wikt coshCosh may refer to Hyperbolic cosine , a mathematical function with notation cosh x A blunt metal stick used as a weapon, also known as a Baton law enforcement Blackjack blackjack Various sorts of blunt instrument Bludgeon weapon bludgeon , Baton law enforcement baton , piece of lead pipe, piece of flexible tubing filled with metal, or the like ref 1991 edition of Chambers Dictionary ref Slang for chlorpromazine , an antipsychotic drug Harry and Cosh , a British children s television series Cosh Boy , a 1953 British film Chrome OS Shell People Chris Cosh born 1956 , American football coach Colby Cosh born 1971 , Canadian writer John Cosh 1915 2005 , British rheumatologist See also COSHH , Control of Substances Hazardous to Health, a set of UK regulations References references disambig ... more details
wikt cosh A cosh as a weapon may mean Various sorts of blunt instruments A blunt metal stick used as a weapon, also known as a blackjack see Baton law enforcement Blackjack Club weapon Baton law enforcement Truncheon From which came derived uses Chemical cosh Slang use to mean chlorpromazine , an antipsychotic drug disambig Category Blunt weapons ... more details
Chemical cosh is a term used primarily by the British. To wikt coshcosh someone means to bang them on the head, resulting in the person being sedated or knocked unconscious. A chemical cosh, then, refers to sedating people with chemicals, or medications. The term is generally used to refer to the situation where sedation is unnecessary. More specifically it refers to the widespread dispensation of antipsychotic antipsychotic drugs in residential care to make people with dementia easier to manage. ref http www.telegraph.co.uk health elderhealth 8086614 Chemical cosh will be cut for dementia sufferers.html Chemical cosh will be cut for dementia sufferers ref the use of ritalin to calm children with attention deficit hyperactivity disorder . ref http www.dailymail.co.uk health article 189282 Fears use Ritalin children.html Fears over use of Ritalin on children ref See also Antipsychotic Controversy Antipsychotic controversy References references Category Antipsychotics Category Neologisms Category Psychiatric terms ... more details
refimprove date October 2011 inline date October 2011 distinguish Colby Coash Colby Cosh born May 2, 1971 is a Canada Canadian commentator, writer and editor of non fiction, and weblog blogger . Life and career Cosh was born in Edmonton , Alberta and grew up in Bon Accord, Alberta , north of Edmonton. He graduated from the University of Alberta in 1993, doing further study in European intellectual history under Libertarianism libertarian scholar Ronald Hamowy . Cosh generally writes political, social and sports commentary for his blog, and professionally for the conservatism conservative press. Cosh s own views tend towards libertarianism. Cosh was the central character of the comic strip Colby Christ , published in The Gateway newspaper The Gateway , the University of Alberta student newspaper. The comic had replaced Space Moose after Adam Thrasher, the author of that comic, left the university in 1991 to work for a company. Donald R. Don Husereau, a pharmacy student and friend of Cosh, drew the strip while Cosh assisted in the formation of the depiction of himself. ref name CCFAQ Thrasher, Adam and Colby Cosh. http web.archive.org web 20030202042543 www.spacemoose.com smfaq.htm Frequently Asked Questions FAQ about SPACE MOOSE . Space Moose. Retrieved on February 4, 2011. ref Cosh ... for the Alberta in the 20th Century book series, a Byfield family project. Cosh then joined the Byfields ..., Cosh became a regular Op Ed contributor to the National Post , and joined the Report influenced ... publications. Cosh left the Post in 2009. He currently contributes a blog to Macleans . His website ColbyCosh.com was started in June 2002. Besides politics, Cosh occasionally writes about ice hockey ... ColbyCosh.com http www.colbycosh.com who.html Colby Cosh fact file from ColbyCosh.com Persondata Metadata see Wikipedia Persondata . NAME Cosh, Colby ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1971 05 02 PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Cosh, Colby Category 1971 births ... more details
