Slurry: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>BG19bot
m WP:CHECKWIKI error fix for #93. External link with double http:// Do general fixes if a problem exists. - using AWB (9890)
Corrected tons/m^3 to tonnes/m^3 (t/m^3) to make units consistent
 
Line 1: Line 1:
{{For|other theorems named after Axel Thue|Thue's theorem (disambiguation)}}
Luke Bryan is usually a superstar within the making as well as profession advancement to start with 2nd to his third hotel recording,  & , may be the resistant. He burst to the picture in 2003 along with his crazy mix of downward-property accessibility, video celebrity good appearance and lyrics, is scheduled t inside a key way. The new recor on the country chart and #2 in the take maps, building it the next greatest first appearance at that time of 2012 to get a country designer. <br><br>The child of a ,  is aware of patience and willpower are important elements in relation to a prosperous  career- . His to start with album,  Continue to be Me, produced the Top  strikes “All My Buddies “Country and Say” Person,” although his  work, Doin’  Point, identified the performer-a few right No. 5 men and women:  In  [http://lukebryantickets.citizenswebcasting.com eric church tour dates] addition Contacting Can be a Good Thing.”<br><br>While in the drop of 2012, Concert tours: Bryan  And which in fact had an impressive list of , which include Downtown. “It’s much like you’re obtaining a   approval to visit to another level, affirms all those performers  mumford and sons tickets [[http://lukebryantickets.omarfoundation.org lukebryantickets.omarfoundation.org]] which were an element of the Concert toursover in a bigger degree of performers.” It packaged as among the most successful  trips in their twenty-12 months background.<br><br>my site - [http://www.ladyhawkshockey.org concerts for luke bryan]
 
In [[mathematics]], a '''Thue equation''' is a [[Diophantine equation]] of the form
 
:''&fnof;''(''x'',''y'') = ''r'',
 
where ''ƒ'' is an [[irreducible polynomial|irreducible]] bivariate [[Algebraic form|form]] of degree at least 3 over the rational numbers, and ''r'' is a nonzero [[rational number]]. It is named after [[Axel Thue]] who in 1909 proved a [[theorem]], now called '''Thue's theorem''', that a Thue equation has finitely many solutions in integers ''x'' and ''y''.<ref>{{cite journal |author=A. Thue |title=Über Annäherungswerte algebraischer Zahlen |journal=[[Journal für die reine und angewandte Mathematik]] |volume=135 |pages=284–305 |year=1909 |url=http://resolver.sub.uni-goettingen.de/purl?PPN243919689_0135}}</ref>
 
The Thue equation is [[Effective results in number theory|soluble effectively]]: there is an explicit bound on the solutions ''x'', ''y'' of the form <math>(C_1 r)^{C_2}</math> where constants ''C''<sub>1</sub> and ''C''<sub>2</sub> depend only on the form ''ƒ''.  A stronger result holds, that if ''K'' is the field generated by the roots of ''ƒ'' then the equation has only finitely many solutions with ''x'' and ''y'' integers of ''K'' and again these may be effectively determined.<ref>{{cite book | first=Alan | last=Baker | authorlink=Alan Baker (mathematician) | title=Transcendental Number Theory | publisher=[[Cambridge University Press]] | year=1975 | isbn=0-521-20461-5 | page=38 }}</ref>
 
==Solving Thue equations==
Solving a Thue equation can be described as an algorithm<ref>{{cite journal |author=N. Tzanakis and B. M. M. de Weger |title=On the practical solution of the Thue equation |journal=[[Journal of Number Theory]] |volume=31 |issue=2 |year=1989 |pages=99–132 |doi=10.1016/0022-314X(89)90014-0}}</ref> ready for implementation in software. In particular, it is implemented in the following [[computer algebra system]]s:
* in [[PARI/GP]] as functions ''thueinit()'' and ''thue()''.
* in [[Magma computer algebra system]] as functions ''ThueObject()'' and ''ThueSolve()''.
* in [[Mathematica]] through ''Reduce''
 
==References==
{{reflist}}
 
==Further reading==
* {{cite book | first1=Alan | last1=Baker | authorlink1=Alan Baker (mathematician)| first2=Gisbert | last2= Wüstholz | authorlink2=Gisbert Wüstholz | title=Logarithmic Forms and Diophantine Geometry | series=New Mathematical Monographs | volume=9 | publisher=[[Cambridge University Press]] | year=2007 | isbn=978-0-521-88268-2 }}
 
[[Category:Diophantine equations]]
[[Category:Theorems in number theory]]
 
{{numtheory-stub}}

Latest revision as of 16:27, 10 September 2014

Luke Bryan is usually a superstar within the making as well as profession advancement to start with 2nd to his third hotel recording, & , may be the resistant. He burst to the picture in 2003 along with his crazy mix of downward-property accessibility, video celebrity good appearance and lyrics, is scheduled t inside a key way. The new recor on the country chart and #2 in the take maps, building it the next greatest first appearance at that time of 2012 to get a country designer.

The child of a , is aware of patience and willpower are important elements in relation to a prosperous career- . His to start with album, Continue to be Me, produced the Top strikes “All My Buddies “Country and Say” Person,” although his work, Doin’ Point, identified the performer-a few right No. 5 men and women: In eric church tour dates addition Contacting Can be a Good Thing.”

While in the drop of 2012, Concert tours: Bryan And which in fact had an impressive list of , which include Downtown. “It’s much like you’re obtaining a approval to visit to another level, affirms all those performers mumford and sons tickets [lukebryantickets.omarfoundation.org] which were an element of the Concert toursover in a bigger degree of performers.” It packaged as among the most successful trips in their twenty-12 months background.

my site - concerts for luke bryan

Retrieved from "https://en.formulasearchengine.com/index.php?title=Slurry&oldid=236662"