Ornstein–Uhlenbeck process: Difference between revisions

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[[File:Three_decades.png|thumb|Three decades: 0.01, 0.1, 1, 10 (10<sup>-2</sup>, 10<sup>-1</sup>, 10<sup>0</sup>, 10<sup>1</sup>).]]
It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>When you have any questions about where in addition to how to utilize [http://www.youtube.com/watch?v=90z1mmiwNS8 dentist DC], you possibly can call us on our site.
[[File:Three_decades_x10.png|thumb|Three decades: One-thousand 0.01's, one-hundred 0.1's, ten 1's, one 10.]]
 
One '''decade''' is a [[factorization|factor]] of 10 difference between two numbers (an [[order of magnitude]] difference) measured on a [[logarithmic scale]]. Along with the [[octave (electronics)|octave]], it is a [[units of measurement|unit]] used to describe [[frequency|frequency bands]] or [[interval ratio|frequency ratios]].<ref name="Levine">Levine, William S. (2010). ''The Control Handbook: Control System Fundamentals'', p.9-29. ISBN 9781420073621.</ref><ref name="Perdikaris">Perdikaris, G. (1991). ''Computer Controlled Systems: Theory and Applications'', p.117. ISBN 9780792314226.</ref> It is especially useful when referring to frequencies and when describing [[frequency response]] of [[electronics|electronic systems]], such as [[audio amplifier]]s and [[electronic filter|filters]].
 
==Calculations==
The factor-of-ten in a decade can be in either direction: so one decade up from 100&nbsp;Hz is 1000&nbsp;Hz, and one decade down is 10&nbsp;Hz. The factor-of-ten is what is important, not the unit used, so 3.14&nbsp;rad/s is one decade down from 31.4&nbsp;rad/s.
 
To determine the number of decades between two frequencies (<math>f_1</math> & <math>f_2</math>), use the [[logarithm]] of the ratio of the two values:
*<math>\log_{10} (f_2/f_1)</math> decades<ref name="Levine"/><ref name="Perdikaris"/>
or, using [[natural logarithm]]s:
*<math>\ln f_2 - \ln f_1\over\ln 10</math> decades<ref>Davis, Don and Patronis, Eugene (2012). ''Sound System Engineering'', p.13. ISBN 9780240808307.</ref>
 
:How many decades is it from 15&nbsp;rad/s to 150,000&nbsp;rad/s?
::<math>\log_{10} (150000/15) = 4</math> decades
:How many decades is it from 3.2&nbsp;GHz to 4.7&nbsp;MHz?
::<math>\log_{10} (4.7\times10^6 / 3.2\times10^9 ) = -2.83</math> decades
:How many decades is one octave?
::One octave is a factor of 2, so <math>\log_{10} (2) = 0.301</math> decades per octave (decade = [[just major third]] + three octaves, 10/1 = 5/4)
 
To find out what frequency is a certain number of decades from the original frequency, multiply by appropriate powers of 10:
:What is 3 decades down from 220&nbsp;Hz?
::<math>220 \times 10^{-3} = 0.22</math> Hz
:What is 1.5 decades up from 10?
::<math>10 \times 10^{1.5} = 316.23</math>
 
To find out the size of a step for a certain number of frequencies per decade, raise 10 to the power of the inverse of the number of steps:
:What is the step size for 30 steps per decade?
::<math> 10^{1/30} = 1.079775</math> - or each step is 7.9775% larger than the last.
 
[[Image:Butterworth filter bode plot.png|350px|thumb|right|[[Bode plot]] showing the concept of a decade: each major division on the horizontal axis is one decade]]
 
==Graphical representation and analysis==
Decades on a logarithmic scale, rather than unit steps (steps of 1) or other [[linear]] scale, are commonly used on the horizontal axis when representing the frequency response of electronic circuits in graphical form, such as in [[Bode plot]]s, since depicting large frequency ranges on a linear scale is often not practical. For example, an [[audio amplifier]] will usually have a frequency band ranging from 20 Hz to 20&nbsp;kHz and representing the entire band using a decade log scale is very convenient. Typically the graph for such a representation would begin at 1 Hz (10<sup>0</sup>) and go up to perhaps 100&nbsp;kHz (10<sup>5</sup>), to comfortably include the full audio band in a standard-sized [[graph paper]], as shown below.  Whereas in the same distance on a linear scale, with 10 as the major step-size, you might only get from 0 to 50.
 
[[Image:Decade vs Linear.svg|400px|1,10,100,1k,10k,100k using decades vs. 0,10,20,30,40,50 using linear scale]]
 
Electronic frequency responses are often described in terms of "per decade".  The example Bode plot shows a slope of -20&nbsp;[[Decibel|dB]]/decade in the stopband, which means that for every factor-of-ten increase in frequency (going from 10 rad/s to 100 rad/s in the figure), the gain decreases by 20&nbsp;dB.
 
==See also==
* [[Savart]]
 
==Sources==
{{reflist}}
 
{{DEFAULTSORT:Decade (Log Scale)}}
[[Category:Charts]]
[[Category:Logarithmic scales of measurement]]

Latest revision as of 09:31, 7 June 2014

It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.

Here are some common dental emergencies:
Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.

At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.

Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.

Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.

Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.

Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.

Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.

In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.

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