source
stringlengths 16
98
| text
stringlengths 40
168k
|
|---|---|
Wikipedia:Izabella Łaba#0
|
Izabella Łaba (born 1966) is a Polish-Canadian mathematician, a professor of mathematics at the University of British Columbia. Her main research specialties are harmonic analysis, geometric measure theory, and additive combinatorics. == Professional career == Łaba earned a master's degree in 1986 from the University of Wrocław. She received her PhD from the University of Toronto in 1994, under the supervision of Israel Michael Sigal, after which she was a postdoctoral scholar at University of California, Los Angeles and then an assistant professor at Princeton University before moving to UBC in 2000. She is one of three founding editors of the Online Journal of Analytic Combinatorics. == Contributions == Łaba's thesis research proved the asymptotic completeness of many n-body systems in the presence of a constant magnetic field. While at UCLA, with Nets Katz and Terence Tao, she made important contributions to the theory of Kakeya sets, including the best known lower bound on these sets in three-dimensional Euclidean spaces. Her more recent work concerns harmonic analysis, periodic tilings, and Falconer's conjecture on sets of distances of points. == Awards and honours == Łaba was the 2004 winner of the Coxeter–James Prize, an annual prize of the Canadian Mathematical Society for outstanding young mathematicians. In 2008, the CMS honoured her again with their Krieger–Nelson Prize, given to an outstanding woman in mathematics. In 2012 she became a fellow of the American Mathematical Society. == References == == External links == Home page The Accidental Mathematician, Łaba's blog
|
Wikipedia:J. B. Lockhart#0
|
James Balfour Lockhart FRSE (1886–27 January 1969) was a Scottish mathematician and teacher. He was generally known as J. B. Lockhart or simply JBL. He was a Fellow of the Royal Society of Edinburgh. == Life == He was born in Cambuslang in 1886. He was educated locally then studied for the civil service at Skerry's College in Glasgow. In 1912 he decided to start studying mathematics and natural philosophy (physics) at the University of Edinburgh. His studies were interrupted by the First World War, during which he served in Egypt and Gallipoli. He appears to have been a Private in the Royal Army Medical Corps Returning to university after the war he graduated with first class honours also receiving the Napier Medal for best mathematician in 1920. After graduation he decided to stay in Edinburgh and began teaching at Edinburgh Academy. In 1930 he became house-master of Dundas House, a boarding facility for the academy at 2 Kinnear Road. In 1932 he was elected a Fellow of the Royal Society of Edinburgh. His proposers were Sir Edmund Taylor Whittaker, Herbert Turnbull, Charles Barkla and Sir Charles Galton Darwin. In 1937 he moved to Inverleith Grove, and in 1940 took over as Head of Mathematics. In October 1950 he fell ill and in 1951 was forced to retire due to a heart condition. He died of complications following an operation on a broken leg in Glenfarg Hospital on 27 January 1969. His wife died in July of the same year. == Family == He was happily married to Adie, whom he had met as a student at Skerrys College. Holidays were spent at his cottage in Kingskettle in Fife. On his retirement they moved to Balmony, a cottage in Glendevon in southern Perthshire (now part of Clackmannanshire). His hobbies included bee-keeping. == References ==
|
Wikipedia:J. E. Jayasuriya#0
|
J. E. Jayasuriya (14 February 1918 - 23 January 1990) was a Sri Lankan educationist. He was the Professor of Education at the University of Ceylon. == Early life and education == Jayasuriya's father was a postmaster and the family moved when he was transferred from post office to post office. He received his education at Nawalapitiya Anuruddha Vidyalaya, Dharmasoka College, Ambalangoda and at Wesley College, Colombo. In 1933, he came third in the British Empire at the Cambridge Senior Examination gaining a scholarship to the University College, Colombo and graduated in 1939 with a first class in mathematics. == Educational career == He accepted an invitation from P. de S. Kularatne to serve as Acting Principal of Dharmapala Vidyalaya, Pannipitiya and thereafter served as Deputy Principal of Sri Sumangala Vidyalaya, Panadura. He was then invited by the Minister of Education Dr. C. W. W. Kannangara to become the Principal of newly established central school in his electorate, the Matugama Central College. Thereafter, he served as the Principal of Wadduwa Central College. In 1947, he left to London for postgraduate studies at the Institute of Education of the University of London, gaining a Postgraduate Diploma in Education and a Master of Arts in Education. On his return, he joined the Government Teacher Training College, Maharagama as a lecturer in mathematics. In 1952, he joined the Faculty of Education, University of Ceylon as a lecturer and in 1957, he succeeded Prof. T. L. Green and was appointed as Professor of Education. In 1961, he was appointed as the Chairman of the National Education Commission. He served as the Dean of the Faculty of Arts and from time to time as acting Vice Chancellor until his retirement in 1971 to join UNESCO as the Regional Advisor in Population Education based in Bangkok. At the end of his contract he returned to Sri Lanka, where he spent his last days writing and researching. He died in January 1989. He has awarded an honorary Doctor of Letters from the University of Colombo and an honorary Doctor of Science from the Open University of Sri Lanka. He was a Chartered Psychologist. == == Books published == Educational Policies and Progress during British Rule in Ceylon, 1796-1948 Education in Ceylon Before and After Independence Dynamics of Nation Building in Malaysia; Education in Korea – A Third World Success Story Population Education through Curriculum Innovation == See also == Bachelor of Education == References ==
|
Wikipedia:J. F. Cameron#0
|
John Forbes Cameron (July 1873 – 21 March 1952) was a Scottish mathematician, academic and academic administrator. He was Master of Gonville and Caius College, Cambridge from 1928 to 1948 and was Vice-Chancellor of the University of Cambridge from 1933 to 1935. == Early life == Cameron was born in July 1873 in Stanley, Perthshire, Scotland. He was educated at Perth Academy, a state high school in Perth, Scotland. He studied mathematics and natural philosophy at the University of Edinburgh. He was awarded a Ferguson Scholarship, available to graduates of Scottish universities, to attend the University of Cambridge. He studied the Mathematical Tripos at Gonville and Caius College, Cambridge from 1895 to 1898. He was tutored by R. R Webb and completed his degree as second wrangler. == Academic career == In 1899, Cameron was elected a Fellow of Gonville and Caius College, Cambridge. The following year, in 1900, he was appointed a lecturer in mathematics and in 1909 was appointed a tutor. During World War I, from 1914 to 1918, he left the college to work at the Ministry of Munitions. After the war, he returned to Gonville and Caius College and was appointed senior tutor in 1919. Between 1921 and 1928, he served as the college bursar. On 23 November 1928, he was elected Master of Gonville and Caius College. From 1933 to 1935, he additionally served as Vice-Chancellor of the University of Cambridge. In 1943, he reached the usual retirement age for a college head, 70 years, but his tenure was extended. He finally retired in 1948, after 20 years as Master. == References ==
|
Wikipedia:J. Stewart Burns#0
|
Joseph Stewart Burns (born December 4, 1969), better known as J. Stewart Burns or simply just Stewart Burns is a television writer and producer most notable for his work on The Simpsons, Futurama, and Unhappily Ever After. == Education == Burns attended Harvard University, where he wrote for the Harvard Lampoon. Noted in the DVD commentaries of "The Deep South" and "Roswell That Ends Well", Burns has an M.A. in Mathematics from the University of California, Berkeley, where he studied under John Rhodes. Burns is partly credited for The Simpsons' inclusion of a number of complex mathematical concepts and jokes within the series. Burns was famously referenced in a 1993 Newsweek article about his decision to jump from pursuing a graduate degree in mathematics to writing comedy: "You could read the entire story of American decline in that one career move." == Career == Burns got his start by writing for Beavis and Butthead. Since then, he has written for The Simpsons, Futurama, and Unhappily Ever After. Aside from writing on the original series, Burns also wrote the script for the Futurama video game as well as one of the Spyro games, Spyro: A Hero's Tail. Burns developed and has served as the game runner of The Simpsons: Tapped Out since its inception. === Awards === Burns has won the Emmy Award for Outstanding Animation Program four times — for Futurama in 2002, and for The Simpsons in 2006, 2008 and 2019. == Writing credits == === Futurama episodes === "My Three Suns" (1999) "Mars University" (1999) "A Head in the Polls" (1999) "The Deep South" (2000) "The Cryonic Woman" (2000) "Roswell That Ends Well" (2002) "Where the Buggalo Roam" (2002) "Neutopia" (2011) === The Simpsons episodes === "Moe Baby Blues" (2003) "The Way We Weren't" (2004) "There's Something About Marrying" (2005) "The Monkey Suit" (2006) "Homerazzi" (2007) "Marge Gamer" (2007) "Eternal Moonshine of the Simpson Mind" (2007) "Waverly Hills 9-0-2-1-D'oh" (2009) "Holidays of Future Passed" (2011) "The D'oh-cial Network" (2012) "What Animated Women Want" (2013) "Steal This Episode" (2014) "Days of Future Future" (2014) "Simpsorama" (2014) "Every Man's Dream" (2015) "Puffless" (2015) "Fland Canyon" (2016) "Friends and Family" (2016) "Dogtown" (2017) "Flanders' Ladder" (2018) "Treehouse of Horror XXX" (2019) "The Miseducation of Lisa Simpson" (2020) "Screenless" (2020) "Mother and Child Reunion" (2021) "Write Off This Episode" (2023) "The Tipping Point" (2024) "The Last Man Expanding" (2025) "Yellow Planet" (2025) == Supervising producer credits == === The Simpsons episodes === "The Great Louse Detective" (2002) "Special Edna" (2003) "The Dad Who Knew Too Little" (2003) "The Strong Arms of the Ma" (2003) "Pray Anything" (2003) "Barting Over" (2003) "I'm Spelling As Fast As I Can" (2003) "A Star Is Born Again" (2003) "Mr. Spritz Goes to Washington" (2003) "C.E. D'oh" (2003) "'Scuse Me While I Miss the Sky" (2003) "Three Gays of the Condo" (2003) "Dude, Where's My Ranch?" (2003) "Old Yeller-Belly" (2003) "Brake My Wife, Please" (2003) "Moe Baby Blues" (2003) "The Bart of War" (2003) "Treehouse of Horror XIV" (2003) (starring as "Here Lies J. Stewart Burns") "My Mother the Carjacker" (2003) "The President Wore Pearls" (2003) "The Regina Monologues" (2003) "The Fat and the Furriest" (2003) "Today I Am a Clown" (2003) "'Tis the Fifteenth Season" (2003) == Co-executive producer credits == === The Simpsons episodes === "Marge vs. Singles, Seniors, Childless Couples and Teens and Gays" (2004) "I, (Annoyed Grunt)-bot" (2004) "Diatribe of a Mad Housewife" (2004) "Margical History Tour" (2004) "Milhouse Doesn't Live Here Anymore" (2004) "Smart and Smarter" (2004) "The Ziff Who Came to Dinner" (2004) "Co-Dependents' Day" (2004) "The Wandering Juvie" (2004) "My Big Fat Geek Wedding" (2004) "Catch 'Em If You Can" (2004) "Simple Simpson" (2004) "The Way We Weren't" (2004) "Bart-Mangled Banner" (2004) "Fraudcast News" (2004) "Treehouse of Horror XV" (2004) (as J. Stewart Burns In Hell) "All's Fair in Oven War" (2004) "Sleeping with the Enemy" (2004) "She Used to Be My Girl" (2004) "Fat Man and Little Boy" (2004) "Midnight Rx" (2005) "Mommie Beerest" (2005) "Homer and Ned's Hail Mary Pass" (2005) "Pranksta Rap" (2005) "There's Something About Marrying" (2005) "On a Clear Day I Can't See My Sister" (2005) "Goo Goo Gai Pan" (2005) "Mobile Homer" (2005) "The Seven-Beer Snitch" (2005) "Future-Drama" (2005) "Don't Fear the Roofer" (2005) "The Heartbroke Kid" (2005) "A Star Is Torn" (2005) "Thank God It's Doomsday" (2005) "Home Away from Homer" (2005) "The Father, the Son and the Holy Guest Star" (2005) "The Bonfire of the Manatees" (2005) "The Girl Who Slept Too Little" (2005) "Milhouse of Sand and Fog" (2005) "Treehouse of Horror XVI" (2005) (as J. Stewart Burns At The Stake) "Marge's Son Poisoning" (2005) "See Homer Run" (2005) "The Last of the Red Hat Mamas" (2005) "The Italian Bob" (2005) "Simpsons Christmas Stories" (2005) "Homer's Paternity Coot" (2006) "We're on the Road to D'ohwhere" (2006) "My Fair Laddy" (2006) "The Seemingly Never-Ending Story" (2006) "Bart Has Two Mommies" (2006) "Homer Simpson, This Is Your Wife" (2006) "Million-Dollar Abie" (2006) "Kiss Kiss Bang Bangalore" (2006) "Girls Just Want to Have Sums" (2006) "Regarding Margie" (2006) "The Monkey Suit" (2006) "Marge and Homer Turn a Couple Play" (2006) "The Mook, the Chef, the Wife and Her Homer" (2006) "Jazzy and the Pussycats" (2006) "Please Homer, Don't Hammer 'Em" (2006) "Treehouse of Horror XVII" (2006) (Starring as J.St=ewart=Bμrns) "G.I. (Annoyed Grunt)" (2006) "Moe'N'a Lisa" (2006) "Ice Cream of Margie (with the Light Blue Hair)" (2006) "The Haw-Hawed Couple" (2006) "Kill Gil, Volumes I & II" (2006) "The Wife Aquatic" (2007) "Revenge Is a Dish Best Served Three Times" (2007) "Little Big Girl" (2007) "Springfield Up" (2007) "Yokel Chords" (2007) "Rome-Old and Juli-Eh" (2007) "Homerazzi" (2007) "Marge Gamer" (2007) "The Boys of Bummer" (2007) "Crook and Ladder" (2007) "Stop or My Dog Will Shoot!" (2007) "24 Minutes" (2007) "You Kent Always Say What You Want" (2007) "He Loves to Fly and He D'ohs" (2007) "The Homer of Seville" (2007) "Midnight Towboy" (2007) "I Don't Wanna Know Why the Caged Bird Sings" (2007) "Treehouse of Horror XVIII" (2007) (Starring as Jth Degree Burns) "Little Orphan Millie" (2007) "Husbands and Knives" (2007) "Funeral for a Fiend" (2007) "Eternal Moonshine of the Simpson Mind" (2007) "E Pluribus Wiggum" (2008) "That '90s Show" "Love, Springfieldian Style" "The Debarted" "Dial 'N' for Nerder" "Smoke on the Daughter" "Papa Don't Leech" "Apocalypse Cow" "Any Given Sundance" "Mona Leaves-a" "All About Lisa" "Sex, Pies and Idiot Scrapes" "Lost Verizon" "Double, Double, Boy in Trouble" "Treehouse of Horror XIX" (Starring as J. Boo-Art-Boo-Urns) "Dangerous Curves" "Homer and Lisa Exchange Cross Words" "MyPods and Boomsticks" "The Burns and the Bees" "Lisa the Drama Queen" "Take My Life, Please" "How the Test Was Won" "No Loan Again, Naturally" "Gone Maggie Gone" "In the Name of the Grandfather" "Wedding for Disaster" "Eeny Teeny Maya Moe" "The Good, the Sad, and the Drugly" "Father Knows Worst" "Waverly Hills 9-0-2-1-D'oh" "Four Great Women and a Manicure" "Coming to Homerica" "Homer the Whopper" "Bart Gets a 'Z'" "The Great Wife Hope" "Treehouse of Horror XX" (Starring as J. O-Lantern Burns) "The Devil Wears Nada" "Pranks and Greens" "Rednecks and Broomsticks" "Oh Brother, Where Bart Thou?" "Thursdays with Abie" "Once Upon a Time in Springfield" "Million Dollar Maybe" "Boy Meets Curl" "The Color Yellow" "Postcards from the Wedge" "Stealing First Base" "The Greatest Story Ever D'ohed" "American History X-cellent" "Chief of Hearts" "The Squirt and the Whale" "To Surveil with Love" "Moe Letter Blues" "The Bob Next Door" "Judge Me Tender" "Elementary School Musical" "Loan-a Lisa" "MoneyBart" "Treehouse of Horror XXI" (Starring as J. Disco Stu Mr. Burns) "Lisa Simpson, This Isn't Your Life" "The Fool Monty" "How Munched Is That Birdie in the Window?" "The Fight Before Christmas" "Donnie Fatso" "Moms I'd Like to Forget" "Flaming Moe" "Homer the Father" "The Blue and the Gray" "Angry Dad: The Movie" "The Scorpion's Tale" "A Midsummer's Nice Dream" "Love Is a Many Strangled Thing" "The Great Simpsina" "The Real Housewives of Fat Tony" "Homer Scissorhands" "500 Keys" "The Ned-liest Catch" "The Falcon and the D'ohman" "Bart Stops to Smell the Roosevelts" "Treehouse of Horror XXII" (Starring as The Gruesome Stewsome) "Replaceable You" "The Food Wife" "The Book Job" "The Man in the Blue Flannel Pants" "The Ten-Per-Cent Solution" "Holidays of Future Passed" "Politically Inept, with Homer Simpson" "The D'oh-cial Network" "Moe Goes from Rags to Riches" "The Daughter Also Rises" "At Long Last Leave" "Exit Through the Kwik-E-Mart" "How I Wet Your Mother" "Them, Robot" "Beware My Cheating Bart" "A Totally Fun Thing That Bart Will Never Do Again" "The Spy Who Learned Me" "Ned 'n' Edna's Blend Agenda" "Lisa Goes Gaga" "Moonshine River" "Treehouse of Horror XXIII" (Starring as The Witch's Stew Burns) "Adventures in Baby-Getting" "Gone Abie Gone" "Penny-Wiseguys" "A Tree Grows in Springfield" "The Day the Earth Stood Cool" "To Cur, with Love" "Homer Goes to Prep School" "A Test Before Trying" "The Changing of the Guardian" "Love Is a Many-Splintered Thing" "Hardly Kirk-ing" "Gorgeous Grampa" "Black-Eyed, Please" "Dark Knight Court" "What Animated Women Want" "Pulpit Friction" "Whiskey Business" "The Fabulous Faker Boy" "Dangers on a Train" "The Saga of Carl" "Homerland" "Treehouse of Horror XXIV" (Starring as J. Screwit Burns) "Four Regrettings and a Funeral" "YOLO" "Labor Pains" "The Kid Is All Right" "Yellow Subterfuge" "White Christmas Blues" "Steal This Episode" "Married to the Blob" "Specs and the City" "The Man Who Grew Too Much" "Diggs" "The Winter of His Content" "The War of Art" "You Don't Have to Live Like a Referee" "Luca$" "Days of Future Future" "What to Expect When Bart's Expecting" "Brick Like Me" "Pay Pal" "The Yellow Badge of Cowardge" "The Simpsons Take the Bowl" "Clown in the Dumps" "The Wreck of the Relationship" "Super Franchise Me" "Treehouse of Horror XXV" (Starring as Jay Stuart Byrnes) "Opposites A-Frack" "Simpsorama" "Blazed and Confused" "Covercraft" "I Won't Be Home for Christmas" "The Man Who Came to Be Dinner" "Bart's New Friend" "The Musk Who Fell to Earth" "Walking Big & Tall" "My Fair Lady" "The Princess Guide" "Sky Police" "Waiting for Duffman" "Peeping Mom" "The Kids Are All Fight" "Let's Go Fly a Coot" "Bull-E" "Mathlete's Feat" "Every Man's Dream" "'Cue Detective" "Puffless" "Halloween of Horror" "Treehouse of Horror XXVI" (Strraing as Junk Status Bonds) "Friend with Benefit" "Lisa with an 'S'" "Paths of Glory" "Barthood" "The Girl Code" "Teenage Mutant Milk-Caused Hurdles" "Much Apu About Something" "Love Is in the N2-O2-Ar-CO2-Ne-He-CH4" "Gal of Constant Sorrow" "Lisa the Veterinarian" "The Marge-ian Chronicles" "The Burns Cage" "How Lisa Got Her Marge Back" "Fland Canyon" "To Courier with Love" "Simprovised" "Orange Is the New Yellow" "Monty Burns' Fleeing Circus" "Friends and Family" "The Town" "Treehouse of Horror XXVII" (Starring as J. Sewer Rat Burns) "Planet of the Couches" "Trust but Clarify" "There Will Be Buds" "Havana Wild Weekend" "Dad Behavior" "The Last Traction Hero" "The Nightmare After Krustmas" "Pork and Burns" "The Great Phatsby" "Fatzcarraldo" "The Cad and the Hat" "Kamp Krustier" "22 for 30" "A Father's Watch" "The Caper Chase" "Looking for Mr. Goodbart" "Moho House" "Dogtown" "The Serfsons" "Springfield Splendor" "Whistler's Father" "Treehouse of Horror XXVIII" (Starring as Trey Newsquirt Burns) "Grampy Can Ya Hear Me" "The Old Blue Mayor She Ain't What She Used to Be" "Singin' in the Lane" "Mr. Lisa's Opus" "Gone Boy" "Haw-Haw Land" "Frink Gets Testy" "Homer Is Where the Art Isn't" "3 Scenes Plus a Tag from a Marriage" "Fears of a Clown" "No Good Read Goes Unpunished" "King Leer" "Lisa Gets the Blues" "Forgive and Regret" "Left Behind" "Throw Grampa from the Dane" "Flanders' Ladder" "Bart's Not Dead" "Heartbreak Hotel" "My Way or the Highway to Heaven" "Treehouse of Horror XXIX" (Starring as Snrub Trawets J) "Baby You Can't Drive My Car" "From Russia Without Love" "Werking Mom" "Krusty the Clown (episode)" "Daddicus Finch" "'Tis the 30th Season" "Mad About the Toy" "The Girl on the Bus" "I'm Dancing as Fat as I Can" "The Clown Stays in the Picture" "101 Mitigations" "I Want You (She's So Heavy)" "E My Sports" "Bart vs. Itchy & Scratchy" "Girl's in the Band" "I'm Just a Girl Who Can't Say D'oh" "D'oh Canada" "Woo-Hoo Dunnit?" "Crystal Blue-Haired Persuasion" "The Winter of Our Monetized Content" "Go Big or Go Homer" "The Fat Blue Line" "Treehouse of Horror XXX" (Starring as J. Strewn Bones) "Gorillas on the Mast" "Marge the Lumberjill" "Livin La Pura Vida" "Thanksgiving of Horror" (Starring as J. Stuffing Birds) "Todd, Todd, Why Hast Thou Forsaken Me?" "Bobby, It's Cold Outside" "Hail to the Teeth" "The Miseducation of Lisa Simpson" "Frinkcoin" "Bart the Bad Guy" "Screenless" "Better Off Ned" "Highway to Well" "The Incredible Lightness of Being a Baby" "Warrin' Priests: Part One" "Warrin' Priests: Part Two" "The Hateful Eight-Year-Olds" "The Way of the Dog" "Undercover Burns" "I, Carumbus" "Now Museum, Now You Don't" "Treehouse of Horror XXXI" (Starring as J. Stewicide Burns) "The 7 Beer Itch" "Podcast News" "Three Dreams Denied" "The Road to Cincinnati" "Sorry Not Sorry" "A Springfield Summer Christmas for Christmas" "The Dad-Feelings Limited" "Diary Queen" "Wad Goals" "Yokel Hero" "Do Pizza Bots Dream of Electric Guitars" "Manger Things" "Uncut Femmes" "Burger Kings" "Panic on the Streets of Springfield" "Mother and Child Reunion" "The Man from G.R.A.M.P.A." "The Last Barfighter" "The Star of the Backstage" "Bart's in Jail!" "Treehouse of Horror XXXII" (Starring as J. Short BTC) "The Wayz We Were" "Lisa's Belly" "A Serious Flanders: Part One" "A Serious Flanders: Part Two" "Portrait of a Lackey on Fire" "Mothers and Other Strangers" "A Made Maggie" "The Longest Marge" "Pixelated and Afraid" "Boyz N the Highlands" "You Won't Believe What This Episode Is About – Act Three Will Shock You!" "Bart the Cool Kid" "Pretty Whittle Liar" "The Sound of Bleeding Gums" "My Octopus and a Teacher" "Girls Just Shauna Have Fun" "Marge the Meanie" "Meat is Murder" "Poorhouse Rock" === Unhappily Ever After episodes === "Meter Maid" "Getting More Than Some" "College!" "Experimenting in College" "Making the Grade" "Teacher's Pet" "Excorsising Jennie" "Shampoo" "Rock 'n' Roll" "Lightning Boy" "The Tell-Tale Lipstick" "Jack The Ripper" "The Great Depression" "The Rat" == References == == External links == J. Stewart Burns at IMDb
|
Wikipedia:J. V. Uspensky#0
|
James Victor Uspensky (Russian: Яков Викторович Успенский, romanized: Yakov Viktorovich Uspensky; April 29, 1883 – January 27, 1947) was a Russian and American mathematician notable for writing Theory of Equations. == Biography == Uspensky graduated from the University of St. Petersburg in 1906 and received his doctorate from the University of St. Petersburg in 1910. He was a member of the Russian Academy of Sciences from 1921. Uspensky joined the faculty of Stanford University in 1929-30 and 1930-31 as acting professor of mathematics. He was professor of mathematics at Stanford from 1931 until his death. Uspensky was the one who kept alive Vincent's theorem of 1834 and 1836, carrying the torch (so to speak) from Serret. == Books == Uspensky, J. V. (1948). Theory of equations. Uspensky, J. V.; Heaslet, M. A. (1939). Elementary Number Theory. Uspensky, J. V. (1937). Introduction to mathematical probability. == Notes == == References == J. V. Uspensky (1931). "On Ch. Jordan's Series for Probability". Annals of Mathematics. Second Series. 32 (2): 306–312. doi:10.2307/1968193. JSTOR 1968193. J. V. Uspensky (1926–1927). "On the Development of Arbitrary Functions in Series of Hermite's and Laguerre's Polynomials". Annals of Mathematics. Second Series. 28 (1/4): 593–619. doi:10.2307/1968401. JSTOR 1968401. Halsey Royden (1988). The History of the Mathematics Department at Stanford, in A Century of Mathematics in America edited by Peter L. Duren, Richard Askey, and Uta C. Merzbach. American Mathematical Society, History of Mathematics Volume 2, Providence, Rhode Island. "A History of Mathematics at Stanford" by Halsey Royden. == External links == J. V. Uspensky at the Mathematics Genealogy Project
|
Wikipedia:Jaak Peetre#0
|
Jaak Peetre (29 July 1935, in Tallinn – 1 April 2019, in Lund) was an Estonian-born Swedish mathematician. He is known for the Peetre theorem and Peetre's inequality. == Biography == Jaak Peetre's father was Arthur Peetre (1907–1989), an Estonian jurist, historian, archivist, and from 1941 to 1942 mayor of Pärnu. Jaak Peetre went to Sweden with his parents and brother in 1944. At Lund University he graduated with BSc in 1956 and PhD in 1959. His thesis advisor was Åke Pleijel. At Lund University, Peetre was an assistant professor from 1956 to 1959, an associate professor from 1960 to 1963, and full professor from 1963 to 1988. He was briefly in 1988 a visiting professor at the University of Madrid and was from 1988 to 1992 a visiting professor at Stockholm University. At Lund University he was a lecturer from 1993 to 1997, an assistant professor from 1997 to 2000, and professor emeritus from 2000. He was also a visiting professor at New York University for the academic year 1960–1961 and at University of Maryland for the academic year 1961–1962. Peetre's research deals with ordinary and partial derivative differential equations, operator interpolation spaces, singular integrals and Besov spaces, differential geometry, Clifford analysis, Fock space and Hankel operators, Fourier and harmonic analysis. Bernard Malgrange, Jacques-Louis Lions, and Peetre were pioneers of modern interpolation theory. In the early 1990s, Peetre's research focused on multilinear forms, especially trilinear forms. He was the author or coauthor of more than 230 research papers. He was the thesis advisor for 8 doctoral students. In 1970 he was an Invited Speaker at the International Congress of Mathematicians in Nice. He gave lectures at more than 30 international mathematical congresses and conferences and in many cases was among the organizers. He was a member of the editorial boards of several international mathematical journals. In 1984 he was elected a member of the Swedish Royal Academy of Sciences. From 1984 to 1987 he was the president of the Swedish Mathematical Society. In 1998 he was awarded the Royal Society of Sciences in Uppsala's Celsius Gold Medal. Jaak Peetre was the most prolific Estonian mathematician of his era, often visiting Estonia and giving lectures there. In 1994 he was a founding member of the Estonian Mathematical Society. In 2001 he was awarded the Order of the White Star, 3rd Class. In 2008 he was elected a foreign member of the Estonian Academy of Science. == Selected publications == === Articles === Peetre, Jaak (1959). "Une Caractérisation Abstraite des Opérateurs Différentiels". Mathematica Scandinavica. 7 (1): 211–218. doi:10.7146/math.scand.a-10574. JSTOR 24489021. Peetre, Jaak (1957). "A Generalization of Courant's Nodal Domain Theorem". Mathematica Scandinavica. 5 (1): 15–20. doi:10.7146/math.scand.a-10484. JSTOR 24490131. Peetre, J. (1961). "Mixed problems for higher order elliptic equations in two variables, I." (PDF). Annali della Scuola Normale Superiore di Pisa-Classe di Scienze. 15 (4): 337–353. Peetre, J. (1962). "On the differentiability of the solutions of quasilinear partial differential equations". Transactions of the American Mathematical Society. 104 (3): 476–482. doi:10.1090/S0002-9947-1962-0146518-1. ISSN 0002-9947. Lions, J. L.; Peetre, J. (1964). "Sur une classe d'espaces d'interpolation" (PDF). Publications Mathématiques de l'IHÉS. 19: 5–68. doi:10.1007/BF02684796. S2CID 124471748. (Over 900 citations) Peetre, J. (1966). "Espaces d'interpolation et théorème de Soboleff". Annales de l'Institut Fourier. 16 (1): 279–317. doi:10.5802/aif.232. Peetre, Jaak (1969). "On the theory of Lp,λ spaces". Journal of Functional Analysis. 4: 71–87. doi:10.1016/0022-1236(69)90022-6. Holmstedt, T.; Peetre, J. (1969). "On certain functionals arising in the theory of interpolation spaces" (PDF). Journal of Functional Analysis. 4 (1): 88–94. doi:10.1016/0022-1236(69)90023-8. Peetre, J.; Sparr, G. (1972). "Interpolation of normed abelian groups". Annali di Matematica Pura ed Applicata. 92: 217–262. doi:10.1007/BF02417949. S2CID 121904777. Peetre, Jaak (1975). "On spaces of Triebel-Lizorkin type". Arkiv för Matematik. 13 (1–2): 123–130. Bibcode:1975ArM....13..123P. doi:10.1007/BF02386201. MR 0380394. Peetre, J. (1975). "A remark on Sobolev spaces. The case 0< p< 1" (PDF). Journal of Approximation Theory. 13 (3): 218–228. doi:10.1016/0021-9045(75)90034-9. Peetre, J. (1979). "Two new interpolation methods based on the duality map" (PDF). Acta Mathematica. 143: 73–91. doi:10.1007/BF02392089. S2CID 121740083. Peetre, J. (1980). "On Hadamard's variational formula" (PDF). Journal of Differential Equations. 36 (3): 335–346. Bibcode:1980JDE....36..335P. doi:10.1016/0022-0396(80)90053-4. Janson, Svante; Peetre, Jaak; Semmes, Stephen (1984). "On the action of Hankel and Toeplitz operators on some function spaces". Duke Mathematical Journal. 51 (4): 937–958. doi:10.1215/S0012-7094-84-05142-1. Fisher, S. D.; Arazy, J.; Peetre, J. (1985). "Möbius invariant function spaces". Journal für die reine und angewandte Mathematik. 1985 (363): 110–145. doi:10.1515/crll.1985.363.110. S2CID 120842922. Janson, Svante; Peetre, Jaak (1987). "A New Generalization of Hankel Operators (the Case of Higher Weights)". Mathematische Nachrichten. 132 (1): 313–328. doi:10.1002/mana.19871320121. ISSN 0025-584X. Janson, Svante; Peetre, Jaak (1988). "Paracommutators―boundedness and Schatten-von Neumann properties". Transactions of the American Mathematical Society. 305 (2): 467. doi:10.1090/S0002-9947-1988-0924766-6. Arazy, J.; Fisher, S. D.; Peetre, J. (1988). "Hankel Operators on Weighted Bergman Spaces". American Journal of Mathematics. 110 (6): 989–1053. doi:10.2307/2374685. JSTOR 2374685. Cobos, Fernando; Peetre, Jaak (1989). "Interpolation of compactness using Aronszajn-Gagliardo functors". Israel Journal of Mathematics. 68 (2): 220–240. doi:10.1007/BF02772662. S2CID 120426208. Peetre, Jaak (1990). "The Berezin Transform and Ha-Plitz Operators". Journal of Operator Theory. 24 (1): 165–186. JSTOR 24714631. Fisher, S. D.; Arazy, J.; Janson, S.; Peetre, J. (1990). "An identity for reproducing kernels in a planar domain and Hilbert-Schmidt Hankel operators". Journal für die reine und angewandte Mathematik. 1990 (406): 179–199. doi:10.1515/crll.1990.406.179. S2CID 117856717. Arazy, Jonathan; Fisher, Stephen D.; Janson, Svante; Peetre, Jaak (1991). "Membership of Hankel Operators on the Ball in Unitary Ideals". Journal of the London Mathematical Society (3): 485–508. doi:10.1112/jlms/s2-43.3.485. Cobos, Fernando; Peetre, Jaak (1991). "Interpolation of Compact Operators: The Multidimensional Case". Proceedings of the London Mathematical Society (2): 371–400. doi:10.1112/plms/s3-63.2.371. Peetre, Jaak; Sjölin, Per S (1992). "Three-line theorems and clifford analysis". Complex Variables, Theory and Application. 19 (3): 92–124. doi:10.1080/17476939208814568. ISSN 0278-1077. Peetre, Jaak; Qian, Tao (1994). "Möbius covariance of iterated Dirac operators". Journal of the Australian Mathematical Society, Series A. 56 (3): 403–414. doi:10.1017/S1446788700035576. Cobos, Fernando; Peetre, Jaak; Persson, Lars Erik (1998). "On the connection between real and complex interpolation of quasi-banach spaces". Bulletin des Sciences Mathématiques. 122: 17–37. doi:10.1016/S0007-4497(98)80075-4. Lindqvist, Peter; Peetre, Jaak (2001). "Two Remarkable Identities, Called Twos, for Inverses to Some Abelian Integrals". The American Mathematical Monthly. 108 (5): 403–410. doi:10.1080/00029890.2001.11919766. S2CID 43677974. Bernhardsson, Bo; Peetre, Jaak (2001). "Singular Values of Trilinear Forms". Experimental Mathematics. 10 (4): 509–517. doi:10.1080/10586458.2001.10504670. S2CID 4455661. === Books === Lumiste, Ülo; Peetre, Jaak, eds. (1994). Edgar Krahn 1894-1961: A Centenary Volume. IOS Press. ISBN 9789051991680. (See Edgar Krahn.) == References == == Further reading == Eesti entsüklopeedia (Estonian Encyclopedia) 14, 364 Eesti teadlased väljaspool kodumaad: biograafiline teatmik (Estonian scholars and scientists abroad: biographical directory). Stockholm, 1984, 91 Eesti teaduse biograafiline leksikon. 3. köide: N–Sap TTEÜ, avaldatud elekrooniliselt 2013
|
Wikipedia:Jaan Sarv#0
|
Jaan Sarv (Võro: Sarvõ Jaan; 21 December 1877 – 23 August 1954) was an Estonian mathematician and educator. Most of his life he worked as a professor at the University of Tartu. Sarv laid the foundation of Estonian language mathematical education. == References == "Eesti koolimatemaatika ajalugu" I-IV, Olaf Prinits, Tartu, 1992–1994
|
Wikipedia:Jaap Murre#0
|
Jacob Pieter "Jaap" Murre (18 September 1929 – 9 April 2023) was a Dutch mathematician specializing in algebraic geometry. He was a professor of mathematics at Leiden University from 1961 to 1994. == Career == Murre was born on 18 September 1929 in Baarland. At his small primary school one of his classmates and friends was later botanist Jan Zeevaart. Murre started studying mathematics at Delft University of Technology in 1947, he however switched to Leiden University where he obtained his degree in 1952. With the Italian school of algebraic geometry being in fashion he was inspired by his promotor to do doctoral research under André Weil at the University of Chicago, which he was able to do because of the Marshall Plan. In 1957 Murre obtained his doctorate under Hendrik Kloosterman with a thesis titled: Over multipliciteiten van maximaal samenhangende bossen. By 1958 Murre became inspired by Alexander Grothendieck and managed to collaborate with him. In 1959 he was appointed associate professor (lector) at Leiden University. In 1961 he became professor of mathematics at the same institute, with a teaching assignment in algebraic geometry. Frans Oort was the first doctoral student he supervised, but Oort had to formally promote under Wil van Est as his promotion came one month before Murre's appointment. During his career Murre traveled frequently. He amongst others went to India to study with C. S. Seshadri and to the United Kingdom where he met David Mumford, who inspired him to work on algebraic cycles. In Italy he collaborated with Alberto Conte, who became a friend. He also befriended American mathematician Spencer Bloch. In the 1990s he published on the Chow group. Murre retired as professor in 1994. Murre was elected a member of the Royal Netherlands Academy of Arts and Sciences in 1971. In 2002 he obtained an honorary doctorate from the University of Turin. Murre was elected a foreign member of the Accademia delle Scienze di Torino in 2004. Murre died on 9 April 2023 at the age of 93. == References == == External links == Profile at Leiden University Jaap Murre at the Mathematics Genealogy Project