Infobox Television show name Harry and Cosh image caption genre Sitcom creator Daniel Peacock starring Harry Capehorn br Coshti Dowden br Lucinda Rhodes Flaherty br Gemma Baker country UK language English language English num series 4 num episodes 46 list episodes executive producer producer camera runtime network Five channel Five picture format 4 3 , 16 9 first aired start date 1999 10 30 df yes last aired end date 2003 7 12 df yes Harry and Cosh was a United Kingdom British children s television series directed by Daniel Peacock shown on Saturday afternoons on Shake on Channel 5 UK It starred Harry Capehorn, Coshti Dowden, Lucinda Rhodes Flaherty and Gemma Baker. It told the story of two teenagers, their relationship problems and dysfunctional families . It ran for 46 episodes from 30 October 1999 to 12 July 2003. Frankie Fitzgerald Ricky Diamond and Carly Hillman appeared in some episodes as guest stars. In 2002, it was nominated for a BAFTA . Characters recur in other Two Hats Productions so it could be said OR? date March 2010 to belong to the same metaseries as Sister Said , Cavegirl , Morris 2274 and Billie Girl from the Future . External links tv.com 21382 Harry and Cosh http ftvdb.bfi.org.uk sift series 32437 BFI Film & TV Database Harry and Cosh imdb title id 0227905 title Harry and Cosh UK tv prog stub Category Television shows set in London Category Channel 5 UK television programmes Category Teen dramas Category 1999 in British television Category 1999 British television programme debuts Category 2003 British television programme endings Category 1990s British television series Category 2000s British television series Category Teen sitcoms ... more details
Infobox college coach image name Chris Cosh caption birth date Birth date and age 1959 5 12 mf y birth place death date sport American football Football current team South Florida Bulls football USF current conference Big East Conference current title Defensive coordinator Defensive Coordinator contract player Y player years 1977&ndash 1981 player teams Virginia Polytechnic Institute and State University ... br USF DC CFBHOF year Chris Cosh born May 12, 1959 , is an American football coach and currently holds the position of defensive coordinator at the University of South Florida . Playing career Cosh ... 3629270 Cosh Added to Wildcat Defensive Staff . Kansas State University Wildcats official athletic .... ref name KSS 2008 12 06 Cosh has moved around a lot, with 13 stops in 25 years, ref http web.archive.org ... ref ref http gamecocksonline.cstv.com sports m footbl mtt cosh chris00.html ref including ... and linebackers coach with head coach Ralph Friedgen . ref name KSS 2008 12 06 While at Maryland, Cosh ... as poor to occasionally impressive . Friedgen praised Cosh s recruiting but showed public frustration with Cosh s in game coaching. ref name wapo cite web url http www.washingtonpost.com wp dyn content article 2008 12 05 AR2008120503504.html title Maryland Assistant Cosh To Depart for Kansas ... ref On December 6, 2008 it was announced that Cosh would return to Kansas State for a second time ... . December 8, 2008 ref Cosh will have now served as a defensive coordinator in five of the six ... 12 06 On January 18, 2012, Cosh was announced as the new defensive coordinator at the University ... http www.tampabay.com blogs bulls content holtz gets his man cosh run usf defense ref Personal Cosh ... 2008 12 06 Cosh and his wife, Mary, have two sons, J.J., who is a member of the Navy Midshipmen football ... References reflist Persondata Metadata see Wikipedia Persondata . NAME Cosh, Chris ALTERNATIVE NAMES ... OF DEATH PLACE OF DEATH DEFAULTSORT Cosh, Chris Category 1959 births Category Living people Category ... more details
John Cosh 1915 2005 was a United Kingdom British rheumatologist . He is known for his long term studies of the effects of rheumatoid arthritis , co discovery of the genes associated with rheumatoid arthritis, and his work on the benefits of herbal medicine s. In 1973, with R K Jacoby and M I Jayson, he published an 11 year follow up of 100 patients newly diagnosed as having rheumatoid arthritis and followed them for a further 30 years, showing that rheumatoid arthritis is a progressive disease impairing function for decades after onset. By 2004 eight of the sample were severely disabled with rheumatoid arthritis, three were less disabled, and only five had normal functioning. Of the 84 who died, median survival was reduced by 10 to 11 years, and the leading cause of death was heart disease . In 1986 he published, with other rheumatologists, a study that showed the association of rheumatoid arthritis with several human lymphocyte antigens the associations were stronger in patients with more advanced disease. John Cosh had originally wanted to be a heart surgeon, but his interests shifted towards cardiology and then to the cardiological aspects of rheumatology. He was born in Bristol , the son of a pharmacist. From Bristol Grammar School