Wiktionary Ell or ELL may refer to Ell , a measure of length Ell, Luxembourg , a commune and town in Luxembourg Ell, Netherlands , a town in the Netherlands Ell architecture , a wing of a building EllEll Scots Ell Scots , a Scottish measure of length ELL gene Elongation factor RNA polymerase II , a human gene Ell surname , a family name Eldar Gasimov , Azerbaijani singer European Lunar Lander East London Line , a train of the London Overground Encyclopedia of Language and Linguistics , a compendium of human communication English language learner , a person acquiring the English language See also Elle disambiguation Aelle disambiguation disambig geo eo ELL fr Ell it ELL lb Ell nl Ell simple Ell disambiguation fi ELL ... more details
Ell Cranell is the trade name of two hair loss treatments in Germany Ell Cranell alpha alfatradiol Ell Cranell dexa alfatradiol and dexamethasone sia ... more details
Unreferenced stub auto yes date December 2009 Infobox Luxembourg commune name Ell luxname Ell map Map Ell.PNG arms Coat of arms ell luxbrg.png LAU2 03003 canton Redange district Diekirch website http www.ell.lu ell.lu Ell is a Communes of Luxembourg commune and small town in western Luxembourg , in the Redange canton canton of Redange . It lies close to the border with Belgium . As of 2005 , the town of Ell, which lies in the south east of the commune, has a population of 340. Other towns within the commune include Colpach Bas , Colpach Haut , and Roodt, Ell Roodt . commonscat Ell Luxembourg Ell Redange commune footer Coord 49 46 N 5 51 E region LU type city display title Category Communes in Redange canton Category Towns in Luxembourg Luxembourg geo stub als Ell Luxemburg ca Ell Luxemburg da Ell de Ell Luxemburg fr Ell Luxembourg it Ell Lussemburgo lb Gemeng Ell nl Ell Luxemburg no Ell pl Ell pt Ell ru ... more details
Pe Ell may refer to Pe Ell, Washington , a town in Washington State. Pe Ell Shannara , a character from the Shannara series of novels by Terry Brooks. See also Piel disambiguation disambig ... more details
Unreferenced stub auto yes date December 2009 Roodt Lang lb Rued is a small town in the Communes of Luxembourg commune of Ell, Luxembourg Ell , in western Luxembourg . As of 2005 , the town has a population of 150. Coord 49.79306 5.82193 display title region LU type city Category Towns in Luxembourg Category Redange canton Luxembourg geo stub fr Roodt lb Rued Ell nl Roodt Ell pl Roodt ... more details
Image Benjamin Stephenson House courtyard .JPG thumb right Benjamin Stephenson House s courtyard formed by an ell . In architecture , an ell is a wing of a building that lies perpendicular to the length of the main portion. ref Ching, Francis D. K. 1995 . A Visual Dictionary of Architecture. Van Nostrand Reinhold Company. p. 26. ISBN 0 442 02462 2. ref In connected farm architecture, the ell is often extended to attach the main house to another building, usually a barn . It takes its name from the shape of the letter L. References reflist External links http www.thisoldhouse.com toh tv house project overview 0,,607636,00.html This Old House Carlisle project connected farm DEFAULTSORT Ell Architecture Category Architectural terminology ... more details
old girl. Then my band and I were assured that it was Lindsay Ell playing a complex Tommy Emmanuel ... Consider This 2006 ref name Lindsay Ell Music cite web url http lindsayell.com blog ?page id 11 title Lindsay Ell Music publisher Lindsayell.com date accessdate 2009 08 09 Dead link date October 2010 bot H3llBot ref Alone 2009 ref name Lindsay Ell Music References Reflist External links Commons category Lindsay Ell http www.lindsayell.com Lindsay Ell Use dmy dates date December 2011 Persondata Metadata see Wikipedia Persondata . NAME Ell, Lindsay ALTERNATIVE NAMES SHORT DESCRIPTION Canadian musician DATE OF BIRTH 20 March 1989 PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Ell ... more details