|
Wikipedia:Jaap Wessels#0
|
Jacobus (Jaap) Wessels (19 January 1939 – 30 July 2009) was a Dutch mathematician and Professor of Stochastic Operations Research at the Eindhoven University of Technology, known for his contributions in the field of Markov decision processes. == Biography == Born in Amsterdam, Wessels started to study Mathematics and Physics at the University of Amsterdam in 1956, where in 1963 he received his MA. He graduated in 1968 at the Eindhoven University of Technology advised by Jacques F. Benders with a thesis entitled "Decision rules in Markovian decision problems with Incompletely known transition probabilities" about Markov decision processes. In 1960, Wessels started his academic career at the University of Amsterdam as assistant to Jan Hemelrijk, an authority in the field of stochastic processes. During his doctoral research, Wessels was employed as research assistant at the Technical University of Eindhoven. In 1973, he was appointed Professor of Applied Probability Theory at the Faculty of Mathematics and Computer Science. In 2000, he retired from the Eindhoven University of Technology. He kept participating in International Institute for Applied Systems Analysis and EURANDOM. On July 30, 2009 he died in Veldhoven. Among his doctoral students were Jo van Nunen, Kees van Hee, Henk Zijm, Eric van Damme and Wil van der Aalst. Wessels was president of the Vereniging voor Statistiek (VVS), and has contributed to the foundation of the National Network Mathematical Decision Making (LNMB), the research school BETA, and European Institute for Statistics, Probability, Stochastic Operations Research and its Applications (EURANDOM). == Work == Wessels' research interests focused on topics such as queuing theory, neural networks and structured Markov processes, and more specifically "decision support methodology and he applies his favorite research topics in operations management, communication processes, manpower policy making and environmental problems." === Model-based decision support methodology === Wessels' most cited work is the 2000 publication Model-based decision support methodology with environmental applications, edited with Andrzej Wierzbicki and Marek Makowski. In the introduction they acknowledge about decision making: Decision making is a major component of living and, therefore, a fascinating topic for discussion and investigation. Several fields in science also occupy themselves with the nature of different aspects of decision making: philosophy, psychology, sociology, economics, etc. There are many types of decision making and all types are equally intriguing, e.g., How do people react when they are threatened? How should one select a spouse? What is the most appropriate factory layout? Which markets would be most profitable?... In most institutional decision-making problems, there are three main aspects of concern: The information about the current situation and, possibly, about the past. The processes that are to be influenced by the decisions. The actual decision-making process ... In the history of decision support and decision analysis, one sees that many tools and methods have been developed to help make decisions. This publication gives in three parts (Methodology, Decision Support Tools, Environmental Applications) an overview of the field. == Publications == Wessel authored and co-authored dozens of publications in the field. Books, a selection: 1968. Decision rules in Markovian decision problems with Incompletely known transition probabilities. 1976. Markov decision theory: proceedings of the Advanced Seminar on Markov Decision Theory held at Amsterdam, the Netherlands, 13–17 September 1976. With Henk Tijms eds. 1991. User-oriented methodology and techniques of decision analysis and support: proceedings of the International IIASA Workshop, held in Serock, Poland, 9–13 September 1991. With Andrzej Wierzbicki eds. 1993. Analysing shortest expected delay routing for Erlang servers. With Ivo Adan. 2000. Model-based decision support methodology with environmental applications. With Andrzej Wierzbicki and Marek Makowski eds. == References == == External links == prof.dr. Jaap Wessels In memoriam (in Dutch)
|
Wikipedia:Jacek Banasiak#0
|
Jacek Banasiak FAAS (born 15 March 1959) is a Polish mathematician who is a Professor and South African Research Chair in Mathematical Models and Methods in Biosciences and Bioengineering at the University of Pretoria, South Africa. == Early life and education == Jacek Banasiak was born on 15 March 1959 in Łódź, Poland. He obtained a Master of Science (MSc) in Math from the Łódź University of Technology in 1981, and Doctor of Philosophy (PhD) in mathematics on 15 March 1989 from the University of Strathclyde, Scotland. He was hablitated (PD) in Physics on 17 June 1999 from the Faculty of Mathematics, Informatics and Mechanics, University of Warsaw with a thesis titled Singularly Perturbed Evolution Equations with Applications in Kinetic Theory and Other Branches of Mathematical Physics. == Career and research == Banasiak became a professor on 21 December 2007, and has been a Professor of Mathematical Sciences at the University of KwaZulu-Natal from 2011 until 2015. After, he joined the University of Pretoria and became the South African Research Chair in Mathematical Models and Methods in Biosciences and Bioengineering at the Department of Mathematics and Applied Mathematics, extraordinary professor at the Łódź University of Technology, and a visiting professor of Mathematics and Statistics at the Strathclyde University. Banasiak research focuses on applied mathematics especially semigroup theory, asymptotic analysis, mathematical biology, fragmentations coagulation equations, and difference and differential equations. Banasiak served as the vice president of the South African Mathematical Society (2001–2005). He is a member of the Academy of Science of South Africa and the African Institute for Mathematical Sciences (AIMS). He is also the Editor-in-Chief of Afrika Matematika since 2010, Associate Editor of Quaestiones Mathematicae and Evolution Equations an Control Theory (EECT), and a member of the Editorial Board of Mathematical Methods for the Applied Sciences and Differential Equations and Dynamical Systems. == Awards and honours == In 2012, Banasiak won the South African Mathematical Society (SAMS) award for Research Distinction. In 2014, he was honoured with the Polish Cross of Merit (Silver) for his contributions to science. Banasiak was elected a Fellow of the African Academy of Sciences in 2016. == Selected publications == Banasiak, J.; Arlotti, Luisa (2006). Perturbations of positive semigroups with applications. London: Springer. ISBN 978-1-85233-993-7. OCLC 67766114. Banasiak, Jacek; Lachowicz, Mirosław (2014). "Methods of Small Parameter in Mathematical Biology". Modeling and Simulation in Science, Engineering and Technology. Cham: Springer International Publishing. doi:10.1007/978-3-319-05140-6. ISBN 978-3-319-05139-0. ISSN 2164-3679. Banasiak, Jacek; Mika, Janusz R. (1998-01-01). "Singularly perturbed telegraph equations with applications in the random walk theory". Journal of Applied Mathematics and Stochastic Analysis. 11 (1). Hindawi Limited: 9–28. doi:10.1155/s1048953398000021. ISSN 1048-9533. Mika, J. R.; Banasiak, J. (1995). Singularly perturbed evolution equations with applications to kinetic theory. Singapore: World Scientific. ISBN 981-02-2125-8. OCLC 32746102. Banasiak, J.; Lamb, Wilson; Laurençot, Philippe (2020). Analytic methods for coagulation-fragmentation models. Volume II. Boca Raton, FL. ISBN 978-0-429-28032-0. OCLC 1119391451.{{cite book}}: CS1 maint: location missing publisher (link) == References == == External links == Explicit solutions of fragmentation models with growth or decay, Professor Jacek Banasiak on YouTube
|
Wikipedia:Jack Yang#0
|
Jack Jung-Kai Yang (simplified Chinese: 杨荣凯; traditional Chinese: 楊榮凱; pinyin: Yáng Róngkǎi) (born 1974) is an American-Canadian actor of Taiwanese ethnicity. He was born in Toronto, Ontario, Canada and currently resides in Los Angeles, California. == Filmography == The Yellow Truth as Jack (2003) Shadow Chaser (2003) Law & Order: Special Victims Unit as Ricky Yao (2004) Skin Trade (short film) as The Designer (2004) The Seat Filler as Page (2004) CSI: Miami as Shawn Kimsey (2005) All of Us as Harry (2005) Grey's Anatomy as Walter (2005-2007) Bones as Ming Tsou (2005-2007) Nip/Tuck as Chiyo (2006) The Evidence as Ha Huang (2006) Scrubs as Patient (2006) ER as Bevan Wong (2007) Seven Pounds as Apogee Engineer (2008) Need for Speed: Undercover (video game) as Chau Wu (2008) Command & Conquer: Red Alert 3 (video game) as Commander Kenji Tenzai (2008) Samurai Girl as Hiko (2008) The Mummy: Tomb of the Dragon Emperor (video game) as General Yang (2008) Cashmere Mafia as Jason Chung (2008) Knight Rider as Cross (2008) Chuck as Jason Wang (2009) Command & Conquer: Red Alert 3 – Uprising (video game) as Commander Kenji Tenzai (2009) Point of Entry Season 4 as Glenn Chua (2013) A Leading Man as GQ (2013) American Ultra as Gangster (2015) Star as Elliot (2017) Lucifer (season 3 episode 6) as police inspector (2017) Justice League (2017) as Garrett Bowman Shadowhunters as Asmodeus (2018–2019) == References == == External links == Jack J. Yang at IMDb
|
Wikipedia:Jack function#0
|
In mathematics, the Jack function is a generalization of the Jack polynomial, introduced by Henry Jack. The Jack polynomial is a homogeneous, symmetric polynomial which generalizes the Schur and zonal polynomials, and is in turn generalized by the Heckman–Opdam polynomials and Macdonald polynomials. == Definition == The Jack function J κ ( α ) ( x 1 , x 2 , … , x m ) {\displaystyle J_{\kappa }^{(\alpha )}(x_{1},x_{2},\ldots ,x_{m})} of an integer partition κ {\displaystyle \kappa } , parameter α {\displaystyle \alpha } , and arguments x 1 , x 2 , … , x m {\displaystyle x_{1},x_{2},\ldots ,x_{m}} can be recursively defined as follows: For m=1 J k ( α ) ( x 1 ) = x 1 k ( 1 + α ) ⋯ ( 1 + ( k − 1 ) α ) {\displaystyle J_{k}^{(\alpha )}(x_{1})=x_{1}^{k}(1+\alpha )\cdots (1+(k-1)\alpha )} For m>1 J κ ( α ) ( x 1 , x 2 , … , x m ) = ∑ μ J μ ( α ) ( x 1 , x 2 , … , x m − 1 ) x m | κ / μ | β κ μ , {\displaystyle J_{\kappa }^{(\alpha )}(x_{1},x_{2},\ldots ,x_{m})=\sum _{\mu }J_{\mu }^{(\alpha )}(x_{1},x_{2},\ldots ,x_{m-1})x_{m}^{|\kappa /\mu |}\beta _{\kappa \mu },} where the summation is over all partitions μ {\displaystyle \mu } such that the skew partition κ / μ {\displaystyle \kappa /\mu } is a horizontal strip, namely κ 1 ≥ μ 1 ≥ κ 2 ≥ μ 2 ≥ ⋯ ≥ κ n − 1 ≥ μ n − 1 ≥ κ n {\displaystyle \kappa _{1}\geq \mu _{1}\geq \kappa _{2}\geq \mu _{2}\geq \cdots \geq \kappa _{n-1}\geq \mu _{n-1}\geq \kappa _{n}} ( μ n {\displaystyle \mu _{n}} must be zero or otherwise J μ ( x 1 , … , x n − 1 ) = 0 {\displaystyle J_{\mu }(x_{1},\ldots ,x_{n-1})=0} ) and β κ μ = ∏ ( i , j ) ∈ κ B κ μ κ ( i , j ) ∏ ( i , j ) ∈ μ B κ μ μ ( i , j ) , {\displaystyle \beta _{\kappa \mu }={\frac {\prod _{(i,j)\in \kappa }B_{\kappa \mu }^{\kappa }(i,j)}{\prod _{(i,j)\in \mu }B_{\kappa \mu }^{\mu }(i,j)}},} where B κ μ ν ( i , j ) {\displaystyle B_{\kappa \mu }^{\nu }(i,j)} equals κ j ′ − i + α ( κ i − j + 1 ) {\displaystyle \kappa _{j}'-i+\alpha (\kappa _{i}-j+1)} if κ j ′ = μ j ′ {\displaystyle \kappa _{j}'=\mu _{j}'} and κ j ′ − i + 1 + α ( κ i − j ) {\displaystyle \kappa _{j}'-i+1+\alpha (\kappa _{i}-j)} otherwise. The expressions κ ′ {\displaystyle \kappa '} and μ ′ {\displaystyle \mu '} refer to the conjugate partitions of κ {\displaystyle \kappa } and μ {\displaystyle \mu } , respectively. The notation ( i , j ) ∈ κ {\displaystyle (i,j)\in \kappa } means that the product is taken over all coordinates ( i , j ) {\displaystyle (i,j)} of boxes in the Young diagram of the partition κ {\displaystyle \kappa } . === Combinatorial formula === In 1997, F. Knop and S. Sahi gave a purely combinatorial formula for the Jack polynomials J μ ( α ) {\displaystyle J_{\mu }^{(\alpha )}} in n variables: J μ ( α ) = ∑ T d T ( α ) ∏ s ∈ T x T ( s ) . {\displaystyle J_{\mu }^{(\alpha )}=\sum _{T}d_{T}(\alpha )\prod _{s\in T}x_{T(s)}.} The sum is taken over all admissible tableaux of shape λ , {\displaystyle \lambda ,} and d T ( α ) = ∏ s ∈ T critical d λ ( α ) ( s ) {\displaystyle d_{T}(\alpha )=\prod _{s\in T{\text{ critical}}}d_{\lambda }(\alpha )(s)} with d λ ( α ) ( s ) = α ( a λ ( s ) + 1 ) + ( l λ ( s ) + 1 ) . {\displaystyle d_{\lambda }(\alpha )(s)=\alpha (a_{\lambda }(s)+1)+(l_{\lambda }(s)+1).} An admissible tableau of shape λ {\displaystyle \lambda } is a filling of the Young diagram λ {\displaystyle \lambda } with numbers 1,2,…,n such that for any box (i,j) in the tableau, T ( i , j ) ≠ T ( i ′ , j ) {\displaystyle T(i,j)\neq T(i',j)} whenever i ′ > i . {\displaystyle i'>i.} T ( i , j ) ≠ T ( i , j − 1 ) {\displaystyle T(i,j)\neq T(i,j-1)} whenever j > 1 {\displaystyle j>1} and i ′ < i . {\displaystyle i'<i.} A box s = ( i , j ) ∈ λ {\displaystyle s=(i,j)\in \lambda } is critical for the tableau T if j > 1 {\displaystyle j>1} and T ( i , j ) = T ( i , j − 1 ) . {\displaystyle T(i,j)=T(i,j-1).} This result can be seen as a special case of the more general combinatorial formula for Macdonald polynomials. == C normalization == The Jack functions form an orthogonal basis in a space of symmetric polynomials, with inner product: ⟨ f , g ⟩ = ∫ [ 0 , 2 π ] n f ( e i θ 1 , … , e i θ n ) g ( e i θ 1 , … , e i θ n ) ¯ ∏ 1 ≤ j < k ≤ n | e i θ j − e i θ k | 2 α d θ 1 ⋯ d θ n {\displaystyle \langle f,g\rangle =\int _{[0,2\pi ]^{n}}f\left(e^{i\theta _{1}},\ldots ,e^{i\theta _{n}}\right){\overline {g\left(e^{i\theta _{1}},\ldots ,e^{i\theta _{n}}\right)}}\prod _{1\leq j<k\leq n}\left|e^{i\theta _{j}}-e^{i\theta _{k}}\right|^{\frac {2}{\alpha }}d\theta _{1}\cdots d\theta _{n}} This orthogonality property is unaffected by normalization. The normalization defined above is typically referred to as the J normalization. The C normalization is defined as C κ ( α ) ( x 1 , … , x n ) = α | κ | ( | κ | ) ! j κ J κ ( α ) ( x 1 , … , x n ) , {\displaystyle C_{\kappa }^{(\alpha )}(x_{1},\ldots ,x_{n})={\frac {\alpha ^{|\kappa |}(|\kappa |)!}{j_{\kappa }}}J_{\kappa }^{(\alpha )}(x_{1},\ldots ,x_{n}),} where j κ = ∏ ( i , j ) ∈ κ ( κ j ′ − i + α ( κ i − j + 1 ) ) ( κ j ′ − i + 1 + α ( κ i − j ) ) . {\displaystyle j_{\kappa }=\prod _{(i,j)\in \kappa }\left(\kappa _{j}'-i+\alpha \left(\kappa _{i}-j+1\right)\right)\left(\kappa _{j}'-i+1+\alpha \left(\kappa _{i}-j\right)\right).} For α = 2 , C κ ( 2 ) ( x 1 , … , x n ) {\displaystyle \alpha =2,C_{\kappa }^{(2)}(x_{1},\ldots ,x_{n})} is often denoted by C κ ( x 1 , … , x n ) {\displaystyle C_{\kappa }(x_{1},\ldots ,x_{n})} and called the Zonal polynomial. == P normalization == The P normalization is given by the identity J λ = H λ ′ P λ {\displaystyle J_{\lambda }=H'_{\lambda }P_{\lambda }} , where H λ ′ = ∏ s ∈ λ ( α a λ ( s ) + l λ ( s ) + 1 ) {\displaystyle H'_{\lambda }=\prod _{s\in \lambda }(\alpha a_{\lambda }(s)+l_{\lambda }(s)+1)} where a λ {\displaystyle a_{\lambda }} and l λ {\displaystyle l_{\lambda }} denotes the arm and leg length respectively. Therefore, for α = 1 , P λ {\displaystyle \alpha =1,P_{\lambda }} is the usual Schur function. Similar to Schur polynomials, P λ {\displaystyle P_{\lambda }} can be expressed as a sum over Young tableaux. However, one need to add an extra weight to each tableau that depends on the parameter α {\displaystyle \alpha } . Thus, a formula for the Jack function P λ {\displaystyle P_{\lambda }} is given by P λ = ∑ T ψ T ( α ) ∏ s ∈ λ x T ( s ) {\displaystyle P_{\lambda }=\sum _{T}\psi _{T}(\alpha )\prod _{s\in \lambda }x_{T(s)}} where the sum is taken over all tableaux of shape λ {\displaystyle \lambda } , and T ( s ) {\displaystyle T(s)} denotes the entry in box s of T. The weight ψ T ( α ) {\displaystyle \psi _{T}(\alpha )} can be defined in the following fashion: Each tableau T of shape λ {\displaystyle \lambda } can be interpreted as a sequence of partitions ∅ = ν 1 → ν 2 → ⋯ → ν n = λ {\displaystyle \emptyset =\nu _{1}\to \nu _{2}\to \dots \to \nu _{n}=\lambda } where ν i + 1 / ν i {\displaystyle \nu _{i+1}/\nu _{i}} defines the skew shape with content i in T. Then ψ T ( α ) = ∏ i ψ ν i + 1 / ν i ( α ) {\displaystyle \psi _{T}(\alpha )=\prod _{i}\psi _{\nu _{i+1}/\nu _{i}}(\alpha )} where ψ λ / μ ( α ) = ∏ s ∈ R λ / μ − C λ / μ ( α a μ ( s ) + l μ ( s ) + 1 ) ( α a μ ( s ) + l μ ( s ) + α ) ( α a λ ( s ) + l λ ( s ) + α ) ( α a λ ( s ) + l λ ( s ) + 1 ) {\displaystyle \psi _{\lambda /\mu }(\alpha )=\prod _{s\in R_{\lambda /\mu }-C_{\lambda /\mu }}{\frac {(\alpha a_{\mu }(s)+l_{\mu }(s)+1)}{(\alpha a_{\mu }(s)+l_{\mu }(s)+\alpha )}}{\frac {(\alpha a_{\lambda }(s)+l_{\lambda }(s)+\alpha )}{(\alpha a_{\lambda }(s)+l_{\lambda }(s)+1)}}} and the product is taken only over all boxes s in λ {\displaystyle \lambda } such that s has a box from λ / μ {\displaystyle \lambda /\mu } in the same row, but not in the same column. == Connection with the Schur polynomial == When α = 1 {\displaystyle \alpha =1} the Jack function is a scalar multiple of the Schur polynomial J κ ( 1 ) ( x 1 , x 2 , … , x n ) = H κ s κ ( x 1 , x 2 , … , x n ) , {\displaystyle J_{\kappa }^{(1)}(x_{1},x_{2},\ldots ,x_{n})=H_{\kappa }s_{\kappa }(x_{1},x_{2},\ldots ,x_{n}),} where H κ = ∏ ( i , j ) ∈ κ h κ ( i , j ) = ∏ ( i , j ) ∈ κ ( κ i + κ j ′ − i − j + 1 ) {\displaystyle H_{\kappa }=\prod _{(i,j)\in \kappa }h_{\kappa }(i,j)=\prod _{(i,j)\in \kappa }(\kappa _{i}+\kappa _{j}'-i-j+1)} is the product of all hook lengths of κ {\displaystyle \kappa } . == Properties == If the partition has more parts than the number of variables, then the Jack function is 0: J κ ( α ) ( x 1 , x 2 , … , x m ) = 0 , if κ m + 1 > 0. {\displaystyle J_{\kappa }^{(\alpha )}(x_{1},x_{2},\ldots ,x_{m})=0,{\mbox{ if }}\kappa _{m+1}>0.} == Matrix argument == In some texts, especially in random matrix theory, authors have found it more convenient to use a matrix argument in the Jack function. The connection is simple. If X {\displaystyle X} is a matrix with eigenvalues x 1 , x 2 , … , x m {\displaystyle x_{1},x_{2},\ldots ,x_{m}} , then J κ ( α ) ( X ) = J κ ( α ) ( x 1 , x 2 , … , x m ) . {\displaystyle J_{\kappa }^{(\alpha )}(X)=J_{\kappa }^{(\alpha )}(x_{1},x_{2},\ldots ,x_{m}).} == References == Demmel, James; Koev, Plamen (2006), "Accurate and efficient evaluation of Schur and Jack functions", Mathematics of Computation, 75 (253): 223–239, CiteSeerX 10.1.1.134.5248, doi:10.1090/S0025-5718-05-01780-1, MR 2176397. Jack, Henry (1970–1971), "A class of symmetric polynomials with a parameter", Proceedings of the Royal Society of Edinburgh, Section A. Mathematics, 69: 1–18, MR 0289462. Knop, Friedrich; Sahi, Siddhartha (19 March 1997), "A recursion and a combinatorial formula for Jack polynomials", Inventiones Mathematicae, 128 (1): 9–22, arXiv:q-alg/9610016, Bibcode:1997InMat.128....9K, doi:10.1007/s002220050134, S2CID 7188322 Macdonald, I. G. (1995), Symmetric functions and Hall polynomials, Oxford Mathematical Monographs (2nd ed.), New York: Oxford University Press, ISBN 978-0-19-853489-1, MR 1354144 Stanley, Richard P. (1989), "Some combinatorial properties of Jack symmetric functions", Advances in Mathematics, 77 (1): 76–115, doi:10.1016/0001-8708(89)90015-7, MR 1014073. == External links == Software for computing the Jack function by Plamen Koev and Alan Edelman. MOPS: Multivariate Orthogonal Polynomials (symbolically) (Maple Package) Archived 2010-06-20 at the Wayback Machine SAGE documentation for Jack Symmetric Functions
|
Wikipedia:Jacob Bernoulli#0
|
Jacob Bernoulli (also known as James in English or Jacques in French; 6 January 1655 [O.S. 27 December 1654] – 16 August 1705) was a Swiss mathematician. He sided with Gottfried Wilhelm Leibniz during the Leibniz–Newton calculus controversy and was an early proponent of Leibnizian calculus, to which he made numerous contributions. A member of the Bernoulli family, he, along with his brother Johann, was one of the founders of the calculus of variations. He also discovered the fundamental mathematical constant e. However, his most important contribution was in the field of probability, where he derived the first version of the law of large numbers in his work Ars Conjectandi. == Biography == Jacob Bernoulli was born in Basel in the Swiss Confederation, the son and grandson of Protestant spice merchants on his fathers side, his mother was born into a family engaged in banking and city governing. Following his father's wish, he studied theology and entered the ministry. But contrary to the desires of his parents, he also studied mathematics and astronomy. He traveled throughout Europe from 1676 to 1682, learning about the latest discoveries in mathematics and the sciences under leading figures of the time. This included the work of Johannes Hudde, Robert Boyle, and Robert Hooke. During this time he also produced an incorrect theory of comets. Bernoulli returned to Switzerland, and began teaching mechanics at the University of Basel from 1683. His doctoral dissertation Solutionem tergemini problematis was submitted in 1684. It appeared in print in 1687. In 1684, Bernoulli married Judith Stupanus; they had two children. During this decade, he also began a fertile research career. His travels allowed him to establish correspondence with many leading mathematicians and scientists of his era, which he maintained throughout his life. During this time, he studied the new discoveries in mathematics, including Christiaan Huygens's De ratiociniis in aleae ludo, Descartes' La Géométrie and Frans van Schooten's supplements of it. He also studied Isaac Barrow and John Wallis, leading to his interest in infinitesimal geometry. Apart from these, it was between 1684 and 1689 that many of the results that were to make up Ars Conjectandi were discovered. People believe he was appointed professor of mathematics at the University of Basel in 1687, remaining in this position for the rest of his life. By that time, he had begun tutoring his brother Johann Bernoulli on mathematical topics. The two brothers began to study the calculus as presented by Leibniz in his 1684 paper on the differential calculus in "Nova Methodus pro Maximis et Minimis" published in Acta Eruditorum. They also studied the publications of von Tschirnhaus. It must be understood that Leibniz's publications on the calculus were very obscure to mathematicians of that time and the Bernoullis were among the first to try to understand and apply Leibniz's theories. Jacob collaborated with his brother on various applications of calculus. However the atmosphere of collaboration between the two brothers turned into rivalry as Johann's own mathematical genius began to mature, with both of them attacking each other in print, and posing difficult mathematical challenges to test each other's skills. By 1697, the relationship had completely broken down. The lunar crater Bernoulli is also named after him jointly with his brother Johann. == Important works == Jacob Bernoulli's first important contributions were a pamphlet on the parallels of logic and algebra published in 1685, work on probability in 1685 and geometry in 1687. His geometry result gave a construction to divide any triangle into four equal parts with two perpendicular lines. By 1689, he had published important work on infinite series and published his law of large numbers in probability theory. Jacob Bernoulli published five treatises on infinite series between 1682 and 1704. The first two of these contained many results, such as the fundamental result that ∑ 1 n {\displaystyle \sum {\frac {1}{n}}} diverges, which Bernoulli believed were new but they had actually been proved by Pietro Mengoli 40 years earlier and was proved by Nicole Oresme in the 14th century already. Bernoulli could not find a closed form for ∑ 1 n 2 {\displaystyle \sum {\frac {1}{n^{2}}}} , but he did show that it converged to a finite limit less than 2. Euler was the first to find the limit of this series in 1737. Bernoulli also studied the exponential series which came out of examining compound interest. In May 1690, in a paper published in Acta Eruditorum, Jacob Bernoulli showed that the problem of determining the isochrone is equivalent to solving a first-order nonlinear differential equation. The isochrone, or curve of constant descent, is the curve along which a particle will descend under gravity from any point to the bottom in exactly the same time, no matter what the starting point. It had been studied by Huygens in 1687 and Leibniz in 1689. After finding the differential equation, Bernoulli then solved it by what we now call separation of variables. Jacob Bernoulli's paper of 1690 is important for the history of calculus, since the term integral appears for the first time with its integration meaning. In 1696, Bernoulli solved the equation, now called the Bernoulli differential equation, y ′ = p ( x ) y + q ( x ) y n . {\displaystyle y'=p(x)y+q(x)y^{n}.} Jacob Bernoulli also discovered a general method to determine evolutes of a curve as the envelope of its circles of curvature. He also investigated caustic curves and in particular he studied these associated curves of the parabola, the logarithmic spiral and epicycloids around 1692. The lemniscate of Bernoulli was first conceived by Jacob Bernoulli in 1694. In 1695, he investigated the drawbridge problem which seeks the curve required so that a weight sliding along the cable always keeps the drawbridge balanced. Bernoulli's most original work was Ars Conjectandi, published in Basel in 1713, eight years after his death. The work was incomplete at the time of his death but it is still a work of the greatest significance in the theory of probability. The book also covers other related subjects, including a review of combinatorics, in particular the work of van Schooten, Leibniz, and Prestet, as well as the use of Bernoulli numbers in a discussion of the exponential series. Inspired by Huygens' work, Bernoulli also gives many examples on how much one would expect to win playing various games of chance. The term Bernoulli trial resulted from this work. In the last part of the book, Bernoulli sketches many areas of mathematical probability, including probability as a measurable degree of certainty; necessity and chance; moral versus mathematical expectation; a priori an a posteriori probability; expectation of winning when players are divided according to dexterity; regard of all available arguments, their valuation, and their calculable evaluation; and the law of large numbers. Bernoulli was one of the most significant promoters of the formal methods of higher analysis. Astuteness and elegance are seldom found in his method of presentation and expression, but there is a maximum of integrity. == Discovery of the mathematical constant e == In 1683, Bernoulli discovered the constant e by studying a question about compound interest which required him to find the value of the following expression (which is in fact e): lim n → ∞ ( 1 + 1 n ) n {\displaystyle \lim _{n\to \infty }\left(1+{\frac {1}{n}}\right)^{n}} One example is an account that starts with $1.00 and pays 100 percent interest per year. If the interest is credited once, at the end of the year, the value is $2.00; but if the interest is computed and added twice in the year, the $1 is multiplied by 1.5 twice, yielding $1.00×1.52 = $2.25. Compounding quarterly yields $1.00×1.254 = $2.4414..., and compounding monthly yields $1.00×(1.0833...)12 = $2.613035.... Bernoulli noticed that this sequence approaches a limit (the force of interest) for more and smaller compounding intervals. Compounding weekly yields $2.692597..., while compounding daily yields $2.714567..., just two cents more. Using n as the number of compounding intervals, with interest of 100% / n in each interval, the limit for large n is the number that Euler later named e; with continuous compounding, the account value will reach $2.7182818.... More generally, an account that starts at $1, and yields (1+R) dollars at compound interest, will yield eR dollars with continuous compounding. == Tombstone == Bernoulli wanted a logarithmic spiral and the motto Eadem mutata resurgo ('Although changed, I rise again the same') engraved on his tombstone. He wrote that the self-similar spiral "may be used as a symbol, either of fortitude and constancy in adversity, or of the human body, which after all its changes, even after death, will be restored to its exact and perfect self". Bernoulli died in 1705, but an Archimedean spiral was engraved rather than a logarithmic one. Translation of Latin inscription: Jacob Bernoulli, the incomparable mathematician. Professor at the University of Basel For more than 18 years; member of the Royal Academies of Paris and Berlin; famous for his writings. Of a chronic illness, of sound mind to the end; succumbed in the year of grace 1705, the 16th of August, at the age of 50 years and 7 months, awaiting the resurrection. Judith Stupanus, his wife for 20 years, and his two children have erected a monument to the husband and father they miss so much. == Works == Conamen novi systematis cometarum (in Latin). Amstelaedami: apud Henr. Wetstenium. 1682. (title roughly translates as "A new hypothesis for the system of comets".) De gravitate aetheris (in Latin). Amstelaedami: apud Henricum Wetstenium. 1683. Ars conjectandi, opus posthumum, Basileae, impensis Thurnisiorum Fratrum, 1713. Opera (in Latin). Vol. 1. Genève: héritiers Cramer & frères Philibert. 1744. Opera (in Latin). Vol. 2. Genève: héritiers Cramer & frères Philibert. 1744. == Notes == == References == == Further reading == Hoffman, J.E. (1970–1980). "Bernoulli, Jakob (Jacques) I". Dictionary of Scientific Biography. Vol. 2. New York: Charles Scribner's Sons. pp. 46–51. ISBN 978-0-684-10114-9. Schneider, I. (2005). "Jakob Bernoulli Ars conjectandi (1713)". In Grattan-Guinness, Ivor (ed.). Landmark Writings in Western Mathematics 1640–1940. Elsevier. pp. 88–104. ISBN 978-0-08-045744-4. == External links == Media related to Jakob Bernoulli at Wikimedia Commons Jacob Bernoulli at the Mathematics Genealogy Project O'Connor, John J.; Robertson, Edmund F., "Jacob Bernoulli", MacTutor History of Mathematics Archive, University of St Andrews Bernoulli, Jacobi. "Tractatus de Seriebus Infinitis" (PDF). Weisstein, Eric Wolfgang (ed.). "Bernoulli, Jakob (1654–1705)". ScienceWorld. Gottfried Leibniz and Jakob Bernoulli Correspondence Regarding the Art of Conjecturing" Archived 2016-04-06 at the Wayback Machine
|
Wikipedia:Jacob Eichenbaum#0
|
Jacob Moiseyovych Eichenbaum (Yiddish: יעקב בן־משה אייכענבוים, Ukrainian: Я́ків Мойсе́йович Ейхенба́ум; 12 October 1796 – 27 December 1861), born Jacob Gelber, was a Galician Jewish maskil, educator, poet and mathematician. == Biography == Jacob Gelber was born in the Galician city of Krystynopil, on 12 October 1796, in the year following the Third Partition of Poland by the Russian Empire. By the age of eleven, he was already in his first marriage, but it didn't last long until the divorce, as his father-in-law suspected that he was a secularist. In 1815, when he was eighteen, he remarried, adopted the name "Eichenbaum" and settled in Zamość. There he encountered a progressive Jewish youth circle, and began studying Hebrew, German, philosophy, and (in particular) mathematics. In 1819, he translated Euclid's Elements from German into Hebrew. He worked as a travelling private tutor, teaching Hebrew subjects and mathematics in wealthy households throughout Ukraine. In 1835, Eichenbaum opened a private school for Jewish children in Odesa, which had become an important educational centre for Ukrainian Jews. In 1836, he published Kol Zimrah, one of the first books of Modern Hebrew poetry published in the Haskalah period. In 1840, he published Ha-Kerav, a poetry book describing a variety of chess moves in verse. Eichenbaum's educational and literary work attracted the attention of the Russian government, which advanced his position in the Jewish education system of the Russian Empire. In 1844, Eichenbaum was appointed as director of the Bessarabian Jewish school in Chișinău, and in 1850, he was appointed as chief inspector of a Yeshiva in Zhytomyr, a position which he maintained until his death. During his final years, he continued to publish works of mathematics and poetry. In 1857, he published a Hebrew arithmetic textbook, Ḥokhmat ha-Shi'urim, which he had adapted from a work in the French language. In 1861, he wrote an allegorical poem, Ha-Kosem, which he published in the Hebrew newspaper Ha-Melitz. On 27 December 1861, Jacob Eichenbaum died in Kyiv. == References == == Sources == Kressel, Getzel (2018). "Eichenbaum (Gelber), Jacob". Encyclopaedia Judaica. Retrieved 15 November 2022 – via Encyclopedia.com. Rosenthal, Herman; Dubnow, Simon (1901–1906). "Eichenbaum, Jacob". Jewish Encyclopedia. Vol. 5. pp. 76–77.
