1973), third edition 2000, Oxford University Press, Oxford UK, ISBN 0-19-850177-3.
*{{cite book
|last1=Sommerfeld |first1=A.
|others=Brose, H. L. (transl.)
|author1-link=Arnold Sommerfeld
|year=1923
|title=Atomic Structure and Spectral Lines
|url=http://books.google.com/books/about/Atomic_structure_and_spectral_lines.html?id=u1UmAAAAMAAJ
|edition=from 3rd German
|publisher=[[Methuen Publishing|Methuen]]
|ref=harv
}}
{{refend}}


{| class="wikitable"
==Other reading==
! Range (m)
| 500
| 600
| 700
| 800
| 900
| 1000
| 1100
| 1200
| 1300
| 1400
| 1500
| 1600
| 1700
| 1800
| 1900
| 2000
|-
! Ballistic coefficient (G1)
| 1.040
| 1.051
| 1.057
| 1.063
| 1.064
| 1.067
| 1.068
| 1.068
| 1.068
| 1.066
| 1.064
| 1.060
| 1.056
| 1.050
| 1.042
| 1.032
|}


The initial rise in the BC value is attributed to a projectile's always present yaw and [[precession]] out of the bore. The test results were obtained from many shots, not just a single shot. The bullet was assigned 1.062 for its BC number by the bullet's manufacturer, Lost River Ballistic Technologies.
{{refbegin}}
 
* {{cite book | author=Condon, E.U. and Shortley, G.H. | title=The Theory of Atomic Spectra | publisher=Cambridge University Press | year=1964 | isbn =0-521-09209-4 }}
Measurements on other bullets can give totally different results. How different speed regimes affect several 8.6&nbsp;mm (.338 in calibre) rifle bullets made by the Finnish ammunition manufacturer Lapua can be seen in the .338 Lapua Magnum product brochure which states Doppler radar established BC data.<ref>[http://www.lapua.com/upload/downloads/brochures/2011/lapuaspecialpurpose2011eng.pdf .338 Lapua Magnum product brochure]</ref>
* {{cite book | author=Rybicki, G.B. and Lightman, A.P. | title=Radiative processes in Astrophysics | publisher=John Wiley & Sons, New York | year=1985 | isbn =0-471-82759-2 }}
 
* {{cite book | author=Shu, F.H. | title=The Physics of Astrophysics - Volume 1 - Radiation | publisher=University Science Books, Mill Valley, CA | year=1991 | isbn =0-935702-64-4 }}
===General trends===
* {{cite journal | author=Robert C. Hilborn | title=Einstein coefficients, cross sections, f values, dipole moments, and all that | journal=physics/0202029 | year=2002 | url = http://arxiv.org/abs/physics/0202029 }}
Sporting bullets, with a [[caliber|calibre]] ''d'' ranging from {{convert|0.172|to|0.50|in|1|disp=flip}}, have BCs in the range 0.12 to slightly over 1.00&nbsp;lb/in². Those bullets with the higher BCs are  the most aerodynamic, and those with low BCs are the least. [[Very-low-drag bullet]]s with BCs ≥ 1.10 can be designed and produced on CNC precision lathes out of mono-metal rods, but they often have to be fired from custom made full bore rifles with special barrels.<ref>[http://www.lima-wiederladetechnik.de/Englisch/LM-Class-Bullets.htm LM Class Bullets, very high BC bullets for windy long ranges.]</ref>
* {{cite journal | author=Taylor, M.A. and Vilchez, J.M. | title=Tutorial: Exact solutions for the populations of the n-level ion | journal=Pub. Astron. Soc. Pac. 121, 885 | pages=1257–1266 | year=2009}}
 
{{refend}}
Ammunition makers often offer several bullet weights and types for a given cartridge.  Heavy-for-caliber pointed (spitzer) bullets with a boattail design have BCs at the higher end of the normal range, whereas lighter bullets with square tails and blunt noses have lower BCs. The 6&nbsp;mm and 6.5&nbsp;mm cartridges are probably the most well known for having high BCs and are often used in long range target matches of {{convert|300|m|yd|0|abbr=on}} – {{convert|1000|m|yd|0|abbr=on}}.  The 6 and 6.5 have relatively light recoil compared to high BC bullets of greater caliber and tend to be shot by the winner in matches where accuracy is key. Examples include the [[6mm PPC]], [[6mm Norma BR]], 6x47mm SM, [[6.5×55mm]] Swedish Mauser, [[6.5x47mm Lapua]], [[6.5 Creedmoor]], [[6.5 Grendel]], [[.260 Remington]], and the [[6.5-284]]. The 6.5&nbsp;mm is also a  popular hunting caliber in Europe.
 