Infobox Politician image only free content images are allowed for depicting living people see WP NONFREE name Monica Ell small caption birth date birth place residence office Legislative Assembly of Nunavut MLA for Iqaluit West term start 2011 term end predecessor Paul Okalik successor incumbent party non partisan br consensus government religion occupation Monica Ell is a Canada Canadian politician, who was elected to represent the district of Iqaluit West in the Legislative Assembly of Nunavut in a by election on September 12, 2011. ref name cbc http www.cbc.ca news canada north story 2011 09 12 north nunavut byelections.html Enook, Ell, Oshutapik win Nunavut byelections . CBC News , September 12, 2011. ref Prior to her election as an MLA, Ell was a director of the Inuit Broadcasting Corporation . ref name nunatsiaq http www.nunatsiaqonline.ca stories article 65674monica ell takes iqaluit west in decisive win Monica Ell takes Iqaluit West in decisive win . Nunatsiaq News , September 12, 2011. ref References reflist Nunavut MLAs Persondata Metadata see Wikipedia Persondata . NAME Ell, Monica ALTERNATIVE NAMES SHORT DESCRIPTION Canadian politician DATE OF BIRTH PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Ell, Monica Category Living people Category Members of the Legislative Assembly of Nunavut Category Canadian Inuit people Category Inuit politicians Category People from Iqaluit Category Women MLAs in Nunavut Nunavut politician stub ... more details
Infobox MP honorific prefix small The Honourable small br name Henry George Harry Ell honorific suffix br small MP small image Harry Ell, 1914.jpg alt Shows a clean shaven man looking towards the camera. He wears a shirt and tie, a waistcoat, and a suit jacket. caption Harry Ell in October 1914 office ... Ell probably 24 September 1862 27 June 1934 , commonly known as Harry Ell , was a Christchurch City ... of the Sign of the Takahe and other road houses along the Summit Road. Early years Ell was born ... turned him into a stern critic of the race relations policies of the time. Ell was a Christchurch ... politician start 1914 end 1919 term 19th NZ parlbox footer Ell stood as a prohibitionist for a seat ... 1950 p 104 Ell stood for the Lyttelton New Zealand electorate Lyttelton electorate , which contained ... 312 313 Ell was associated with the New Liberal Party New Zealand New Liberal Party in 1905. As a Member of the New Zealand Parliament House of Representatives , Ell spoke against the relaxation of liquor ... Cabinet of Thomas Mackenzie . The Summit Road rest houses Ell is most remembered for his strong interest in recreation and conservation. From 1900 onwards, Ell pushed for the creation of a network ... by architect Samuel Hurst Seager , were completed during Ell s lifetime the Sign of the Bellbird ... until long after Ell s death, in 1949. All four houses were built of local stone, and designed .... Quotes Ell s political philosophy was simple Our aim in life is to effect such social and economic ... 20 February 1900. ref As a parliamentarian, Ell was proud of his Independent politician independent ... 1899 p.3. ref gallery title Harry Ell picture gallery width 300 height 300 File SignOfTheTakahe02 gobeirne.jpg The Sign of the Takahe, one of Ell s achievements File HGEllMemorialGates01 gobeirne.jpg Plaque commemorating Harry Ell at the Sign of the Takahe File PortHillsFromCavendish.jpg View ... isbn oclc Harry Ell and His Summit Road a Biography of Henry George Ell by Lenore Oakley, published ... more details
PBB geneid 8178 RNA polymerase II elongation factor ELL is an enzyme that in humans is encoded by the ELL ... JD title Cloning of ELL, a gene that fuses to MLL in a t 11 19 q23 p13.1 in acute myeloid leukemia ... by the human ELL gene journal Science volume 271 issue 5257 pages 1873 6 year 1996 month Apr pmid 8596958 pmc doi 10.1126 science.271.5257.1873 ref ref name entrez cite web title Entrez Gene ELL elongation ... ELL gene has been shown to Protein protein interaction interact with P53 . ref name pmid10358050 ... II elongation factor ELL and p53 journal J. Biol. Chem. volume 274 issue 24 pages 17003 10 ... ELL. Identification of two overlapping ELL functional domains that govern its interaction with polymerase ... of the Holo ELL complex. Evidence for the presence of ELL associated proteins that suppress the transcriptional inhibitory activity of ELL journal J. Biol. Chem. volume 273 issue 18 pages 11212 7 year ... the RNA polymerase II elongation factor ELL and p53 journal J. Biol. Chem. volume 274 issue 24 ..., Miller T, Schmidt SL, et al. title Cloning and characterization of the EAP30 subunit of the ELL complex ... mediated gene transfer of MLL ELL transforms primary myeloid progenitors and causes acute myeloid leukemias ... al. title EAF1, a novel ELL associated factor that is delocalized by expression of the MLL ELL fusion ... cite journal author Luo RT, Lavau C, Du C, et al. title The elongation domain of ELL is dispensable but its ELL associated factor 1 interaction domain is essential for MLL ELL induced leukemogenesis ... MCB.21.16.5678 5687.2001 pmc 87288 cite journal author Simone F, Luo RT, Polak PE, et al. title ELL associated factor 2 EAF2 , a functional homolog of EAF1 with alternative ELL binding properties journal ... cite journal author Polak PE, Simone F, Kaberlein JJ, et al. title ELL and EAF1 are Cajal body components that are disrupted in MLL ELL leukemia journal Mol. Biol. Cell volume 14 issue 4 pages 1517 28 ... MLL ELL journal Mol. Cell. Biol. volume 23 issue 12 pages 4230 46 year 2003 pmid 12773566 doi 10.1128 ... more details
Image Ell Pond Rhode Island kettle hole.jpeg thumb 300px right Ell Pond in Rhode Island. Ell Pond is a kettle hole in Hopkinton, Rhode Island Hopkinton , Washington County, Rhode Island . It is surrounded by a swamp of red maple and Atlantic white cypress , and by steep granitic monadnock s. The small area contains communities of both hydrophytic plant hydrophytic and xeric plant s, which makes it ideal for ecological research and education. It was designated a National Natural Landmark in May 1974. ref http www.nature.nps.gov nnl Registry USA Map States RhodeIsland NNL EP index.cfm NPS NNL Summary ref In 1972, the Nature Conservancy purchased convert 50 acres ha including the pond to extend convert 218 acres ha of protected land owned by the Audubon Society of Rhode Island and the convert 1002 acres ha of Rockville Wildlife Management Area owned by the state. ref http www.visitrhodeisland.com what to do bird watching and nature walks 1529 rockville management area Rockville Management Area ref The preserve is jointly managed by all three entities. There are hiking trails in the preserve, but Ell pond is specifically not reachable due to its fragile environment. References reflist External links http www.nature.org wherewework northamerica states rhodeisland preserves art4091.html Nature Conservancy site http www.asri.org refuges long pond woods.html Audubon Society of Rhode Island Long Pond preserve http www.mdc.net dbrier yawgoog trails long ell.html Description of hiking trails coord 41.505331 71.782908 name Ell Pond type landmark display title Category National Natural Landmarks in Rhode Island Category Nature Conservancy preserves Category Protected areas of Washington County, Rhode Island Category Nature reserves in Rhode Island RhodeIsland geo stub ... more details
Infobox settlement name Ell image map LocatieEll.png coordinates display inline,title coordinates region NL subdivision type List of sovereign states Country subdivision name Netherlands subdivision type1 Province subdivision name1 Limburg subdivision type2 Municipality subdivision name2 Leudal population 1240 population as of 1 January 2006 coordinates Coor dms 51 13 7 N 5 47 35 E type city EG scale 100000 NB OL blank name sec1 Transport blank1 name sec1 Major roads blank1 info sec1 Rijksweg 2 A2 dialling code 0495 postal code 6010 6011 Ell Coord 51 13 N 5 48 E type city 1074 is a town in the Netherlands Dutch province of Limburg Netherlands Limburg . It is a part of the municipality of Hunsel , and lies about 7 km southeast of Weert . In 2001, Ell had 1074 inhabitants. The built up area of the town was 0.28 km , and contained 381 residences. ref name CBS Statistics Netherlands CBS , Bevolkingskernen in Nederland 2001 http www.cbs.nl nl NL menu themas milieu natuur ruimte ruimte publicaties cartografie geografie geografische data 2001 bevolkingskernen in nederland.htm . Statistics are for the continuous built up area. ref References references Category Populated places in Limburg Netherlands LimburgNL geo stub fr Ell Pays Bas li l nl Ell Limburg ... more details