|
Wikipedia:Jacob Tsimerman#0
|
Jacob Tsimerman (born 1988) is a Canadian mathematician at the University of Toronto specialising in number theory and related areas. He was awarded the SASTRA Ramanujan Prize in the year 2015 in recognition for his work on the André–Oort conjecture and for his work in both analytic number theory and algebraic geometry. == Education == He studied at the University of Toronto, graduating in 2006 with a bachelor's degree in math. He obtained his PhD from Princeton in 2011 under the guidance of Peter Sarnak. == Career == Jacob Tsimerman was born in Kazan, Russia, on April 26, 1988. In 1990 his family first moved to Israel and then in 1996 to Canada. In 2003 and 2004 he represented Canada in the International Mathematical Olympiad (IMO) and won gold medals both years, with a perfect score in 2004. Following his PhD, he had a post-doctoral position at Harvard University as a Junior Fellow of the Harvard Society of Fellows. In July 2014 he was awarded a Sloan Fellowship and he started his term as assistant professor at the University of Toronto, where he is now a full professor. In 2018, Tsimerman was an invited speaker at the International Congress of Mathematicians. In 2019, he was awarded the Coxeter–James Prize by the Canadian Mathematical Society. He is also one of winners of the 2022 New Horizons in Mathematics Prize, associated with the Breakthrough Prize in Mathematics. He was awarded for "outstanding work in analytic number theory and arithmetic geometry, including breakthroughs on the André-Oort and Griffiths conjectures". In 2023, Tsimerman received the Ostrowski Prize. == Research == Together with Jonathan Pila, Tsimerman demonstrated the André–Oort conjecture for Siegel modular varieties. Later, he completed the proof of the full André-Oort conjecture for all moduli spaces of abelian varieties by reducing the problem to the averaged Colmez conjecture which was proved by Xinyi Yuan and Shou-Wu Zhang as well as independently by Andreatta, Goren, Howard and Madapusi-Pera. == References ==
|
Wikipedia:Jacobi triple product#0
|
In mathematics, the Jacobi triple product is the identity: ∏ m = 1 ∞ ( 1 − x 2 m ) ( 1 + x 2 m − 1 y 2 ) ( 1 + x 2 m − 1 y 2 ) = ∑ n = − ∞ ∞ x n 2 y 2 n , {\displaystyle \prod _{m=1}^{\infty }\left(1-x^{2m}\right)\left(1+x^{2m-1}y^{2}\right)\left(1+{\frac {x^{2m-1}}{y^{2}}}\right)=\sum _{n=-\infty }^{\infty }x^{n^{2}}y^{2n},} for complex numbers x and y, with |x| < 1 and y ≠ 0. It was introduced by Jacobi (1829) in his work Fundamenta Nova Theoriae Functionum Ellipticarum. The Jacobi triple product identity is the Macdonald identity for the affine root system of type A1, and is the Weyl denominator formula for the corresponding affine Kac–Moody algebra. == Properties == Jacobi's proof relies on Euler's pentagonal number theorem, which is itself a specific case of the Jacobi triple product identity. Let x = q q {\displaystyle x=q{\sqrt {q}}} and y 2 = − q {\displaystyle y^{2}=-{\sqrt {q}}} . Then we have ϕ ( q ) = ∏ m = 1 ∞ ( 1 − q m ) = ∑ n = − ∞ ∞ ( − 1 ) n q 3 n 2 − n 2 . {\displaystyle \phi (q)=\prod _{m=1}^{\infty }\left(1-q^{m}\right)=\sum _{n=-\infty }^{\infty }(-1)^{n}q^{\frac {3n^{2}-n}{2}}.} The Rogers–Ramanujan identities follow with x = q 2 q {\displaystyle x=q^{2}{\sqrt {q}}} , y 2 = − q {\displaystyle y^{2}=-{\sqrt {q}}} and x = q 2 q {\displaystyle x=q^{2}{\sqrt {q}}} , y 2 = − q q {\displaystyle y^{2}=-q{\sqrt {q}}} . The Jacobi Triple Product also allows the Jacobi theta function to be written as an infinite product as follows: Let x = e i π τ {\displaystyle x=e^{i\pi \tau }} and y = e i π z . {\displaystyle y=e^{i\pi z}.} Then the Jacobi theta function ϑ ( z ; τ ) = ∑ n = − ∞ ∞ e π i n 2 τ + 2 π i n z {\displaystyle \vartheta (z;\tau )=\sum _{n=-\infty }^{\infty }e^{\pi {\rm {i}}n^{2}\tau +2\pi {\rm {i}}nz}} can be written in the form ∑ n = − ∞ ∞ y 2 n x n 2 . {\displaystyle \sum _{n=-\infty }^{\infty }y^{2n}x^{n^{2}}.} Using the Jacobi triple product identity, the theta function can be written as the product ϑ ( z ; τ ) = ∏ m = 1 ∞ ( 1 − e 2 m π i τ ) [ 1 + e ( 2 m − 1 ) π i τ + 2 π i z ] [ 1 + e ( 2 m − 1 ) π i τ − 2 π i z ] . {\displaystyle \vartheta (z;\tau )=\prod _{m=1}^{\infty }\left(1-e^{2m\pi {\rm {i}}\tau }\right)\left[1+e^{(2m-1)\pi {\rm {i}}\tau +2\pi {\rm {i}}z}\right]\left[1+e^{(2m-1)\pi {\rm {i}}\tau -2\pi {\rm {i}}z}\right].} There are many different notations used to express the Jacobi triple product. It takes on a concise form when expressed in terms of q-Pochhammer symbols: ∑ n = − ∞ ∞ q n ( n + 1 ) 2 z n = ( q ; q ) ∞ ( − 1 z ; q ) ∞ ( − z q ; q ) ∞ , {\displaystyle \sum _{n=-\infty }^{\infty }q^{\frac {n(n+1)}{2}}z^{n}=(q;q)_{\infty }\;\left(-{\tfrac {1}{z}};q\right)_{\infty }\;(-zq;q)_{\infty },} where ( a ; q ) ∞ {\displaystyle (a;q)_{\infty }} is the infinite q-Pochhammer symbol. It enjoys a particularly elegant form when expressed in terms of the Ramanujan theta function. For | a b | < 1 {\displaystyle |ab|<1} it can be written as ∑ n = − ∞ ∞ a n ( n + 1 ) 2 b n ( n − 1 ) 2 = ( − a ; a b ) ∞ ( − b ; a b ) ∞ ( a b ; a b ) ∞ . {\displaystyle \sum _{n=-\infty }^{\infty }a^{\frac {n(n+1)}{2}}\;b^{\frac {n(n-1)}{2}}=(-a;ab)_{\infty }\;(-b;ab)_{\infty }\;(ab;ab)_{\infty }.} == Proof == Let f x ( y ) = ∏ m = 1 ∞ ( 1 − x 2 m ) ( 1 + x 2 m − 1 y 2 ) ( 1 + x 2 m − 1 y − 2 ) {\displaystyle f_{x}(y)=\prod _{m=1}^{\infty }\left(1-x^{2m}\right)\left(1+x^{2m-1}y^{2}\right)\left(1+x^{2m-1}y^{-2}\right)} Substituting xy for y and multiplying the new terms out gives f x ( x y ) = 1 + x − 1 y − 2 1 + x y 2 f x ( y ) = x − 1 y − 2 f x ( y ) {\displaystyle f_{x}(xy)={\frac {1+x^{-1}y^{-2}}{1+xy^{2}}}f_{x}(y)=x^{-1}y^{-2}f_{x}(y)} Since f x {\displaystyle f_{x}} is meromorphic for | y | > 0 {\displaystyle |y|>0} , it has a Laurent series f x ( y ) = ∑ n = − ∞ ∞ c n ( x ) y 2 n {\displaystyle f_{x}(y)=\sum _{n=-\infty }^{\infty }c_{n}(x)y^{2n}} which satisfies ∑ n = − ∞ ∞ c n ( x ) x 2 n + 1 y 2 n = x f x ( x y ) = y − 2 f x ( y ) = ∑ n = − ∞ ∞ c n + 1 ( x ) y 2 n {\displaystyle \sum _{n=-\infty }^{\infty }c_{n}(x)x^{2n+1}y^{2n}=xf_{x}(xy)=y^{-2}f_{x}(y)=\sum _{n=-\infty }^{\infty }c_{n+1}(x)y^{2n}} so that c n + 1 ( x ) = c n ( x ) x 2 n + 1 = ⋯ = c 0 ( x ) x ( n + 1 ) 2 {\displaystyle c_{n+1}(x)=c_{n}(x)x^{2n+1}=\dots =c_{0}(x)x^{(n+1)^{2}}} and hence f x ( y ) = c 0 ( x ) ∑ n = − ∞ ∞ x n 2 y 2 n {\displaystyle f_{x}(y)=c_{0}(x)\sum _{n=-\infty }^{\infty }x^{n^{2}}y^{2n}} === Evaluating c0(x) === To show that c 0 ( x ) = 1 {\displaystyle c_{0}(x)=1} , use the fact that the infinite expansion ∏ m = 1 ∞ ( 1 + x 2 m − 1 y 2 ) ( 1 + x 2 m − 1 y − 2 ) {\displaystyle \prod _{m=1}^{\infty }\left(1+x^{2m-1}y^{2}\right)\left(1+x^{2m-1}y^{-2}\right)} has the following infinite polynomial coefficient at y 0 {\displaystyle y^{0}} = ∑ m = 0 ∞ x 2 m 2 ( 1 − x 2 ) 2 ( 1 − x 4 ) 2 ⋯ ( 1 − x 2 m ) 2 {\displaystyle =\sum _{m=0}^{\infty }{\frac {x^{2m^{2}}}{(1-x^{2})^{2}(1-x^{4})^{2}\cdots (1-x^{2m})^{2}}}} which is the Durfee square generating function with x 2 {\displaystyle x^{2}} instead of x {\displaystyle x} . = ∏ m = 1 ∞ ( 1 − x 2 m ) − 1 {\displaystyle =\prod _{m=1}^{\infty }\left(1-x^{2m}\right)^{-1}} Therefore at y 0 {\displaystyle y^{0}} we have f x ( y ) = 1 {\displaystyle f_{x}(y)=1} , and so c 0 ( x ) = 1 {\displaystyle c_{0}(x)=1} . === Other proofs === A different proof is given by G. E. Andrews based on two identities of Euler. For the analytic case, see Apostol. == References == Peter J. Cameron, Combinatorics: Topics, Techniques, Algorithms, (1994) Cambridge University Press, ISBN 0-521-45761-0 Jacobi, C. G. J. (1829), Fundamenta nova theoriae functionum ellipticarum (in Latin), Königsberg: Borntraeger, ISBN 978-1-108-05200-9, Reprinted by Cambridge University Press 2012 {{citation}}: ISBN / Date incompatibility (help) Carlitz, L (1962), "A note on the Jacobi theta formula", Bulletin of the American Mathematical Society, vol. 68, no. 6, American Mathematical Society, pp. 591–592 Wright, E. M. (1965), "An Enumerative Proof of An Identity of Jacobi", Journal of the London Mathematical Society, London Mathematical Society: 55–57, doi:10.1112/jlms/s1-40.1.55
|
Wikipedia:Jacobian matrix and determinant#0
|
In vector calculus, the Jacobian matrix (, ) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. If this matrix is square, that is, if the number of variables equals the number of components of function values, then its determinant is called the Jacobian determinant. Both the matrix and (if applicable) the determinant are often referred to simply as the Jacobian. They are named after Carl Gustav Jacob Jacobi. The Jacobian matrix is the natural generalization to vector valued functions of several variables of the derivative and the differential of a usual function. This generalization includes generalizations of the inverse function theorem and the implicit function theorem, where the non-nullity of the derivative is replaced by the non-nullity of the Jacobian determinant, and the multiplicative inverse of the derivative is replaced by the inverse of the Jacobian matrix. The Jacobian determinant is fundamentally used for changes of variables in multiple integrals. == Definition == Let f : Rn → Rm be a function such that each of its first-order partial derivatives exists on Rn. This function takes a point x = ( x 1 , … , x n ) ∈ R n {\displaystyle \mathbf {x} =(x_{1},\ldots ,x_{n})\in \mathbf {R} ^{n}} as input and produces the vector f ( x ) = ( f 1 ( x ) , … , f m ( x ) ) ∈ R m {\displaystyle \mathbf {f} (\mathbf {x} )=(f_{1}(\mathbf {x} ),\ldots ,f_{m}(\mathbf {x} ))\in \mathbf {R} ^{m}} as output. Then the Jacobian matrix of f, denoted Jf, is the m × n {\displaystyle m\times n} matrix whose (i, j) entry is ∂ f i ∂ x j ; {\textstyle {\frac {\partial f_{i}}{\partial x_{j}}};} explicitly J f = [ ∂ f ∂ x 1 ⋯ ∂ f ∂ x n ] = [ ∇ T f 1 ⋮ ∇ T f m ] = [ ∂ f 1 ∂ x 1 ⋯ ∂ f 1 ∂ x n ⋮ ⋱ ⋮ ∂ f m ∂ x 1 ⋯ ∂ f m ∂ x n ] {\displaystyle \mathbf {J_{f}} ={\begin{bmatrix}{\dfrac {\partial \mathbf {f} }{\partial x_{1}}}&\cdots &{\dfrac {\partial \mathbf {f} }{\partial x_{n}}}\end{bmatrix}}={\begin{bmatrix}\nabla ^{\mathsf {T}}f_{1}\\\vdots \\\nabla ^{\mathsf {T}}f_{m}\end{bmatrix}}={\begin{bmatrix}{\dfrac {\partial f_{1}}{\partial x_{1}}}&\cdots &{\dfrac {\partial f_{1}}{\partial x_{n}}}\\\vdots &\ddots &\vdots \\{\dfrac {\partial f_{m}}{\partial x_{1}}}&\cdots &{\dfrac {\partial f_{m}}{\partial x_{n}}}\end{bmatrix}}} where ∇ T f i {\displaystyle \nabla ^{\mathsf {T}}f_{i}} is the transpose (row vector) of the gradient of the i {\displaystyle i} -th component. The Jacobian matrix, whose entries are functions of x, is denoted in various ways; other common notations include Df, ∇ f {\displaystyle \nabla \mathbf {f} } , and ∂ ( f 1 , … , f m ) ∂ ( x 1 , … , x n ) {\textstyle {\frac {\partial (f_{1},\ldots ,f_{m})}{\partial (x_{1},\ldots ,x_{n})}}} . Some authors define the Jacobian as the transpose of the form given above. The Jacobian matrix represents the differential of f at every point where f is differentiable. In detail, if h is a displacement vector represented by a column matrix, the matrix product J(x) ⋅ h is another displacement vector, that is the best linear approximation of the change of f in a neighborhood of x, if f(x) is differentiable at x. This means that the function that maps y to f(x) + J(x) ⋅ (y – x) is the best linear approximation of f(y) for all points y close to x. The linear map h → J(x) ⋅ h is known as the derivative or the differential of f at x. When m = n, the Jacobian matrix is square, so its determinant is a well-defined function of x, known as the Jacobian determinant of f. It carries important information about the local behavior of f. In particular, the function f has a differentiable inverse function in a neighborhood of a point x if and only if the Jacobian determinant is nonzero at x (see inverse function theorem for an explanation of this and Jacobian conjecture for a related problem of global invertibility). The Jacobian determinant also appears when changing the variables in multiple integrals (see substitution rule for multiple variables). When m = 1, that is when f : Rn → R is a scalar-valued function, the Jacobian matrix reduces to the row vector ∇ T f {\displaystyle \nabla ^{\mathsf {T}}f} ; this row vector of all first-order partial derivatives of f is the transpose of the gradient of f, i.e. J f = ∇ T f {\displaystyle \mathbf {J} _{f}=\nabla ^{\mathsf {T}}f} . Specializing further, when m = n = 1, that is when f : R → R is a scalar-valued function of a single variable, the Jacobian matrix has a single entry; this entry is the derivative of the function f. These concepts are named after the mathematician Carl Gustav Jacob Jacobi (1804–1851). == Jacobian matrix == The Jacobian of a vector-valued function in several variables generalizes the gradient of a scalar-valued function in several variables, which in turn generalizes the derivative of a scalar-valued function of a single variable. In other words, the Jacobian matrix of a scalar-valued function of several variables is (the transpose of) its gradient and the gradient of a scalar-valued function of a single variable is its derivative. At each point where a function is differentiable, its Jacobian matrix can also be thought of as describing the amount of "stretching", "rotating" or "transforming" that the function imposes locally near that point. For example, if (x′, y′) = f(x, y) is used to smoothly transform an image, the Jacobian matrix Jf(x, y), describes how the image in the neighborhood of (x, y) is transformed. If a function is differentiable at a point, its differential is given in coordinates by the Jacobian matrix. However, a function does not need to be differentiable for its Jacobian matrix to be defined, since only its first-order partial derivatives are required to exist. If f is differentiable at a point p in Rn, then its differential is represented by Jf(p). In this case, the linear transformation represented by Jf(p) is the best linear approximation of f near the point p, in the sense that f ( x ) − f ( p ) = J f ( p ) ( x − p ) + o ( ‖ x − p ‖ ) ( as x → p ) , {\displaystyle \mathbf {f} (\mathbf {x} )-\mathbf {f} (\mathbf {p} )=\mathbf {J} _{\mathbf {f} }(\mathbf {p} )(\mathbf {x} -\mathbf {p} )+o(\|\mathbf {x} -\mathbf {p} \|)\quad ({\text{as }}\mathbf {x} \to \mathbf {p} ),} where o(‖x − p‖) is a quantity that approaches zero much faster than the distance between x and p does as x approaches p. This approximation specializes to the approximation of a scalar function of a single variable by its Taylor polynomial of degree one, namely f ( x ) − f ( p ) = f ′ ( p ) ( x − p ) + o ( x − p ) ( as x → p ) . {\displaystyle f(x)-f(p)=f'(p)(x-p)+o(x-p)\quad ({\text{as }}x\to p).} In this sense, the Jacobian may be regarded as a kind of "first-order derivative" of a vector-valued function of several variables. In particular, this means that the gradient of a scalar-valued function of several variables may too be regarded as its "first-order derivative". Composable differentiable functions f : Rn → Rm and g : Rm → Rk satisfy the chain rule, namely J g ∘ f ( x ) = J g ( f ( x ) ) J f ( x ) {\displaystyle \mathbf {J} _{\mathbf {g} \circ \mathbf {f} }(\mathbf {x} )=\mathbf {J} _{\mathbf {g} }(\mathbf {f} (\mathbf {x} ))\mathbf {J} _{\mathbf {f} }(\mathbf {x} )} for x in Rn. The Jacobian of the gradient of a scalar function of several variables has a special name: the Hessian matrix, which in a sense is the "second derivative" of the function in question. == Jacobian determinant == If m = n, then f is a function from Rn to itself and the Jacobian matrix is a square matrix. We can then form its determinant, known as the Jacobian determinant. The Jacobian determinant is sometimes simply referred to as "the Jacobian". The Jacobian determinant at a given point gives important information about the behavior of f near that point. For instance, the continuously differentiable function f is invertible near a point p ∈ Rn if the Jacobian determinant at p is non-zero. This is the inverse function theorem. Furthermore, if the Jacobian determinant at p is positive, then f preserves orientation near p; if it is negative, f reverses orientation. The absolute value of the Jacobian determinant at p gives us the factor by which the function f expands or shrinks volumes near p; this is why it occurs in the general substitution rule. The Jacobian determinant is used when making a change of variables when evaluating a multiple integral of a function over a region within its domain. To accommodate for the change of coordinates the magnitude of the Jacobian determinant arises as a multiplicative factor within the integral. This is because the n-dimensional dV element is in general a parallelepiped in the new coordinate system, and the n-volume of a parallelepiped is the determinant of its edge vectors. The Jacobian can also be used to determine the stability of equilibria for systems of differential equations by approximating behavior near an equilibrium point. == Inverse == According to the inverse function theorem, the matrix inverse of the Jacobian matrix of an invertible function f : Rn → Rn is the Jacobian matrix of the inverse function. That is, the Jacobian matrix of the inverse function at a point p is J f − 1 ( p ) = J f − 1 ( f − 1 ( p ) ) , {\displaystyle \mathbf {J} _{\mathbf {f} ^{-1}}(\mathbf {p} )={\mathbf {J} _{\mathbf {f} }^{-1}(\mathbf {f} ^{-1}(\mathbf {p} ))},} and the Jacobian determinant is det ( J f − 1 ( p ) ) = 1 det ( J f ( f − 1 ( p ) ) ) . {\displaystyle \det(\mathbf {J} _{\mathbf {f} ^{-1}}(\mathbf {p} ))={\frac {1}{\det(\mathbf {J} _{\mathbf {f} }(\mathbf {f} ^{-1}(\mathbf {p} )))}}.} If the Jacobian is continuous and nonsingular at the point p in Rn, then f is invertible when restricted to some neighbourhood of p. In other words, if the Jacobian determinant is not zero at a point, then the function is locally invertible near this point. The (unproved) Jacobian conjecture is related to global invertibility in the case of a polynomial function, that is a function defined by n polynomials in n variables. It asserts that, if the Jacobian determinant is a non-zero constant (or, equivalently, that it does not have any complex zero), then the function is invertible and its inverse is a polynomial function. == Critical points == If f : Rn → Rm is a differentiable function, a critical point of f is a point where the rank of the Jacobian matrix is not maximal. This means that the rank at the critical point is lower than the rank at some neighbour point. In other words, let k be the maximal dimension of the open balls contained in the image of f; then a point is critical if all minors of rank k of f are zero. In the case where m = n = k, a point is critical if the Jacobian determinant is zero. == Examples == === Example 1 === Consider a function f : R2 → R2, with (x, y) ↦ (f1(x, y), f2(x, y)), given by f ( [ x y ] ) = [ f 1 ( x , y ) f 2 ( x , y ) ] = [ x 2 y 5 x + sin y ] . {\displaystyle \mathbf {f} \left({\begin{bmatrix}x\\y\end{bmatrix}}\right)={\begin{bmatrix}f_{1}(x,y)\\f_{2}(x,y)\end{bmatrix}}={\begin{bmatrix}x^{2}y\\5x+\sin y\end{bmatrix}}.} Then we have f 1 ( x , y ) = x 2 y {\displaystyle f_{1}(x,y)=x^{2}y} and f 2 ( x , y ) = 5 x + sin y . {\displaystyle f_{2}(x,y)=5x+\sin y.} The Jacobian matrix of f is J f ( x , y ) = [ ∂ f 1 ∂ x ∂ f 1 ∂ y ∂ f 2 ∂ x ∂ f 2 ∂ y ] = [ 2 x y x 2 5 cos y ] {\displaystyle \mathbf {J} _{\mathbf {f} }(x,y)={\begin{bmatrix}{\dfrac {\partial f_{1}}{\partial x}}&{\dfrac {\partial f_{1}}{\partial y}}\\[1em]{\dfrac {\partial f_{2}}{\partial x}}&{\dfrac {\partial f_{2}}{\partial y}}\end{bmatrix}}={\begin{bmatrix}2xy&x^{2}\\5&\cos y\end{bmatrix}}} and the Jacobian determinant is det ( J f ( x , y ) ) = 2 x y cos y − 5 x 2 . {\displaystyle \det(\mathbf {J} _{\mathbf {f} }(x,y))=2xy\cos y-5x^{2}.} === Example 2: polar-Cartesian transformation === The transformation from polar coordinates (r, φ) to Cartesian coordinates (x, y), is given by the function F: R+ × [0, 2π) → R2 with components x = r cos φ ; y = r sin φ . {\displaystyle {\begin{aligned}x&=r\cos \varphi ;\\y&=r\sin \varphi .\end{aligned}}} J F ( r , φ ) = [ ∂ x ∂ r ∂ x ∂ φ ∂ y ∂ r ∂ y ∂ φ ] = [ cos φ − r sin φ sin φ r cos φ ] {\displaystyle \mathbf {J} _{\mathbf {F} }(r,\varphi )={\begin{bmatrix}{\frac {\partial x}{\partial r}}&{\frac {\partial x}{\partial \varphi }}\\[0.5ex]{\frac {\partial y}{\partial r}}&{\frac {\partial y}{\partial \varphi }}\end{bmatrix}}={\begin{bmatrix}\cos \varphi &-r\sin \varphi \\\sin \varphi &r\cos \varphi \end{bmatrix}}} The Jacobian determinant is equal to r. This can be used to transform integrals between the two coordinate systems: ∬ F ( A ) f ( x , y ) d x d y = ∬ A f ( r cos φ , r sin φ ) r d r d φ . {\displaystyle \iint _{\mathbf {F} (A)}f(x,y)\,dx\,dy=\iint _{A}f(r\cos \varphi ,r\sin \varphi )\,r\,dr\,d\varphi .} === Example 3: spherical-Cartesian transformation === The transformation from spherical coordinates (ρ, φ, θ) to Cartesian coordinates (x, y, z), is given by the function F: R+ × [0, π) × [0, 2π) → R3 with components x = ρ sin φ cos θ ; y = ρ sin φ sin θ ; z = ρ cos φ . {\displaystyle {\begin{aligned}x&=\rho \sin \varphi \cos \theta ;\\y&=\rho \sin \varphi \sin \theta ;\\z&=\rho \cos \varphi .\end{aligned}}} The Jacobian matrix for this coordinate change is J F ( ρ , φ , θ ) = [ ∂ x ∂ ρ ∂ x ∂ φ ∂ x ∂ θ ∂ y ∂ ρ ∂ y ∂ φ ∂ y ∂ θ ∂ z ∂ ρ ∂ z ∂ φ ∂ z ∂ θ ] = [ sin φ cos θ ρ cos φ cos θ − ρ sin φ sin θ sin φ sin θ ρ cos φ sin θ ρ sin φ cos θ cos φ − ρ sin φ 0 ] . {\displaystyle \mathbf {J} _{\mathbf {F} }(\rho ,\varphi ,\theta )={\begin{bmatrix}{\dfrac {\partial x}{\partial \rho }}&{\dfrac {\partial x}{\partial \varphi }}&{\dfrac {\partial x}{\partial \theta }}\\[1em]{\dfrac {\partial y}{\partial \rho }}&{\dfrac {\partial y}{\partial \varphi }}&{\dfrac {\partial y}{\partial \theta }}\\[1em]{\dfrac {\partial z}{\partial \rho }}&{\dfrac {\partial z}{\partial \varphi }}&{\dfrac {\partial z}{\partial \theta }}\end{bmatrix}}={\begin{bmatrix}\sin \varphi \cos \theta &\rho \cos \varphi \cos \theta &-\rho \sin \varphi \sin \theta \\\sin \varphi \sin \theta &\rho \cos \varphi \sin \theta &\rho \sin \varphi \cos \theta \\\cos \varphi &-\rho \sin \varphi &0\end{bmatrix}}.} The determinant is ρ2 sin φ. Since dV = dx dy dz is the volume for a rectangular differential volume element (because the volume of a rectangular prism is the product of its sides), we can interpret dV = ρ2 sin φ dρ dφ dθ as the volume of the spherical differential volume element. Unlike rectangular differential volume element's volume, this differential volume element's volume is not a constant, and varies with coordinates (ρ and φ). It can be used to transform integrals between the two coordinate systems: ∭ F ( U ) f ( x , y , z ) d x d y d z = ∭ U f ( ρ sin φ cos θ , ρ sin φ sin θ , ρ cos φ ) ρ 2 sin φ d ρ d φ d θ . {\displaystyle \iiint _{\mathbf {F} (U)}f(x,y,z)\,dx\,dy\,dz=\iiint _{U}f(\rho \sin \varphi \cos \theta ,\rho \sin \varphi \sin \theta ,\rho \cos \varphi )\,\rho ^{2}\sin \varphi \,d\rho \,d\varphi \,d\theta .} === Example 4 === The Jacobian matrix of the function F : R3 → R4 with components y 1 = x 1 y 2 = 5 x 3 y 3 = 4 x 2 2 − 2 x 3 y 4 = x 3 sin x 1 {\displaystyle {\begin{aligned}y_{1}&=x_{1}\\y_{2}&=5x_{3}\\y_{3}&=4x_{2}^{2}-2x_{3}\\y_{4}&=x_{3}\sin x_{1}\end{aligned}}} is J F ( x 1 , x 2 , x 3 ) = [ ∂ y 1 ∂ x 1 ∂ y 1 ∂ x 2 ∂ y 1 ∂ x 3 ∂ y 2 ∂ x 1 ∂ y 2 ∂ x 2 ∂ y 2 ∂ x 3 ∂ y 3 ∂ x 1 ∂ y 3 ∂ x 2 ∂ y 3 ∂ x 3 ∂ y 4 ∂ x 1 ∂ y 4 ∂ x 2 ∂ y 4 ∂ x 3 ] = [ 1 0 0 0 0 5 0 8 x 2 − 2 x 3 cos x 1 0 sin x 1 ] . {\displaystyle \mathbf {J} _{\mathbf {F} }(x_{1},x_{2},x_{3})={\begin{bmatrix}{\dfrac {\partial y_{1}}{\partial x_{1}}}&{\dfrac {\partial y_{1}}{\partial x_{2}}}&{\dfrac {\partial y_{1}}{\partial x_{3}}}\\[1em]{\dfrac {\partial y_{2}}{\partial x_{1}}}&{\dfrac {\partial y_{2}}{\partial x_{2}}}&{\dfrac {\partial y_{2}}{\partial x_{3}}}\\[1em]{\dfrac {\partial y_{3}}{\partial x_{1}}}&{\dfrac {\partial y_{3}}{\partial x_{2}}}&{\dfrac {\partial y_{3}}{\partial x_{3}}}\\[1em]{\dfrac {\partial y_{4}}{\partial x_{1}}}&{\dfrac {\partial y_{4}}{\partial x_{2}}}&{\dfrac {\partial y_{4}}{\partial x_{3}}}\end{bmatrix}}={\begin{bmatrix}1&0&0\\0&0&5\\0&8x_{2}&-2\\x_{3}\cos x_{1}&0&\sin x_{1}\end{bmatrix}}.} This example shows that the Jacobian matrix need not be a square matrix. === Example 5 === The Jacobian determinant of the function F : R3 → R3 with components y 1 = 5 x 2 y 2 = 4 x 1 2 − 2 sin ( x 2 x 3 ) y 3 = x 2 x 3 {\displaystyle {\begin{aligned}y_{1}&=5x_{2}\\y_{2}&=4x_{1}^{2}-2\sin(x_{2}x_{3})\\y_{3}&=x_{2}x_{3}\end{aligned}}} is | 0 5 0 8 x 1 − 2 x 3 cos ( x 2 x 3 ) − 2 x 2 cos ( x 2 x 3 ) 0 x 3 x 2 | = − 8 x 1 | 5 0 x 3 x 2 | = − 40 x 1 x 2 . {\displaystyle {\begin{vmatrix}0&5&0\\8x_{1}&-2x_{3}\cos(x_{2}x_{3})&-2x_{2}\cos(x_{2}x_{3})\\0&x_{3}&x_{2}\end{vmatrix}}=-8x_{1}{\begin{vmatrix}5&0\\x_{3}&x_{2}\end{vmatrix}}=-40x_{1}x_{2}.} From this we see that F reverses orientation near those points where x1 and x2 have the same sign; the function is locally invertible everywhere except near points where x1 = 0 or x2 = 0. Intuitively, if one starts with a tiny object around the point (1, 2, 3) and apply F to that object, one will get a resulting object with approximately 40 × 1 × 2 = 80 times the volume of the original one, with orientation reversed. == Other uses == === Dynamical systems === Consider a dynamical system of the form x ˙ = F ( x ) {\displaystyle {\dot {\mathbf {x} }}=F(\mathbf {x} )} , where x ˙ {\displaystyle {\dot {\mathbf {x} }}} is the (component-wise) derivative of x {\displaystyle \mathbf {x} } with respect to the evolution parameter t {\displaystyle t} (time), and F : R n → R n {\displaystyle F\colon \mathbb {R} ^{n}\to \mathbb {R} ^{n}} is differentiable. If F ( x 0 ) = 0 {\displaystyle F(\mathbf {x} _{0})=0} , then x 0 {\displaystyle \mathbf {x} _{0}} is a stationary point (also called a steady state). By the Hartman–Grobman theorem, the behavior of the system near a stationary point is related to the eigenvalues of J F ( x 0 ) {\displaystyle \mathbf {J} _{F}\left(\mathbf {x} _{0}\right)} , the Jacobian of F {\displaystyle F} at the stationary point. Specifically, if the eigenvalues all have real parts that are negative, then the system is stable near the stationary point. If any eigenvalue has a real part that is positive, then the point is unstable. If the largest real part of the eigenvalues is zero, the Jacobian matrix does not allow for an evaluation of the stability. === Newton's method === A square system of coupled nonlinear equations can be solved iteratively by Newton's method. This method uses the Jacobian matrix of the system of equations. === Regression and least squares fitting === The Jacobian serves as a linearized design matrix in statistical regression and curve fitting; see non-linear least squares. The Jacobian is also used in random matrices, moments, local sensitivity and statistical diagnostics. == See also == Center manifold Hessian matrix Pushforward (differential) == Notes == == References == == Further reading == Gandolfo, Giancarlo (1996). "Comparative Statics and the Correspondence Principle". Economic Dynamics (Third ed.). Berlin: Springer. pp. 305–330. ISBN 3-540-60988-1. Protter, Murray H.; Morrey, Charles B. Jr. (1985). "Transformations and Jacobians". Intermediate Calculus (Second ed.). New York: Springer. pp. 412–420. ISBN 0-387-96058-9. == External links == "Jacobian", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Mathworld A more technical explanation of Jacobians
|
Wikipedia:Jacobi–Anger expansion#0
|
In mathematics, the Jacobi–Anger expansion (or Jacobi–Anger identity) is an expansion of exponentials of trigonometric functions in the basis of their harmonics. It is useful in physics (for example, to convert between plane waves and cylindrical waves), and in signal processing (to describe FM signals). This identity is named after the 19th-century mathematicians Carl Jacobi and Carl Theodor Anger. The most general identity is given by: e i z cos θ ≡ ∑ n = − ∞ ∞ i n J n ( z ) e i n θ , {\displaystyle e^{iz\cos \theta }\equiv \sum _{n=-\infty }^{\infty }i^{n}\,J_{n}(z)\,e^{in\theta },} where J n ( z ) {\displaystyle J_{n}(z)} is the n {\displaystyle n} -th Bessel function of the first kind and i {\displaystyle i} is the imaginary unit, i 2 = − 1. {\textstyle i^{2}=-1.} Substituting θ {\textstyle \theta } by θ − π 2 {\textstyle \theta -{\frac {\pi }{2}}} , we also get: e i z sin θ ≡ ∑ n = − ∞ ∞ J n ( z ) e i n θ . {\displaystyle e^{iz\sin \theta }\equiv \sum _{n=-\infty }^{\infty }J_{n}(z)\,e^{in\theta }.} Using the relation J − n ( z ) = ( − 1 ) n J n ( z ) , {\displaystyle J_{-n}(z)=(-1)^{n}\,J_{n}(z),} valid for integer n {\displaystyle n} , the expansion becomes: e i z cos θ ≡ J 0 ( z ) + 2 ∑ n = 1 ∞ i n J n ( z ) cos ( n θ ) . {\displaystyle e^{iz\cos \theta }\equiv J_{0}(z)\,+\,2\,\sum _{n=1}^{\infty }\,i^{n}\,J_{n}(z)\,\cos \,(n\theta ).} == Real-valued expressions == The following real-valued variations are often useful as well: cos ( z cos θ ) ≡ J 0 ( z ) + 2 ∑ n = 1 ∞ ( − 1 ) n J 2 n ( z ) cos ( 2 n θ ) , sin ( z cos θ ) ≡ − 2 ∑ n = 1 ∞ ( − 1 ) n J 2 n − 1 ( z ) cos [ ( 2 n − 1 ) θ ] , cos ( z sin θ ) ≡ J 0 ( z ) + 2 ∑ n = 1 ∞ J 2 n ( z ) cos ( 2 n θ ) , sin ( z sin θ ) ≡ 2 ∑ n = 1 ∞ J 2 n − 1 ( z ) sin [ ( 2 n − 1 ) θ ] . {\displaystyle {\begin{aligned}\cos(z\cos \theta )&\equiv J_{0}(z)+2\sum _{n=1}^{\infty }(-1)^{n}J_{2n}(z)\cos(2n\theta ),\\\sin(z\cos \theta )&\equiv -2\sum _{n=1}^{\infty }(-1)^{n}J_{2n-1}(z)\cos \left[\left(2n-1\right)\theta \right],\\\cos(z\sin \theta )&\equiv J_{0}(z)+2\sum _{n=1}^{\infty }J_{2n}(z)\cos(2n\theta ),\\\sin(z\sin \theta )&\equiv 2\sum _{n=1}^{\infty }J_{2n-1}(z)\sin \left[\left(2n-1\right)\theta \right].\end{aligned}}} == See also == Plane wave expansion == Notes == == References == Abramowitz, Milton; Stegun, Irene Ann, eds. (1983) [June 1964]. "Chapter 9". Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. Vol. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. p. 355. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253. Colton, David; Kress, Rainer (1998), Inverse acoustic and electromagnetic scattering theory, Applied Mathematical Sciences, vol. 93 (2nd ed.), ISBN 978-3-540-62838-5 Cuyt, Annie; Petersen, Vigdis; Verdonk, Brigitte; Waadeland, Haakon; Jones, William B. (2008), Handbook of continued fractions for special functions, Springer, ISBN 978-1-4020-6948-2 == External links == Weisstein, Eric W. "Jacobi–Anger expansion". MathWorld — a Wolfram web resource. Retrieved 2008-11-11.