he won a scholarship to St John s College, Cambridge , for his pre clinical studies, and went to St Thomas s Hospital Medical School , London , for his clinical training. He qualified in 1940 and became a house physician at Lambeth Hospital, a satellite hospital of St Thomas s. From there he went to the Royal Hampshire County Hospital in Winchester ... College of Physicians Heberden medal for his research in rheumatology. He retired in 1982. John Cosh ... cgi content full 331 7523 1026 John Cosh s obituary ref References references Persondata Metadata see Wikipedia Persondata . NAME Cosh, John ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1915 PLACE OF BIRTH DATE OF DEATH 2005 PLACE OF DEATH DEFAULTSORT Cosh, John Category 1915 births Category ... more details
Unreferenced date January 2009 Cosh Boy is a 1953 British film starring James Kenney actor James Kenney , Joan Collins , Hermione Baddeley , Hermione Gingold , Betty Ann Davies and Robert Ayres actor Robert Ayres . It was directed by Lewis Gilbert , and produced by Daniel M. Angel . Plot Based on an original play by Bruce Walker , the film tells of the exploits of 16 year old delinquent youth Roy Walsh James Kenney and his gang in post World War II London . The gang starts off by mugging women. Later, Roy becomes infatuated with Rene, the sister of one of the gang members. Already having a boyfriend, Brian, she rejects Roy, to his fury. Later the gang beat up Brian. Roy menaces Rene, who eventually submits to him. When she informs him that he has made her pregnant, and urges him to marry her, he decides he wants nothing more to do with her. Roy s mother, Elsie Walsh Betty Ann Davies , is involved with Canadian Bob Stevens Robert Ayres , who urges her to marry him so he can take Roy in hand before it s too late. Roy hates Bob. Bob works as an assistant manager at the Palidrome dance hall, which becomes a target for the gang. Another member of staff appears on the scene, and is shot and wounded by the gang. Later that night a mob of women arrive on the doorstep with Rene s mother, who adds that the police are on their way. Bob arrives, removes Rene s mother from the premises and decides to give Roy a thrashing for his own good before the police arrive in the belief that if the judge hears he has already received a thrashing, his sentence might be lighter, which will be easier for his mother to stomach. The police arrive just as Bob is brandishing his belt in readiness. Bob lets them in, and they ask who he is. He tells him he is the boy s stepfather, as his mother and I were ... Sergeant Reception Cosh Boy has also been named The Tough Guy , or The Slasher . It was the first ... 482602 index.html Cosh Boy at screenonline Lewis Gilbert DEFAULTSORT Cosh Boy Category 1953 films Category ... more details
Co kun mer , more commonly known as Cosh Omar , ref cite news author Kibris Gazetesi title K br sl T rk akt rden rk l k zerine cesur oyun url http www.kibrisgazetesi.com index.php cat 2 news 79993 PageName Ic Haberler accessdate 2011 09 14 ref born in London , United Kingdom is a United Kingdom British actor and playwright of Turkish Cypriot descent. ref cite news author The Telegraph title The Great Extension at the Theatre Royal Stratford & My Wonderful Day at the Stephen Joseph Theatre, review url http www.telegraph.co.uk culture theatre theatre reviews 6439370 The Great Extension at the Theatre Royal Stratford and My Wonderful Day at the Stephen Joseph Theatre review.html accessdate 2011 02 28 location London work The Daily Telegraph date 26 October 2009 ref ref cite news author The Guardian title The Battle of Green Lanes url http www.guardian.co.uk stage 2004 oct 23 theatre1?INTCMP ILCNETTXT3487 accessdate 2011 02 28 location London date 23 October 2004 ref Omar s most notable plays include The Battle of Green Lanes and The Great Extension which deal with multicultural issues in London with the use of comedy . ref cite web author The Stage title The Battle of Green Lanes url http www.thestage.co.uk reviews review.php 4918 the battle of green lanes accessdate 2011 02 28 ref ref cite web author The Stage title The Great Extension url http www.thestage.co.uk reviews review.php 25979 the great extension accessdate 2011 02 28 ref ref cite news author Daily Mail title The Great Extension tackles the hottest issues with humour url http www.dailymail.co.uk tvshowbiz reviews article 1226663 The Great Extension tackles hottest issues humour.html accessdate 2011 02 28 location London date 10 November 2009 ref He has also appeared in several TV episodes including The Bill ... Metadata see Wikipedia Persondata . NAME Omar, Cosh ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Omar, Cosh Category Living people Category ... more details