Unreferenced date December 2009 Infobox character name Pe Ell series Shannara image nickname gender Male first The Druid of Shannara last Killed either by Quickening s magic after her death or by a Shannara creatures Kodens Koden species Human lbl21 Loyalty data21 Himself, secondly Rimmer Dall lbl22 Magic item or equipment data22 Enchanted dagger Stiehl Pe Ell is a character from The Druid of Shannara by Terry Brooks . Biography Pe Ell is an assassin, the number one mercernary assassin in service to Rimmer Dall . He originally lived with a drunkard claiming to be his uncle who beat him as a boy ... as an assassin for hire. It was in this way that Pe Ell met Dall, for the two both came to kill the same man. After that time, Pe Ell forged a partnership with Dall, serving him because he was intrigued. Pe Ell s opinion that death was more interesting than life clashed with Dall s, but the two worked together just the same. Dall constantly tried to convert Pe Ell to his cause, but the assassin ... either. Pe Ell came into contact with the Ohmsford family when Dall sent him to kill Quickening Shannara Quickening , the daughter of the King of the Silver River . Since Pe Ell s magic was external, he could approach her and kill her after finding her purpose. Pe Ell became enchanted with her, becoming ... as first Morgan Leah and then Walker Boh joined their company as they headed for Eldwist. Pe Ell ... Black Elfstone . Pe Ell s temper grew as Horner Dees and Carisman the tunesmith joined their group ..., Pe Ell did not know that he was meant to kill Quickening, that she had manipulated him from the beginning ... on his hands, Pe Ell ran into the Koden that guarded Eldwist. When the others came upon him, he did ... Pe Ell is a main character, is dedicated to Peter and Ellen . Pe Ell is also a city in Washington, Brooks home state. Category Characters from The Heritage of Shannara Ell Category Shannara characters Ell it Pe Ell ... more details
Carl Stephens Ell papers, 1912 1981 are located in the Northeastern University Libraries, Archives and Special Collections Department, Boston, MA. Carl Stephens Ell Obituary, Boston Globe, April 19, 1981, p.1 External links http www.northeastern.edu president images Ellhead.jpg Photograph of Ell ... Metadata see Wikipedia Persondata . NAME Ell, Carl Stephens ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1887 PLACE OF BIRTH DATE OF DEATH 1981 PLACE OF DEATH DEFAULTSORT Ell, Carl Stephens ... more details
Infobox settlement official name Pe Ell, Washington settlement type Town nickname motto Images image skyline imagesize image caption image flag image seal Maps image map Lewis County Washington Incorporated and Unincorporated areas Pe Ell Highlighted.svg mapsize 250px map caption Location of Pe Ell, Washington image map1 mapsize1 map caption1 Location subdivision type List of countries Country subdivision name United States subdivision type1 US state State subdivision name1 Washington U.S. state Washington subdivision type2 List of counties in Washington County subdivision name2 Lewis County, Washington Lewis Government government footnotes government type leader title leader name leader title1 leader name1 established title established date Area unit pref Imperial area footnotes area magnitude area total km2 1.5 area land km2 1.5 area water km2 0.0 area total sq mi 0.6 area land sq mi 0.6 ... Names Information System GNIS feature ID blank1 info 1507338 GR 3 website footnotes Pe Ell is a town ... Census 2010 census . History Pe Ell was officially incorporated on March 9, 1906. There have long been several versions of how Pe Ell was named, none of which can be authenticated. One of those versions ... it into Pe Ell. Another version is that P and L were the first initials for Pierre Charles and his Indian wife. Two words were made from the initials Pe Ell . Another distinct version is that Charlie ... to sound out the sh in Pershell so it became Pe Ell. ref A History of Pe Ell, Washington and the Upper ... a railroad depot in the town. In 1907 Pe Ell s population was around 1,000 larger than it is today ... Pe Ell is located at coord 46 34 17 N 123 17 49 W city 46.571415, 123.296842 . GR 1 According .... Politics Pe Ell is a predominantly Republican Party United States Republican area, although less ... in Washington state bg ca Pe Ell es Pe Ell Washington ht Pe Ell, Washington nl Pe Ell pt Pe Ell vo Pe Ell ... more details