|
Wikipedia:Jacobson–Bourbaki theorem#0
|
In algebra, the Jacobson–Bourbaki theorem is a theorem used to extend Galois theory to field extensions that need not be separable. It was introduced by Nathan Jacobson (1944) for commutative fields and extended to division rings by Jacobson (1947), and Henri Cartan (1947) who credited the result to unpublished work by Nicolas Bourbaki. The extension of Galois theory to normal extensions is called the Jacobson–Bourbaki correspondence, which replaces the correspondence between some subfields of a field and some subgroups of a Galois group by a correspondence between some sub division rings of a division ring and some subalgebras of an associative algebra. The Jacobson–Bourbaki theorem implies both the usual Galois correspondence for subfields of a Galois extension, and Jacobson's Galois correspondence for subfields of a purely inseparable extension of exponent at most 1. == Statement == Suppose that L is a division ring. The Jacobson–Bourbaki theorem states that there is a natural 1:1 correspondence between: Division rings K in L of finite index n (in other words L is a finite-dimensional left vector space over K). Unital K-algebras of finite dimension n (as K-vector spaces) contained in the ring of endomorphisms of the additive group of K. The sub division ring and the corresponding subalgebra are each other's commutants. Jacobson (1956, Chapter 7.2) gave an extension to sub division rings that might have infinite index, which correspond to closed subalgebras in the finite topology. == Bibliography == Cartan, Henri (1947), "Les principaux théorèmes de la théorie de Galois pour les corps non nécessairement commutatifs", Comptes rendus de l'Académie des Sciences, 224: 249–251, MR 0020983 Cartan, Henri (1947), "Théorie de Galois pour les corps non commutatifs", Annales Scientifiques de l'École Normale Supérieure, Série 3, 64: 59–77, doi:10.24033/asens.942, ISSN 0012-9593, MR 0023237 Jacobson, Nathan (1944), "Galois theory of purely inseparable fields of exponent one", American Journal of Mathematics, 66 (4): 645–648, doi:10.2307/2371772, ISSN 0002-9327, JSTOR 2371772, MR 0011079 Jacobson, Nathan (1947), "A note on division rings", American Journal of Mathematics, 69 (1): 27–36, doi:10.2307/2371651, ISSN 0002-9327, JSTOR 2371651, MR 0020981 Jacobson, Nathan (1956), Structure of rings, American Mathematical Society, Colloquium Publications, vol. 37, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-1037-8, MR 0081264 {{citation}}: ISBN / Date incompatibility (help) Jacobson, Nathan (1964), Lectures in abstract algebra. Vol III: Theory of fields and Galois theory, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London-New York, ISBN 978-0-387-90168-8, MR 0172871 {{citation}}: ISBN / Date incompatibility (help) Kreimer, F. (2001) [1994], "Jacobson-Bourbaki_theorem", Encyclopedia of Mathematics, EMS Press
|
Wikipedia:Jacobson–Morozov theorem#0
|
In mathematics, the Jacobson–Morozov theorem is the assertion that nilpotent elements in a semi-simple Lie algebra can be extended to sl2-triples. The theorem is named after Jacobson 1951, Morozov 1942. == Statement == The statement of Jacobson–Morozov relies on the following preliminary notions: an sl2-triple in a semi-simple Lie algebra g {\displaystyle {\mathfrak {g}}} (throughout in this article, over a field of characteristic zero) is a homomorphism of Lie algebras s l 2 → g {\displaystyle {\mathfrak {sl}}_{2}\to {\mathfrak {g}}} . Equivalently, it is a triple e , f , h {\displaystyle e,f,h} of elements in g {\displaystyle {\mathfrak {g}}} satisfying the relations [ h , e ] = 2 e , [ h , f ] = − 2 f , [ e , f ] = h . {\displaystyle [h,e]=2e,\quad [h,f]=-2f,\quad [e,f]=h.} An element x ∈ g {\displaystyle x\in {\mathfrak {g}}} is called nilpotent, if the endomorphism [ x , − ] : g → g {\displaystyle [x,-]:{\mathfrak {g}}\to {\mathfrak {g}}} (known as the adjoint representation) is a nilpotent endomorphism. It is an elementary fact that for any sl2-triple ( e , f , h ) {\displaystyle (e,f,h)} , e must be nilpotent. The Jacobson–Morozov theorem states that, conversely, any nilpotent non-zero element e ∈ g {\displaystyle e\in {\mathfrak {g}}} can be extended to an sl2-triple. For g = s l n {\displaystyle {\mathfrak {g}}={\mathfrak {sl}}_{n}} , the sl2-triples obtained in this way are made explicit in Chriss & Ginzburg (1997, p. 184). The theorem can also be stated for linear algebraic groups (again over a field k of characteristic zero): any morphism (of algebraic groups) from the additive group G a {\displaystyle G_{a}} to a reductive group H factors through the embedding G a → S L 2 , x ↦ ( 1 x 0 1 ) . {\displaystyle G_{a}\to SL_{2},x\mapsto \left({\begin{array}{cc}1&x\\0&1\end{array}}\right).} Furthermore, any two such factorizations S L 2 → H {\displaystyle SL_{2}\to H} are conjugate by a k-point of H. == Generalization == A far-reaching generalization of the theorem as formulated above can be stated as follows: the inclusion of pro-reductive groups into all linear algebraic groups, where morphisms G → H {\displaystyle G\to H} in both categories are taken up to conjugation by elements in H ( k ) {\displaystyle H(k)} , admits a left adjoint, the so-called pro-reductive envelope. This left adjoint sends the additive group G a {\displaystyle G_{a}} to S L 2 {\displaystyle SL_{2}} (which happens to be semi-simple, as opposed to pro-reductive), thereby recovering the above form of Jacobson–Morozov. This generalized Jacobson–Morozov theorem was proven by André & Kahn (2002, Theorem 19.3.1) by appealing to methods related to Tannakian categories and by O'Sullivan (2010) by more geometric methods. == References == André, Yves; Kahn, Bruno (2002), "Nilpotence, radicaux et structures monoïdales", Rend. Semin. Mat. Univ. Padova, 108: 107–291, arXiv:math/0203273, Bibcode:2002math......3273A, MR 1956434 Chriss, Neil; Ginzburg, Victor (1997), Representation theory and complex geometry, Birkhäuser, ISBN 0-8176-3792-3, MR 1433132 Bourbaki, Nicolas (2007), Groupes et algèbres de Lie: Chapitres 7 et 8, Springer, ISBN 9783540339779 Jacobson, Nathan (1935), "Rational methods in the theory of Lie algebras", Annals of Mathematics, Second Series, 36 (4): 875–881, doi:10.2307/1968593, JSTOR 1968593, MR 1503258 Jacobson, Nathan (1951), "Completely reducible Lie algebras of linear transformations", Proceedings of the American Mathematical Society, 2: 105–113, doi:10.1090/S0002-9939-1951-0049882-5, MR 0049882 Jacobson, Nathan (1979), Lie algebras (Republication of the 1962 original ed.), Dover Publications, Inc., New York, ISBN 0-486-63832-4 Morozov, V. V. (1942), "On a nilpotent element in a semi-simple Lie algebra", C. R. (Doklady) Acad. Sci. URSS, New Series, 36: 83–86, MR 0007750 O'Sullivan, Peter (2010), "The generalised Jacobson-Morosov theorem", Memoirs of the American Mathematical Society, 207 (973), doi:10.1090/s0065-9266-10-00603-4, ISBN 978-0-8218-4895-1
|
Wikipedia:Jacquelien Scherpen#0
|
Jacquelien Maria Aleida Scherpen is a Dutch applied mathematician specializing in nonlinear control theory. She is a professor in the faculty of science and engineering at the University of Groningen, director of the Groningen Engineering Center, and former scientific director of the Engineering and Technology Institute Groningen (ENTEG). She has been rector magnificus of the university since September 2023. == Education and career == Scherpen studied applied mathematics at the University of Twente, earning a master's degree in 1990 and completing her Ph.D. in 1994. Her doctoral dissertation, Balancing for Nonlinear Systems, was jointly promoted by Huibert Kwakernaak and Arjan van der Schaft. She was affiliated with the Delft University of Technology from 1994 until 2006, when she moved to her present position at the University of Groningen. She was scientific director of ENTEG from 2013 to 2019, and has directed the Groningen Engineering Center since 2016. On 1 September 2023 she became rector magnificus of the university, succeeding Cisca Wijmenga. == Recognition == Scherpen was named an IEEE Fellow in 2021 "for contributions to nonlinear model reduction and passivity-based control". She is also a knight of the Order of the Netherlands Lion. In 2022, she was elected Chair of the Society for Industrial and Applied Mathematics Activity Group on Control and Systems Theory (SIAM SIAG/CST). == References == == External links == Home page Jacquelien Scherpen publications indexed by Google Scholar
|
Wikipedia:Jacqueline Ferrand#0
|
Jacqueline Lelong-Ferrand (17 February 1918, Alès, France – 26 April 2014, Sceaux, France) was a French mathematician who worked on conformal representation theory, potential theory, and Riemannian manifolds. She taught at universities in Caen, Lille, and Paris. == Education and career == Ferrand was born in Alès, the daughter of a classics teacher, and went to secondary school in Nîmes. In 1936 the École Normale Supérieure began admitting women, and she was one of the first to apply and be admitted. In 1939 she and Roger Apéry placed first in the mathematics agrégation; she began teaching at a girls' school in Sèvres, while continuing to do mathematics research under the supervision of Arnaud Denjoy, publishing three papers in 1941 and defending a doctoral thesis in 1942. In 1943 she won the Girbal-Baral Prize of the French Academy of Sciences, and obtained a faculty position at the University of Bordeaux. She moved to the University of Caen in 1945, was given a chair at the University of Lille in 1948, and in 1956 moved to the University of Paris as a full professor. She retired in 1984. == Contributions == Ferrand had nearly 100 mathematical publications, including ten books, and was active in mathematical research into her late 70s. One of her accomplishments, in 1971, was to prove the compactness of the group of conformal mappings of a non-spherical compact Riemannian manifold, resolving a conjecture of André Lichnerowicz, and on the basis of this work she became an invited speaker at the 1974 International Congress of Mathematicians in Vancouver. == Personal life == She married mathematician Pierre Lelong in 1947, taking his surname alongside hers in her subsequent publications until their separation in 1977. == References == == Links == ChronoMath, une chronologie des MATHÉMATIQUES (in French); accessed 5 May 2014
|
Wikipedia:Jacques F. Benders#0
|
Jacobus Franciscus (Jacques) Benders (1 June 1924 – 9 January 2017) was a Dutch mathematician and Emeritus Professor of Operations Research at the Eindhoven University of Technology. He was the first Professor in the Netherlands in the field of Operations Research and is known for his contributions to mathematical programming. == Biography == Benders studied mathematics at the Utrecht University, where he later also received his PhD in 1960 with the thesis entitled "Partitioning in Mathematical Programming" under supervision of Hans Freudenthal. Late 1940s had started his career as statistician for the Rubber Foundation. In 1955, he moved to Shell laboratory in Amsterdam, where he researched mathematical programming problems concerning the logistics of oil refinery. He developed the technique known as Benders' decomposition, and used the results in his doctoral thesis. In 1963, Benders was appointed Professor of Operations Research at the Eindhoven University of Technology, being the first Professor in the Netherlands in that field. Among his PhD students were Israel Herschberg (1966), Jaap Wessels (1968), Freerk Lootsma (1970), Joseph Evers (1973), Jan van Geldrop (1980), Robert van der Vet (1980) Johannes van der Wal (1980), and Jacob Koene (1982). He retired at the Eindhoven University of Technology on May 31, 1989. In 2009 he was awarded the EURO Gold Medal, the highest distinction within Operations Research in Europe. == Publications == Benders has authored and co-authored dozens publications. Books, a selection: 1960. Partitioning in mathematical programming. Doctoral thesis Utrecht University. 1961. Mathematische programmering: syllabus college Rijksuniversiteit Utrecht 1960–1961 1964. De taak van de wiskunde in de operations research. Inaugurele rede. 1982. Een decision support systeem voor locatie en allocatieproblemen bij een drankenconcern. With Jo van Nunen. Articles, a selection: Benders, Jacques F. "Partitioning procedures for solving mixed-variables programming problems." Numerische mathematik 4.1 (1962): 238–252. == References == == External links == Jacques F. Benders at the Mathematics Genealogy Project
|
Wikipedia:Jacques Frédéric Français#0
|
Jacques Frédéric Français (20 June 1775 – 9 March 1833) was a French engineer and mathematician. == Biography == Born on 20 June 1775, Jacques Frédéric Français was the son of a grocer of Saverne. He attended the Royal College of Strasbourg and enrolled voluntarily in the Army of the Rhine in 1793. In September 1794 he was transferred to the military engineering corps. Admitted to the École Polytechnique in the autumn of 1797, he moved in the spring of 1798 to the École du Génie de Metz and graduated with the brevet of first lieutenant. It was at this time that he wrote about the integration of differential equations. In January 1801 he took part in the Egyptian Campaign of the French Army. On his return in 1801 he was assigned to the port of Toulon. Named captain of the sappers in December 1801, he became second in command of the headquarters of the corps of engineers in November 1802. Under the orders of Admiral Pierre-Charles de Villeneuve, he took part in the naval battles of Cape Finisterre and Trafalgar. In 1807, he was transferred to the regiment of the Colonel Étienne Louis Malus in Strasbourg. He became in 1811 professor of military art at the École d’Application du Génie et de l’Artillerie in Metz until his death in 1833. His mathematical work focused on the study of the changes of Cartesian coordinates applied to systems of planes and lines and the geometric representation of complex numbers based on original ideas of his uncle Louis François Antoine Arbogast. They have been published for the most part in the Annales de Gergonne. After the death of his brother François;in 1810, he published his treatise Recherches sur la poussée des terres (1817). == Publications == Mémoire sur le mouvement de rotation d’un corps solide libre autour de son centre de masse, Paris, 1813 == Bibliography ==
|
Wikipedia:Jacques Neveu#0
|
Jacques Jean-Pierre Neveu (14 November 1932 – 17 May 2016) was a Belgian (and then French) mathematician, specializing in probability theory. He is one of the founders of the French school (post WW II) of probability and statistics. == Education and career == Jacques Neveu received in 1955 from the Sorbonne his doctorate in mathematics under Robert Fortet with dissertation Étude des semi-groupes de Markov. In 1960, Neveu was, with Robert Fortet, one of the first two members of the Laboratoire de Probabilités et Modèles Aléatoires (LPMA). He was the LPMA's director from 1980 until 1989 when Jean Jacod became the director. In 1962, Neveu was a chargé de cours (university lecturer) at the Collège de France. He taught at the Sorbonne and, after the reorganization of the University of Paris, at the University of Paris VI at the Laboratory for Probability of the Institut de mathématiques de Jussieu. He was a professor at the École Polytechnique. In 1976, he gave a course at l'école d'été de Saint-Flour (a summer school in probability theory sponsored by the University of Clermont Auvergne). He was a visiting professor in Brussels, São Paulo, and Leuven. From 1969 to 1987, Neveu was the thesis advisor for 19 doctoral students. In 1977 he was the president of the Société mathématique de France. In 1991, he founded the group Modélisation Aléatoire et Statistique (MAS) of the Société de Mathématiques Appliquées et Industrielles (SMAI). In 2012 he was elected a Fellow of the American Mathematical Society. == Research == Neveu is one of the founders of the modern theory of probability. His research deals with Markov processes, Markov chains, Gaussian processes, martingales, ergodic theory, random trees (especially Galton-Watson processes and Galton-Watson trees), and Dirac measures, as well as applications of probability theory to statistics, computer science, combinatorics, and statistical physics. In 1986 he introduced the concept of arbre de Galton-Watson (Galton-Watson tree) within the framework of discrete random trees; within the mathematical formalism of Galton-Watson trees, the notation de Neveu is named in his honor. == Commemoration == Several mathematicians have paid tribute to Neveu for his influence on the modern theory of probability. He was outstanding in teaching as well as research. In honor of Neveu, a prize is awarded by the MAS group of the SMAI to the year's best of the new French holders of doctorates in mathematicians or statistics on the basis of the judged quality of the dissertation. === Prix Jacques Neveu === The laureates are: 2008: Pierre Nolin; 2009: Amandine Véber; 2010: Sébastien Bubeck & Kilian Raschel; 2011: Nicolas Curien; 2012: Pierre Jacob et Quentin Berger; 2013: Adrien Kassel; 2014: Emilie Kaufmann & Julien Reygner; 2015: Erwin Scornet; 2016: Anna Ben-Hamou; 2017: Aran Raoufi; 2018: Elsa Cazelles. == Selected publications == === Articles === "Lattice methods and submarkovian processes." In Fourth Berkeley Symposium on Mathematical Statistics and Probability, pp. 347–391. 1961. "Existence of bounded invariant measures in ergodic theory." In Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), vol. 2, no. Part 2, pp. 461–472. 1967. "Temps d'arrêt d'un système dynamique." Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 13, no. 2, 1969, pp. 81–94. doi:10.1007/BF00537013 "Potentiel Markovien récurrent des chaînes de Harris." Ann. Inst. Fourier, vol. 22, no. 2, 1972, pp. 85–130. "Sur l’espérance conditionelle par rapport à un mouvement brownien." Ann. Inst. H. Poincaré, section B, vol. 12, no. 2, 1976, pp. 105–109. "Processus ponctuels." In École d’Eté de Probabilités de Saint-Flour VI-1976, pp. 249–445. Springer, Berlin, Heidelberg, 1977. doi:10.1007/BFb0097494 Arbres et processus de Galton-Watson, Annales de l'IHP, section B, vol. 22, 1986, pp. 199–207. "Multiplicative martingales for spatial branching processes." In Seminar on Stochastic Processes, 1987, pp. 223–242. Birkhäuser Boston, 1988. doi:10.1007/978-1-4684-0550-7_10 with Francis Comets: The Sherrington-Kirkpatrick model of spin glasses and stochastic calculus: the high temperature case. Communications in Mathematical Physics, vol. 166, no. 3, 1995, pp. 549–564. doi:10.1007/BF02099887 === Books === Théorie des semi-groups de Markov, University of California Press 1958 (and Gauthier-Villars 1958) Bases mathématiques du calcul des probabilités, Masson, 1964, 1970 English translation: Mathematical foundations of the calculus of probability, Holden-Day 1965 Processus aléatoires gaulliens, Montréal: Presses de l'Université de Montréal, 1968 Cours de probabilités, École Polytechnique, 1970, 1978 Martingales à temps discret, Masson, 1972 English translation: Discrete-parameter martingales, Elsevier, 1975 Théorie de la mesure et intégration, cours de l'École polytechnique, 1983 Introduction aux processus aléatoires, École Polytechnique 1985 == References ==
|
Wikipedia:Jacques Tits#0
|
Jacques Tits (French: [ʒak tits]) (12 August 1930 – 5 December 2021) was a Belgian-born French mathematician who worked on group theory and incidence geometry. He introduced Tits buildings, the Tits alternative, the Tits group, and the Tits metric. == Early life and education == Tits was born in Uccle, Belgium to Léon Tits, a professor, and Lousia André. Jacques attended the Athénée of Uccle and the Free University of Brussels. His thesis advisor was Paul Libois, and Tits graduated with his doctorate in 1950 with the dissertation Généralisation des groupes projectifs basés sur la notion de transitivité. == Career == Tits held professorships at the Free University of Brussels (now split into the Université libre de Bruxelles and the Vrije Universiteit Brussel) (1962–1964), the University of Bonn (1964–1974) and the Collège de France in Paris, until becoming emeritus in 2000. He changed his citizenship to French in 1974 in order to teach at the Collège de France, which at that point required French citizenship. Because Belgian nationality law did not allow dual nationality at the time, he renounced his Belgian citizenship. Tits was an "honorary" member of the Nicolas Bourbaki group; as such, he helped popularize H.S.M. Coxeter's work, introducing terms such as Coxeter number, Coxeter group, and Coxeter graph. == Death == Tits died on 5 December 2021, at the age of 91 in the 13th arrondissement, Paris. == Awards and honors == Tits received the Wolf Prize in Mathematics in 1993, the Cantor Medal from the Deutsche Mathematiker-Vereinigung (German Mathematical Society) in 1996, and the German distinction "Pour le Mérite". In 2008 he was awarded the Abel Prize, along with John Griggs Thompson, "for their profound achievements in algebra and in particular for shaping modern group theory". Tits became a member of the French Academy of Sciences in 1979. He was a member of the Norwegian Academy of Science and Letters. He became a foreign member of the Royal Netherlands Academy of Arts and Sciences in 1988. == Contributions == He introduced the theory of buildings (sometimes known as Tits buildings), which are combinatorial structures on which groups act, particularly in algebraic group theory (including finite groups, and groups defined over the p-adic numbers). The related theory of (B, N) pairs is a basic tool in the theory of groups of Lie type. Of particular importance is his classification of all irreducible buildings of spherical type and rank at least three, which involved classifying all polar spaces of rank at least three. The existence of these buildings initially depended on the existence of a group of Lie type in each case, but in joint work with Mark Ronan he constructed those of rank at least four independently, yielding the groups directly. In the rank-2 case spherical building are generalized n-gons, and in joint work with Richard Weiss he classified these when they admit a suitable group of symmetries (the so-called Moufang polygons). In collaboration with François Bruhat he developed the theory of affine buildings, and later he classified all irreducible buildings of affine type and rank at least four. Another of his well-known theorems is the "Tits alternative": if G is a finitely generated subgroup of a linear group, then either G has a solvable subgroup of finite index or it has a free subgroup of rank 2. The Tits group and the Kantor–Koecher–Tits construction are named after him. He introduced the Kneser–Tits conjecture. == Publications == Tits, Jacques (1964). "Algebraic and abstract simple groups". Annals of Mathematics. Second Series. 80 (2): 313–329. doi:10.2307/1970394. ISSN 0003-486X. JSTOR 1970394. MR 0164968. Tits, Jacques (1974). Buildings of spherical type and finite BN-pairs. Lecture Notes in Mathematics, Vol. 386. Vol. 386. Berlin, New York: Springer-Verlag. doi:10.1007/978-3-540-38349-9. ISBN 978-3-540-06757-3. MR 0470099. Tits, Jacques; Weiss, Richard M. (2002). Moufang polygons. Springer Monographs in Mathematics. Berlin, New York: Springer-Verlag. ISBN 978-3-540-43714-7. MR 1938841. J. Tits, Oeuvres - Collected Works, 4 vol., Europ. Math. Soc., 2013. J. Tits, Résumés des cours au Collège de France, S.M.F., Doc.Math. 12, 2013. == References == == External links == Jacques Tits at the Mathematics Genealogy Project O'Connor, John J.; Robertson, Edmund F., "Jacques Tits", MacTutor History of Mathematics Archive, University of St Andrews Biography at the Abel Prize site Archived 18 February 2020 at the Wayback Machine (pdf) List of publications at the Université libre de Bruxelles Weiss, Richard M. (January 2023). "Jacques Tits (1930–2021)" (PDF). Notices of the American Mathematical Society. 70 (1): 77–93. doi:10.1090/noti2601.
|
Wikipedia:Jade Mirror of the Four Unknowns#0
|
Jade Mirror of the Four Unknowns, Siyuan yujian (simplified Chinese: 四元玉鉴; traditional Chinese: 四元玉鑒), also referred to as Jade Mirror of the Four Origins, is a 1303 mathematical monograph by Yuan dynasty mathematician Zhu Shijie. Zhu advanced Chinese algebra with this Magnum opus. The book consists of an introduction and three books, with a total of 288 problems. The first four problems in the introduction illustrate his method of the four unknowns. He showed how to convert a problem stated verbally into a system of polynomial equations (up to the 14th order), by using up to four unknowns: 天 Heaven, 地 Earth, 人 Man, 物 Matter, and then how to reduce the system to a single polynomial equation in one unknown by successive elimination of unknowns. He then solved the high-order equation by Southern Song dynasty mathematician Qin Jiushao's "Ling long kai fang" method published in Shùshū Jiǔzhāng (“Mathematical Treatise in Nine Sections”) in 1247 (more than 570 years before English mathematician William Horner's method using synthetic division). To do this, he makes use of the Pascal triangle, which he labels as the diagram of an ancient method first discovered by Jia Xian before 1050. Zhu also solved square and cube roots problems by solving quadratic and cubic equations, and added to the understanding of series and progressions, classifying them according to the coefficients of the Pascal triangle. He also showed how to solve systems of linear equations by reducing the matrix of their coefficients to diagonal form. His methods predate Blaise Pascal, William Horner, and modern matrix methods by many centuries. The preface of the book describes how Zhu travelled around China for 20 years as a teacher of mathematics. Jade Mirror of the Four Unknowns consists of four books, with 24 classes and 288 problems, in which 232 problems deal with Tian yuan shu, 36 problems deal with variable of two variables, 13 problems of three variables, and 7 problems of four variables. == Introduction == The four quantities are x, y, z, w can be presented with the following diagram x y 太w z The square of which is: === The Unitary Nebuls === This section deals with Tian yuan shu or problems of one unknown. Question: Given the product of huangfan and zhi ji equals to 24 paces, and the sum of vertical and hypotenuse equals to 9 paces, what is the value of the base? Answer: 3 paces Set up unitary tian as the base( that is let the base be the unknown quantity x) Since the product of huangfang and zhi ji = 24 in which huangfan is defined as： ( a + b − c ) {\displaystyle (a+b-c)} zhi ji： a b {\displaystyle ab} therefore ( a + b − c ) a b = 24 {\displaystyle (a+b-c)ab=24} Further, the sum of vertical and hypotenuse is b + c = 9 {\displaystyle b+c=9} Set up the unknown unitary tian as the vertical x = a {\displaystyle x=a} We obtain the following equation （ x 5 − 9 x 4 − 81 x 3 + 729 x 2 = 3888 {\displaystyle x^{5}-9x^{4}-81x^{3}+729x^{2}=3888} ） 太 Solve it and obtain x=3 === The Mystery of Two Natures === 太 Unitary equation: − 2 y 2 − x y 2 + 2 x y + 2 x 2 y + x 3 = 0 {\displaystyle -2y^{2}-xy^{2}+2xy+2x^{2}y+x^{3}=0} ; from the given 太 equation: 2 y 2 − x y 2 + 2 x y + x 3 = 0 {\displaystyle 2y^{2}-xy^{2}+2xy+x^{3}=0} ; we get: 太 8 x + 4 x 2 = 0 {\displaystyle 8x+4x^{2}=0} and 太 2 x 2 + x 3 = 0 {\displaystyle 2x^{2}+x^{3}=0} by method of elimination, we obtain a quadratic equation x 2 − 2 x − 8 = 0 {\displaystyle x^{2}-2x-8=0} solution: x = 4 {\displaystyle x=4} . === The Evolution of Three Talents === Template for solution of problem of three unknowns Zhu Shijie explained the method of elimination in detail. His example has been quoted frequently in scientific literature. Set up three equations as follows 太 − y − z − y 2 x − x + x y z = 0 {\displaystyle -y-z-y^{2}x-x+xyz=0} .... I − y − z + x − x 2 + x z = 0 {\displaystyle -y-z+x-x^{2}+xz=0} .....II 太 y 2 − z 2 + x 2 = 0 ; {\displaystyle y^{2}-z^{2}+x^{2}=0;} ....III Elimination of unknown between II and III by manipulation of exchange of variables We obtain 太 − x − 2 x 2 + y + y 2 + x y − x y 2 + x 2 y {\displaystyle -x-2x^{2}+y+y^{2}+xy-xy^{2}+x^{2}y} ...IV and 太 − 2 x − 2 x 2 + 2 y − 2 y 2 + y 3 + 4 x y − 2 x y 2 + x y 2 {\displaystyle -2x-2x^{2}+2y-2y^{2}+y^{3}+4xy-2xy^{2}+xy^{2}} .... V Elimination of unknown between IV and V we obtain a 3rd order equation x 4 − 6 x 3 + 4 x 2 + 6 x − 5 = 0 {\displaystyle x^{4}-6x^{3}+4x^{2}+6x-5=0} Solve to this 3rd order equation to obtain x = 5 {\displaystyle x=5} ; Change back the variables We obtain the hypothenus =5 paces === Simultaneous of the Four Elements === This section deals with simultaneous equations of four unknowns. { − 2 y + x + z = 0 − y 2 x + 4 y + 2 x − x 2 + 4 z + x z = 0 x 2 + y 2 − z 2 = 0 2 y − w + 2 x = 0 {\displaystyle {\begin{cases}-2y+x+z=0\\-y^{2}x+4y+2x-x^{2}+4z+xz=0\\x^{2}+y^{2}-z^{2}=0\\2y-w+2x=0\end{cases}}} Successive elimination of unknowns to get 4 x 2 − 7 x − 686 = 0 {\displaystyle 4x^{2}-7x-686=0} Solve this and obtain 14 paces == Book I == === Problems of Right Angle Triangles and Rectangles === There are 18 problems in this section. Problem 18 Obtain a tenth order polynomial equation: 16 x 10 − 64 x 9 + 160 x 8 − 384 x 7 + 512 x 6 − 544 x 5 + 456 x 4 + 126 x 3 + 3 x 2 − 4 x − 177162 = 0 {\displaystyle 16x^{10}-64x^{9}+160x^{8}-384x^{7}+512x^{6}-544x^{5}+456x^{4}+126x^{3}+3x^{2}-4x-177162=0} The root of which is x = 3, multiply by 4, getting 12. That is the final answer. === Problems of Plane Figures === There are 18 problems in this section === Problems of Piece Goods === There are 9 problems in this section === Problems on Grain Storage === There are 6 problems in this section === Problems on Labour === There are 7 problems in this section === Problems of Equations for Fractional Roots === There are 13 problems in this section == Book II == === Mixed Problems === === Containment of Circles and Squares === === Problems on Areas === === Surveying with Right Angle Triangles === There are eight problems in this section Problem 1 Question: There is a rectangular town of unknown dimension which has one gate on each side. There is a pagoda located at 240 paces from the south gate. A man walking 180 paces from the west gate can see the pagoda, he then walks towards the south-east corner for 240 paces and reaches the pagoda; what is the length and width of the rectangular town? Answer: 120 paces in length and width one li Let tian yuan unitary as half of the length, we obtain a 4th order equation x 4 + 480 x 3 − 270000 x 2 + 15552000 x + 1866240000 = 0 {\displaystyle x^{4}+480x^{3}-270000x^{2}+15552000x+1866240000=0} solve it and obtain x=240 paces, hence length =2x= 480 paces=1 li and 120 paces. Similarity, let tian yuan unitary(x) equals to half of width we get the equation: x 4 + 360 x 3 − 270000 x 2 + 20736000 x + 1866240000 = 0 {\displaystyle x^{4}+360x^{3}-270000x^{2}+20736000x+1866240000=0} Solve it to obtain x=180 paces, length =360 paces =one li. Problem 7 Identical to The depth of a ravine (using hence-forward cross-bars) in Haidao Suanjing. Problem 8 Identical to The depth of a transparent pool in Haidao Suanjing. === Hay Stacks === === Bundles of Arrows === === Land Measurement === === Summon Men According to Need === Problem No 5 is the earliest 4th order interpolation formula in the world men summoned : n a + 1 2 ! n ( n − 1 ) b + 1 3 ! n ( n − 1 ) ( n − 2 ) c + 1 4 ! n ( n − 1 ) ( n − 2 ) ( n − 3 ) d {\displaystyle na+{\tfrac {1}{2!}}n(n-1)b+{\tfrac {1}{3!}}n(n-1)(n-2)c+{\tfrac {1}{4!}}n(n-1)(n-2)(n-3)d} In which a=1st order difference b=2nd order difference c=3rd order difference d=4th order difference == Book III == === Fruit pile === This section contains 20 problems dealing with triangular piles, rectangular piles Problem 1 Find the sum of triangular pile 1 + 3 + 6 + 10 + . . . + 1 2 n ( n + 1 ) {\displaystyle 1+3+6+10+...+{\frac {1}{2}}n(n+1)} and value of the fruit pile is: v = 2 + 9 + 24 + 50 + 90 + 147 + 224 + ⋯ + 1 2 n ( n + 1 ) 2 {\displaystyle v=2+9+24+50+90+147+224+\cdots +{\frac {1}{2}}n(n+1)^{2}} Zhu Shijie use Tian yuan shu to solve this problem by letting x=n and obtained the formular v = 1 2 ⋅ 3 ⋅ 4 ( 3 x + 5 ) x ( x + 1 ) ( x + 2 ) {\displaystyle v={\frac {1}{2\cdot 3\cdot 4}}(3x+5)x(x+1)(x+2)} From given condition v = 1320 {\displaystyle v=1320} , hence 3 x 4 + 14 x 3 + 21 x 2 + 10 x − 31680 = 0 {\displaystyle 3x^{4}+14x^{3}+21x^{2}+10x-31680=0} Solve it to obtain x = n = 9 {\displaystyle x=n=9} . Therefore, v = 2 + 9 + 24 + 50 + 90 + 147 + 224 + 324 + 450 = 1320 {\displaystyle v=2+9+24+50+90+147+224+324+450=1320} 。 === Figures within Figure === === Simultaneous Equations === === Equation of two unknowns === === Left and Right === === Equation of Three Unknowns === === Equation of Four Unknowns === Six problems of four unknowns. Question 2 Yield a set of equations in four unknowns: . { − 3 y 2 + 8 y − 8 x + 8 z = 0 4 y 2 − 8 x y + 3 x 2 − 8 y z + 6 x z + 3 z 2 = 0 y 2 + x 2 − z 2 = 0 2 y + 4 x + 2 z − w = 0 {\displaystyle {\begin{cases}-3y^{2}+8y-8x+8z=0\\4y^{2}-8xy+3x^{2}-8yz+6xz+3z^{2}=0\\y^{2}+x^{2}-z^{2}=0\\2y+4x+2z-w=0\end{cases}}} == References == Sources
|
Wikipedia:Jahar Saha#0
|
Jahar Saha is a professor and former director of the Indian Institute of Management (IIM), Ahmedabad, a position he held from 1998 to 2002. == Biography == Jahar Saha was born on 14 December 1943 at Kaladi in Matlab (now in Bangladesh). While his grandparents were in business, his father was a lawyer who later became a school teacher. His elder brother was a senior government official and his younger sister is a professor in a medical college at Kolkata. == Education == Saha did a four-year professional degree in Statistics (B.Stat.), Masters in Statistics (M.stat), and a one-year Post-Graduate Diploma in Statistical Quality Control and Operations Research from the Indian Statistical Institute, Kolkata. Jahar Saha obtained his Ph.D. in Operations Research from Case Western Reserve University, Cleveland, Ohio. His Ph.D. thesis was titled "Some Problems in Railway Networks" which focused on two kinds of problems in railway networks: (i) scheduling trains, (ii) selecting an optimal configuration for railway networks. Many of the problems were structured mathematical programming problems and Saha made attempts to develop efficient algorithms to the problems. == Career == Saha started his career as a Trainee Technical Officer of SQC Unit, Indian Statistical Institute, Mumbai. He also worked as a Junior System Consultant with a consulting company in Mumbai. Since 1975, Saha has been teaching in the Production and Quantitative Methods Area of the Indian Institute of Management, Ahmedabad (lIMA). During his tenure at the Institute, he held the position of Director between 1998 and 2002. He had also taught at Lake Erie College, USA and had been Visiting Associate Professor at the University ofNew Brunswick, Canada. Professor Saha has been associated with the development of first-year courses on Mathematics and Statistics for Management (MSM). He also developed second-year courses on Linear Programming, Applications of Operations Research, Advanced Topic in Operations Research and Selected Topics in Operations Research, and Quality Management. He is a member of the Operations research Society of India. == References == == External links == Profile at the Operations research Society of India, Ahmedabad Chapter website
|
Wikipedia:Jaina school of mathematics#0
|
The Jain school of mathematics is a school of mathematics whose members are distinguished by the fact that they are followers of the Jain religion. All members of the Jain school of mathematics are also members of the larger community of Indian mathematicians. The mathematics developed by this school forms a subset of the body of mathematical knowledge developed in India since ancient times. However, certain aspects of the cosmological and philosophical speculations of the Jain religion has impacted the mathematical thinking of the adherents of the Jain religion. As an example, one can site the fascination of the Jains (followers of the Jain religion) for very large numbers and their speculations relating to the concept of infinity. == References == == Additional reading == Datta, B B. (1929). "The Jaina school of mathematics". Bulletin of the Calcutta Mathematical Society. 21: 115–145. (Reprinted with the title: “The mathematical achievements of the Jainas”. In: Studies in the History of Science in India (ed. D. Chattopadhyaya), New Delhi, 1982, pp. 684–716.) Jadhav, Dipak (2017). "Historical Notes: The Jaina School of Indian Mathematics". Indian Journal of History of Science. 52 (3): 316–334. doi:10.16943/ijhs/2017/v52i3/49161. Jain, L C. On the Jaina school of mathematics. In: Babu Chote Lāla Jaina Smrti Grantha, Kolkata, 1967, pp. 265–292. Jain, L. C. (1973). "Set theory in Jaina school of mathematics". Indian Journal of History of Science. 8 (2): 1–27. Jain, L. C. (1976). "On certain mathematical topics of the Dhavalā texts (the Jaina school of mathematics)". Indian Journal of History of Science. 11 (2): 85–111. Jain, L. C. (1979). "System theory in Jaina school of mathematics". Indian Journal of History of Science. 14: 31–65. Jain, L. C. and Jain, Meena. (1989). "System theory in Jaina school of mathematics II". Indian Journal of History of Science. 24 (3): 163–180.{{cite journal}}: CS1 maint: multiple names: authors list (link) O'Connor, J J; Robertson, E F (November 2000). "Jaina mathematics". Maths History. School of Mathematics and Statistics - University of St Andrews, Scotland. Retrieved 11 January 2025.