, and C denotes the constant of integration . math int sinh ax ,dx frac 1 a cosh ax C , math math int cosh ax ,dx frac 1 a sinh ax C , math math int sinh 2 ax ,dx frac 1 4a sinh 2ax frac x 2 C , math math int cosh 2 ax ,dx frac 1 4a sinh 2ax frac x 2 C , math math int tanh 2 ax ,dx x frac tanh ax a C , math math int sinh n ax ,dx frac 1 an sinh n 1 ax cosh ax frac n 1 n int sinh n 2 ax ,dx qquad mbox for n 0 mbox , math also math int sinh n ax ,dx frac 1 a n 1 sinh n 1 ax cosh ax frac n 2 n 1 int sinh n 2 ax ,dx qquad mbox for n 0 mbox , n neq 1 mbox , math math int cosh n ax ,dx frac 1 an sinh ax cosh n 1 ax frac n 1 n int cosh n 2 ax ,dx qquad mbox for n 0 mbox , math also math int cosh n ax ,dx frac 1 a n 1 sinh ax cosh n 1 ax frac n 2 n 1 int cosh n 2 ax ,dx qquad mbox for n ... also math int frac dx sinh ax frac 1 a ln left frac cosh ax 1 sinh ax right C , math also math int frac dx sinh ax frac 1 a ln left frac sinh ax cosh ax 1 right C , math also math int frac dx sinh ax frac 1 a ln left frac cosh ax 1 cosh ax 1 right C , math math int frac dx cosh ax frac 2 a arctan e ax C , math also math int frac dx cosh ax frac 1 a arctan sinh ax C , math math int frac dx sinh n ax frac cosh ax a n 1 sinh n 1 ax frac n 2 n 1 int frac dx sinh n 2 ax qquad mbox for n neq 1 mbox , math math int frac dx cosh n ax frac sinh ax a n 1 cosh n 1 ax frac n 2 n 1 int frac dx cosh n 2 ax qquad mbox for n neq 1 mbox , math math int frac cosh n ax sinh m ax dx frac cosh n 1 ax a n m sinh m 1 ax frac n 1 n m int frac cosh n 2 ax sinh m ax dx qquad mbox for m neq n mbox , math also math int frac cosh n ax sinh m ax dx frac cosh n 1 ax a m 1 sinh m 1 ax frac n m 2 m 1 int frac cosh n ax sinh m 2 ax dx qquad mbox for m neq 1 mbox , math also math int frac cosh n ax sinh m ax dx frac cosh n 1 ax a m 1 sinh m 1 ax frac n 1 m 1 int frac cosh n 2 ax sinh m 2 ax dx qquad mbox for m neq 1 mbox , math math int frac sinh m ax cosh n ax dx frac sinh m 1 ax a m n cosh n 1 ax frac m 1 n m int ... more details
Expert subject Mathematics date November 2008 Image Breather surface.PNG thumb 250px right Breather surface when math a frac 2 5 text and 14 le u 14 math math text and 37.4 le v 37.4 math In differential equations , a breather surface is a mathematical surface relating to breather s. Parameterization math begin align x & u frac 2 left 1 a 2 right cosh au sinh au a left left 1 a 2 right cosh 2 au a 2 , sin 2 left sqrt 1 a 2 v right right y & frac 2 sqrt 1 a 2 cosh au left sqrt 1 a 2 cos v cos left sqrt 1 a 2 v right sin v sin left sqrt 1 a 2 v right right a left left 1 a 2 right cosh 2 au a 2 , sin 2 left sqrt 1 a 2 v right right z & frac 2 sqrt 1 a 2 cosh au left sqrt 1 a 2 sin v cos left sqrt 1 a 2 v right cos v sin left sqrt 1 a 2 v right right a left left 1 a 2 right cosh 2 au a 2 , sin 2 left sqrt 1 a 2 v right right end align math where 0 a 1. See also Breather References http xahlee.org surface breather p breather p.html Xah Lee Web Surface Gallery Category Surfaces Category Mathematics articles needing expert attention Category Differential equations mathanalysis stub ... more details
math scriptstyle x 2 y 2 1 math in the point math scriptstyle cosh ,a, , sinh ,a math , where math scriptstyle ... s n t or IPAc en a n , and the hyperbolic cosine cosh IPAc en icon k , from which ... other languages, like French and Russian. Standard algebraic expressions image sinh cosh tanh.svg 256px thumb font color b30000 sinh font , font color 00b300 cosh font and font color 0000b3 tanh font ... a cosh and b sinh obtained using exponential functions math e x math and math e x math image1 Hyperbolic and exponential cosh.svg caption1 a cosh x is the Arithmetic mean average of e sup x sup and e sup x sup alt1 a cosh x is the Arithmetic mean average of e sup x sup and e sup x sup image2 Hyperbolic ... math cosh x frac e x e x 2 frac e 2x 1 2e x math Hyperbolic tangent math tanh x frac sinh x cosh x frac e x e x e x e x frac e 2x 1 e 2x 1 math Hyperbolic cotangent math coth x frac cosh x sinh x frac e x e x e x e x frac e 2x 1 e 2x 1 math Hyperbolic secant math operatorname sech ,x left cosh ... i x math Hyperbolic cosine math cosh x cos rm i x math Hyperbolic tangent math tanh x rm i tan rm ... math cosh x cosh x , math Hence math tanh x tanh x , math math coth x coth x , math math operatorname ... be seen that cosh x and sech x are even function s the others are odd functions . math operatorname ... the identity math cosh 2 x sinh 2 x 1 , math which is similar to the Pythagorean trigonometric identity ... int a b cosh x dx int a b sqrt 1 left frac d dx cosh x right 2 dx text arc length . math Sums of arguments math cosh x y sinh x cdot sinh y cosh x cdot cosh y , math math sinh x y cosh x cdot sinh y sinh x cdot cosh y , math Sum and difference of cosh and sinh math cosh x sinh x e x, math math cosh ... math frac d dx sinh x cosh x , math math frac d dx cosh x sinh x , math math frac d dx tanh x 1 tanh 2 x hbox sech 2 x 1 cosh 2 x , math from http www.pen.k12.va.us Div Winchester jhhs math lessons ... of hyperbolic functions, see list of integrals of hyperbolic functions math int sinh ax ,dx a 1 cosh ... more details