Infobox NFL player name Ell Roberson image caption currentteam Free Agent currentnumber currentpositionplain Quarterback Wide Receiver birth date Birth date and age 1980 8 13 mf y birth place Baytown, Texas heightft 6 heightin 1 weight 205 college Kansas State University Kansas State undraftedyear 2005 pastteams nowiki nowiki Montreal Alouettes 2005 2006 status Active cflstatus highlights nowiki nowiki Big 12 Football Championship Game Big 12 Championship Game MVP 2003 cfl Ell Roberson III born August 13, 1980 is a former quarterback for the Kansas State Wildcats from 1999 to 2003. During his senior year, he was 6 1 tall and weighed 209 pounds. He was the starting quarterback at K State from 2001 to 2003, before starting a career in the Canadian Football League. ref http sports.espn.go.com ncf player profile?playerId 18862 ESPN Ell Roberson Stats, News, Photos Kansas State Wildcats NCAA College Football Bot generated title ref College career Roberson was a top recruit of Kansas State and Bill Snyder , who was an advocate of fast, mobile quarterbacks. He is in the K State record books, such as 4 on the single season quarterback rating of 143.2 in 2003 and he is also 6 with a rating of 136.5 in 2002. He also holds the school record for touchdown passes in a season with 24 in 2003. 2003 Big 12 Championship game Roberson was named the Most Valuable Player of the 2003 Big 12 Championship Game , completing 10 of 17 passes with no interceptions and four touchdown passes, which accounted for all Kansas State offensive scores in the game. He also rushed 17 times for 62 yards. ref http www.big12sports.com sports m footbl stats 120603aaa.htm Big 12 Conference Official Athletic Site Bot ... robersonell Ell Roberson s Facebook profile References Reflist Kansas State Wildcats quarterback navbox Persondata Metadata see Wikipedia Persondata . NAME Roberson, Ell ALTERNATIVE NAMES SHORT DESCRIPTION ... DEFAULTSORT Roberson, Ell Category 1980 births Category Living people Category American football quarterbacks ... more details
Infobox song Name Fuckin Ell It s Fred Titmus Cover Border Caption Type Artist Half Man Half Biscuit alt Artist Album Back in the DHSS Gramophone record Vinyl Published 1985, 1988 Released track no 2 Recorded Genre Indie pop Language Length 2 41 Writer Composer Label Probe Plus records Producer prev God Gave Us Life prev no 1 next Sealclubbing next no 3 Misc Extra tracklisting Album ACD album ACD Compact Disc Type live prev track Architecture And Morality, Ted And Alice live prev no 13 this track Fuckin Ell It s Fred Titmus live track no 14 next track Time Flies By When You re The Driver Of A Train live next no 15 Audio sample? File Half Man Half Biscuit.jpg 200px thumb Half Man Half Biscuit playing live in London Fuckin Ell It s Fred Titmus is a song by UK Indie pop indie band Half Man Half Biscuit . It was on the 1985 album Back in the DHSS , and the 1988 CD ACD album ACD . ref Harvnb Robbins 1991 page 299 ref The subject of the song was cricketer Fred Titmus . ref name Bale Harvnb Bale 2008 page 187 ref The band line up for both the album track and the live recording was Paul Wright on drums, Neil Crossley on bass guitar and vocals, Nigel Blackwell on rhythm guitar and lead vocals, Simon Blackwell on lead guitar and David Lloyd on keyboards. Release and performances In 1985, the band released a 33RPM vinyl LP entitled Back in the DHSS . ref name Discogs Harvnb Discogs DHSS ref This was the second track on Side A of the album, following God Gave Us Life and preceding Sealclubbing , 99 Of Gargoyles Look Like Bob Todd and Time Flies By When You re A Driver Of A Train . ref ... Ell featured as track number 14, following Architecture And Morality, Ted And Alice live and preceding ... Listen filename FuckinEllItsFredTitmus.ogg title Half Man Half Biscuit Fuckin Ell It s Fred Titmus 1985 description 16 second sample from Half Man Half Biscuit s Fuckin Ell It s Fred Titmus . format Ogg ... www.chrisrand.com hmhb back in the dhss fuckin ell its fred titmus This song, at the Half Man Half ... more details