|
Wikipedia:Jakub Kresa#0
|
Jakub Kresa (Spanish: Jacobo Kresa, Latin: Jacobo Kreysa; 19 July 1648 – 28 July 1715) was a Czech mathematician. He was one of the most important Czech mathematicians of the Baroque era. == Biography == === Early life === Jakub Kresa was born into a smallholder's family at Smržice, not far from Prostějov. He studied at the Jesuit gymnasium (school) in Brno. There he proved to be an extraordinary student. He not only displayed rare skills in mathematics, but he also became a polyglot, able to speak fluently Hebrew, German, Latin, Italian, Spanish, French and Portuguese, in addition to his Czech mother-tongue. In 1669–70 he taught at the gymnasium (school) in Litoměřice. Then he went to Prague, where he studied at the Faculty of Philosophy of Charles University between 1670 and 1673. After spending a short time back in Litoměřice, he returned to Prague in 1675 and continued his studies in mathematics and theology. Kresa was ordained a priest in 1680. After this he spent a short time in Telč. === In the Czech Crown lands === In 1681 Jakub Kresa started to teach Hebrew at the University of Olomouc. There he obtained his first doctorate and between 1682 and 1684 taught mathematics. In Olomouc Kresa's other high points included presiding at the academic dissertation of the mathematician and astronomer Jan Taletius, who devised a model to predict eclipses of the sun and of the moon. Jakub Kresa was also often entrusted with diplomatic tasks. During the peasants' uprising in northern Bohemia in 1680, he served as mediator between the cavalry regiment of general Vilém Harant z Polžic and the peasant leaders. In 1684 Kresa left Olomouc to become head of the Departments of Mathematics and of Hebreistics at the Charles University. He was also preaching at the St. Salvador church in Prague. By this time he was already well known for his extraordinary skills regarding mathematics, languages and diplomacy, and he was offered the position of head of Department of Mathematics at the Colegio Imperial de Madrid. He relocated to Spain in 1686 and stayed there for fifteen years. === In Spain === In order to make the study of mathematics easier for the Spanish students, Kresa translated the 8 books of Euclid's Elements into Spanish. This brought him recognition and he soon became renowned in the whole country, being dubbed the Euclid of the West. At that time it became a custom in Spain to let Kresa assess mathematical treatises ahead of publication. Apart from the Colegio Imperial de Madrid, Kresa was also giving lectures at the Naval academy of Cadiz. === Back in the Czech Crown lands === Following the death of spanish king Charles II in 1700 Kresa went back to Prague. He obtained a doctorate in theology at Charles University and also started to teach theology there. At the same time he was privately teaching mathematics and was acquiring mathematical apparatus for the Department of Mathematics. He was engaged in arithmetic, fractions and logarithms, trigonometry, astronomy, algebra, as well as military architecture. One of his private students, Count Ferdinand Herbert, published Kresa's ideas in magazine Acta Eruditorum in 1711. === Late life === The Emperor Leopold I appointed Kresa as confessor of his second son, the Archduke Charles. He remained in this position after Charles took over the Spanish throne, within the War of the Spanish Succession, and therefore returned to Spain with him (1704–13). After nine years in Spain, and the defeat of Charles, Kresa went back to the Czech Crown lands, working with the help of Karel Slavíček on mathematical theories in Brno, where he died in 1715. == Legacy == Kresa's manuscripts were transcribed for printing by his students František Tillisch and Karel Slavíček, who both later taught at Olomouc. The lectures Kresa gave at Charles University were recorded by student called Kryštof John, who published them under the title Mathematica in universitate Pragensi tradica a P. Jacobo Kreysa ... excerpta anno 1685. The manuscript is today stored at the library of Strahov Monastery. In Kresa's era the Trigonometric functions were derived using geometry. Kresa was the first to introduce algebraic number to trigonometry. Kresa's death was followed by a decline in mathematics and science in the Czech Crown lands due to the dogmatic application of Catholic Church doctrines. With Slavíček having gone to China, scientific work largely disappeared from the Czech lands for two decades. Although the theories of Isaac Newton, Jacques Cassini and Edmond Halley were well known, local scientists (such as Josef Player or Jan Slezina) were continued to work with the obsolete theories of Ptolemaios and Aristoteles. It was only a quarter of a century later, that scientific work was resumed by peoples such as Jan Antonín Scrinci (1697–1773) and Joseph Stepling (1716–1778). === Major works === Theses mathematicae defendidas por el Ex. mo Seňor Don Innigo de la Cruz ... en colegio de la Compaňia de Jesus de Ciudad de Cadiz, 1688 Elementes geometricos de Euclides, los seis primeros Libros de los planos, etc., Brussels 1689 Arithmetica Tyro-Brunensis curiosa varietate et observatione communi quidem omnium fructui, sed praeprimis Tyronibus Mathemetum utilis, Prague 1715 Analysis speciosa trigonometriae sphericae, etc. Prague 1720 == References ==
|
Wikipedia:Jakša Cvitanić#0
|
Jakša Cvitanić (born 1962 in Split, Croatia, Yugoslavia) is a Richard N. Merkin Professor of Mathematical Finance at the California Institute of Technology. His main research interests are in mathematical finance, contract theory, stochastic control theory, and stochastic differential equations. From 1992 to 1999 he was an Assistant and Associate Professor of Statistics at Columbia University. From 1999 until 2005, when he joined Caltech, Cvitanić was a Professor of Mathematics and Economics at the University of Southern California. During the academic year 2012-2013 he was a professor of finance at EDHEC Business School in France. He was also the director of the Ronald and Maxine Linde Institute of Economic and Management Sciences. and the president of the Bachelier Finance Society. Cvitanić has co-authored some fundamental papers on financial markets with portfolio constraints, transaction costs, and other market imperfections. He is the author of over fifty articles in academic finance, economics and mathematics journals,[1], a co-author, with Fernando Zapatero, of the textbook Introduction to the Economics and Mathematics of Financial Markets, and, with Jianfeng Zhang, of the monograph Contract Theory in Continuous-time Models. He was or has been a co-editor of Finance and Stochastics [2], Mathematical Finance, Mathematics and Financial Economics [3] and Frontiers of Mathematical Finance. Cvitanić earned a B.Sc. (1985) and M.Sc. (1988) in Mathematics from the University of Zagreb, Croatia, and a PhD in Statistics (1992) from Columbia University in New York City. He received the American Statistical Association Scholastic Excellence Award in 1992. == Selected publications == Introduction to the Economics and Mathematics of Financial Markets (with Fernando Zapatero). Cambridge, Mass.: MIT Press, 2004. ISBN 0-262-53265-4. Contract Theory in Continuous-Time Models (with Jianfeng Zhang). Springer Science+Business Media, 2013. ISBN 978-3-642-14200-0. == References == == Further reading == "Computational Finance Expert Joins Math Department". news.usc.edu. October 25, 1999. Retrieved July 7, 2017. == External links == Cvitanic's web site, caltech.edu Research papers, ideas.repec.org Portal hrvatskih znanstvenika Archived 2006-08-29 at the Wayback Machine (out of date)
|
Wikipedia:James B. Carrell#0
|
James B. Carrell (born 1940) is an American and Canadian mathematician, who is currently an emeritus professor of mathematics at the University of British Columbia, Vancouver, British Columbia, Canada. His areas of research are algebraic geometry, Lie theory, transformation groups and differential geometry. He obtained his Ph.D. at the University of Washington (Seattle) under the supervision of Allendoefer. In 1971, together with Jean Dieudonné, he received the Leroy P. Steele Prize for the article Invariant theory, old and new. He proved theorems in Schubert calculus about singularities of Schubert varieties. The Carrell–Liebermann theorem on the zero set of a holomorphic vector field is used in complex algebraic geometry. He is a fellow of the American Mathematical Society. == References == == External links == Jim Carrell at math.ubc.ca Jim Carrell in ca.linkedin.com
|
Wikipedia:James Colliander#0
|
James Ellis Colliander (born 22 June 1967) is an American-Canadian mathematician. He is currently Professor of Mathematics at University of British Columbia and served as Director of the Pacific Institute for the Mathematical Sciences (PIMS) during 2016-2021. He was born in El Paso, Texas, and lived there until age 8 and then moved to Hastings, Minnesota. He graduated from Macalester College in 1989. He worked for two years at the United States Naval Research Laboratory on fiber optic sensors and then went to graduate school to study mathematics. He received his PhD from the University of Illinois at Urbana–Champaign in 1997 and was advised by Jean Bourgain. Colliander was a postdoctoral fellow at the University of California, Berkeley and spent semesters at the University of Chicago, the Institute for Advanced Study and the Mathematical Sciences Research Institute. He is also an award-winning teacher. == Research == Colliander's research mostly addresses dynamical aspects of solutions of Hamiltonian partial differential equations, especially non-linear Schrödinger equation. Colliander is a collaborator with Markus Keel, Gigliola Staffilani, Hideo Takaoka, and Terence Tao, forming a group known as the "I-team". The name of this group has been said to come from a mollification operator used in the team's method of almost conserved quantities, or as an abbreviation for "interaction", referring both to the teamwork of the group and to the interactions of light waves with each other. The group's work was featured in the 2006 Fields Medal citations for group member Tao. == Organization creation == Colliander is co-founder of the education technology company called Crowdmark. Colliander, with colleagues from PIMS, created Syzygy, a project that provides interactive computing for students and teachers at universities across Canada. Syzygy operates on infrastructure provided by Compute Canada. Colliander, with colleagues from PIMS and Cybera, created Callysto, a project designed to improve computational thinking for students and teachers in grades 5-12. Colliander is co-founder of the International Interactive Computing Collaboration (2i2c). == Major publications == Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Global well-posedness for Schrödinger equations with derivative. SIAM J. Math. Anal. 33 (2001), no. 3, 649–669. Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. A refined global well-posedness result for Schrödinger equations with derivative. SIAM J. Math. Anal. 34 (2002), no. 1, 64–86. Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation. Math. Res. Lett. 9 (2002), no. 5-6, 659–682. Christ, Michael; Colliander, James; Tao, Terence. Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations. Amer. J. Math. 125 (2003), no. 6, 1235–1293. Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Sharp global well-posedness for KdV and modified KdV on R {\displaystyle \mathbb {R} } and T {\displaystyle \mathbb {T} } . J. Amer. Math. Soc. 16 (2003), no. 3, 705–749. Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Multilinear estimates for periodic KdV equations, and applications. J. Funct. Anal. 211 (2004), no. 1, 173–218. Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on R 3 {\displaystyle \mathbb {R} ^{3}} . Comm. Pure Appl. Math. 57 (2004), no. 8, 987–1014. Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. (2008), "Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in ℝ3", Annals of Mathematics, Second Series, 167 (3): 767–865, doi:10.4007/annals.2008.167.767, MR 2415387. Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. (2010), "Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation", Inventiones Mathematicae, 181 (1): 39–113, Bibcode:2010InMat.181...39C, doi:10.1007/s00222-010-0242-2, hdl:1721.1/71665, MR 2651381. == References == == External links == Official website MathSciNet: "Items authored by Colliander, James." James Colliander at the Mathematics Genealogy Project James Colliander introducing Crowdmark at 2013 Launch Education and Kids on YouTube James Colliander publications indexed by Google Scholar
|
Wikipedia:James Harkness (mathematician)#0
|
James Harkness (1864–1923) was a Canadian mathematician, born in Derby, England, and educated at Trinity College, Cambridge with a B.A. in 1885 and an M.A. in 1889. Coming early to the United States, he was connected with Bryn Mawr College from 1888 to 1903, for the last seven years as professor of mathematics. The study of the Theory of Functions received a new impetus in America through the arrival of James Harkness (1864–1923), a man who from his boyhood had shown unusual ability in the field of mathematics. At the age of eight he mastered the first book of Euclid's Elements without any help. He studied under Dr. E. J. Routh at Trinity College, Cambridge, graduating as eighth wrangler in 1885. Harkness complemented Scott with a course on "Abelian Integrals and Functions" that also drew on the latest literature in German — the work of Alfred Clebsch and Paul Gordan, Bernhard Riemann, Hermann Amandus Schwarz and others — and "aimed to prepare the students for the recent Memoirs of Felix Klein in the Mathematische Annalen". In 1903, he was appointed Peter Redpath professor of pure mathematics at McGill University, Montreal, Quebec. Harkness was for a time a vice president of the American Mathematical Society and associate editor of its Transactions, was elected a member of the London Mathematical Society and in 1908 became a fellow of the Royal Society of Canada. He published, with Professor Frank Morley, two treatises on the Theory of Functions and collaborated on the article "Elliptic Functions", in the German Encyclopædia of Mathematics (1914–15). == References == == External links == Frank Morley and James Harkness A treatise on the theory of functions (New York: Macmillan, 1893) Frank Morley and James Harkness Introduction To The Theory of Analytic Functions (G.E.Stechert And Company, 1898)
|
Wikipedia:James McCaw#0
|
Richard Hugh McCaw (born 31 December 1980) is a retired New Zealand professional rugby union player. He captained the New Zealand national team, the All Blacks, in 110 out of his 148 test matches, and won two Rugby World Cups. He has won the World Rugby Player of the Year award a joint record three times and was the most capped test rugby player of all time from August 2015 to October 2020. McCaw was awarded World Rugby player of the decade (2011–2020) in 2021. McCaw is also a winner of the New Zealand sportsman of the decade award. McCaw was the first All Black to reach 100 caps, and the first rugby union player to win 100 tests. He was the most-capped player in rugby union history with 148 caps, having overtaken Brian O'Driscoll's record in 2015 and losing the record to Alun Wyn Jones in 2020. McCaw has also equaled the record for most appearances at the Rugby World Cup, with Jason Leonard. McCaw predominantly played in the openside flanker position for the New Zealand, Crusaders and Canterbury teams, but also played as a blindside flanker and no. 8. During McCaw's career, Canterbury won the NPC (later Mitre10 Cup) five times, and the Crusaders won four Super Rugby titles. In addition to winning two world cups, the All Blacks won seven Tri-Nations titles, completed three successful Grand Slam tours and won the Bledisloe Cup eight times. He made his debut in 2001 for the Crusaders, and was selected for the All Blacks' 2001 end-of-year tour, despite having played only eight minutes of Super 12 rugby. His debut for New Zealand was against Ireland, where he was awarded man-of-the-match. McCaw became a regular selection for New Zealand, only missing a few games due to recurring concussions. In 2004 he was appointed captain of the All Blacks, whom he led at the 2007 Rugby World Cup. After their elimination in the quarter-finals, his captaincy came under criticism, but he was retained and eventually led the team to consecutive Rugby World Cup titles in 2011 and 2015, becoming one of only 43 players who have won the Rugby World Cup on multiple occasions. McCaw is however one of the two only captains to have won two Rugby World Cups, the other one being Siya Kolisi. McCaw holds the international record for most game wins as a player at 131. He also holds the international record for most games as a captain at 110. == Family and early years == His paternal fourth great-grandfather was Seth Smith, who built large proportions of Belgravia & Mayfair in London in the 1830s, related through his great, great-grandmother Sarah Annette Seth-Smith McCaw. McCaw's great-great-grandfather immigrated to New Zealand from the Scottish Borders in 1893, and settled in the Hakataramea Valley, Waimate District, South Canterbury. McCaw's father took over the family farm and his mother was a teacher at Kurow. On New Year's Eve 1980, Richard Hugh McCaw was born in the nearby town of Oamaru. He grew up on his parents' farm along with his sister Joanna. McCaw started flying gliders with his grandfather J H 'Jim' McCaw, a Tempest pilot during World War II credited with shooting down 20 V1 missiles, when he was nine years old. He played rugby for the local Kurow rugby club as a youngster, but it was not until 1994, when he boarded at Otago Boys' High School in Dunedin, that he started to take the game seriously. In his last year at Otago Boys' High, McCaw was head boy, proxime accessit (runner up) to the dux and played in the school's 1st XV. McCaw came to the attention of national selectors during a 5-all draw with Rotorua Boys' High School in the 1998 New Zealand secondary schools rugby final in Christchurch. However, he failed to make the New Zealand Secondary Schools Team, losing out to Sam Harding, Angus McDonald and Hale T-Pole. With Sam Harding moving south to study at the University of Otago, McCaw headed to Christchurch's Lincoln University to study agricultural science and pursue his rugby interests. He achieved all but two papers for his Bachelor of Agricultural Science degree before deciding to pursue his rugby career instead. He received an honorary doctorate in recognition of his sporting achievements in April 2012. In 1999, McCaw was selected in the New Zealand under-19 squad (coached by Mark Shaw), which won the world championship in Wales. During that series, McCaw realised his All Blacks dream could be attainable. The following year he was selected in the New Zealand under-21 squad and debuted for Canterbury in the National Provincial Championship (NPC) against North Harbour. On 31 March 2001, he made his Super Rugby debut with the Crusaders, playing a few minutes in a losing effort against the Hurricanes. That year he only played twice for the Crusaders, both times as a substitute, for a total of just eight minutes playing time. He did however play a full season with NPC champions Canterbury and captained the New Zealand Under 21s. == Playing career == === International debut === Although the then 20-year-old McCaw had only played seventeen matches for Canterbury, John Mitchell, the new All Black coach, selected him for the 2001 end of year tour to Ireland, Scotland and Argentina. This led Josh Kronfeld, a former All Black openside flanker, to criticise the selection: "You might as well just give All Black jerseys to everybody. The fact they picked guys off one NPC season is bloody incredible". McCaw's debut international test was against Ireland at Lansdowne Road on 17 November 2001. His first touch of the game resulted in a knock-on when he was hit in a tackle and New Zealand were trailing the Irish 16–7 at half-time. In the second half the All Blacks recovered to win 40–29 and McCaw was named man of the match, receiving a standing ovation at the post-match function. A turning point came in the second half when McCaw was able to steal the ball from Ireland, which led to a try to left wing Jonah Lomu. After the match McCaw recalled the experience: "it was a hell of a stadium to play at, a real rugby stadium, a big crowd – something I'll always remember, very special." McCaw played all three tests on the tour, with the All Blacks beating Scotland 37–6 and winning 24–20 against Argentina. At the end of season rugby awards, McCaw was selected as both the New Zealand Rugby Football Union Under-21 and Air New Zealand NPC Division One Player of the Year. === 2002–2003 === In the lead-up to the 2003 World Cup McCaw was a regular player for Canterbury, the Crusaders and the All Blacks. In 2002 and 2003 the Crusaders competed in the Super Rugby final, beating the Brumbies in 2002 and losing to the Blues in 2003. The Canterbury provincial rugby team lost the semi-final to the eventual winners Auckland in 2002. McCaw and the other All Blacks were "rested" during the 2003 national provincial championship. In 2002 McCaw played for the All Blacks against the touring Ireland team (15–6 and 40–8 victories) and in the Tri Nations against Australia and South Africa. Of the six 2002 test matches McCaw played in, five were won by New Zealand with the only loss to Australia. The 14–16 loss occurred in New Zealand's third Tri Nations match and ensured the Bledisloe Cup stayed with Australia. During the All Blacks match against South Africa in Durban a pitch invader attacked Irish referee David McHugh as a scrum was being set, dislocating his shoulder in the process. McCaw and A.J. Venter wrestled the assailant off the referee and, according to McHugh, if they had not got involved his shoulder would have been broken. McCaw was rested, along with 20 other members of the Tri Nations squad, from the 2002 end-of-year tour to Europe. In 2002 McCaw was voted as Newcomer of the Year by the International Rugby Players Association. This award is voted on by all international players, with players not allowed to vote for members of their own team. After another successful campaign with the Crusaders in 2003 (reaching the Super 12 finals), McCaw was again selected as first choice openside flanker for the All Blacks. In June he was involved in a narrow 13–15 defeat at home to England, was a non-playing reserve in a 55–3 victory against Wales and played in a 31–23 win over France. The 2003 All Blacks retained the Tri Nations title, regained the Bledisloe Cup for the first time since 1997 and were ranked second behind England leading into the World Cup. McCaw was selected as openside flanker for the 2003 All Blacks World Cup squad and played in every game at the tournament. New Zealand won all their pool games and beat South Africa in the quarter-finals to qualify for a semi-final match-up against Australia. In an upset, the Australians defeated the All Blacks, knocking them out of the tournament. At the end of the season awards McCaw received the Kel Tremain Trophy for the New Zealand Rugby Union player of the year. === 2004–2005 === The Crusaders finished as runner-ups in the 2004 Super 12 season, losing the final to the Brumbies. Following the World Cup, John Mitchell was dropped as All Black coach and replaced by Graham Henry. McCaw was selected as first choice openside flanker and made vice captain. In the first test against England he was escorted off the field after suffering concussion following a clash of heads with fellow All Black Xavier Rush. He was a late withdrawal from the second England test and then played 70 minutes against Argentina before again leaving the field due to dizziness. Still suffering headaches a month later, he withdrew from the rest of the home campaign and the 2004 Tri Nations to focus on recovery. McCaw returned to captain Canterbury to the finals at the tail end of the NPC season. In November 2004 he returned for the All Blacks' end-of-season tour to Italy, Wales and France. He was made captain at the age of 23 for the first time against Wales as regular captain Tana Umaga was rested. In April 2005, while captaining the Crusaders, McCaw again suffered a concussion. He was stretchered off the field two minutes into the game after attempting a tackle on Bulls prop Richard Bands. After the incident, McCaw visited a young boy in hospital who had broken his neck playing rugby and started to question whether he should be playing the game. Another paraplegic in the ward told him he had broken his neck swimming on holiday in Fiji, convincing McCaw that it could happen anywhere, and you may as well "do what you enjoy". A month later, in May 2005, McCaw returned to training with the Crusaders and led them in their semi-final and final victories. McCaw returned to international rugby in 2005, playing in the 91–0 victory over Fiji before the British and Irish Lions arrived. He then played the first two test against the Lions, including a record 48–18 victory in Wellington. The All Blacks defeated the touring Lions 3–0 in the series. McCaw was part of the successful Tri Nations campaign (losing just one game) and Grand Slam (when victory is achieved against the four home nations) end of year tour. He missed the game against England after suffering his third serious head knock against Ireland. Despite his injury concerns, McCaw was shortlisted for the 2005 IRB International Player of the Year, which was won by All Black teammate Dan Carter. === 2006–2007 === McCaw led the Crusaders to the Super Rugby title again in 2006. In May 2006, at the age of 25 and after 36 test matches, McCaw was named captain of the All Blacks. His first two games as regular captain were against Ireland in New Zealand, while a separate squad led by Jerry Collins was named to travel to Argentina for a one-off game. McCaw started his captaincy with victory over Ireland and then mentored stand-in captain Jerry Collins in Argentina. New Zealand emerged as 2006 Tri Nations champions (the only loss away to South Africa by one point) and retained the Bledisloe Cup. A successful European tour saw comfortable victories against England, France twice and Wales. McCaw was captain in every match and after being short listed in 2002, 2003 and 2005 was named the 2006 IRB International Player of the Year. Because 2007 was a World Cup year, All Black management decided that a select group of 22 players, including McCaw, would undergo "reconditioning" by not playing in the first seven rounds of the Super 14. McCaw returned to the Crusaders in the eighth round and helped them reach the semi-finals. New Zealand then beat a below-strength France team in two tests and won a one-off test against Canada. McCaw started on the bench for the Canadian match, with Reuben Thorne returning as captain. The Tri Nations was shortened because of the World Cup, with each team playing the other two teams twice (one home and one away game). Led by McCaw, New Zealand again dropped just one game (this time a five-point loss against Australia in Melbourne) retaining the Tri Nations crown and the Bledisloe cup. ==== 2007 World Cup ==== The 2007 World Cup was held in France, Scotland and Wales. The All Blacks were in a pool that included Italy, Portugal, Scotland and Romania. The All Blacks comfortably made it through the pool play with scores of 76–14, 108–13, 40–0 and 85–8 respectively. McCaw made just three appearances (two starts and one as a reserve) due to Henry's rotation policy. In the quarter-finals the All Blacks lost to France 18–20, resulting in New Zealand's earliest exit from a World Cup. With semi-final exits after being among the favourites at the 1991, 1999 and 2003 World Cups, they were once again accused of "choking on the world's biggest stage". An emotional McCaw could not hide his disappointment at the after-match press conference: "If I knew the answers we would have sorted it out. We will be thinking about it for a long time". McCaw denied New Zealand's easy run into the quarter-finals played a part in the loss "A lot of the guys have been through this before, they've played big test matches." Graham Henry's policy of using squad rotation and resting key players during the Super 14 was criticised. McCaw also came under attack. He was accused of not inspiring his team, lacking the ability to change policy when plan A was not working and not providing enough leadership on the field. === 2008 === Despite much speculation that Henry would lose the All Black coaching job to coach Robbie Deans, he was retained on a contract for the next two years, later extended to include the 2011 World Cup. He immediately stated that he would retain McCaw as his captain. Robbie Deans instead signed with the Australian Rugby Union, becoming head coach of Australia. In Deans' last season (2008) as Crusaders coach they won the Super Rugby title for the seventh time. Ireland and England toured to New Zealand in June 2008 and the All Blacks came away with a hard-fought win against Ireland, and two comfortable victories against England. McCaw tore a ligament in his ankle against England and missed the start of the Tri Nations. Rodney So'oialo was made stand-in captain and started the Tri Nations with a win and two losses. McCaw returned for the fourth game and the All Blacks won the remaining three matches to retain the Tri Nations title and Bledisloe Cup. McCaw was seen as an inspiration after his return from injury, with Henry rating his performance in the 19–0 win in South Africa (the first time the South Africans had been kept scoreless on home soil in 105 years) as his best so far for the All Blacks. In 2008 a fourth Bledisloe match was played in Hong Kong with the intention of expanding the game of rugby and in a close 19–14 game McCaw scored the match winning try. The Grand Slam tour to the United Kingdom and Ireland resulted in victories over Scotland (32–6), Ireland (22–3), Wales (29–9) and England (32–6). During 2008 McCaw won every test he captained and a total of 26 out of 28 games he played in at all levels. The All Blacks won 13 of a record 15 tests, retained the Bledisloe Cup and Tri Nations Trophy, completed the Grand Slam and reclaimed the world No. 1 ranking from South Africa. McCaw finished 2008 by making his debut for the Barbarians against Australia at Twickenham in an 11–18 loss. === 2009–2010 === The Crusaders, under new coach Todd Blackadder, had a slow start to the 2009 season, losing four of their first five games. They recovered to finish fourth on the table, losing the semi-final at Loftus Versfeld to the Bulls. McCaw injured his knee and missed the start of the international season, returning for the Tri Nations tournament. South Africa beat the All Blacks in every match to win the title and regain the number 1 ranking, with New Zealand beating Australia three times to finish second. It was the first time New Zealand had not won the competition in five years and the fifth time since the Tri Nations started in 1996. A fourth Bledisloe Test against Australia was played in Japan before New Zealand toured Europe. Although New Zealand won every match on tour, an earlier loss to France and three defeats by the South Africans were the most suffered by the All Blacks in a season since McCaw joined the team in 2001. Despite the team's relatively poor season, McCaw was named the IRB International Player of the Year for a second time. The 2010 season started in much the same way with the Crusaders finishing fourth during the round robin stage and losing to the Bulls in the semi-final. During the season McCaw played his 100th Super Rugby game in a losing effort against the Cape Town-based Stormers. New Zealand recorded victories over the touring Ireland and Wales teams, Ireland losing their match by a record 66–28 after number eight Jamie Heaslip received a red card for kneeing McCaw in the head. The All Blacks went through the Tri Nations undefeated with the final game of the tournament against Australia marking McCaw's 52nd time captaining the All Blacks, surpassing Sean Fitzpatrick as New Zealand's most-capped test captain. The fourth Bledisloe Cup match was again scheduled for Hong Kong and Australia ended a ten match losing streak to the All Blacks. It was to be the only loss the All Blacks would suffer that season as they went on to win another Grand Slam tour, defeating England, Scotland, Ireland and Wales. In the match against Ireland McCaw, along with teammate Mils Muliaina played in their 93rd test match passing Sean Fitzpatrick to become the most capped All Blacks. At the end of the year McCaw was named the IRB International Player of the Year for the second successive season and the New Zealand sportsperson of the year at the Halberg Awards. === 2011 Rugby World Cup === During preseason training in January 2011 McCaw injured his foot, subsequent x-rays revealed that he had received a stress fracture in the fifth metatarsal of his right foot. It was determined his best chance of recovery was to undergo an operation where a pin was inserted. As a result, McCaw missed the opening two months of the Super Rugby season. During the All Black's third Rugby World Cup pool match against France, McCaw became the first All Black to reach 100 test caps. However, it was also during this match McCaw re-aggravated his foot injury. In order to rest his injury, he was forced to skip the more physical aspects of training and miss the All Blacks' final pool match against Canada. Prior to the quarter-final against Argentina McCaw decided against having another x-ray. Following the re-occurrence of his injury it was uncertain whether McCaw could continue to play for the All Blacks, this forced the coaching staff to develop contingency plans and Matt Todd was called into the All Black training squad. McCaw was able to continue to play throughout the World Cup tournament and lifted the Webb Ellis trophy after a tense 8–7 victory over France. This was the lowest score in a final in World Cup history. After the final, the All Black coach Graham Henry stated "He can hardly walk and how he played today I just don't know," and he acknowledged the All Blacks probably would not have won without him. Following the World Cup x-rays showed that the screw in his foot, necessary to stop the deterioration of the original injury had caused a second fracture. The fracture again, required a further operation. After the Rugby World Cup McCaw was selected in the RWC Dream Team. This team was determined by public vote, with over 160,000 votes cast. In addition, for the second successive year McCaw was named the New Zealand sportsperson of the year at the Halberg Awards. === 2012–2015 === Under new coach Steve Hansen, the All Blacks won 12 tests, drew one and only lost one test in 2012, as well as winning the new Rugby Championship with a 100% winning record. During this time McCaw overtook George Gregan for most times on the winning side with 94. He also recorded his 100th win against South Africa in Dunedin. McCaw was a nominee for the IRB Player of the Year award but lost out to teammate Dan Carter. In the first half of 2013, in order to rest his body and improve his chances of playing in the 2015 Rugby World Cup McCaw enforced the sabbatical clause in his NZRFU contract. As a result, he only played the latter rounds of Super Rugby, and missed the 2013 French Test Series. He later returned to captain the All Blacks as they successfully defended the Rugby Championship. During this campaign, McCaw equalled (with Brian O'Driscoll of Ireland and John Smit of South Africa) the record as captaining the most test matches (83). McCaw subsequently overtook this record when playing in Japan on 2 November 2013. Following the All Blacks victory over the Springboks in Ellis Park, McCaw has played and won at every major Rugby Test stadium. Along with Kieran Read, McCaw led the All Blacks to a perfect season in 2013, winning 14 out of 14. McCaw captained New Zealand for the 100th time on 22 November 2014 in the end of year international against Wales. He is the first rugby union player to achieve 100 caps as captain. On 15 August 2015, McCaw surpassed Ireland's Brian O'Driscoll world record, as the most capped rugby player when he won his 142nd cap against Australia in the Bledisloe Cup. He would go on to hold this title for five years until 31 October 2020 when Welsh captain Alun Wyn Jones got his 149th cap. On 31 October 2015, McCaw captained New Zealand to retain the Rugby World Cup after a 34–17 win against Australia in the final at Twickenham. This match was the thirteenth Rugby World Game as captain and is the current world record for this statistic. During the tournament he received a yellow card for foottripping in the opening game against Argentina. On 19 November 2015, McCaw announced his retirement from rugby. === Leading of haka === Despite McCaw often being captain in tests, he generally turned down the role of haka leader (kaea). He only served as the kaea in 11 tests, only when the All Blacks performed 'Ka Mate'. == Playing style == McCaw predominately played at openside flanker, although he has played in the other "loose forward" positions of blindside flanker and number eight for the Crusaders. The openside flanker binds to the side of the scrum farthest from the touch-line and is usually one of the first players to reach a breakdown. In 2008, McCaw told the IRB:"My main role as a flanker is, defensively, to tie in with the back line to ensure that the defence works well. On attack I think my primary role at first phase is to look after our ball. You attack the back line and I'm usually the first person there to make sure we secure that ball. Thirdly I put pressure on break downs and make sure I disturb their ball and try to turn their ball over." McCaw has been described as the best openside flanker of all time. He has been awarded the IRB Player of the Year a record three times and has been nominated on eight occasions. When he received the IRB Player of The Year award for the third time former Australian lock and award chairperson John Eales described him as "an outstanding captain, a world class player and a role model for our sport". Along with Dan Carter, he is seen as one of the most influential members of the All Blacks. McCaw considers his ability to anticipate play as one of his most important skills. Australian openside David Pocock, who was also shortlisted for the IRB award, admires the way he reads the game as well as his ability to read the referee. One of McCaw's strengths is his ability to re-invent himself. For example, he adapted quickly to changes in the breakdown laws (e.g., the 2008 the Experimental Law Variations (ELVS) and the 2010 New IRB Law Interpretations) and, over time, other areas of his game. Not all agree with McCaw's playing style and many believe that he pushes the boundaries of legality. He has been labelled a "cheat" by both former South Africa coach Peter de Villiers and former Australian coach Bob Dwyer. Longtime Springboks lock Victor Matfield said in 2010 that the referees let "him get away with murder" at the breakdown. Shortly after the 2011 Rugby World Cup final, veteran France back-rower Imanol Harinordoquy criticised McCaw saying that "he played the whole match in our [Frances] camp." Former Australian coach Eddie Jones and flanker Phil Waugh say he does no more than any other good openside, but his skill at judging how the referee will interpret the breakdown is the main reason for his success. McCaw admits that he tests the referee early "to know what you can get away with" and that only an "idiot" would not adapt to their rulings. Teammate Aaron Mauger, along with many New Zealand fans, have suggested that McCaw's influence and playing style has made him a target for illegitimate play. International players Phil Waugh, Jamie Heaslip, Marcus Horan, Lote Tuqiri, Andy Powell, Dylan Hartley, Quade Cooper, Dean Greyling, Kevin McLaughlin and Scott Higginbotham have been accused of making "cheap shots" on McCaw. He has even been on the receiving end from his All Black teammates when playing for the Crusaders, with Neemia Tialata, Jerry Collins and Ali Williams becoming frustrated with his play. According to McCaw "what happens on the field stays on the field" and if he gets extra attention it is because he "must be doing something right". In 2012, Wallabies coach Robbie Deans and selectors wagered the potential returns in finishing games with two openside flankers on the field as a way to counter McCaw. In September 2012 after the All Blacks v South African Test in Dunedin, then South African coach Heyneke Meyer said that McCaw was the greatest rugby player the world has ever seen. Following the All Blacks win over Wallabies to claim their 3rd World Cup, All Blacks Coach Steve Hansen praised McCaw's and Dan Carter's career efforts, distinguishing McCaw from Carter:“Richie is the best All Black we have ever had and Dan is a close second,” said Hansen. “The only thing that separates them is Richie has played 148 matches at flanker, which is unheard of - you put your body on the line every time you go there. The challenge for the other guys now is to try and become as great as him and Dan.” == International record by opposition == == Playing achievements == == Personal life == In January 2013 it was reported that he had been seeing hockey player Gemma Flynn for the past six months. McCaw announced his engagement to Flynn in January 2016. They married on 14 January 2017. Their daughter was born in December 2018 and a second daughter in May 2021. Their third daughter Ella Mae was born in April 2023. In December 2024, McCaw's family said they were soon to move to Wānaka after 10 years living in Christchurch. His other sporting passion is flying and he was made an honorary Squadron Leader in the Royal New Zealand Air Force in 2010 and was promoted to honorary Wing Commander in September 2016. McCaw was taught to fly gliders by his grandfather J H 'Jim' McCaw who flew more than 300 missions in the Second World War. In 2009 he convinced the head of the Discovery network in Australia and New Zealand to do a show about gliding. They filmed McCaw gliding at Omarama on the extreme sports series Sportstar Insider, which was hosted by Australian former rugby league footballer Andrew Ettingshausen. After the 2010 Canterbury earthquake he auctioned a personal flying lesson through Trade Me to raise money for the badly damaged Hororata St Johns Church. He is also raising money for a young Samoan who broke his neck playing rugby and whose village was destroyed in the 2009 Samoa earthquake and tsunami. It was revealed at his retirement announcement in 2015 that McCaw would work at Christchurch Helicopters, where he is a Director and Shareholder, and was obtaining a commercial helicopter licence. McCaw has since obtained said licence and has continued working as a helicopter pilot. He flew several rescue and reconnaissance missions following the 2016 Kaikōura earthquake that struck the South Island. He also performed milk drops around rural areas of New Zealand while having an endorsement with Fonterra, in which his sister and her husband are dairy farmers. In 2010, McCaw and Dan Carter were on a NZ$750,000 a year contract that saw them through to the end of the 2011 Rugby World Cup, making them the highest paid rugby players in New Zealand at the time. This contract would still have applied if they had not been selected for the World Cup squad. == Honours and awards == In 2019, World Rugby inducted McCaw to its Hall of Fame, alongside Shiggy Konno, Os du Randt, Peter Fatialofa, Graham Henry, and Diego Ormaechea. === Order of New Zealand === In December 2011, then Prime Minister John Key revealed that he had asked McCaw about the possibility of a knighthood in the 2012 New Year Honours, but that McCaw had turned it down. According to Key, "He made the call that he's still in his playing career and it didn't feel quite right for him, that day where he's no longer on the pitch may be the right time for him." No formal offer was ultimately made. McCaw was appointed a member of New Zealand's highest honour, the Order of New Zealand, in the 2016 New Year Honours. The honour surpassed the knighthood he had previously turned down prior to his retirement because only 20 living New Zealanders can gain membership at any one time. McCaw represented the Order in the Royal Procession at the 2023 Coronation. == Notes == == References == == External links == Richie McCaw at the All Blacks (archive) Richie McCaw at ESPNscrum