In the United States, hunting cartridges such as the [[.25-06 Remington]] (a 6.35&nbsp;mm caliber), the [[.270 Winchester]] (a 6.8&nbsp;mm caliber), and the [[.284 Winchester]] (a 7&nbsp;mm caliber) are used when high BCs and moderate recoil are desired. The [[.30-06 Springfield]] and [[.308 Winchester]] cartridges also offer several high-BC loads, although the bullet weights are on the heavy side.
 
In the larger caliber category, the [[.338 Lapua Magnum]] and the [[.50 BMG]] are popular with very high BC bullets for shooting beyond 1,000 meters. Newer chamberings in the larger caliber category are the [[.408 Chey Tac|.375 and .408 Cheyenne Tactical]] and the [[.416 Barrett]].
 
==Satellites and reentry vehicles==
Satellites in [[Low Earth Orbit]] (LEO) with high ballistic coefficients experience smaller perturbations to their orbits due to atmospheric drag.
 
The ballistic coefficient of an [[atmospheric reentry]] vehicle has a significant effect on its behavior. A very high ballistic coefficient vehicle would lose velocity very slowly and would impact the Earth's surface at higher speeds. In contrast a low ballistic coefficient would reach subsonic speeds before reaching the ground.
 
In general, reentry vehicles that carry human beings back to Earth from space have high drag and a correspondingly low ballistic coefficient. Vehicles that carry nuclear weapons launched by an [[intercontinental ballistic missile]] (ICBM), by contrast, have a high ballistic coefficient, which enables them to travel rapidly from space to a target on land. That makes the weapon less affected by crosswinds or other weather phenomena, and harder to track, intercept, or otherwise defend against.
 
==See also==
*[[External ballistics]] - The behavior of a projectile in flight.
*[[Trajectory of a projectile]]
 
==References==
{{reflist|30em}}


==External links==
==External links==
*[http://www.reentrynews.com/Defs.html Aerospace Corporation Definition]
* [http://ioannis.virtualcomposer2000.com/spectroscope/amici.html#colorphotos Emission Spectra from various light sources]
*[http://www.chuckhawks.com/bc.htm Chuck Hawks Article on Ballistic Coefficient]
*[http://www.frfrogspad.com/bcdata.htm Ballistic Coefficient Tables]
*[http://www.exteriorballistics.com/ebexplained/index.cfm Exterior Ballistics.com]
*[http://www.nennstiel-ruprecht.de/bullfly/ballcoeff.htm#header How do bullets fly? The ballistic coefficient (bc) by Ruprecht Nennstiel, Wiesbaden, Germany]
*[http://www.precisionshooting.com.au/downloads/ballisticcoefficients-explained(4).pdf Ballistic Coefficients - Explained]
[http://www.jbmballistics.com/ballistics/calculators/calculators.shtml Ballistic calculators]


[[Category:Emission spectroscopy]]


{{DEFAULTSORT:Ballistic Coefficient}}
[[bg:Атомна спектрална линия]]
[[Category:Projectiles]]
[[it:Linea spettrale atomica]]
[[Category:Aerodynamics]]
[[pl:Widmo liniowe]]
[[Category:Ballistics]]
[[zh:原子谱线]]

Revision as of 10:11, 14 August 2014

Template:More footnotes

Emission lines and absorption lines compared to a continuous spectrum.

In physics, one thinks of atomic spectral lines from two viewpoints.

  • An emission line is formed when an electron makes a transition from a particular discrete energy level Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

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    A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

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    Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. of an atom, to a lower energy level Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

    Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

    There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

    This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

    A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

    If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

    Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer., emitting a photon of a particular energy and wavelength. A spectrum of many such photons will show an emission spike at the wavelength associated with these photons.
  • An absorption line is formed when an electron makes a transition from a lower, Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

    Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

    There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

    This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

    A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

    If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

    Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer., to a higher discrete energy state, Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

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    There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

    This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

    A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

    If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

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The two states must be bound states in which the electron is bound to the atom, so the transition is sometimes referred to as a "bound–bound" transition, as opposed to a transition in which the electron is ejected out of the atom completely ("bound–free" transition) into a continuum state, leaving an ionized atom, and generating continuum radiation.

A photon with an energy equal to the difference Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. between the energy levels is released or absorbed in the process. The frequency Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. at which the spectral line occurs is related to the photon energy by Bohr's frequency condition where Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. denotes Planck's constant.[1][2][3][4][5][6]

Emission and absorption coefficients

An atomic spectral line refers to emission and absorption events in a gas in which is the density of atoms in the upper energy state for the line, and is the density of atoms in the lower energy state for the line.