Ell Persons was an African American man who was Lynching in the United States lynched on 22 May 1917, after he was accused of having raped and murdered a 16 year old white girl, Antoinette Rappel, in Memphis, Tennessee , United States. He was arrested and was awaiting trial when he was captured by a lynch party, who burned him alive and scattered his dismembered remains around town, throwing his decapitated head at a group of African Americans. A large crowd attended his lynching, which had the atmosphere of a carnival. The lynching, which was described as one of the most vicious in American history, by whom date November 2010 did not lead to a single person being charged, but did play a part in the foundation of the Memphis chapter of the National Association for the Advancement of Colored People NAACP . Death of Rappel and arrest of Persons Described as i nnocent, pure, pretty, by turns playful and pensive and as someone who must have reminded many readers of their own daughters, nieces, or cousins , Rappel was a student at Treadwell School in Memphis. On the morning of 30 April 1917, she left for school and did not return on 2 May 1917 a newspaper published a story which said she left to join the war, a story her mother, Mrs Wood, reportedly believed. Later, Rappel was found dead ... Mob captures slayer of the Rappel girl Ell Persons to be lynched near scene of murder May resort ... read Thousands cheered when negro burned Ell Persons pays death penalty for killing girl ... Ell 20Persons.PDF Memphis 506 KB , The Crisis NAACP newspaper The Crisis Supplement 14 3 1 4, July ... citation 1 4 1 9 7 p141971 index.html The Lynching of Ell Persons and the Rise of the Memphis ... of Ell Persons in http quod.lib.umich.edu cgi t text text idx?c acls cc acls view toc idno heb90036.0001.001 ... States Persondata Metadata see Wikipedia Persondata . NAME Persons, Ell, Lynching Of ALTERNATIVE NAMES ... DEFAULTSORT Persons, Ell, Lynching Of Category 1917 deaths Category 1917 in Tennessee Category ... more details
Infobox settlement official name Ell Township settlement type Civil township Township nickname motto Images image skyline imagesize image caption image flag image seal Maps image map Map highlighting Ell Township, Hancock County, Iowa.svg mapsize map caption Location in Hancock County image map1 mapsize1 map caption1 Location coordinates display inline,title coordinates region US IA subdivision type List of countries Country subdivision name USA subdivision type1 Political divisions of the United States State subdivision name1 flag Iowa subdivision type2 List of counties in Iowa County subdivision name2 Hancock County, Iowa Hancock government footnotes government type leader title leader name leader title1 leader name1 established title established date Area area footnotes area magnitude area total km2 94.25 area land km2 94.25 area water km2 0 unit pref Imperial area total sq mi 36.39 area land sq mi 36.39 area water sq mi 0 area water percent 0 Population population as of United States Census, 2000 2000 population footnotes population total 870 population density km2 9.2 population density sq mi 23.9 General information elevation footnotes elevation m 373 elevation ft 1224 latd 43 latm 02 lats 06 latNS N longd 93 longm 32 longs 49 longEW W Area postal codes & others timezone North American Central Time Zone CST utc offset 6 timezone DST North American Central Time Zone CDT utc offset DST 5 postal code type ZIP codes postal code 50438, 50449 area code blank name Geographic Names ... NO P3 FID 0467783 0467783 website footnotes Ell Township is one of sixteen Civil township townships ... American FactFinder ref . Geography According to the United States Census Bureau , Ell Township covers ... data.com township Ell Hancock IA.html City Data.com Geographic Location Centre Ell Township ... Category Townships in Hancock County, Iowa es Municipio de Ell condado de Hancock, Iowa pl Gmina Ell ... more details
3 j symbol Wigner 3jm symbols . math c k ell,m, ell ,m int d 2 Omega Y ell m Omega Y ell ... such a product over a spherical harmonic basis math Y ell m Y ell m sum ell ,m hat A ell,m, ell ,m , ell ,m Y ell m , math one may then multiply by math Y math and integrate, using the conjugate property and being careful with phases and normalisations math int Y ell m Y ell m Y L M hat A ell,m, ell ,m ,L,M c L ell,m, ell ,m math These coefficient obey a number of identities. They include math begin align c k ell,m, ell ,m & c k ell, m, ell , m & 1 m m c k ell ,m , ell,m & 1 m m sqrt frac 2 ell 1 2k 1 c ellell ,m ,k,m m & 1 m sqrt frac 2 ell 1 2k 1 c ell k,m m , ell,m sum m ellell c k ell,m, ell,m & 2 ell 1 delta k,0 sum m ellell sum m ellell c k ell,m, ell ,m 2 & sqrt 2 ell 1 2 ell 1 cdot c k ell,0, ell ,0 sum m ellell c k ell,m, ell ,m 2 & sqrt frac 2 ell 1 2 ell 1 cdot c k ell,0, ell ,0 sum m ellell c k ell,m, ell ,m c k ell,m, tilde ell,m & delta ell , tilde ell cdot sqrt frac 2 ell 1 2 ell 1 cdot c k ell,0, ell ,0 sum m c k ell,m r, ell ,m c k ell,m r, tilde ell,m & delta ell, tilde ell cdot frac sqrt 2 ell 1 2 ell 1 2k 1 cdot c k ell,0, ell ,0 sum m c k ell,m r, ell ,m c q ell,m r, ell ,m & delta k,q cdot frac sqrt 2 ell 1 2 ell 1 2k 1 cdot c k ell,0, ell ,0 end ... more details