|
Wikipedia:James Mercer (mathematician)#0
|
James Mercer FRS (15 January 1883 – 21 February 1932) was a mathematician, born in Bootle, close to Liverpool, England. He was educated at University of Manchester, and then University of Cambridge. He became a Fellow, saw active service at the Battle of Jutland in World War I and, after decades of ill health, died in London. He proved Mercer's theorem, which states that positive-definite kernels can be expressed as a dot product in a high-dimensional space. This theorem is the basis of the kernel trick (applied by Aizerman), which allows linear algorithms to be easily converted into non-linear algorithms. == References ==
|
Wikipedia:James Milne (mathematician)#0
|
James S. Milne (born 10 October 1942 in Invercargill, New Zealand) is a New Zealand mathematician working in arithmetic geometry. == Life == Milne attended high school in Invercargill in New Zealand until 1959, and then studied at the University of Otago in Dunedin (B.A. 1964) and Harvard University (Masters 1966, Ph.D. 1967 under John Tate). From then to 1969 he was a lecturer at University College London. After that he was at the University of Michigan, as Assistant Professor (1969–1972), Associate Professor (1972–1977), Professor (1977–2000), and Professor Emeritus (since 2000). He has also been a visiting professor at King's College London, at the Institut des hautes études scientifiques in Paris (1975, 1978), at the Mathematical Sciences Research Institute in Berkeley, California (1986–87), and the Institute for Advanced Study in Princeton, New Jersey (1976–77, 1982, 1988). In his dissertation, entitled "The conjectures of Birch and Swinnerton-Dyer for constant abelian varieties over function fields," he proved the conjecture of Birch and Swinnerton–Dyer for constant abelian varieties over function fields in one variable over a finite field. He also gave the first examples of nonzero abelian varieties with finite Tate–Shafarevich group. He went on to study Shimura varieties (certain hermitian symmetric spaces, low-dimensional examples being modular curves) and motives. For 2025 Milne was awarded the Leroy P. Steele Prize for Mathematical Exposition of the American Mathematical Society. His students include Piotr Blass, Michael Bester, Matthew DeLong, Pierre Giguere, William Hawkins Jr, Matthias Pfau, Victor Scharaschkin, Stefan Treatman, Anthony Vazzana, and Wafa Wei. Milne is also an avid mountain climber. == Writings == Étale Cohomology. Princeton Mathematical Series. Vol. 33. Princeton, NJ: Princeton University Press. 1980. ISBN 0-691-08238-3. MR 0559531. Abelian Varieties, Jacobian Varieties, in Arithmetic Geometry Proc. Conference Storrs 1984, Springer 1986 With Pierre Deligne, Arthur Ogus, Kuang-yen Shih, Hodge Cycles, Motives and Shimura Varieties, Springer Verlag, Lecture Notes in Mathematics vol. 900, 1982 (therein by Deligne: Tannakian Categories) Arithmetic Duality Theorems, Academic Press, Perspectives in Mathematics, 1986 Editor with Laurent Clozel, Automorphic Forms, Shimura Varieties and L-Functions, 2 volumes, Elsevier 1988 (Conference University of Michigan, 1988) Elliptic Curves, BookSurge Publishing 2006 Shimura Varieties and Motives in Jannsen, Kleiman, Serre (editor) motif, Proc. Symp. Pure vol. 55 Math, AMS, 1994 == References == The original article was a Google translation of the corresponding article in German Wikipedia. == External links == Personal website
|
Wikipedia:James Moffat (mathematician)#0
|
James Moffat is a mathematician. He was a researcher for the Ministry of Defence during the 1982 Falklands War. He wrote Complexity Theory and Network Centric Warfare, which has 275 scholarly citations. Moffat is currently Professor of Physics at the University of Aberdeen, where he studies quantum gravity. He has published 135 articles. He is a recipient of the Napier Medal in Mathematics and the President’s Medal of the ORS; the 'nobel medal in analytics'. He is also a Fellow of OR, a Fellow of the Institute of Mathematics and its Applications, and a Chartered Mathematician. His contributions to the literature cited 560 times include new theories for Loop Quantum Gravity based on the Mathematics of Operator Algebras. Moffat was an early writer on the topic of the Agile Organization. Business agility, generally, had been discussed before, but agility, specifically in the context of military organizations, was a new field in 2005. == Selected publications == Complexity Theory and Network Centric Warfare, citation count of 275 The Agile Organization: From Informal Networks to Complex Effects and Agility, citation count of 138 Command And Control In The Information Age: Representing Its Impact, citation count of 60 == References ==
|
Wikipedia:James Oxley#0
|
James G. Oxley is an Australian–American mathematician, Boyd Professor of Mathematics at Louisiana State University. He is known for his expertise in matroid theory and graph theory. Oxley did his undergraduate studies in Australia, and earned a doctorate from the University of Oxford in 1978, under the supervision of Dominic Welsh. He joined the Louisiana State University faculty in 1982. Oxley is the author of the book Matroid Theory (Oxford University Press, 1992). In 2012 he became a fellow of the American Mathematical Society. == References ==
|
Wikipedia:James Stewart (mathematician)#0
|
James Drewry Stewart, (March 29, 1941 – December 3, 2014) was a Canadian mathematician, violinist, and professor emeritus of mathematics at McMaster University. Stewart is best known for his series of calculus textbooks used for high school, college, and university-level courses. == Career == Stewart received his master of science at Stanford University and his doctor of philosophy from the University of Toronto in 1967. He worked for two years as a postdoctoral fellow at the University of London, where his research focused on harmonic and functional analysis. His books are standard textbooks in universities in many countries. One of his best-known textbooks is Calculus: Early Transcendentals (1995), a set of textbooks which is accompanied by a website for students. Stewart was also a violinist and a former member of the Hamilton Philharmonic Orchestra. == Integral House == From 2003 to 2009 a house designed by Brigitte Shim and Howard Sutcliffe was constructed for Stewart in the Rosedale neighbourhood of Toronto at a cost of $32 million. He paid an additional $5.4 million for the existing house and lot which was torn down to make room for his new home. Called Integral House (a reference to its curved walls, and their similarity to the mathematical integral symbol), the house includes a concert hall that seats 150. Stewart has said, "My books and my house are my twin legacies. If I hadn't commissioned the house I'm not sure what I would have spent the money on." Glenn Lowry, director of the Museum of Modern Art, called the house "one of the most important private houses built in North America in a long time." == Personal life and political activism == Stewart was gay and involved in LGBT activism. According to Joseph Clement, a documentary filmmaker who is working on a film about Stewart and Integral House, Stewart brought gay rights activist George Hislop to speak at McMaster in the early 1970s, when the LGBT liberation movement was in its infancy, and was involved in protests and demonstrations. == Death == In the summer of 2013, Stewart was diagnosed with multiple myeloma, a blood cancer. He died on December 3, 2014, aged 73. == Honours == In 2015, he was posthumously awarded the Meritorious Service Cross. == Publications == === Books === Stewart, James (2012). Essential Calculus (2nd ed.). Cengage Learning. ISBN 978-1-133-11229-7. Stewart, James (2012). Essential Calculus: Early Transcendentals (2nd ed.). Cengage Learning. ISBN 978-1-133-11228-0. Stewart, James; Watson, Saleem; Clegg, Daniel (2020). CALCULUS (9th ed.). Cengage Learning. ISBN 978-1-337-62418-3. Stewart, James; Watson, Saleem; Clegg, Daniel (2020). CALCULUS: Early Transcendentals (9th ed.). Cengage Learning. ISBN 978-1-337-61392-7. Stewart, James; Kokoska, Stephen (2023). CALCULUS: CONCEPTS AND CONTEXTS (5th ed.). Cengage Learning. ISBN 978-0-357-63249-9. == References == == Further reading == Peterson, Ivars (August–September 2009). "James Stewart and the House That Calculus Built" (PDF). MAA Focus. 29 (4): 4–6. ISSN 0731-2040. Archived from the original (PDF) on 2015-10-14. Retrieved 2009-07-27. Article about Stewart's "Integral House". == External links == James Stewart at the Mathematics Genealogy Project Stewart Calculus Official Biography The house that math built by Katie Daubs at the Toronto Star Integral Man Archived 2018-05-18 at the Wayback Machine, a documentary about Stewart and Integral House
|
Wikipedia:Jan Brinkhuis#0
|
Jan Brinkhuis (born 1952) is a Dutch mathematician, and Associate Professor of Finance and Mathematical Methods and Techniques at the Econometric Institute of Erasmus University Rotterdam, specialized in the theory and application of optimization theory and game theory. Born in Veenendaal, Brinkhuis received his PhD in mathematics in 1981 at King's College London under supervisor of Albrecht Fröhlich with the thesis Embedding Problems and Galois Modules. After graduation, he started his academic career as research associate at King's College London on a SERC grant. In 1983 he moved back to The Netherlands and joined the Econometric Institute of Erasmus University Rotterdam. Since early 2000s Brinkhuis is also teacher at the Tinbergen Institute. In 2000 Brinkhuis was awarded Education and Research award by the Erasmus University Rotterdam, and in 2009 he was elected Tinbergen Professor of the Year 2008/2009 by the first-year students. In 2005 Brinkhuis and Vladimir Tikhomirov wrote Optimization: Insights and Applications an introduction to mathematical optimization, published by Princeton University Press. == Publications == Books 1981. Embedding Problems and Galois Modules. PhD thesis King's College London. 1986. Normal integral bases and complex conjugation. Econometric Institute. 2005. Optimization: Insights and Applications, Jan Brinkhuis and Vladimir Tikhomirov, Princeton University Press Articles, a selection: 1983. "Non-repetitive sequences on three symbols." Quarterly Journal of Mathematics 34.2: 145-149. 1992. "On the Galois module structure over CM-fields." manuscripta mathematic 75.1 (1992): 333-347. == References == == External links == Jan Brinkhuis at erim.eur.nl
|
Wikipedia:Jan Camiel Willems#0
|
Jan Camiel Willems (18 September 1939 – 31 August 2013) was a Belgian mathematical system theorist who has done most of his scientific work while residing in the Netherlands and the United States. He is most noted for the introduction of the notion of a dissipative system and for the development of the behavioral approach to systems theory. == Biography == Jan Willems was born in Bruges in 1939. He studied engineering at the University of Ghent, obtained the M.Sc. degree from the University of Rhode Island, and the Ph.D. degree from the Massachusetts Institute of Technology in electrical engineering in 1968. He was an assistant professor in the department of electrical engineering at MIT from 1968 to 1973. On 1 February 1973 he was appointed professor of systems and control in the mathematics department of the University of Groningen. In 2003 he became emeritus professor. Afterwards, he became guest professor at the KU Leuven. He served terms as chairperson of the European Union Control Association and of the Dutch Mathematical Society (Wiskundig Genootschap). He was managing editor of the SIAM Journal of Control and Optimization and as founding and managing editor of Systems & Control Letters. == Research contributions == In his Ph.D. dissertation, Willems worked on input/output stability. In an often-cited 1972 paper he introduced the notion of a dissipative system. This notion is a generalization of Lyapunov function to input/state/output systems. The construction of the storage function, as the analogue of a Lyapunov function is called, led to the study of the linear matrix inequality (LMI) in control theory. Applied to linear-quadratic-Gaussian control, the construction of the storage function leads to the Kalman–Yakubovich–Popov lemma. In the 1980s Willems worked on the geometric theory of linear systems, where he introduced the notion of almost invariant subspace. Since the 1990s, he has devoted his interest to the development of the behavioral approach to systems theory and control. In the behavioral approach a dynamical system is simply viewed as a family of trajectories. This approach avoids having to separate the system variables into inputs and outputs. == Awards and honors == Willems was a fellow of the IEEE, the Society for Industrial and Applied Mathematics, the American Mathematical Society and International Federation of Automatic Control. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. In 1998, he received the IEEE Control Systems Award "for seminal contributions to control theory and leadership in systems research". In 2010, he became doctor honoris causa of the University of Liège. == Selected publications == == References == == External links == Jan Willems' homepage S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory (book in pdf)
|
Wikipedia:Jan Hemelrijk#0
|
Jan Hemelrijk (28 May 1918 – 16 March 2005) was a Dutch mathematician, Professor of Statistics at the University of Amsterdam, and authority in the field of stochastic processes. == Biography == Hemelrijk received his PhD in 1950 at the University of Amsterdam with a thesis entitled "Symmetry Keys and other applications of the theory of Neyman and Pearson" under supervision of David van Dantzig. After graduation Hemelrijk started his academic career as assistant to David van Dantzig at the Centrum Wiskunde & Informatica in Amsterdam, and later Head of the Statistical Consulting Department. He was Professor at the Delft University of Technology from 1952 to 1960. In 1960, he was appointed Professor of Statistics at the University of Amsterdam as successor of David van Dantzig. Among his doctoral students were Gijsbert de Leve (1964), Willem van Zwet (1964), R. Doornbos (1966), Ivo Molenaar (1970), Robert Mokken (1970) and J. Dik (1981). Jaap Wessels in 1960 started his academic career Wessels as assistant to Jan Hemelrijk. Hemelrijk was President of the Netherlands Society for Statistics and Operations Research, and chief editor of the Journal of the association Statistica Neerlandica. He also provided the first television course Statistics of Teleac, broadcast in 1969 and 1970. In 1963, he was elected as a Fellow of the American Statistical Association. == Publications == 1950. Symmetry Keys and other applications of the theory of Neyman and Pearson Doctoral thesis University of Amsterdam. 1957. Elementaire statistische opgaven met uitgewerkte oplossingen. Gorinchem : Noorduijn 1977. Oriënterende cursus mathematische statistiek. Amsterdam : Mathematisch Centrum 1998. Statistiek eenvoudig. With Jan Salomon Cramer. Amsterdam : Nieuwezijds Articles, a selection: Hemelrijk, Jan. "In memoriam prof. dr. D van Dantzig (1900-1959)." Statistica Neerlandica 13, 1954, p. 415-432 Hemelrijk, Jan. "Statistical methods applied to the mixing of solid particles, 1." Stichting Mathematisch Centrum. Statistische Afdeling S 159/54 (1954): 1-16. Hemelrijk, Jan. "Het begrip nauwkeurigheid." Stichting Mathematisch Centrum. Statistische Afdeling S 228/58 (1958): 1-19. == References == == External links == In Memoriam Prof. dr. Jan Hemelrijk (in Dutch)
|
Wikipedia:Jan Karel Lenstra#0
|
Jan Karel Lenstra (born 19 December 1947, in Zaandam) is a Dutch mathematician and operations researcher, known for his work on scheduling algorithms, local search, and the travelling salesman problem. Lenstra received his Ph.D. from the University of Amsterdam in 1976, advised by Gijsbert de Leve. He then became a researcher at the Centrum Wiskunde & Informatica, where he remained until 1989. After taking positions at the Eindhoven University of Technology (where he became Dean of the Faculty of Mathematics and Computer Science) and the Georgia Institute of Technology, he returned to CWI as its director in 2003. He stepped down in 2011, and at that time became a CWI Fellow. He was editor-in-chief of Mathematics of Operations Research from 1993 to 1998, and is editor-in-chief of Operations Research Letters since 2002. Lenstra became an INFORMS fellow in 2004. In 1997, he was awarded the EURO Gold Medal, the highest distinction within Operations Research in Europe. In 2011, he was made a knight of the Order of the Netherlands Lion, and the CWI organized a symposium in his honor. Lenstra is the brother of Arjen Lenstra, Andries Lenstra, and Hendrik Lenstra, all of whom are also mathematicians. He is married to Karen Aardal, in 2020 professor at Delft University. == Publications == Jan Karel Lenstra // DBLP, Universität Trier Peter J. M. van Laarhoven, Emile H. L. Aarts, Jan Karel Lenstra. - Job Shop Scheduling by Simulated Annealing (info) // Operations Research, 40 (1992), pp. 113-125. Emile H. L. Aarts, Peter J. M. van Laarhoven, Jan Karel Lenstra, Nico L. J. Ulder: A Computational Study of Local Search Algorithms for Job Shop Scheduling. // INFORMS Journal on Computing 6(2): 118-125 (1994) (dblp) == References == == Sources == Album Academicum (website University of Amsterdam)
|
Wikipedia:Jan Koenderink#0
|
Jan Johan Koenderink (born 10 February 1943, Stramproy) is a Dutch physicist and psychologist known for his research in visual perception, computer vision, and geometry. Koenderink earned a bachelor's degree from Utrecht University in 1964, a master's in 1967, and a Ph.D. in 1972 on a thesis titled Models of the visual system. He was a full professor of physics and astronomy at Utrecht University from 1978 until his mandatory retirement in 2008; since then, he has held fellow or visiting professor positions at Utrecht, the Delft University of Technology, the Massachusetts Institute of Technology, and Katholieke Universiteit Leuven. Koenderink is the author of the books Color for the Sciences (MIT Press, 2010), on colorimetry, and Solid Shape (MIT Press, 1990), on differential geometry. In 1987, the Katholieke Universiteit Leuven awarded Koenderink an honorary doctorate. Koenderink became a fellow of the Royal Netherlands Academy of Arts and Sciences in 1990, and of the Royal Flemish Academy of Belgium for Science and the Arts in 2010. Koenderink is the 2013 recipient of the Azriel Rosenfeld Award for lifetime achievement in computer vision. In 2017, Koenderink, along with Andrea Van Doorn, was awarded the Kurt-Koffka medal from Justus Liebig University Giessen. == References == == External links == Gestalt ReVision co-PI: Jan Koenderink Archived 2015-12-08 at the Wayback Machine Jan Koenderink publications indexed by Google Scholar
|
Wikipedia:Jan Mandel#0
|
Janhilly "Jan" Manual (born January 13, 1986) is a Filipino actor and comedian. He made his first showbiz appearance on the fourth season of the Philippine reality show StarStruck where he finished as an avenger. He was a contract artist of GMA Artist Center. He is also the nephew of Survivor Philippines Season 1 Castaway Rob Sy. Manual is known for being a mainstay in longest-running gag show Bubble Gang. == Biography == === 2006—2007: StarStruck === On September 3, 2006, GMA Network formally announced the return of their reality-based talent show now titled StarStruck: The Next Level (aka StarStruck 4), a new and improved edition of the popular show. Hosted by the same hosts and headed by The Council members' Lorna Tolentino, Louie Ignacio and Douglas Quijano, the show had its pilot episode on December 4, 2006. In the 4th year of the reality-talent search, the age bracket for star wannabes was adjusted from 15 to 18 in previous batches to 16–21, a milestone in StarStruck History. Unlike the previous batches which launched 14, this batch were trimmed down to twenty, dubbed as the "Top 20". Also, four winners were picked in this season — Ultimate Sweetheart, Ultimate Hunk, and Ultimate Loveteam. Just like in previous seasons, voting is via the internet and mobile phones and this constitutes 50% of the total scores of the survivors. Jan made it through to the Top 14 but was eliminated. At the Final Judgment, he received an award for Dats Entertaining Award along with Dex Quindoza for Male with the Most Dramatic Exit, Stef Prescott for Female With the Most Dramatic Exit, and Jesi Corcuera for the Best Taktak Award. === 2007—2018: Post—StarStruck === He is presently making his own mark and signature in the Philippine show business through his role as Pacboy, the comic imitation of Manny Pacquiao in his segment in Startalk. He is joined with his fellow StarStruck alumni Chariz Solomon with StarStruck V's graduates Nina Kodaka and Princess Snell. Jan also voiced the character Chad from Bleach anime. Jan had some offerings which were sexy roles but he refused because he thought that he was too sexy to be in it, "sexy of fats". While celebrating the KapusOlympics Watermania 2008 in Golden Sunset Resort, the torch accidentally fell onto Jan's face and to some part of his body. He stayed in hospital for three weeks and couldn't do anything but to rest while fighting for his life thinking that it was his end. After three weeks of medication, Jan back to work and there were no marks that made by the accident. That experience for him is considered as a miracle. Jan was included in I Laugh Sabado. that served as his biggest break as he was one of the main hosts. According to him in an interview, he said he could be free from the shadows of his character in Startalk who is "Pacboy". He joined the casts of Wally Bayola, Paolo Paraiso, Janna Dominguez, Gee Canlas, Alfred Marquez and Archie Alemania. I Laugh Sabado was directed by Bibeth Orteza. In the said show, he also said that he was able to show his other abilities as a comedian. Aside from his stint in I Laugh Sabado, he was seen more often in some shows of GMA as an extended cast such as The Last Prince and in Panday Kids. Jan appeared in Take Me Out, a TV dating game show hosted by Jay-R. Being a comedian, Jan also served as guest in Bubble Gang where he admitted he wanted to be part of the country's best gag show. In 2011, Jan was cast in the country's first epic-serye and the most expensive project GMA has done yet before Indio — Amaya starred by Marian Rivera and Sid Lucero. In 2012, Jan was part of the early prime time show, My Daddy Dearest as Jing. In 2013, Jan was expected to be part of a new series to be led by his StarStruck batch-mates, Aljur Abrenica and Kris Bernal. The title of the series was Prinsesa ng Buhay Ko. Aside from his then upcoming prime time series, in July 2013, Bubble Gang revealed that Manual is part of the show's search for a new batch of comedians. Their search is called "Bagong Gang The Search for New Recruits". However, Manual shared that he might eliminate himself in Bubble Gang because of the possible schedule conflict with his Prinsesa ng Buhay Ko role, although he said that nothing was definite yet as of that moment. In the end, Jan was able to finish his soap and at the same time, winning the competition in the gag show. In mid-2013, Jan appeared in Wagas, a romance drama anthology aired in GMA News TV with Frank Magalona and Kylie Padilla, and in Pepito Manaloto as Lawrence. Jan also portrayed the role of Charice Pempengco's manager in Charice's life story in Magpakailanman. In early 2014, Jan had his first movie project via Basement. He portrayed the character of Migs, the nurse of Pilita Corrales' character. The said film was released on February 12, 2013, making it as the Valentine movie offering of GMA Films. By the end the first quarter of 2014, Jan had his first starring role via the Lenten season offering of The 700 Club Asia's Tanikala, My Sister, My Lover. He starred opposite Sheena Halili, another StarStruck alumna. Jan played the character of Art Duyan, a gay before who got married and eventually getting a family. Art is now a pastor. Jan is a no stranger to gay roles as he played several gay roles before. According to him, his role in My Sister, My Lover is special to him because the show has a different purpose which is not just to entertain. He also said that he accepted the role because he knows that that show would do something good and there would be a lot of viewers who would be able to relate to the story. According to CBN Asia's website, Tanikala (Shackles) is their annual TV drama special that airs nationwide in the Philippines every Holy Week. It "features true-to-life stories of Filipinos who fought their way out of the darkness of their lives, and found the light of the truth in Jesus". After months of not having an acting project aside from his Bubble Gang stint, Jan becomes part of the weekly drama anthology, Seasons of Love, where he is in the second installment entitled "I Do, I Don't" which starred by Louise delos Reyes, Geoff Eigenmann and Mike Tan. His character's name is Badoy, the best friend of Mike Tan's character, Gary. == Personal life == Jan has stated that he wants to concentrate on comedy. He said that Michael V. and Jim Carrey are his idols when it comes to make people laugh. He has plans in relocating to the United States if his showbiz career does not work out. Though Jan is most interested in comedy roles, he still hopes to do drama series as well. He enjoys working out through Taekwondo and boxing. Jan married Jamey Santiago in June 2018. They met due to attending the same church. Santiago is one of the hosts of Christian TV show 700 Club Asia. == Filmography == === Television === === Film === == See also == Sheena Halili Kevin Santos (actor) Arci Muñoz Kim Domingo Sef Cadayona == References == == External links == Jan Manual at GMANetwork.com Jan Manual at IMDb
|
Wikipedia:Jan Nekovář#0
|
Jan Nekovář (1963 – 14 November 2022) was a Czech academic and mathematician who specialized in number theory. == Biography == Nekovář first studied at Charles University in Prague and was an exchange student at Moscow State University from 1984 to 1985. He obtained his doctorate from the Czechoslovak Academy of Sciences in 1991 with a thesis titled Modulární formy necelé váhy. From 1991 to 1993, he was a postdoctoral researcher at the University of California, Berkeley. In 1993, he became an assistant professor at Charles University, where he became a lecturer in 1995. He taught at Christ's College, Cambridge from 1995 to 2002 and subsequently became a professor at Pierre and Marie Curie University. Nekovář was a visiting researcher at the Steklov Institute of Mathematics from 1988 to 1989, at the Max Planck Institute for Mathematics from 1989 to 1990, at the Isaac Newton Institute in 1998, the École normale supérieure in 1991, as well as the University of Minnesota, the Centre de Recerca Matemàtica, the Fields Institute, and the Erwin Schrödinger International Institute for Mathematical Physics. Jan Nekovář died in Paris on 14 November 2022, at the age of 59. == Awards == Whitehead Prize (1998) G. de B. Robinson Award (2014) Neuron Prize for Important Scientific Discovery (2019) == Publications == "Class numbers of quadratic fields and Shimura's correspondence." (1990) "On p-adic height pairings" (1991) Selmer complexes (2006) "The Euler system method for CM points on Shimura curves" (2007) "Eichler-Shimura relations and semisimplicity of étale cohomology of quaternionic Shimura varieties" (2018) "Semisimplicity of certain Galois representations occurring in étale cohomology of unitary Shimura varieties" (2019) == References ==
|
Wikipedia:Jan Poleszczuk#0
|
Jan Poleszczuk (born 19 October 1986) is a Polish mathematician and biologist known for his contributions in mathematical biology. == Early life and education == Poleszczuk was born on 19 October 1986. In June 2010, he graduated from Warsaw University's Faculty of Mathematics, Informatics and Mechanics with a Master of Science in mathematical methods in biology and social sciences based on the thesis "Modeling of tumor angiogenesis and antiangiogenic therapy on the basis of Hahnfeldt et al. mode". == Academic career == Under supervision of Maria Wideł and coadvisor Urszula Alicja Foryś, Jan Poleszczuk defended the Ph.D. in Biocybernetics and Biomedical Engineering at Faculty of Automatic Control, Electronics and Computer Science, Silesian University of Technology, based on dissertation: "Mathematical modeling of cancer cell response to therapy induced stress" February 2014, Next, under supervision of Urszula Alicja Foryś with coadvisor Maria Wideł, he defended the Ph.D. in Mathematics at Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, based on thesis ""Exploring potential tumor growth modulating mechanisms in cells having different status of TP53 gene"" in December 2015. Since February 2012, he has been a research fellow at the Nalecz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences. On 2020-06-26, his dissertation Mathematical modeling in the study of evolution and treatment of cancer with radio and immunotherapy was presented to the scientific council of the Maciej Nalecz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences. He was habilitated in the field of engineering sciences, discipline of biomedical engineering, receiving the degree of doctor of science. == Contributions == His publications are listed in various data bases. The author and co-author of more than 60 scientific articles. Most of the works are interdisciplinary. The most cited works are in the area of mathematical modeling of gene expression Stochastic models of gene expression with delayed degradation, immune reaction Mathematical modelling of immune reaction against gliomas: sensitivity analysis and influence of delays. As a mathematician working in the field of oncology, he supports biologists, medical doctors, physicists and chemists. His aim is to understand how gene mutations interact and how they affect cancer growth. His work is focused on increasing the effectiveness of existing therapies (radiotherapy and chemotherapy), which may improve the situation of many more patients more quickly than with new targeted drug therapies with limited effects. In radiotherapy, he created a model aimed at selecting, from among many metastases, this tumor in the patient's body, the irradiation of which will maximize the overall effectiveness of the therapy. He also used mathematical and computer methods to calculate and propose radiation therapy plans to harm the cancer as much as possible but preserve healthy tissues and organs. He is currently working on improving the dosage of chemotherapy so that it does not result in tumor resistance to treatment in relapses. He is member of Polish Mathematical Society (Treasurer for years 2017–2020), Polish Radiation Research Society, Society for Mathematical Biology and American Association for Cancer Research. == References ==
|
Wikipedia:Jan Reiterman#0
|
Jan Reiterman (8 October 1948 – 14 September 1992) was a Czech mathematician and computer scientist. He is best known for his contributions to categorical methods in algebra and the eponymous Reiterman's Theorem, which generalized Birkhoff's Variety Theorem to varieties of finite algebras. == Life == Reiterman was born on 8 October 1948 in Prague, Czechoslovakia. He died on 14 September 1992 of lung cancer. == References ==
|
Wikipedia:Jan Rusinek#0
|
Jan Rusinek (born 2 December 1950) is a Polish mathematician and chess composer, particularly noted for his brilliant endgame studies. He was editor of the study section of Szachy (Chess) from 1971 to the magazine's closure in 1990. Rusinek became an International Judge of chess composition in 1983, and a Grandmaster of chess composition in 1992. He won over 30 first prizes in composing tourneys. The Oxford Companion to Chess opines that "his achievements are likely to rival those of his greatest predecessors". == Endgame studies == To the left is one of Rusinek's better known studies. Black threatens Nb5-d6# or Ne4-d6# and 1.Kb7 Bd5+ does not help, so 1.a7 is necessary. Now 1...Bd5 can be answered with, among other lines, 2.g8Q Bxg8 3.a8Q Nxb6+ 4.Kb7 Nxa8 5.Kxa8 Be6 6.Kb8 and Black must give up a piece for the c pawn, so instead 1...Ba6+ 2.b7. Now 2...Nb5 threatens 3...Nd6# but is met with 3.g8N+ Ke8 4.Nf6+ when 4...Nxf6 loses to 5.a8Q. Instead, therefore, Black plays 2...Ne4 3.g8N+! Ke8 4.Nf6+ and now 4...Nexf6 is possible. This seems to put White in a dilemma, since 5.a8Q loses to 5...Nd5 with 6...Ne7# next move. But instead there is 5.a8B!! when 5...Nd5 is stalemate, so therefore 5...Ne5 6.Kb8 Nc6+ 7.Kc8 Bf1 and again White has a problem because 8.b8Q will lose to 8...Ba6+ 9.Qb7 Ne4 10.Qxa6 Nd6#. 8.b8N is no better: 8...Ne7+ 9.Kb7 Bg2+ 10.Ka7 (10.Nc6 Bxc6+ 11.Ka7 Bd7) 10...Nc8+ 11.Ka6 Bxa8. However, white can draw with a third underpromotion: 8.b8R!!. Now after 8...Ba6+ 9.Rb7, 9...Ne4 is stalemate, and there is no useful way for Black to avoid this. White draws. White's being required to make all three underpromotions in order to draw is exceptionally unusual. In Endgame Magic (Batsford, 1996), John Beasley and Timothy Whitworth comment that it "represents a very much greater feat of composition than might at first appear. That it was accomplished with the use of only nine men adds still more to the composer's achievement." Beasley and Whitworth also comment that "It is quite easy to construct a position in which White must promote to a rook or bishop in order to avoid giving stalemate," but "It is much more difficult to create a position in which White must underpromote to create a stalemate," which is done on two occasions in this study. Rusinek subsequently (64, 27 July 1978) added an introduction to this study which added a promotion to queen to the already existing underpromotions, thus creating an Allumwandlung. This later version is shown to the right. 1.h8R+ is insufficient, since 1...Ke7 will mate quickly. 1.h8Q+ is therefore necessary, and after the forced continuation 1...Qxh8 2.g7+ Qxg7 3.hxg7+ Ke7, the initial position of the original study is reached. Rusinek himself considered this version inferior to the original (aesthetics versus task). == Articles by Rusinek == "Stalemate by pinning in the middle of the board", in EG No. 51 (June 1978) "Studies in the FIDE Album 1986-88", in EG No. 105 (May 1992) "Grzegorz Grzeban, 1902-1991", in EG No. 106 (October 1992) == References == David Hooper and Kenneth Whyld, The Oxford Companion to Chess (Oxford University Press, 1992) == External links == Jan Rusinek at the Mathematics Genealogy Project
|
Wikipedia:Jan S. Hesthaven#0
|
Jan S. Hesthaven (born 10 December 1965) is a Danish mathematician, currently president of the Karlsruhe Institute of Technology. He was previously Vice President for Academic Affairs (starting in 2021) at EPFL (École polytechnique fédérale de Lausanne) and held the Chair of Computational Mathematics and Simulation Science (MCSS). He is particularly known for contributions to the development, analysis and application of high-order accurate computational methods for time-dependent partial differential equations. He has also contributed substantially to the development of reduced order models and the application of neural networks and machine learning techniques to problems in science and engineering. == Career == Prof. Hesthaven obtained a Master of Science degree in computational physics from the Technical University of Denmark (DTU) in 1991. In 1995, he received a Ph.D. in Numerical Analysis from the Institute of Mathematical Modelling (DTU) and in 2009 he was awarded the degree of Dr.Techn. from DTU for substantial and lasting contributions that has helped to move his research area forward and penetrated into applications. After graduation, he was appointed in 1995 as Visiting Assistant Professor at Brown University, then in 1999 as assistant professor and in 2003 he was promoted associate professor of applied mathematics with tenure at Brown University where in July 2005 he was promoted to professor of applied mathematics. In 2006, he founded the Center for Computation and Visualization (CCV) at Brown University and was its director until 2013. He served from Aug 2010 to June 2013 as founding deputy director of the Institute of Computational and Experimental Research in Mathematics ICERM, an NSF Mathematical Sciences Research Institute. In 2013, he joined EPFL (École polytechnique fédérale de Lausanne) where he was appointed full professor of computational mathematics and simulation science, and shortly later, in February 2014, he founded the new unit of Scientific IT and Application Support (SCITAS) From 2016 to 2021 he served as Editor in Chief of SIAM Journal of Scientific Computing. In February 2017, he became dean of the School of Basic Sciences (SB). In September 2020, he was appointed as Vice President for Academic Affairs at EPFL for a term starting in 2021. In January 2024, he was elected as the future president of the German Karlsruhe Institute of Technology (KIT) by the supervisory board. The election was confirmed by the Senate on 19 February 2024. He has assumed the presidency as of the 1st of October 2024. == Recognition == Brown University gave him their Philip J. Bray Award for Teaching Excellence in 2004. He was elected as a SIAM Fellow in 2014. He was named to the 2023 class of Fellows of the American Mathematical Society, "for contributions to computational methods for PDEs, high-order accurate methods, and the reduced order method". In 2022 he as inducted as member of the Royal Danish Academy of Sciences and Letters. In 2023, he was elected as a member of Academia Europaea and the European Academy of Sciences. In 2024, the Technical University of Denmark awarded him an honorary doctorate in recognition of his scientific contributions == Books == Hesthaven, Jan. (2007). Spectral methods for time-dependent problems. Gottlieb, Sigal., Gottlieb, David. Cambridge: Cambridge University Press. ISBN 978-0-511-26107-7. OCLC 162144521. Hesthaven, Jan S. (2008). Nodal discontinuous Galerkin methods : algorithms, analysis, and applications. Warburton, Tim. New York: Springer. ISBN 978-0-387-72067-8. OCLC 233971312. Hesthaven, Jan S. (2016). Certified reduced basis methods for parametrized partial differential equations. Rozza, Gianluigi, Stamm, Benjamin. Cham: Springer. ISBN 978-3-319-22470-1. OCLC 919086945. Hesthaven, Jan S. (2018). Numerical methods for conservation laws : from analysis to algorithms. Philadelphia: Society for Industrial and Applied Mathematics. ISBN 978-1-61197-509-3. OCLC 1012713065. == Notes and references == == External links == "Prof. Jan S Hesthaven's personal page". EPFL. "Prof. Jan S Hesthaven". LinkedIn. "Prof. Jan S Hesthaven". Google Scholar. "Prof. Jan S Hesthaven". Scopus.