The emission of atomic line radiation at frequency Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. may be described by an emission coefficient with units of energy/time/volume/solid angle. ε dt dV dΩ is then the energy emitted by a volume element in time into solid angle . For atomic line radiation:

where is the Einstein coefficient for spontaneous emission, which is fixed by the intrinsic properties of the relevant atom for the two relevant energy levels.

The absorption of atomic line radiation may be described by an absorption coefficient with units of 1/length. The expression κ' dx gives the fraction of intensity absorbed for a light beam at frequency ν while traveling distance dx. The absorption coefficient is given by:

where and are the Einstein coefficients for photo absorption and induced emission respectively. Like the coefficient , these are also fixed by the intrinsic properties of the relevant atom for the two relevant energy levels. For thermodynamics and for the application of Kirchhoff's law, it is necessary that the total absorption be expressed as the algebraic sum of two components, described respectively by and , which may be regarded as positive and negative absorption, which are, respectively, the direct photon absorption, and what is commonly called stimulated or induced emission.[7][8][9]

The above equations have ignored the influence of the spectral line shape. To be accurate, the above equations need to be multiplied by the (normalized) spectral line shape, in which case the units will change to include a 1/Hz term.

For conditions of thermodynamic equilibrium, together the number densities and , the Einstein coefficients, and the spectral energy density provide sufficient information to determine the absorption and emission rates.

Equilibrium conditions

The number densities and are set by the physical state of the gas in which the spectral line occurs, including the local spectral radiance (or, in some presentations, the local spectral radiant energy density). When that state is either one of strict thermodynamic equilibrium, or one of so-called 'local thermodynamic equilibrium',[10][11][12] then the distribution of atomic states of excitation (which includes and ) determines the rates of atomic emissions and absorptions to be such that Kirchhoff's law of equality of radiative absorptivity and emissivity holds. In strict thermodynamic equilibrium, the radiation field is said to be black-body radiation, and is described by Planck's law. For local thermodynamic equilibrium, the radiation field does not have to be a black-body field, but the rate of interatomic collisions must vastly exceed the rates of absorption and emission of quanta of light, so that the interatomic collisions entirely dominate the distribution of states of atomic excitation. Circumstances occur in which local thermodynamic equilibrium does not prevail, because the strong radiative effects overwhelm the tendency to the Maxwell-Boltzmann distribution of molecular velocities. For example, in the atmosphere of the sun, the great strength of the radiation dominates. In the upper atmosphere of the earth, at altitudes over 100 km, the rarity of intermolecular collisions is decisive.

In the cases of thermodynamic equilibrium and of local thermodynamic equilibrium, the number densities of the atoms, both excited and unexcited, may be calculated from the Maxwell–Boltzmann distribution, but for other cases, (e.g. lasers) the calculation is more complicated.

Einstein coefficients

In 1916, Albert Einstein proposed that there are three processes occurring in the formation of an atomic spectral line. The three processes are referred to as spontaneous emission, stimulated emission, and absorption. With each is associated an Einstein coefficient which is a measure of the probability of that particular process occurring. Einstein considered the case of isotropic radiation of frequency Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer., and spectral energy density Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer..[2][13] Note that in some treatments, the black-body spectral radiance is used rather than the spectral radiation energy density.[14][12]

Spontaneous emission

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church.

Schematic diagram of atomic spontaneous emission

Spontaneous emission is the process by which an electron "spontaneously" (i.e. without any outside influence) decays from a higher energy level to a lower one. The process is described by the Einstein coefficient A21 (s−1) which gives the probability per unit time that an electron in state 2 with energy will decay spontaneously to state 1 with energy , emitting a photon with an energy Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer.. Due to the energy-time uncertainty principle, the transition actually produces photons within a narrow range of frequencies called the spectral linewidth. If is the number density of atoms in state i  then the change in the number density of atoms in state 2 per unit time due to spontaneous emission will be:

The same process results in increasing of the population of the state 1:

Stimulated emission

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church.

Schematic diagram of atomic stimulated emission

Stimulated emission (also known as induced emission) is the process by which an electron is induced to jump from a higher energy level to a lower one by the presence of electromagnetic radiation at (or near) the frequency of the transition. From the thermodynamic viewpoint, this process must be regarded as negative absorption. The process is described by the Einstein coefficient (J−1 m3 s−1), which gives the probability per unit time per unit spectral energy density of the radiation field that an electron in state 2 with energy will decay to state 1 with energy , emitting a photon with an energy Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer.. The change in the number density of atoms in state 1 per unit time due to induced emission will be:


where denotes the spectral energy density of the isotropic radiation field at the frequency of the transition (see Planck's law).

Stimulated emission is one of the fundamental processes that led to the development of the laser. Laser radiation is, however, very far from the present case of isotropic radiation.