and numerically stable way. However, for reference, we may write the matrix as math Q k ell begin bmatrix ... be written math q ij delta ij delta ik delta jk delta i ell delta j ell c 1 delta ik delta j ell delta i ell delta jk s . , math Suppose h is an index other than k or which must themselves be distinct . Then the similarity update produces, algebraically, math a hk a kh c a hk s a h ell , math math a h ell a ell h c a h ell s a hk , math math a k ell a ell k c 2 s 2 a k ell sc a kk a ellell 0 , math math a kk c 2 a kk s 2 a ellell 2 s c a k ell , math math a ellell s 2 a kk c 2 a ellell 2 s c a k ell , math Numerically stable computation To determine the quantities needed for the update, we ... frac c 2 s 2 sc frac a ellell a kk a k ell . math Set to half this quantity, math beta frac a ellell a kk 2 a k ell . math If a sub k sub is zero we can stop without performing an update ... update equations are math a hk a kh a hk s a h ell rho a hk , math math a h ell a ell h a h ell s a hk rho a h ell , math math a k ell a ell k 0 , math math a kk a kk t a k ell , math math a ellell a ellell t a k ell , math As previously remarked, we need never explicitly compute the rotation ... more details
See also Laplace expansion Laplace expansion of determinant . In physics, the Laplace expansion of a 1 r type potential is applied to expand Newton s law of universal gravitation Gravitational field Newton s gravitational potential or Coulomb s law Table of derived quantities Coulomb s electrostatic potential . In quantum mechanical calculations on atoms the expansion is used in the evaluation of integrals of the interelectronic repulsion. The Laplace expansion is in fact the expansion of the inverse distance between two points. Let the points have position vectors r and r , then the Laplace expansion is math frac 1 mathbf r mathbf r sum ell 0 infty frac 4 pi 2 ell 1 sum m ell ell 1 m frac r scriptscriptstyle ell r scriptscriptstyle ell 1 Y m ell theta, varphi Y m ell theta , varphi . math Here r has the spherical polar coordinates r , &theta , &phi and r has r , &theta , &phi . Further r sub < sub is min r , r and r sub > sub is max r , r . The function math Y m ell math is a normalized spherical harmonics spherical harmonic function . The expansion takes a simpler form when written in terms of solid harmonics , math frac 1 mathbf r mathbf r sum ell 0 infty sum m ell ell 1 m I m ell mathbf r R m ell mathbf r quad hbox with quad mathbf r mathbf r . math Derivation The derivation of this expansion is simple. One writes math frac 1 mathbf r mathbf r frac 1 sqrt r 2 r 2 2 r r cos gamma frac 1 r scriptscriptstyle sqrt 1 h 2 2 h cos gamma quad hbox with quad h equiv frac r scriptscriptstyle r scriptscriptstyle . math We find here the generating function of the Legendre polynomials Applications of Legendre polynomials in physics Legendre polynomials math P ell cos gamma math math frac 1 sqrt 1 h 2 2 h cos gamma sum ell 0 infty h ell P ell cos gamma . math Use of the Spherical multipole moments Spherical multipole moments of a point charge spherical harmonic addition theorem math P ell cos gamma frac 4 pi 2 ell 1 sum m ell ell 1 m Y m ell theta, varphi Y m ell theta , ... more details
Unreferenced stub auto yes date December 2009 A fall or fa a Scottish measurement of length. Other variants of the name include faw , faa and fa , the spelling with an apologetic apostrophe is not favoured now. The measurement was mostly out of use by the 19th century, and English measurements were imposed in 1824 by an act of parliament. There were 320 falls in a Mile Scots mile Scots mile . Equivalent to Obsolete Scottish units of measurement Scottish measures 18 ft 6 Ell Ell Scots ell s Metric system 5.6479 metres Imperial system 6.1766 yards 1.123 poles See also Ell Ell Scots Ell Scots Inch Scottish inch Scottish inch Mile Scots mile Scots mile DEFAULTSORT Fall Unit Category Scottish weights and measures Category Units of length Scotland stub Standard stub ... more details
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