|
Wikipedia:Jan Saxl#0
|
Jan Saxl (5 June 1948 – 2 May 2020) was a Czech-British mathematician, and a professor at the University of Cambridge. He was known for his work in finite group theory, particularly on consequences of the classification of finite simple groups. == Education and career == Saxl was born in Brno, in what was at the time Czechoslovakia. He came to the United Kingdom in 1968, during the Prague Spring. After undergraduate studies at the University of Bristol, he completed his DPhil in 1973 at the University of Oxford under the direction of Peter M. Neumann, with the title of Multiply Transitive Permutation Groups. Saxl held postdoctoral positions at Oxford and the University of Illinois at Chicago, and a lecturer position at the University of Glasgow. He moved to the University of Cambridge in 1976, and spent the rest of his career there. He was elected as a fellow of Gonville and Caius College in 1986, and he retired in 2015. Saxl published around 100 papers, and according to MathSciNet, these have been cited over 1900 times. He is noted for his work in finite group theory, particularly on permutation groups, and often coauthored with Robert Guralnick, Martin Liebeck, and Cheryl Praeger. Some notable and highly-cited examples of this work are as follows. Liebeck, Saxl and Praeger gave a relatively simple and self-contained proof of the O'Nan–Scott theorem. It had long been known that every maximal subgroup of a symmetric group or alternating group was intransitive, imprimitive, or primitive, and the same authors in 1988 gave a partial description of which primitive subgroups could occur. == Personal life == Saxl was married to Cambridge mathematician Ruth M. Williams and they had one daughter, Miriam. == Death == Saxl died on 2 May 2020, after a long period of poor health. == Awards and honors == A three-day conference in the joint honor of Saxl and Martin Liebeck was held at the University of Cambridge in July 2015. == Publications == Books Liebeck, Martin; Praeger, Cheryl; Saxl, Jan (2010). "Regular subgroups of primitive permutation groups". Memoirs of the American Mathematical Society. 203 (952). American Mathematical Society (AMS). doi:10.1090/s0065-9266-09-00569-9. ISBN 978-0-8218-4654-4. ISSN 0065-9266. MR 2588738. OCLC 457767029. Guralnick, Robert M.; Müller, Peter; Saxl, Jan (2003). "The rational function analogue of a question of Schur and exceptionality of permutation representations". Memoirs of the American Mathematical Society. 162 (773). American Mathematical Society (AMS). arXiv:math/0201069. doi:10.1090/memo/0773. ISBN 9780821832882. ISSN 0065-9266. MR 1955160. S2CID 7113361. Ivanov, Alexander A.; Liebeck, Martin W.; Saxl, Jan, eds. (2003). Groups combinatorics & geometry : Durham 2001. New Jersey London: World Scientific. ISBN 981-238-312-3. OCLC 228115554. Liebeck, Martin W.; Saxl, Jan, eds. (1992). Groups, combinatorics & geometry : Durham, 1990. Cambridge England New York: Cambridge University Press. ISBN 978-0-521-40685-7. OCLC 839544039. Liebeck, Martin W.; Praeger, Cheryl E.; Saxl, Jan (1990). "The maximal factorizations of the finite simple groups and their automorphism groups". Memoirs of the American Mathematical Society. 86 (432). American Mathematical Society (AMS). doi:10.1090/memo/0432. ISBN 9780821861554. ISSN 0065-9266. MR 1016353. Selected articles Liebeck, Martin W.; Praeger, Cheryl E.; Saxl, Jan (1988). "On the O'Nan-Scott theorem for finite primitive permutation groups". Journal of the Australian Mathematical Society, Series A. 44 (3). Cambridge University Press (CUP): 389–396. doi:10.1017/s144678870003216x. ISSN 0263-6115. == References ==
|
Wikipedia:Jan Trlifaj#0
|
Jan Trlifaj (born 30 December 1954) is a professor of Mathematics at Charles University whose research interests include Commutative algebra, Homological algebra and Representation theory. == Career and research == Jan Trlifaj studied mathematics at the Faculty of Mathematics and Physics, Charles University, from which he received MSc. in 1979, Ph.D. in 1989 under Ladislav Bican. and Prof. of Mathematics in the field Algebra and number theory in 2009. In the academic year 1994/95 he had the position as Postdoctoral Fellow of the Royal Society at Department of Mathematics at University of Manchester. In Fall 1998 he received the J.W.Fulbright Scholarship at the Department of Mathematics, University California at Irvine. During Fall 2002 and 2006 he was a visiting professor at Centre de Recerca Matemàtica, Barcelona. Since 1990, he has completed numerous short term visiting appointments and given over 100 invited lectures at conferences and seminars worldwide. Since 2017, he is Fellow of Learned Society of the Czech Republic. He served in the organizing committee of 18th International Conference on Representations of Algebras (ICRA 2018), held for 250 participants from 34 countries in August 2018 in Prague, Czech Republic. He has been elected Fellow of the American Mathematical Society (AMS) in 2020, for contributions to homological algebra and tilting theory for non finitely generated modules. He serves as Member of the Science board for Neuron prize that is awarded to best Czech scientists by Neuron Endowment Fund. == Selected publications == === Papers === 1994: "Every *-module is finitely generated", Journal of Algebra, 169 (2): 392–398, doi:10.1006/jabr.1994.1291 1996: Trlifaj, Jan (1996), "Whitehead test modules", Transactions of the American Mathematical Society, 348 (4): 1521–1554, doi:10.1090/S0002-9947-96-01494-8 2001: Eklof, Paul C.; Trlifaj, Jan (2001), "How to make Ext vanish", Bulletin of the London Mathematical Society, 33 (1): 41–51, doi:10.1112/blms/33.1.41, S2CID 11541149 (with Paul C. Eklof), Shelah, Saharon; Trlifaj, Jan (2001), "Spectra of the Γ-invariant of uniform modules", Journal of Pure and Applied Algebra, 162 (2–3): 367–379, doi:10.1016/S0022-4049(00)00118-3 (with Saharon Shelah) 2007: Šťovíček, Jan; Trlifaj, Jan (2007), "All tilting modules are of countable type", Bulletin of the London Mathematical Society, 39 (1): 121–132, doi:10.1112/blms/bdl019 (with Jan Šťovíček) 2012: Herbera, Dolors; Trlifaj, Jan (2012), "Almost free modules and Mittag-Leffler conditions", Advances in Mathematics, 229 (6): 3436–3467, arXiv:0910.4277, doi:10.1016/j.aim.2012.02.013 (with Dolors Herbera), Estrada, Sergio; Guil Asensio, Pedro A.; Prest, Mike; Trlifaj, Jan (2012), "Model category structures arising from Drinfeld vector bundles" (PDF), Advances in Mathematics, 231 (3–4): 1417–1438, doi:10.1016/j.aim.2012.06.011 (with Sergio Estrada, Pedro A. Guil Asensio, and Mike Prest) 2014: Angeleri Hügel, Lidia; Pospíšil, David; Šťovíček, Jan; Trlifaj, Jan (2014), "Tilting, cotilting, and spectra of commutative noetherian rings", Transactions of the American Mathematical Society, 366 (7): 3487–3517, arXiv:1203.0907, doi:10.1090/S0002-9947-2014-05904-7 (with Lidia Angeleri Hügel, David Pospíšil, and Jan Šťovíček) 2016: Slávik, Alexander; Trlifaj, Jan (2016), "Very flat, locally very flat, and contraadjusted modules", Journal of Pure and Applied Algebra, 220 (12): 3910–3926, arXiv:1601.00783, doi:10.1016/j.jpaa.2016.05.020, S2CID 119176440 (with Alexander Slávik) === Books === 2006, 2012: Approximations and Endomorphism Algebras of Modules, de Gruyter Expositions in Mathematics 41, Vol. 1 - Approximations, Vol. 2 - Predictions, W. de Gruyter Berlin - Boston, xxviii + 972 pp. (with Rüdiger Göbel) == Awards and distinctions == Prize of the Dean of MFF for the best monograph 2006 MFF UK Silver medal at the Sexagennial anniversary Fellow of the American Mathematical Society, 2020 == References == == External links == Jan Trlifaj at the Mathematics Genealogy Project Personal web page [[Category:21st-century Czech mathematicians]]
|
Wikipedia:Jan Śleszyński#0
|
Ivan Vladislavovich Sleshinsky or Jan Śleszyński (Russian: Иван Владиславович Слешинский) (23 July 1854 – 9 March 1931) was a Polish-Russian mathematician. He was born in Lysianka, Russian Empire to Polish parents. == Life == Śleszyński's main work was on continued fractions, least squares and axiomatic proof theory based on mathematical logic. He and Alfred Pringsheim, working separately, proved what is now called the Śleszyński–Pringsheim theorem. His most important publications include: "Teoria dowodu" ("The theory of proof") in two volumes (1925, 1929), and "Teoria wyznaczników" ("The theory of determinants") (1926). He is buried at Rakowicki Cemetery. == See also == History of philosophy in Poland List of Poles == References == == External links == O'Connor, John J.; Robertson, Edmund F., "Jan Śleszyński", MacTutor History of Mathematics Archive, University of St Andrews
|
Wikipedia:Jan Šindel#0
|
Jan Šindel (1370s – between 1455 and 1457), also known as Jan Ondřejův (Latin: Iohannes Andreae dictus Schindel or Joannes de Praga), was a Czech medieval scientist and Catholic priest. He was a professor at Charles University in Prague and became the rector of the university in 1410. He lectured on mathematics and astronomy and was also a personal astrologer and physician of kings Wenceslaus IV of Bohemia and his brother Holy Roman Emperor Sigismund. == Life == Jan Šindel was born in Hradec Králové probably in the 1370s. As a young man he came to Prague to study at Charles University. In 1395 or 1399, he became the Master of Arts at Prague University. In 1406, he worked at the parish school of the St. Nicolas Church in Malá Strana in Prague. Later he worked as a teacher of mathematics in Vienna, where he also studied medicine. Then he came back to Prague and became the professor of astronomy at Charles University, where he became Doctor of Medicine and rector of the university in 1410. At the beginning he was a supporter of John Hus but later he stayed Catholic. He avoided religious disputes and preferred science. In 1418 he became a canon of Prague St. Vitus Chapter. Because of the Hussite Wars he had to leave Prague and came to Olomouc. In 1423–1436 he worked in Nuremberg as a physician. In 1432, he became the personal physician of the Emperor Sigismund. In 1441 he became the dean of the Vyšehrad Chapter in Prague. He had a good relationship with Enea Silvio Bartolomeo Piccolomini (later Pope Pius II), their correspondence from the years 1445–1447 has been preserved. He died probably between 1455 and 1457 in Prague. == Legacy == Šindel's astronomical tables and maps were allegedly still used by Tycho Brahe. He had a special liking for astronomical devices. Based on his suggestion and calculations, Mikuláš of Kadaň constructed the Prague Orloj clock in 1410. The Šindel sequences in mathematics are named from the appearance of one of these sequences in this clock. In 1982, an asteroid (3847 Šindel) was named after him. == References == Šolcová, Alena (2009). "Jan Šindel – pravděpodobný autor matematického modelu pražského orloje". Pokroky Matematiky, Fyziky a Astronomie (in Czech). 54 (4): 307–317.
|
Wikipedia:Jan-Erik Roos#0
|
Jan-Erik Ingvar Roos (16 October 1935 – 15 December 2017) was a Swedish mathematician whose research interests were in abelian category theory, homological algebra, and related areas. He was born in Halmstad, in the province of Halland on the Swedish west coast. Roos enrolled at Lund University in 1954, and started studying mathematics with Lars Gårding in 1957. Under Gårding's direction he wrote a thesis on ordinary differential equation, and graduated in 1958 with a licentiate degree. Later that year he went to Paris on a doctoral scholarship; there, he gravitated towards the mathematical environment at the Institut Henri Poincaré, and the various seminars held there. After a while, he started attending Alexander Grothendieck's seminar at the Institut des hautes études scientifiques in Bures-sur-Yvette, where he became interested in abstract algebra and algebraic geometry. In 1967 he was invited by Saunders Mac Lane to visit the University of Chicago for three months; Mac Lane was impressed by Roos and later wrote a very positive letter of recommendation for him. Upon his return to Sweden, Roos was appointed Professor of Mathematics at Stockholm University in 1970, and started building a strong algebra school. He was elected to the Royal Swedish Academy of Sciences in 1980 and was its President from 1980 to 1982. While serving on the Academy, he was on the committees deciding the Rolf Schock Prizes in Mathematics and the Crafoord Prize in Astronomy and Mathematics. Roos made important contributions to homological algebra, and did extensive computer-assisted studies of Hilbert–Poincaré series and their rationality. A special issue of the journal Homology, Homotopy and Applications ("The Roos Festschrift volume") was published in 2002, on the occasion of his 65th birthday. He died on 15 December 2017 at his home in Uppsala and is buried at the Uppsala old cemetery. == Publications == Roos, Jan-Erik (1961). "Sur les foncteurs dérivés de lim ← {\displaystyle \varprojlim } . Applications". Comptes rendus de l'Académie des Sciences. 252: 3702–3704. MR 0132091. Roos, Jan-Erik (1993). "Commutative non-Koszul algebras having a linear resolution of arbitrarily high order. Applications to torsion in loop space homology". Comptes rendus de l'Académie des Sciences. 316 (11): 1123–1128. MR 1221635. Löfwall, Clas; Roos, Jan-Erik (1997). "A Nonnilpotent 1-2-Presented Graded Hopf Algebra Whose Hilbert Series Converges in the Unit Circle". Advances in Mathematics. 130 (2): 161–200. doi:10.1006/aima.1997.1667. MR 1472316. Roos, Jan-Erik; Sturmfels, Bernd (1998). "A toric ring with irrational Poincaré-Betti series". Comptes rendus de l'Académie des Sciences. 326 (2): 141–146. Bibcode:1998CRASM.326..141R. doi:10.1016/S0764-4442(97)89459-1. MR 1646972. Roos, Jan-Erik (2006). "Derived functors of inverse limits revisited". Journal of the London Mathematical Society. 73 (1): 65–83. doi:10.1112/S0024610705022416. MR 2197371. S2CID 122666355. Roos, Jan-Erik (2008). "The homotopy Lie algebra of a complex hyperplane arrangement is not necessarily finitely presented". Experimental Mathematics. 17 (2): 129–143. arXiv:math/0610126. doi:10.1080/10586458.2008.10129030. MR 2433880. S2CID 7626968. Roos, Jan-Erik (2010). "Three-dimensional manifolds, skew-Gorenstein rings and their cohomology". Journal of Commutative Algebra. 2 (4): 473–499. arXiv:1005.2919. doi:10.1216/JCA-2010-2-4-473. MR 2753719. == References ==
|
Wikipedia:Jane Kister#0
|
Jane Elizabeth Kister (born and also published as Jane Bridge, 18 October 1944 – 1 December 2019) was a British and American mathematical logician and mathematics editor who served for many years as an editor of Mathematical Reviews. == Early life and education == Jane Bridge was originally from Weybridge, England, where she was born on 18 October 1944; her father was a lawyer and later a judge. Her family moved to London when she was four, and she studied at St Paul's Girls' School in London. She matriculated at Somerville College, Oxford in 1963, but her studies were interrupted by a diagnosis of lupus; she resumed reading mathematics there in 1964, tutored by Anne Cobbe. She earned a first, won a Junior Mathematical Prize, and continued at Oxford for graduate study. She was given the Mary Somerville Research Fellowship in 1969, and completed her doctorate (D.Phil.) at Oxford in 1972. Her dissertation, Some Problems in Mathematical Logic: Systems of Ordinal Functions and Ordinal Notations, was supervised by Robin Gandy. She then became a tutorial fellow in mathematics at Somerville College, taking Anne Cobbe's position after Cobbe's retirement, and a member of the Mathematical Institute, University of Oxford, working among others there with Dana Scott. == Marriage and later life == In 1977, mathematician James Kister from the University of Michigan visited Oxford on sabbatical; they married in 1978 and she returned with him to the US, giving up her position at Oxford and in 1992 taking US citizenship. She obtained a visiting professorship at the Massachusetts Institute of Technology, and then in 1979 began working at Mathematical Reviews, where she would remain for the rest of her career. She became associate executive editor in 1984, and executive editor in 1998, the first woman to hold that position. When Mathematical Reviews shifted from being a paper review journal to an online electronic database, MathSciNet, in 1996, Kister was heavily involved in this advance. She also held an adjunct professorship at the University of Michigan. She retired in 2004, and died of a heart attack on 1 December 2019. == Books == As Jane Bridge, she was the author of the book Beginning Model Theory: The Completeness Theorem and Some Consequences (Clarendon Press, 1977), the first volume in the Oxford Logic Guides book series. She also co-edited the Ω-Bibliography of Mathematical Logic, Volume VI: Proof Theory, Constructive Mathematics (Perspectives in Mathematical Logic, Springer, 1987). == References ==
|
Wikipedia:Jane Purcell Coffee#0
|
Jane C. Purcell Coffee (1944–2022) was an American mathematician, one of the first women to earn a doctorate in mathematics at the University of Pennsylvania, and the founder of the Teacher Education Honors Academy at the College of Staten Island. == Early life and education == Coffee was the daughter of James Purcell, a civil engineer and Democratic Party politician, who died when she was young. She was born in Meriden, Connecticut in 1944, and became the valedictorian of O.H. Platt High School in Meriden. She attended Smith College on a scholarship, where mathematics professor Neal McCoy became a faculty mentor. There, she met her future husband, legal scholar John C. Coffee Jr., a student at Amherst College. She graduated from Smith in 1966. Next, she went to the University of Pennsylvania for graduate study in mathematics, while John Coffee studied law at Yale University. She persisted as "one of the first women in her PhD program" despite facing discriminatory practices such as segregating her with the mathematicians' wives at regular gatherings where the male mathematicians in the department would discuss their research. She completed her Ph.D. in 1970, with a thesis on abstract algebra, A Condition for a Filtered Ring to be Isomorphic to its Associated Graded Ring, supervised by Murray Gerstenhaber. == Career and later life == In order to avoid hiring discrimination, Coffee applied to faculty positions using only her first initial, "J.". This led to a job offer at Richmond College, which later became the College of Staten Island, and she began working there in 1970. During this time, she lived with her husband in Maplewood, New Jersey, commuting to their jobs in Staten Island and in New York City, respectively. Their daughter, Megan Coffee (now a medical researcher at Columbia University) was born in 1976. In the late 1970s, Coffee took a new faculty position, at the United States Naval Academy in Annapolis, Maryland, at about the same time as her husband became a professor at Georgetown University in Washington, DC. As child care, she sat her daughter at the back of her classroom at the academy. After this, Coffee returned to the College of Staten Island, as chair of mathematics, and her husband moved to Columbia University. An incident from this time spurred her creation of the college's Teacher Education Honors Academy: she met a woman on a train who freely confessed her innumeracy, only to discover later that the same woman was a teacher at her daughter's elementary school. The academy aimed at improving that situation by preparing college students for a career as a secondary school STEM educator. She died on September 23, 2022. == References == == External links ==
|
Wikipedia:Janet McDonald (mathematician)#0
|
Janet McDonald (1905–2006) was an American mathematician who specialized in geometry, specifically the concept of Conjugate Nets. She taught at Vassar College for 27 years and was named professor emerita in 1971. == Life and work == McDonald (sometimes spelled MacDonald) was born in Wesson, Mississippi, on September 3, 1905, and was the first child of Joseph McDonald and Bessie Walden McDonald. She earned her bachelor's degree from Belhaven College for Young Ladies in Jackson in 1925, and then she taught for three years in secondary schools in nearby Jefferson Davis County. She completed her M.A. degree in mathematics from Tulane University in 1929 and joined the faculty of Mississippi Synodical College (1929-1932) to head the math department. In 1932, she was named department head and registrar at Hinds Junior College in Raymond, Mississippi (1932-1941). With the start of World War II, McDonald enrolled at University of Chicago to pursue her Ph.D. but after two years of study, she took on a teaching role there. She completed her doctorate in 1943 (showing her name as Janet MacDonald) with her dissertation titled Conjugate nets in asymptotic parameters. She was immediately hired by Vassar College in New York, first as an instructor and moving to professorships, chair and then professor emerita (1971). She particularly enjoyed teaching geometry and encouraged students to pursue advanced degrees in math. She remained there in a teaching capacity for 27 years. Throughout her life, she enjoyed studying and traveling abroad, "spending much of her leisure in England, Scotland (home of her paternal grandfather), France, Greece, and Spain. Her extended studies took her to the University of Rome and Indiana University." For example, in 1951, she spent the summer in her native Mississippi studying. She spent most of her time doing work in mathematics on projective differential geometry, especially conjugate nets, and studying Italian in preparation for her leave of absence second semester next year. At that time, she went to study projective differential geometry and algebraic geometry at the University of Rome. She chose Rome because Professors Enrico Bompina and Francesco Severi, leaders in her field of study, were lecturing there. On her retirement in 1971, she returned to Jackson, Mississippi and taught some classes at her alma mater, Belhaven College. McDonald died October 29, 2006, in Madison, Mississippi, after a brief illness at 101 years of age. == References ==
|
Wikipedia:Janet basis#0
|
In mathematics, a Janet basis is a normal form for systems of linear homogeneous partial differential equations (PDEs) that removes the inherent arbitrariness of any such system. It was introduced in 1920 by Maurice Janet. It was first called the Janet basis by Fritz Schwarz in 1998. The left hand sides of such systems of equations may be considered as differential polynomials of a ring, and Janet's normal form as a special basis of the ideal that they generate. By abuse of language, this terminology will be applied both to the original system and the ideal of differential polynomials generated by the left hand sides. A Janet basis is the predecessor of a Gröbner basis introduced by Bruno Buchberger for polynomial ideals. In order to generate a Janet basis for any given system of linear PDEs a ranking of its derivatives must be provided; then the corresponding Janet basis is unique. If a system of linear PDEs is given in terms of a Janet basis its differential dimension may easily be determined; it is a measure for the degree of indeterminacy of its general solution. In order to generate a Loewy decomposition of a system of linear PDEs its Janet basis must be determined first. == Generating a Janet basis == Any system of linear homogeneous PDEs is highly non-unique, e.g. an arbitrary linear combination of its elements may be added to the system without changing its solution set. A priori it is not known whether it has any nontrivial solutions. More generally, the degree of arbitrariness of its general solution is not known, i.e. how many undetermined constants or functions it may contain. These questions were the starting point of Janet's work; he considered systems of linear PDEs in any number of dependent and independent variables and generated a normal form for them. Here mainly linear PDEs in the plane with the coordinates x {\displaystyle x} and y {\displaystyle y} will be considered; the number of unknown functions is one or two. Most results described here may be generalized in an obvious way to any number of variables or functions. In order to generate a unique representation for a given system of linear PDEs, at first a ranking of its derivatives must be defined. Definition: A ranking of derivatives is a total ordering such that for any two derivatives δ {\displaystyle \delta } , δ 1 {\displaystyle \delta _{1}} and δ 2 {\displaystyle \delta _{2}} , and any derivation operator θ {\displaystyle \theta } the relations δ ≤ θ δ {\displaystyle \delta \leq \theta \delta } and δ 1 ≤ δ 2 → δ δ 1 ≤ δ δ 2 {\displaystyle \delta _{1}\leq \delta _{2}\rightarrow \delta \delta _{1}\leq \delta \delta _{2}} are valid. A derivative δ 2 {\displaystyle \delta _{2}} is called higher than δ 1 {\displaystyle \delta _{1}} if δ 2 > δ 1 {\displaystyle \delta _{2}>\delta _{1}} . The highest derivative in an equation is called its leading derivative. For the derivatives up to order two of a single function z {\displaystyle z} depending on x {\displaystyle x} and y {\displaystyle y} with x > y {\displaystyle x>y} two possible order are the LEX order z x x > z x y > z x > z y y > z y > z {\displaystyle z_{xx}>z_{xy}>z_{x}>z_{yy}>z_{y}>z} and the GRLEX order z x x > z x y > z y y > z x > z y > z {\displaystyle z_{xx}>z_{xy}>z_{yy}>z_{x}>z_{y}>z} . Here the usual notation ∂ x z = z x , ∂ y z = z y , … {\displaystyle \partial _{x}z=z_{x},\partial _{y}z=z_{y},\ldots } is used. If the number of functions is higher than one, these orderings have to be generalized appropriately, e.g. the orderings T O P {\displaystyle TOP} or P O T {\displaystyle POT} may be applied. The first basic operation to be applied in generating a Janet basis is the reduction of an equation e 1 {\displaystyle e_{1}} w.r.t. another one e 2 {\displaystyle e_{2}} . In colloquial terms this means the following: Whenever a derivative of e 1 {\displaystyle e_{1}} may be obtained from the leading derivative of e 2 {\displaystyle e_{2}} by suitable differentiation, this differentiation is performed and the result is subtracted from e 1 {\displaystyle e_{1}} . Reduction w.r.t. a system of PDEs means reduction w.r.t. all elements of the system. A system of linear PDEs is called autoreduced if all possible reductions have been performed. The second basic operation for generating a Janet basis is the inclusion of integrability conditions. They are obtained as follows: If two equations e 1 {\displaystyle e_{1}} and e 2 {\displaystyle e_{2}} are such that by suitable differentiations two new equations may be obtained with like leading derivatives, by cross-multiplication with its leading coefficients and subtraction of the resulting equations a new equation is obtained, it is called an integrability condition. If by reduction w.r.t. the remaining equations of the system it does not vanish it is included as a new equation to the system. It may be shown that repeating these operations always terminates after a finite number of steps with a unique answer which is called the Janet basis for the input system. Janet has organized them in terms of the following algorithm. Janet's algorithm: Given a system of linear differential polynomials S ≡ { e 1 , e 2 , … } {\displaystyle S\equiv \{e_{1},e_{2},\ldots \}} , the Janet basis corresponding to S {\displaystyle S} is returned. S1: (Autoreduction) Assign S := Autoreduce ( S ) {\displaystyle S:=\operatorname {Autoreduce} (S)} S2: (Completion) Assign S := CompleteSystem ( S ) {\displaystyle S:=\operatorname {CompleteSystem} (S)} S3: (Integrability conditions) Find all pairs of leading terms v i {\displaystyle v_{i}} of e i {\displaystyle e_{i}} and v j {\displaystyle v_{j}} of e j {\displaystyle e_{j}} such that differentiation w.r.t. a nonmultiplier x i k {\displaystyle x_{i_{k}}} and multipliers x j 1 , … , x j l {\displaystyle x_{j_{1}},\ldots ,x_{j_{l}}} leads to ∂ v i ∂ x i k = ∂ p 1 + ⋯ + p l v j ∂ x j 1 p 1 ⋯ ∂ x j l p l {\displaystyle {\frac {\partial v_{i}}{\partial x_{i_{k}}}}={\frac {\partial ^{p_{1}+\cdots +p_{l}}v_{j}}{\partial x_{j_{1}}^{p_{1}}\cdots \partial x_{j_{l}}^{p_{l}}}}} and determine the integrability conditions c i , j = Lcoef ( e j ) ⋅ ∂ e i ∂ x i k − Lcoef ( e i ) ⋅ ∂ p 1 + ⋯ + p l e j ∂ x j 1 p 1 ⋯ ∂ x j l p l {\displaystyle c_{i,j}=\operatorname {Lcoef} (e_{j})\cdot {\frac {\partial e_{i}}{\partial x_{i_{k}}}}-\operatorname {Lcoef} (e_{i})\cdot {\frac {\partial ^{p_{1}+\cdots +p_{l}}e_{j}}{\partial x_{j_{1}}^{p_{1}}\cdots \partial x_{j_{l}}^{p_{l}}}}} S4: (Reduction of integrability conditions). For all c i , j {\displaystyle c_{i,j}} assign c i , j := Reduce ( c i , j , S ) {\displaystyle c_{i,j}:=\operatorname {Reduce} (c_{i,j},S)} S5: (Termination?) If all c i , j {\displaystyle c_{i,j}} are zero return S {\displaystyle S} , otherwise make the assignment S := S ∪ { c i , j ∣ c i , j ≠ 0 } {\displaystyle S:=S\cup \{c_{i,j}\mid c_{i,j}\neq 0\}} , reorder S {\displaystyle S} properly and goto S1 Here A u t o r e d u c e {\displaystyle Autoreduce} is a subalgorithm that returns its argument with all possible reductions performed, C o m p l e t i o n {\displaystyle Completion} adds certain equations to the system in order to facilitate determining the integrability conditions. To this end the variables are divides into multipliers and non-multipliers; details may be found in the above references. Upon successful termination a Janet basis for the input system will be returned. Example 1: Let the system { e 1 ≡ z x y − x 2 y 2 z x − x − y y 2 z = 0 , e 2 ≡ z x + 1 x z y + x z = 0 } {\displaystyle \left\{e_{1}\equiv z_{xy}-{\frac {x^{2}}{y^{2}}}z_{x}-{\frac {x-y}{y^{2}}}z=0,e_{2}\equiv z_{x}+{\frac {1}{x}}z_{y}+xz=0\right\}} be given with ordering GRLEX and x > y {\displaystyle x>y} . Step S1 returns the autoreduced system { e 3 ≡ z y y + 1 y 2 ( x y 3 − x 2 − y ) z y − 1 y ( x 3 − x + y ) z = 0 , e 2 = z x + 1 y z y + x z = 0 } . {\displaystyle \left\{e_{3}\equiv z_{yy}+{\frac {1}{y^{2}}}(xy^{3}-x^{2}-y)z_{y}-{\frac {1}{y}}(x^{3}-x+y)z=0,e_{2}=z_{x}+{\frac {1}{y}}z_{y}+xz=0\right\}.} Steps S3 and S4 generate the integrability condition c 3 , 2 ≡ ∂ e 3 ∂ x − ∂ 2 e 2 ∂ y 2 {\displaystyle c_{3,2}\equiv {\frac {\partial e_{3}}{\partial x}}-{\frac {\partial ^{2}e_{2}}{\partial y^{2}}}} and reduces it to z = 0 {\displaystyle z=0} , i.e. the Janet basis for the originally given system is { z = 0 } {\displaystyle \{z=0\}} with the trivial solution z = 0 {\displaystyle z=0} . The next example involves two unknown functions w {\displaystyle w} and z {\displaystyle z} , both depending on x {\displaystyle x} and y {\displaystyle y} . Example 2: Consider the system { f 1 ≡ w x x − 2 z x y − 1 2 x w x + 1 2 x 2 w = 0 , f 2 ≡ w x y − 1 2 z y y − 1 2 x w y − 6 x 2 z x , f 3 ≡ w y y + 4 x 2 w x − 8 x 2 z y − 8 x w = 0 , f 4 ≡ z x x + 1 2 x z x = 0 } {\displaystyle {\begin{aligned}{\Big \{}&f_{1}\equiv w_{xx}-2z_{xy}-{\frac {1}{2x}}w_{x}+{\frac {1}{2x^{2}}}w=0,f_{2}\equiv w_{xy}-{\frac {1}{2}}z_{yy}-{\frac {1}{2x}}w_{y}-6x^{2}z_{x},\\[5pt]&f_{3}\equiv w_{yy}+4x^{2}w_{x}-8x^{2}z_{y}-8xw=0,f_{4}\equiv z_{xx}+{\frac {1}{2x}}z_{x}=0{\Big \}}\end{aligned}}} in GRLEX, w > z , x > y {\displaystyle w>z,x>y} ordering. The system is already autoreduced, i.e. step S1 returns it unchanged. Step S3 generates the two integrability conditions c 1 , 2 ≡ ∂ f 1 ∂ y − ∂ f 2 ∂ x and c 2 , 3 ≡ ∂ f 2 ∂ y − ∂ f 3 ∂ x . {\displaystyle c_{1,2}\equiv {\frac {\partial f_{1}}{\partial y}}-{\frac {\partial f_{2}}{\partial x}}{\text{ and }}c_{2,3}\equiv {\frac {\partial f_{2}}{\partial y}}-{\frac {\partial f_{3}}{\partial x}}.} Upon reduction in step S4 they are c 1 , 2 = z x y y − 6 x z x = 0 , c 2 , 3 = z y y y + 3 x 2 z x y − 24 x z y − 12 w = 0. {\displaystyle c_{1,2}=z_{xyy}-6xz_{x}=0,c_{2,3}=z_{yyy}+3x^{2}z_{xy}-24xz_{y}-12w=0.} In step S5 they are included into the system and the algorithms starts again with step S1 with the extended system. After a few more iterations finally the Janet basis { z y + 1 2 x w = 0 , z x = 0 , w y = 0 , w x − 1 x w = 0 } {\displaystyle \left\{z_{y}+{\frac {1}{2x}}w=0,z_{x}=0,w_{y}=0,w_{x}-{\frac {1}{x}}w=0\right\}} is obtained. It yields the general solution z = C 1 − C 2 x , w = 2 C 2 y {\displaystyle z=C_{1}-C_{2}x,w=2C_{2}y} with two undetermined constants C 1 {\displaystyle C_{1}} and C 2 {\displaystyle C_{2}} . == Application of Janet bases == The most important application of a Janet basis is its use for deciding the degree of indeterminacy of a system of linear homogeneous partial differential equations. The answer in the above Example 1 is that the system under consideration allows only the trivial solution. In the second Example 2 a two-dimensional solution space is obtained. In general, the answer may be more involved, there may be infinitely many free constants in the general solution; they may be obtained from the Loewy decomposition of the respective Janet basis. Furthermore, the Janet basis of a module allows to read off a Janet basis for the syzygy module. Janet's algorithm has been implemented in Maple. == External links == www.alltypes.de – Implementation of Janet's basis == References ==
|
Wikipedia:Janice B. Walker#0
|
Janice B. Walker is an American mathematician who taught and served as an administrator at Xavier University in Cincinnati and Assistant to the President and Chief Diversity and Inclusion Officer there. == Biography == Janice Anita Brown Walker was born in Meridian, Mississippi, and raised in Florida. She earned her BS in mathematics at Tuskegee University and her MA and Ph.D. in mathematics at the University of Michigan - Ann Arbor (1982). The title of her dissertation was Closure and Expansions in Series of Complex Exponentials and her advisor was Douglas Grassel Dickson. Before earning her Ph.D., Walker held several University of Michigan positions in Ann Arbor. In 1982, Walker moved to Cincinnati, Ohio to become an assistant professor at Xavier University. In 1986, she was named associate professor, and beginning in 1992, she served as chair of the Mathematics and Computer Science department for seven years. In 1999, she became dean of the College of Arts and Sciences and served for 17 years. Walker was Xavier's vice president for Institutional Diversity and Inclusion for five years after which she rejoined the mathematics department before retiring from the university. In 2019, Walker contributed to Xavier's purchase of ten works of art for an exhibit titled, “Art at the X: Celebrating Women,” which was staged along with the university's 50th anniversary of the admission of women as traditional day students. The ten pieces were later added to the university's permanent art collection. Walker retired from Xavier in 2022. She serves as a board member of Breakthrough Cincinnati and other community organizations. == Publications == Walker, Janice B. "A note on neighborhoods of analytic functions having positive real part." International Journal of Mathematics and Mathematical Sciences 13 (1990): 425-429. Walker, Janice Anita Brown. Closure and Expansions in Series of Complex Exponentials. University of Michigan, 1982. == References ==
|
Wikipedia:Janvière Ndirahisha#0
|
Janvière Ndirahisha (born 1966) is a Burundian academic and politician. From 2015 to 2020 she was a Minister of Education for Burundi. She is President of the National Women's Forum (FNF). == Life == Janvière Ndirahisha was born in 1966 in Burundi. She was educated at the University of Burundi before undertaking a PhD at the University of Antwerp. Her thesis on Grothiendiek representations was supervised by Fred Van Oystaeyen. Ndirahisha was elected President of Burundi's new National Women's Forum in 2013. In August 2015 Ndirahisha was announced as Minister of Education, Higher Education and Scientific Research in Pierre Nkurunziza's' cabinet. By 2019 she had moved to be Minister of Education, Technical & Vocational Training, with Gaspard Banyankimbona as Minister of Education, Higher Education and Scientific Research. In 2017 Ndirahisha announced that headmasters of schools which had achieved under 30% in national tests would be dismissed, and her ministry closed several failing schools. In 2018 her ministry banned pregnant girls from attending school, a move which was criticised by equal rights campaigners in the country. Nkurunziza's successor Évariste Ndayishimiye removed Ndirahisha from the cabinet in 2020. == References ==