In physics and mathematics , the Poincar group , named after Henri Poincar , is a quantum group , obtained by deformation of the Poincar group into an Hopf algebra . It is generated by the elements math a mu math and math Lambda mu nu math with the usual constraint math eta rho sigma Lambda mu rho Lambda nu sigma eta mu nu , math where math eta mu nu math is the Minkowski space Minkowskian metric math eta mu nu left begin array cccc 1 & 0 & 0 & 0 0 & 1 & 0 & 0 0 & 0 & 1 & 0 0 & 0 & 0 & 1 end array right . math The commutation rules reads math a j ,a 0 i lambda a j , a j,a k 0 , math math a mu , Lambda rho sigma i lambda left left Lambda rho 0 delta rho 0 right Lambda mu sigma left Lambda alpha sigma eta alpha 0 eta sigma 0 right eta rho mu right , math In the 1 1 dimensional case the commutation rules between math a mu math and math Lambda mu nu math are particularly simple. The Lorentz generator in this case is math Lambda mu nu left begin array cc cosh tau & sinh tau sinh tau & cosh tau end array right , math and the commutation rules reads math a 0 , left begin array c cosh tau sinh tau end array right i lambda sinh tau left begin array c sinh tau cosh tau end array right , math math a 1 , left begin array c cosh tau sinh tau end array right i lambda left 1 cosh tau right left begin array c sinh tau cosh tau end array right , math The coproducts are classical, and encode the group composition law math Delta a mu Lambda mu nu otimes a nu a mu otimes 1 , math math Delta Lambda mu nu Lambda mu rho otimes Lambda rho nu , math Also the Hopf algebra antipodes and the Hopf algebra counits are classical, and represent the group inversion law and the map to the identity math S a mu Lambda 1 mu nu a nu , math math S Lambda mu nu Lambda 1 mu nu Lambda nu mu , math math varepsilon a mu 0 math math varepsilon Lambda mu nu delta mu nu , math The Poincar group is the dual Hopf algebra to the K Poincar algebra , and can be interpreted as its finite version. R ... more details
h tau frac a cosh tau cos sigma math whereas the azimuthal scale factor equals math h phi frac a sin sigma cosh tau cos sigma math Thus, the infinitesimal volume element equals math dV frac a 3 sin sigma left cosh tau cos sigma right 3 , d sigma , d tau , d phi math and the Laplacian is given by math begin align nabla 2 Phi frac left cosh tau cos sigma right 3 a 2 sin sigma & left frac partial partial sigma left frac sin sigma cosh tau cos sigma frac partial Phi partial sigma right right. 8pt & quad left. sin sigma frac partial partial tau left frac 1 cosh tau cos sigma frac partial Phi partial tau right frac 1 sin sigma left cosh tau cos sigma right frac partial 2 Phi partial phi 2 right ... more details
law of cosines law of cosines math cosh c cosh a cosh b sinh a sinh b cos C, , math its dual math cos C cos A cos B sin A sin B cosh c, , math a law of sines math frac sin A sinh a frac sin B sinh b frac sin C sinh c , math and a four parts formula math cos C cosh a sinh a coth b ... function s sinh, cosh and tanh, a hyperbolic triangle is a right triangle in the first quadrant ... of the base of such a triangle is math sqrt 2 cosh a, , math and the altitude triangle altitude ... more details
Image Catenoid.svg thumb right A catenoid A catenoid is a three dimension al surface made by rotating a catenary curve about its directrix. Not counting the plane, it is the first minimal surface to be discovered. It was found and proved to be minimal by Leonhard Euler in 1744. ref L. Euler, Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, 1744, in Opera omnia I, 24 ref Early work on the subject was published also by Jean Baptiste Meusnier . ref Meusnier, J. B. M moire sur la courbure des surfaces. M m. des savans trangers 10 lu 1776 , 477 510, 1785 ref There are only two surface of revolution surfaces of revolution which are also minimal surfaces the Plane geometry plane and the catenoid. ref http mathworld.wolfram.com Catenoid.html Catenoid at