Photo absorption

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church.

Schematic diagram of atomic absorption

Absorption is the process by which a photon is absorbed by the atom, causing an electron to jump from a lower energy level to a higher one. The process is described by the Einstein coefficient (J−1 m3 s−1), which gives the probability per unit time per unit spectral energy density of the radiation field that an electron in state 1 with energy will absorb a photon with an energy Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. and jump to state 2 with energy . The change in the number density of atoms in state 1 per unit time due to absorption will be:


Detailed balancing

The Einstein coefficients are fixed probabilities associated with each atom, and do not depend on the state of the gas of which the atoms are a part. Therefore, any relationship that we can derive between the coefficients at, say, thermodynamic equilibrium will be valid universally.

At thermodynamic equilibrium, we will have a simple balancing, in which the net change in the number of any excited atoms is zero, being balanced by loss and gain due to all processes. With respect to bound-bound transitions, we will have detailed balancing as well, which states that the net exchange between any two levels will be balanced. This is because the probabilities of transition cannot be affected by the presence or absence of other excited atoms. Detailed balance (valid only at equilibrium) requires that the change in time of the number of atoms in level 1 due to the above three processes be zero:

Along with detailed balancing, at temperature Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. we may use our knowledge of the equilibrium energy distribution of the atoms, as stated in the Maxwell–Boltzmann distribution, and the equilibrium distribution of the photons, as stated in Planck's law of black body radiation to derive universal relationships between the Einstein coefficients.

From the Maxwell–Boltzmann distribution we have for the number of excited atomic species i:

where n is the total number density of the atomic species, excited and unexcited, k is Boltzmann's constant, T is the temperature, is the degeneracy (also called the multiplicity) of state i, and Z is the partition function. From Planck's law of black-body radiation at temperature Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. we have for the spectral energy density at frequency Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer.

where:

where is the speed of light and is Planck's constant.

Substituting these expressions into the equation of detailed balancing and remembering that Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. yields:

separating to:

The above equation must hold at any temperature, so

Therefore the three Einstein coefficients are interrelated by:

and

When this relation is inserted into the original equation, one can also find a relation between and , involving Planck's law.

Oscillator strengths

The oscillator strength is defined by the following relation to the cross section for absorption:

where is the electron charge and is the electron mass. This allows all three Einstein coefficients to be expressed in terms of the single oscillator strength associated with the particular atomic spectral line:

See also

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

Cited bibliography

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  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • Chandrasekhar, S. (1950). Radiative Transfer, Oxford University Press, Oxford.
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang Also One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang And a version nearly identical to the latter at One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang Translated in 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 Also in Boorse, H.A., Motz, L. (1966). The world of the atom, edited with commentaries, Basic Books, Inc., New York, pp. 888–901.
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang Translated as "Quantum-theoretical Re-interpretation of kinematic and mechanical relations" in 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • Loudon, R. (1973/2000). The Quantum Theory of Light, (first edition 1973), third edition 2000, Oxford University Press, Oxford UK, ISBN 0-19-850177-3.
  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

Template:Refend

Other reading

Template:Refbegin

  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

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  1. ↑ Template:Harvnb
  2. ↑ 2.0 2.1 Template:Harvnb
  3. ↑ Template:Harvnb
  4. ↑ Template:Harvnb
  5. ↑ Template:Harvnb
  6. ↑ Template:Harvnb
  7. ↑ Weinstein, M.A. (1960). On the validity of Kirchhoff's law for a freely radiating body, American Journal of Physics, 28: 123-25.
  8. ↑ Burkhard, D.G., Lochhead, J.V.S., Penchina, C.M. (1972). On the validity of Kirchhoff's law in a nonequilibrium environment, American Journal of Physics, 40: 1794-1798.
  9. ↑ Baltes, H.P. (1976). On the validity of Kirchhoff's law of heat radiation for a body in a nonequilibrium environment, Chapter 1, pages 1-25 of Progress in Optics XIII, edited by E. Wolf, North-Holland, ISSN 00796638.
  10. ↑ Milne, E.A. (1928). The effect of collisions on monochromatic radiative equilibrium, Monthly Notices of the Royal Astronomical Society, 88: 493-502. [1]
  11. ↑ Chandrasekhar, S. (1950), p. 7.
  12. ↑ 12.0 12.1 Mihalas, D., Weibel-Mihalas, B. (1984). Foundations of Radiation Hydrodynamics, Oxford University Press, New York, ISBN 0-19-503437-6.
  13. ↑ Loudon, R. (2000), Section 1.5, pp. 16–19.
  14. ↑ Chandrasekhar, S. (1950), p. 354.
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