MathWorld ref The catenoid may be defined by the following parametric equations math x c cosh frac v c cos u math math y c cosh frac v c sin u math math z v math where u and v are real parameters and c is a non zero real constant. In cylindrical coordinates math rho c cosh frac z c math Where c is a real constant. A physical model of a catenoid can be formed by dipping two circle s into a soap solution and slowly drawing the circles apart. The catenoid may be also defined approximately by the Stretched grid method as a facet 3D model Helicoid transformation Image helicatenoid.gif thumb right 256px Animation showing the deformation of a helicoid into a catenoid. One can bend a catenoid into the shape of a helicoid without stretching. In other words, one can make a continuous function continuous and Isometry isometric deformation of a catenoid to a helicoid such that every member of the deformation family is Minimal surface minimal having a mean curvature of zero . A Parametric equation parametrization of such a deformation is given by the system math x u,v cos theta , sinh v , sin u sin theta , cosh v , cos u math math y u,v cos theta , sinh v , cos u sin theta , cosh v , sin u math math z u,v u cos t ... more details
In hyperbolic geometry , the law of cosines is a pair of theorems relating the sides and angles of triangles on a Hyperbolic geometry hyperbolic plane , analogous to the planar law of cosines from plane trigonometry , or the spherical law of cosines in spherical trigonometry . Take a hyperbolic plane whose Gaussian curvature is math frac1 k 2 math . Then given a hyperbolic triangle ABC with angles &alpha , &beta , &gamma , and side lengths BC a , AC b , and AB c , the following two rules hold math cosh frac ak cosh frac bk cosh frac ck sinh frac bk sinh frac ck cos alpha, , math considering the sides, while math cos alpha cos beta cos gamma sin beta sin gamma cosh frac ak, , math for the angles. Christian Houzel page 8 indicates that the hyperbolic law of cosines implies the angle of parallelism in the case of an ideal hyperbolic triangle When &alpha 0, that is when the vertex A is rejected to infinity and the sides BA and CA are parallel , the first member equals 1 let us suppose in addition that &gamma &pi 2 so that cos &gamma 0 and sin &gamma 1. The angle at B takes a value &beta given by 1 sin &beta cosh a k this angle was later called angle of parallelism and Lobachevsky noted it by F a or &Pi a . See also Law of sines Hyperbolic case Hyperbolic law of sines External links http www.math.tu berlin.de geometrie Lehre SS04 VisMath mwiki index.php NonEuclideanGeometry Non Euclidean Geometry, Math Wiki at TU Berlin References Houzel, Christian 1992 The Birth of Non Euclidean Geometry , pages 3 to 21 in 1830&ndash 1930 A Century of Geometry , Lecture Notes in Physics 402, Springer Verlag ISBN 3540554084 . Cite book last Anderson first James W. title Hyperbolic geometry year 2005 publisher Springer location London isbn 1852339349 edition 2nd ed. Cite book last Reiman first Istv n year 1999 title Geometria s hat rter letei publisher Szalay K nyvkiad s Keresked h z Kft. isbn 9789632370125 Category Hyperbolic geometry es Teorema del coseno Geometr a hiperb lica fr Th ... more details
http www.abc.net.au local audio 2011 06 23 3251962.htm?site alicesprings dablink For other uses of the term freeform, see Freeform disambiguation . Orphan date February 2009 Unreferenced date July 2007 Freeform crochet and knitting is a seemingly random combination of crochet , knitting and possibly other fibre arts to make a piece that is not constrained by patterns, colours, stitches or other limitations. The roots of this art are thought to be in the 1960s and 1970s but the late 20th and early 21st centuries have seen a revival and progression of this form of textile expression. Well known freeformers are Penny O neill, James Walters, Sylvia Cosh, Jenny Dowde, Jan Messent, Margaret Hubert, http www.eject.com.au e motive prudence gallery.htm Prudence Mapstone and others. One feature of this freeform art is that group pieces can be made by people of varying expertise and experience. Leftover and scrap yarn can be made into scrumbles that can later be joined together. The name scrumbles was coined by James Walter and Syliva Cosh during the 1990s and has remained the term since. Although, it is interesting that Jenny Dowde in her books Freeform Knitting & Crochet , Freeformations and Surface Work http www.sallymilner.com.au framecatbyauthor.php?Author ID 125 has coined her terminology of the word Scrumbling as Fragments. knitting crochet http www.beautifulsilks.com workshops pennyo 27neill.html Category Crochet Category Knitting fi Vapaavirkkaus ... more details
, math x a cosh xi cos eta, math math y a sinh xi sin eta, math the potential energy can be written as math V xi, eta frac mu 1 a left cosh xi cos eta right frac mu 2 a left cosh xi cos eta right frac mu 1 left cosh xi cos eta right mu 2 left cosh xi cos eta right a left cosh 2 xi cos 2 eta right , math and the kinetic energy as math T frac ma 2 2 left cosh 2 xi cos 2 eta right left dot xi ... sub 2 sub , respectively thus, the function Y equals math Y cosh 2 xi cos 2 eta math and the function W equals math W mu 1 left cosh xi cos eta right mu 2 left cosh xi cos eta right math Using the general solution for a Liouville dynamical system below, one obtains math frac ma 2 2 left cosh 2 xi cos 2 eta right 2 dot xi 2 E cosh 2 xi left frac mu 1 mu 2 a right cosh xi gamma math math frac ma 2 2 left cosh 2 xi cos 2 eta right 2 dot eta 2 E cos 2 eta left frac mu 1 mu 2 a right cos eta gamma math Introducing a parameter u by the formula math du frac d xi sqrt E cosh 2 xi left frac mu 1 mu 2 a right cosh xi gamma frac d eta sqrt E cos 2 eta left frac mu 1 mu 2 a right cos eta gamma , math gives the parametric solution math u int frac d xi sqrt E cosh 2 xi left frac mu 1 mu 2 a right cosh ... more details
tau cosh tau cos sigma cos phi math math y a frac sinh tau cosh tau cos sigma sin phi math math z a frac sin sigma cosh tau cos sigma math where the math sigma math coordinate of a point math P math ... tau math are equal math h sigma h tau frac a cosh tau cos sigma math whereas the azimuthal scale factor equals math h phi frac a sinh tau cosh tau cos sigma math Thus, the infinitesimal volume element equals math dV frac a 3 sinh tau left cosh tau cos sigma right 3 , d sigma , d tau , d phi math and the Laplacian is given by math begin align nabla 2 Phi frac left cosh tau cos sigma right 3 a 2 sinh tau & left sinh tau frac partial partial sigma left frac 1 cosh tau cos sigma frac partial Phi partial sigma right right. 8pt & quad left. frac partial partial tau left frac sinh tau cosh tau cos sigma frac partial Phi partial tau right frac 1 sinh tau left cosh tau cos sigma right frac partial ... sqrt cosh tau cos sigma math A separable equation is then obtained. A particular solution obtained by separation of variables is math V sqrt cosh tau cos sigma , ,S nu sigma T mu nu tau Phi mu phi , math ... i nu sigma math math T mu nu tau P nu 1 2 mu cosh tau , , , , mathrm and , , , ,Q nu 1 2 mu cosh tau math math Phi mu phi e i mu phi , , , , mathrm and , , , ,e i mu phi math Where P and Q are associated ... substitution math , 1 z cosh eta , math then, for instance, with vanishing order the convention ... 2 frac cosh tau cos sigma a sinh tau . math Again, a separable equation is obtained. A particular solution ... tau math rather than math cosh tau math and the math mu math and math nu math indices are exchanged ... more details
Notability Companies date January 2011 Unreferenced date January 2011 Moksha Recordings is an English people English electronic music record company . They mainly release alternative electronic music , an example of this would be S.O.L Arranguez 1996 , which uses the classical guitar and vocals from Concierto de Aranjuez mixed with modern house music . They have also released music for big bands like The Shamen . The record company was founded in 1986 by Charles Cosh and is still going today. External links http www.moksha.co.uk Website http www.discogs.com label Moksha Recordings Discogs Category British record labels Category Electronic music record labels Category Record labels established in 1986 ... more details
In mathematics, the Bateman polynomials are a family F sub n sub of orthogonal polynomials introduced by harvs txt last Bateman authorlink Harry Bateman year 1933 . The Bateman Pasternack polynomials are a generalization introduced by harvtxt Pasternack 1939 . Bateman polynomials are given by math F n left frac d dx right cosh 1 x cosh 1 x P n tanh x math where P sub n sub is a Legendre polynomial . harvtxt Pasternack 1939 generalized the Bateman polynomials to polynomials F su b n p m with math F n m left frac d dx right cosh 1 m x cosh 1 m x P n tanh x math harvtxt Carlitz 1957 showed that the polynomials Q sub n sub studied by harvtxt Touchard 1956 are the same as Bateman polynomials up to a change of variable more precisely math Q n x 1 n2 nn binom 2n n 1 F n 2x 1 math Bateman and Pasternack s polynomials are special cases of the symmetric continuous Hahn polynomials . References Citation last1 Bateman first1 H. title Some properties of a certain set of polynomials. url http www.journalarchive.jst.go.jp english jnlabstract en.php?cdjournal tmj1911&cdvol 37&noissue 0&startpage 23 jfm 59.0364.02 year 1933 journal T hoku Mathematical Journal volume 37 pages 23 38 Citation last1 Carlitz first1 Leonard title Some polynomials of Touchard connected with the Bernoulli numbers url http cms.math.ca 10.4153 CJM 1957 021 9 doi 10.4153 CJM 1957 021 9 mr 0085361 year 1957 journal Canadian Journal of Mathematics issn 0008 414X volume 9 pages 188 190 Citation last1 Koelink first1 H. T. title On Jacobi and continuous Hahn polynomials doi 10.1090 S0002 9939 96 03190 5 mr 1307541 year 1996 journal Proceedings of the American Mathematical Society issn 0002 9939 volume 124 issue 3 pages 887 898 Citation last1 Pasternack first1 Simon title A generalization of the polynomial F sub n sub x mr 0000698 year 1939 journal London, Edinburgh, Dublin Philosophical Magazine and Journal of Science volume 28 pages 209 226 Citation last1 Touchard first1 Jacques title Nombres exponentiels et nombr ... more details
In celestial mechanics , the Stumpff functions c sub k sub x , developed by Karl Stumpff , are used for analyzing orbit s using the universal variable formulation ref name Danby cite author Danby, J.M.A title Fundamentals of Celestial Mechanics publisher Willman Bell date 1988 ref . They are defined by the formula math c k x frac 1 k frac x k 2 frac x 2 k 4 ... sum i 0 infty frac 1 i x i k 2i math for math k 0, 1, 2, 3.... math The series mathematics series above absolute convergence converges absolutely for all real number real x . By comparing the Taylor series expansion of the trigonometric functions sin and cos with c sub 0 sub x and c sub 1 sub x , a relationship can be found math c 0 x cos sqrt x math , for math x 0 math math c 1 x frac sin sqrt x sqrt x math , for math x 0 math Similarly, by comparing with the expansion of the hyperbolic functions sinh and cosh we find math c 0 x cosh sqrt x math , for math x 0 math math c 1 x frac sinh sqrt x sqrt x math , for math x 0 math The Stumpff functions satisfy the recursive definition recursive relations math x c k 2 x frac 1 k c k x math , for math k 0, 1, 2, .... math References references astronomy stub Category Celestial mechanics fr Fonction de Stumpff ... more details
In physics, the Euler Heisenberg Lagrangian describes the non linear dynamics of electromagnetic fields in vacuum. It takes into account vacuum polarization to one loop, and it is valid for electromagnetic fields that change slowly compared to the inverse electron mass. It was first obtained by Werner Heisenberg and Hans Heinrich Euler , ref W. Heisenberg and H. Euler, Folgerungen aus der Diracschen Theorie des Positrons Z. Phys. 98 , 714 1936 . ref and can be expressed as math mathcal L mathcal F frac 1 8 pi 2 int 0 infty frac ds s 3 exp left m 2 s right left es 2 frac operatorname Re cosh left es sqrt 2 left mathcal F i mathcal G right right operatorname Im cosh left es sqrt 2 left mathcal F i mathcal G right right mathcal G frac 2 3 es 2 mathcal F 1 right math Here m is the electron mass, e the electron charge, math mathcal F frac 1 2 left mathbf B 2 mathbf E 2 right math , and math mathcal G mathbf E cdot mathbf B math In the weak field limit, this becomes math mathcal L frac 1 2 left mathbf E 2 mathbf B 2 right frac 2 alpha 2 45 m 4 left left mathbf E 2 mathbf B 2 right 2 7 left mathbf E cdot mathbf B right 2 right math References references Category Quantum electrodynamics electromagnetism stub quantum stub ... more details
Inversive distance usually denoted as is a way of measuring the distance between two non intersecting circle s and . If and are inversive geometry inverted with respect to a circle centered at one of the limiting point s of the Apollonian circles Pencils of circles pencil of and , then and will invert into concentric circles. If those concentric circles have radii a nowiki nowiki and b nowiki nowiki , then the inversive distance is defined as math alpha, beta left ln frac a b right . math In addition, if a and b are the radii of and as opposed to their images , and c is the distance between their centers, then the inversive distance is given by math cosh delta left frac a 2 b 2 c 2 2ab right . math See also Coaxal circles Inversive geometry References cite book title Geometry Revisited last Coxeter first H. S. M. coauthors S. L. Greitzer year 1967 publisher Mathematical Association of America MAA location Washington, D.C. Washington isbn 0883856190 geometry stub Category Inversive geometry es Distancia inversiva ... more details
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