|
Wikipedia:Japanese mathematics#0
|
Japanese mathematics (和算, wasan) denotes a distinct kind of mathematics which was developed in Japan during the Edo period (1603–1867). The term wasan, from wa ("Japanese") and san ("calculation"), was coined in the 1870s and employed to distinguish native Japanese mathematical theory from Western mathematics (洋算 yōsan). In the history of mathematics, the development of wasan falls outside the Western realm. At the beginning of the Meiji period (1868–1912), Japan and its people opened themselves to the West. Japanese scholars adopted Western mathematical technique, and this led to a decline of interest in the ideas used in wasan. == History == === Pre-Edo period (552-1600) === Records of mathematics in the early periods of Japanese history are nearly nonexistent. Though it was at this time that a large influx of knowledge from China reached Japan, including that of reading and writing, little sources exist of usage of mathematics within Japan. However, it is suggested that this period saw the use of an exponential numbering system following the law of a m ∗ a n = a m + n {\displaystyle a^{m}*a^{n}=a^{m+n}} . === Edo period === The Japanese mathematical schema evolved during a period when Japan's people were isolated from European influences, but instead borrowed from ancient mathematical texts written in China, including those from the Yuan dynasty and earlier. The Japanese mathematicians Yoshida Shichibei Kōyū, Imamura Chishō, and Takahara Kisshu are among the earliest known Japanese mathematicians. They came to be known to their contemporaries as "the Three Arithmeticians". Yoshida was the author of the oldest extant Japanese mathematical text, the 1627 work called Jinkōki. The work dealt with the subject of soroban arithmetic, including square and cube root operations. Yoshida's book significantly inspired a new generation of mathematicians, and redefined the Japanese perception of educational enlightenment, which was defined in the Seventeen Article Constitution as "the product of earnest meditation". Seki Takakazu founded enri (円理: circle principles), a mathematical system with the same purpose as calculus at a similar time to calculus's development in Europe. However Seki's investigations did not proceed from the same foundations as those used in Newton's studies in Europe. Mathematicians like Takebe Katahiro played an important role in developing Enri (" circle principle"), an analog to the Western calculus. He obtained power series expansion of ( arcsin ( x ) ) 2 {\displaystyle (\arcsin(x))^{2}} in 1722, 15 years earlier than Euler. He used Richardson extrapolation in 1695, about 200 years earlier than Richardson. He also computed 41 digits of π, based on polygon approximation and Richardson extrapolation. == Select mathematicians == The following list encompasses mathematicians whose work was derived from wasan. Yoshida Mitsuyoshi (1598–1672) Seki Takakazu (1642–1708) Takebe Kenkō (1664–1739) Matsunaga Ryohitsu (fl. 1718-1749) Kurushima Kinai (d. 1757) Arima Raido (1714–1783) Fujita Sadasuke (1734-1807) Ajima Naonobu (1739–1783) Aida Yasuaki (1747–1817) Sakabe Kōhan (1759–1824) Fujita Kagen (1765–1821) Hasegawa Ken (c. 1783-1838) Wada Nei (1787–1840) Shiraishi Chochu (1796–1862) Koide Shuke (1797–1865) Omura Isshu (1824–1871) == See also == Japanese theorem for cyclic polygons Japanese theorem for cyclic quadrilaterals Hungarian mathematics Sangaku, the custom of presenting mathematical problems, carved in wood tablets, to the public in Shinto shrines Soroban, a Japanese abacus Category:Japanese mathematicians == Notes == == References == Campbell, Douglas M. and John C. Iggins. (1984). Mathematics: People, Problems, Results. Belmont, California: Warsworth International. ISBN 9780534032005; ISBN 9780534032012; ISBN 9780534028794; OCLC 300429874 Endō Toshisada (1896). History of mathematics in Japan (日本數學史, Dai Nihon sūgakush). Tōkyō: _____. OCLC 122770600 Fukagawa, Hidetoshi, and Dan Pedoe. (1989). Japanese temple geometry problems = Sangaku. Winnipeg: Charles Babbage. ISBN 9780919611214; OCLC 474564475 __________ and Dan Pedoe. (1991) How to resolve Japanese temple geometry problems? (日本の幾何ー何題解けますか?, Nihon no kika nan dai tokemasu ka) Tōkyō. ISBN 9784627015302; OCLC 47500620 __________ and Tony Rothman. (2008). Sacred Mathematics: Japanese Temple Geometry. Princeton: Princeton University Press. ISBN 069112745X; OCLC 181142099 Horiuchi, Annick. (1994). Les Mathematiques Japonaises a L'Epoque d'Edo (1600–1868): Une Etude des Travaux de Seki Takakazu (?-1708) et de Takebe Katahiro (1664–1739). Paris: Librairie Philosophique J. Vrin. ISBN 9782711612130; OCLC 318334322 __________. (1998). "Les mathématiques peuvent-elles n'être que pur divertissement? Une analyse des tablettes votives de mathématiques à l'époque d'Edo." Extrême-Orient, Extrême-Occident, volume 20, pp. 135–156. Kobayashi, Tatsuhiko. (2002) "What kind of mathematics and terminology was transmitted into 18th-century Japan from China?", Historia Scientiarum, Vol.12, No.1. Kobayashi, Tatsuhiko. Trigonometry and Its Acceptance in the 18th-19th Centuries Japan. Ogawa, Tsukane. "A Review of the History of Japanese Mathematics". Revue d'histoire des mathématiques 7, fascicule 1 (2001), 137-155. Restivo, Sal P. (1992). Mathematics in Society and History: Sociological Inquiries. Dordrecht: Kluwer Academic Publishers. ISBN 9780792317654; OCLC 25709270 Selin, Helaine. (1997). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Dordrecht: Kluwer/Springer. ISBN 9780792340669; OCLC 186451909 David Eugene Smith and Yoshio Mikami. (1914). A History of Japanese Mathematics. Chicago: Open Court Publishing. OCLC 1515528; see online, multi-formatted, full-text book at archive.org == External links == Japan Academy, Collection of native Japanese mathematics JapanMath, Math program focused on Math Fact Fluency and Japanese originated logic games Sangaku Sansu Math, translated Tokyo Shoseki Japanese math curriculum Kümmerle, Harald. Bibliography on traditional mathematics in Japan (wasan)
|
Wikipedia:Japanese theorem for cyclic polygons#0
|
In geometry, the Japanese theorem states that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle. It was originally stated on a sangaku tablet on a temple in Yamagata prefecture, Japan, in 1880. Triangulating an arbitrary cyclic quadrilateral by its diagonals yields four overlapping triangles (each diagonal creates two triangles). The centers of the incircles of those triangles form a rectangle. Specifically, let □ABCD be an arbitrary cyclic quadrilateral and let M1, M2, M3, M4 be the incenters of the triangles △ABD, △ABC, △BCD, △ACD. Then the quadrilateral formed by M1, M2, M3, M4 is a rectangle. Proofs are given by Bogomolny and Reyes. This theorem may be extended to prove the Japanese theorem for cyclic polygons, according to which the sum of inradii of a triangulated cyclic polygon does not depend on how it is triangulated. The special case of the theorem for quadrilaterals states that the two pairs of opposite incircles of the theorem above have equal sums of radii. To prove the quadrilateral case, simply construct the parallelogram tangent to the corners of the constructed rectangle, with sides parallel to the diagonals of the quadrilateral. The construction shows that the parallelogram is a rhombus, which is equivalent to showing that the sums of the radii of the incircles tangent to each diagonal are equal. This related result comes from an earlier sangaku tablet, also from Yamagata, from 1800. The quadrilateral case immediately proves the general case, as any two triangulations of an arbitrary cyclic polygon can be connected by a sequence of flips that change one diagonal to another, replacing two incircles in a quadrilateral by the other two incircles with equal sum of radii. == See also == Carnot's theorem Japanese mathematics == References == == Further reading == Mangho Ahuja, Wataru Uegaki, Kayo Matsushita: "In Search of the Japanese Theorem". In: Missouri Journal of Mathematical Sciences, vol 18, no. 2, May 2006 (online at project Euclid) Wataru Uegaki: "Japanese Theoremの起源と歴史" (On the Origin and History of the Japanese Theorem). Departmental Bulletin Paper, Mie University Scholarly E-Collections, 2001-03-01 笹部貞市郎 (1976). "几何学辞典: 问题解法". Archive.org. Problem 587. == External links == Japanese theorem, interactive proof with animation Dynamic Geometry Sketch, Cyclic Quadrilateral Incentres Rectangle
|
Wikipedia:Japanese theorem for cyclic quadrilaterals#0
|
In geometry, the Japanese theorem states that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle. It was originally stated on a sangaku tablet on a temple in Yamagata prefecture, Japan, in 1880. Triangulating an arbitrary cyclic quadrilateral by its diagonals yields four overlapping triangles (each diagonal creates two triangles). The centers of the incircles of those triangles form a rectangle. Specifically, let □ABCD be an arbitrary cyclic quadrilateral and let M1, M2, M3, M4 be the incenters of the triangles △ABD, △ABC, △BCD, △ACD. Then the quadrilateral formed by M1, M2, M3, M4 is a rectangle. Proofs are given by Bogomolny and Reyes. This theorem may be extended to prove the Japanese theorem for cyclic polygons, according to which the sum of inradii of a triangulated cyclic polygon does not depend on how it is triangulated. The special case of the theorem for quadrilaterals states that the two pairs of opposite incircles of the theorem above have equal sums of radii. To prove the quadrilateral case, simply construct the parallelogram tangent to the corners of the constructed rectangle, with sides parallel to the diagonals of the quadrilateral. The construction shows that the parallelogram is a rhombus, which is equivalent to showing that the sums of the radii of the incircles tangent to each diagonal are equal. This related result comes from an earlier sangaku tablet, also from Yamagata, from 1800. The quadrilateral case immediately proves the general case, as any two triangulations of an arbitrary cyclic polygon can be connected by a sequence of flips that change one diagonal to another, replacing two incircles in a quadrilateral by the other two incircles with equal sum of radii. == See also == Carnot's theorem Japanese mathematics == References == == Further reading == Mangho Ahuja, Wataru Uegaki, Kayo Matsushita: "In Search of the Japanese Theorem". In: Missouri Journal of Mathematical Sciences, vol 18, no. 2, May 2006 (online at project Euclid) Wataru Uegaki: "Japanese Theoremの起源と歴史" (On the Origin and History of the Japanese Theorem). Departmental Bulletin Paper, Mie University Scholarly E-Collections, 2001-03-01 笹部貞市郎 (1976). "几何学辞典: 问题解法". Archive.org. Problem 587. == External links == Japanese theorem, interactive proof with animation Dynamic Geometry Sketch, Cyclic Quadrilateral Incentres Rectangle
|
Wikipedia:Jaqueline Mesquita#0
|
Jaqueline Godoy Mesquita (born 1985) is a Brazilian mathematician specializing in differential equations and functional differential equations. She is a professor of mathematics at the University of Brasília. == Education and career == Mesquita was born on 20 September 1985. After graduating from the University of Brasília in 2007, she earned a Ph.D. at the University of São Paulo in 2012, with the dissertation Measure functional differential equations and impulsive functional dynamic equations on time scales, jointly supervised by Marcia Cristina Anderson Braz Federson and Antonín Slavík, based in part on work as a visiting student at the Czech Academy of Sciences. After postdoctoral study at the University of São Paulo and the University of Santiago, Chile, she became a professor at the University of Brasília in 2015. == Recognition == The International Society of Differential Equations gave Mesquita their Bernd Aulbach student prize in 2012. Mesquita became an affiliate member of the Brazilian Academy of Sciences in 2018. She is also a young affiliate of The World Academy of Sciences. She was a 2019 winner of the Brazilian L'Oréal-UNESCO For Women in Science Awards. She is the current president of the Brazilian Mathematical Society. == References == == External links == Jaqueline Mesquita publications indexed by Google Scholar
|
Wikipedia:Jared Mansfield#0
|
Jared Mansfield (May 23, 1759 – February 3, 1830) was an American teacher, mathematician and surveyor. His career was shaped by two interventions by President Thomas Jefferson. In 1801 Jefferson appointed Mansfield as professor at the newly founded United States Military Academy at West Point. Again at Jefferson's appointment, Mansfield served as the Surveyor General of the United States from 1803 to 1812, charged with extending the survey of United States land in the Northwest Territory. == Early life == Mansfield was born in New Haven, Connecticut, son of a sea captain, Stephen Mansfield of New Haven and Hannah Beach of Wallingford, Connecticut. He entered Yale in 1773, but his father died suddenly near the end of his freshman year. He fell into "bad company" and was expelled from college in January of his senior year for complicity in a theft of books from the Library and "other discreditable escapades". Little is known of his life in New Haven for the next nine years, but he is said to have fought the British in the invasion of New Haven of July 5, 1779, and been taken prisoner but quickly released. Apparently reforming, he may have taught in New Haven, perhaps at the Episcopal Trinity Church on the Green schools where he is listed as a "clerk of the vestry" appointed by Rev. Bela Hubbard from 1786 to 1794, and as a vestryman from 1790 to 1794. In 1786, he became the rector of the Hopkins Grammar School in New Haven, where he remained save for a brief period teaching in Philadelphia, until 1802. Forgiven by Yale, in 1787 he was awarded the degree of Master of Arts and enrolled as graduating with his class of 1777. In 1800 he married Elizabeth Phipps of New Haven, daughter of an American naval officer. == Promotion by Jefferson == In 1801 he had printed some scientific papers titled Essays Mathematical and Physical, which were brought to Jefferson's attention by Senator Abraham Baldwin. Jefferson appointed Mansfield captain of engineers, so he might become a professor at West Point. After moving to West Point, Mansfield was appointed Surveyor General in Summer of 1803. Jefferson was dissatisfied with the performance of Rufus Putnam, whose surveys in the Congress Lands of Ohio were poorly executed. Putnam was also a Federalist. In 1801, the position had been offered to Andrew Ellicott by Jefferson, but he refused, because he was upset at slow pay for work he had done for the Federal Government. Mansfield's Essays included sections on determining longitude and latitude, which would be useful in improving precision in surveying. Jefferson made a recess appointment, which was confirmed by the Senate November 15, 1803. He was told to "survey Ohio and lands north of the Ohio River", with later extensions to Indiana Territory and Illinois Territory. Mansfield and his family moved to Marietta, Ohio (1803-1805), Ludlow Station (1805-1809) and near Cincinnati (1809-1812). Under Mansfield's direction the survey was continued down the Ohio River, with grids laid out northward from the river, thus dividing the territory into rectangular townships. Mansfield is credited with "considerable scientific ability and high standards of workmanship." He laid out baselines and Meridians astronomically, adapting principles of celestial navigation to surveying, which Ellicott and others had used to extend the Mason–Dixon line decades earlier. Among his deputies were Thomas Worthington, Lewis Cass, and Ethan Allen Brown. In 1816, Mansfield was elected a member of the American Philosophical Society in Philadelphia. Jonathan Williams, Superintendent of the U.S. Military Academy sent Mansfield a letter March 20, 1809, "...your rank in the Corps doubtless settled, and I wish you were here to take direction of the Academy." The War of 1812 in the West made surveying difficult. Mansfield returned to West Point in 1814 as professor of mathematics and natural and experimental philosophy, continuing in this position until his retirement in 1828. He never was to direct the academy. He and his wife moved back to Cincinnati, and he died February 3, 1830, while visiting New Haven. He arranged for Thomas Jefferson to sit at Monticello for the painter Thomas Sully, and the resulting full-length portrait now hangs in the USMA Museum. The city of Mansfield, Ohio, is named for Jared Mansfield. He was father of author Edward Deering Mansfield. == Notes == == References == Dexter, Franklin Bowditch, Biographical Sketches of the Graduates of Yale College: May 1745-May 1763, Volume 2 (Holt, 1896) Croswell, Frederick, “A History of Trinity Church, New Haven, Read March 8, 1868”, Papers of the New Haven Colony Historical Society, Volume I (New Haven Colony Historical Society, 1865) Dudley, Charlotte W (1998). "Jared Mansfield: United States Surveyor General". Ohio History. 85: 231–246. Archived from the original on 2014-10-29. Retrieved 2014-10-28. Stewart, Lowell O (1935). Public Land Surveys History Instructions Methods. Ames, Iowa: Collegiate Press Inc. ISBN 9780598975874. {{cite book}}: ISBN / Date incompatibility (help) Mathews, Catherine Van Courtlandt (1908). Andrew Ellicott, His Life and Letters. New York: The Grafton Press. p. 204.
|
Wikipedia:Jarkko Kari#0
|
Jarkko J. Kari is a Finnish mathematician and computer scientist, known for his contributions to the theory of Wang tiles and cellular automata. Kari is currently a professor at the Department of Mathematics, University of Turku. == Biography == Kari received his Ph.D. in 1990 from the University of Turku; his dissertation, supervised by Arto Salomaa. He married Lila Kari, a later mathematics student at Turku; they divorced, and afterwards Lila Kari became a professor of computer science at the University of Western Ontario in Canada. == Research == Wang tiles are unit squares with colored markings on each side; they may be used to tesselate the plane, but only with tiles that have matching colors on adjoining edges. The problem of determining whether a set of Wang tiles forms a valid tessellation is undecidable, and its undecidability rests on finding sets of Wang tiles that can only tesselate the plane aperiodically, in such a way that no translation of the plane is a symmetry of the tiling. The first set of aperiodic Wang tiles found, by Robert Berger, had over 20,000 different tiles in it. Kari reduced the size of this set to only 14, by finding a set of tiles that (when used to tile the plane) simulates the construction of a Beatty sequence by Mealy machines. The same approach was later shown to lead to aperiodic sets of 13 tiles, the minimum known. Kari has also shown that the Wang tiling problem remains undecidable in the hyperbolic plane, and has discovered sets of Wang tiles with additional mathematical properties. Kari has also used the Wang tiling problem as the basis of proofs that several algorithmic problems in the theory of cellular automata are undecidable. In particular, in his thesis research, he showed that it is undecidable to determine whether a given cellular automaton rule in two or more dimensions is reversible. For one-dimensional cellular automata, reversibility is known to be decidable, and Kari has provided tight bounds on the size of the neighborhood needed to simulate the reverse dynamics of reversible one-dimensional automata. == References == == External links == Jarkko Kari's personal homepage
|
Wikipedia:Jarl Waldemar Lindeberg#0
|
Jarl Waldemar Lindeberg (4 August 1876, Helsinki – 24 December 1932, Helsinki) was a Finnish mathematician known for work on the central limit theorem. == Life and work == Lindeberg was son of a teacher at the Helsinki Polytechnical Institute and at an early age showed mathematical talent and interest. The family was well off and later Jarl Waldemar would prefer to be a reader than a full professor. Lindeberg's career centred on the University of Helsinki. His early interests were in partial differential equations and the calculus of variations but from 1920 he worked in probability and statistics. In 1920 he published his first paper on the central limit theorem. His result was similar to that obtained earlier by Lyapunov whose work he did not then know. However, their approaches were quite different; Lindeberg's was based on a convolution argument while Lyapunov used the characteristic function. Two years later Lindeberg used his method to obtain a stronger result: the so-called Lindeberg condition. His work on probability led to him becoming involved in applied fields. He developed what we know as Kendall's τ and he found the first two moments of its sampling distribution. Lindeberg used line transect methods in forestry, and when in 1926 determining the necessary number of transects to obtain a sufficiently precise confidence interval, he seems to have rediscovered Student's t-distribution. The Swedish mathematician Harald Cramér met Lindeberg in 1922. He later recalled this story about Lindeberg and the beautiful farm he owned. "When he was reproached for not being sufficiently active in his scientific work, he said 'Well, I am really a farmer.' And if somebody happened to say that his farm was not properly cultivated, his answer was 'Of course my real job is to be a professor.' I was very fond of him and saw him often during the following years." Lindeberg's work was unknown to Alan Turing, who proved the central limit theorem in his dissertation in 1935. == Writing available on the web == Lindeberg, J. W. (1922). "Eine neue Herleitung des Exponentialgesetzes in der Wahrscheinlichkeitsrechnung". Mathematische Zeitschrift. 15 (1): 211–225. doi:10.1007/BF01494395. S2CID 119730242. == Commentary == Le Cam, L. (1986). "The Central Limit Theorem around 1935". Statistical Science. 1 (1): 78–91. doi:10.1214/ss/1177013818. JSTOR 2245503. Elfving, Gustav (1981). The History of Mathematics in Finland 1828–1918. Helsinki: Societas Scientarium Fennica. ISBN 951-653-098-2. == Biography == Elfving, G. (2001). "Jarl Waldemar Lindeberg". In Heyde, C. C.; Seneta, E. (eds.). Statisticians of the Centuries. New York: Springer. pp. 318–321. ISBN 0-387-95283-7. Cramér, Harald (1976). "Half a Century with Probability Theory: Some Personal Recollections". Annals of Probability. 4 (4): 509–546. doi:10.1214/aop/1176996025. == References == == External links == Photograph of Lindeberg on the Portraits of Statisticians page ISI: Milestones of the history of statistics in Finland Archived 2015-06-26 at the Wayback Machine Tore Schweder: Early Statistics in the Nordic Countries Archived 2013-10-30 at the Wayback Machine
|
Wikipedia:Jaroslav Kožešník#0
|
Jaroslav Kožešník (8 June 1907 in Kněžice – 26 June 1985 in Prague) was a Czech and Czechoslovak scientist, mathematician, an expert in mechanics and automation (cybernetics), chairman of the Czechoslovak Academy of Sciences (1969–1970, 1970–1977, 1977–1980), a Communist Party functionary in Communist Czechoslovakia and a member of the parliament during the Normalization period, recipient of several state awards, editor-in-chief of the Kybernetika journal. == Books == 1983: Teorie podobnosti a modelování 1979: Kmitání mechanických soustav 1965: Základy teorie přístrojů (Principles of the Theory of Machines) 1960: Dynamika strojů (Dynamics of Machines), translated into English, German, Russian, Polish 1960: Mechanika elektrických strojů točivých (The Mechanics of Electrical Rotating Machines), translated into several languages 1947: Fysikální podobnost a stavba modelů == Awards == Honorary title of the Hero of Socialist Labor of Czechoslovak Socialist Republic, the Order of the Republic, the Order of the Victorious February, Order of Labour, A. Zápotockého medal with ribbon, the Soviet Order of the Red Banner of Labour, Order of Friendship of Peoples (awarded by the Presidium of the Supreme Soviet of the Soviet Union), Star friendship Nations in gold (awarded by the State Council of the GDR). For scientific merit is twice laureate of the Klement Gottwald State Prize, received the highest scientific honors the Academy of Sciences of the Soviet Union, Lomonosov Gold Medal, two honorary gold plaques of the SCAS "For Merits of science and humanity" and a plaque of Zdeněk Nejedlý. == References ==
|
Wikipedia:Javier González Garza#0
|
Javier González Garza (born 12 July 1945) is a Mexican mathematician and politician affiliated with the Party of the Democratic Revolution. In 2006–2009 he served as a deputy in the 60th Congress, representing the Federal District's second district. == References ==
|
Wikipedia:Jean Du Breuil#0
|
Jean Dubreuil, also known as Jean Du Breuil (22 July 1602 – 27 April 1670), was a French mathematician, music theorist, writer and essayist. == Life == Son of the bookseller Claude Du Breuil, he continued his father's profession until he joined the Society of Jesus. He lived for a long time in Rome where he studied architecture. He is known for his work about the theory and practice of perspective. == Works == Breuil, Jean (1642). Diverses methodes universelles et nouvelles, en tout ou en partie pour faire des perspectives (in French). A Paris: François Langlois. Du Breuil, Jean (1642). Advis charitables sur les diverses œuvres, et feuilles volantes du sr. Girard Desargues (in French). A Paris: François Langlois, Melchior Tavernier. La perspective practique, 1642–1649 L'Art universel des fortifications == References ==
|
Wikipedia:Jean François Niceron#0
|
Jean-François Niceron (5 July 1613 – 22 September 1646) was a French mathematician, Minim friar, and painter of anamorphic art, on which he wrote the ground-breaking book La Perspective Curieuse (Curious Perspectives). == Biography == Jean-François Niceron was a mathematical prodigy. He studied under Father Marin Mersenne, a famed mathematician and Minim friar, at the College de Nevers. In 1632, at the age of nineteen, he joined the Order of Minims. Niceron was also an artist, with a particular interest in the use of anamorphosis in religious art. He was acquainted with the leading scientists in France and Italy, such as Fermat, Descartes, Cavalieri, and Kircher, and was aware of the latest theoretical developments. Intent on finding a scientific solution to the problems presented by perspective, Niceron worked out the geometric algorithms for producing anamorphic art and in 1638, at the age of 25, published a treatise titled La perspective curieuse, ou magie artificielle des effets merveilleux (roughly translated as "The curious perspective or artificial magic of marvelous effects"). As a number of scientific societies formed in the early 1630s, Niceron became a member of the Circle of Mersenne, which was named after his mentor, Father Marin Mersenne. His connection with these societies led to associations with some of the top intellectuals from Paris and Rome. These relationships with the academic world helped him stay up to date with intellectual advancements. He closely followed optics and geometry, and used this knowledge to create the anamorphic paintings for which he is known. He died in 1646 in Aix-en-Provence, aged 33. His portrait was engraved by Lasne. The lexicographer Jean-Pierre Nicéron was a relative. == Publications == La perspective curieuse, ou magie artificielle des effets merveilleux (Paris, 1638, in-fol., reissued together with l'Optique and Catoptrique by P. Mersenne, ibid., 1652, in-fol.) Niceron reworked La perspective curieuse, augmented it with new observations, and translated it into Latin under the title Thaumaturgus opticus, sive amiranda optices, etc. (Paris, 1646, in-fol.) This was to have been followed by two other editions, but Niceron died before he could complete them. The 1638 and 1663 editions are both available online.[1] [2] La perspective curieuse, a richly illustrated manual on perspective, revealed for the first time the secrets of anamorphosis and trompe l'oeil. It contained the first published reference to Descartes's derivation of the law of refraction. First published in 1638 with 25 plates, Niceron's work was enlarged by Roberval and republished in 1663, along with the first edition, posthumously published, of a scholarly work on optics and catoptrics by Mersenne (1588–1648). In the original work, Niceron concentrated primarily on the practical applications of perspective, catoptrics, and dioptrics, and on the illusory effects of optics, then traditionally associated with natural magic. The work's first book (out of four) presents briefly the fundamental geometrical theorems and then develops a general method of perspective, borrowing heavily from Alberti and Dürer. The second book addresses the problem of establishing perspective for paintings executed on curved or irregular surfaces, like vaults and niches, and presents the general technique of anamorphosis. Here Niceron shows, for example, how to construct on the interior surface of a cone a distorted image that, when viewed from the end through the base, appears in proper proportion. Book three discusses and explains the anamorphosis of figures that are viewed by reflection from plane, cylindrical, and conical mirrors. Book four deals with the distortions created by refraction. The added work on optics by Mersenne contained the author's final contributions to optics, including experimental studies of visual acuity and binocular vision and a critical discussion of contemporary hypotheses on the nature of light. L'Interprétation des chiffres, ou Règle pour bien entendre et expliquer facilement toutes sortes de chiffres simples, tirée de italien et augmentée, particulièrement à l'usage des langues française et espagnole (Paris, 1641, in-8°). This work has been translated in part by Ant.-Marie Cospi. == See also == List of Roman Catholic scientist-clerics == References == == Further reading == Louis Gabriel Michaud. "name". Biographie universelle ancienne et moderne : histoire par ordre alphabétique de la vie publique et privée de tous les hommes avec la collaboration de plus de 300 savants et littérateurs français ou étrangers (in French) (2 ed.). P. J. S. Whitmore: The Order of Minims in Seventeenth-Century France [3] A. De Rosa, edited by : Jean François Nicéron. Perspective, Catoptric and Artificial Magic, with critical editions of La Perspective Curieuse (Paris 1638) and of the Thaumaturgus Opticus (Paris 1646), Aracne edizioni, ISBN 978-88-548-6032-2, 24 x 28 cm, 488 pp, Roma 2013 [4]. A. De Rosa, Through a glass darkly: the life and work of Minim Jean François Nicéron, in "Bollettino Ufficiale dell’Ordine dei Minimi", n° 5, year LI, January–March 2005. A. De Rosa, The Optik's Apocalipse. The twin anamorphosis by Emmanuel Maignan and Jean-François Nicéron, in "Ikhnos", Siracusa 2006. A. Bortot, C. Boscaro, A. De Rosa, C. Monteleone, E. Trevisan, Memory and oblivion. Discovery and digital survey of J.-F. Niceron's mural anamorphosis, in "Acts of XVI ASITA National Conference", ISBN 978-88-903132-7-1, Vicenza 2012 [5] G. D’Acunto, Jean-François Nicéron's Thaumaturgus opticus: between scientific precision and natural magic, in "Bollettino Ufficiale dell’Ordine dei Minimi", n° 2, year LII, April–June 2006. I. Rizzini, Jean-François Nicéron's Thaumaturgus opticus: notes on translation from Latin, in "Bollettino Ufficiale dell’Ordine dei Minimi", n° 4, year LI, October–December 2004. A. De Rosa, G. D'Acunto, La vertigine dello sguardo. Saggi sulla rappresentazione anamorfica, Cafoscarina, ISBN 8888613315, Venezia 2002 [6]. == Other sources == The painting at the Museum of the History of Science in Florence [7] The Galileo project [8] Mersenne's ‘'catoptrique'’ contains Niceron's plates First World Exhibition on Jean François Niceron at University Iuav of Venezia from 22 April until 31 May 2013 [9] “Jean François Niceron and Emmanuel Maignan: two Minim fathers, between science and faith”, exhibition curated by Alessio Bortot, Agostino De Rosa and Imago rerum, from 7 October 2023 to 6 January 2024 and from 27 March to 8 September 2024, in the Exhibition Hall of the Sanctuary of San Francesco di Paola in Paola, (CS). The exhibition offers an unprecedented experience which, through physical works and digital reconstructions, will allow visitors to take a journey between science, art and faith. [10] Joe Frawley, "Curious Perspectives", Joe Frawley Music (ca476) (7 November 2011). Music composed by Joe Frawley [11] for the exhibition "Jean François Niceron: Perspective, catoptrics & artificial magic", University Iuav, Venice, Italy, 22 April – 31 May 2013 [12].
|
Wikipedia:Jean Gallier#0
|
Jean Henri Gallier (born 1949) is a researcher in computational logic at the University of Pennsylvania, where he holds appointments in the Computer and Information Science Department and the Department of Mathematics. == Biography == Gallier was born January 5, 1949, in Nancy, France, and holds dual French and American citizenship. He earned his baccalauréat at the Lycée de Sèvres in 1966, and a degree in civil engineering at the École Nationale des Ponts et Chaussées in 1972. He then moved to the University of California, Los Angeles for his graduate studies, earning a Ph.D. in computer science in 1978 under the joint supervision of Sheila Greibach and Emily Perlinski Friedman. His dissertation was entitled Semantics and Correctness of Classes of Deterministic and Nondeterministic Recursive Programs. After postdoctoral study at the University of California, Santa Barbara, he joined the University of Pennsylvania Department of Computer and Information Science in 1978. At Pennsylvania, he was promoted to full professor in 1990, gained a secondary appointment to the Department of Mathematics in 1994, and directed the French Institute of Culture and Technology from 2001 to 2004. == Contributions == Gallier's most heavily cited research paper, with his student William F. Dowling, gives a linear time algorithm for Horn-satisfiability.[DG84] This is a variant of the Boolean satisfiability problem: its input is a Boolean formula in conjunctive normal form with at most one positive literal per clause, and the goal is to assign truth values to the variables of the formula to make the whole formula true. Solving Horn-satisfiability problems is the central computational paradigm in the Prolog programming language. Gallier is also the author of five books in computational logic,[G86] computational geometry,[G99][G00] low-dimensional topology,[GX13] and discrete mathematics.[G11] == Selected publications == === Research papers === === Books === == References == == External links == Home page Jean Gallier publications indexed by Google Scholar
|
Wikipedia:Jean Ginibre#0
|
Jean Ginibre (4 March 1938 — 26 March 2020) was a French mathematical physicist. He is known for his contributions to random matrix theory (see circular law), statistical mechanics (see FKG inequality, Ginibre inequality), and partial differential equations. With Martine Le Berre and Yves Pomeau, he provided a kinetic theory for the emission of photons by an atom maintained in an excited state by an intense field that creates Rabi oscillations. He received the Paul Langevin Prize in 1969. Jean Ginibre was Emeritus Professor at Paris-Sud 11 University. He directed the thesis of Monique Combescure. == See also == Classical XY model == References ==
|
Wikipedia:Jean Giraud (mathematician)#0
|
Jean Giraud (French: [ʒiʁo]; 2 February 1936 – 27 or 28 March 2007) was a French mathematician, a student of Alexander Grothendieck. His research focused on non-abelian cohomology and the theory of topoi. In particular, he authored the book Cohomologie non-abélienne (Springer, 1971) and proved the theorem that bears his name, which gives a characterization of a Grothendieck topos. From 1969 to 1989, he was a professor at École normale supérieure de Saint-Cloud. From 1993 to 1994, he was deputy director for research of École normale supérieure de Lyon, where he was made interim director in 1994 and director from 1995 to 2000. == See also == Fibred category == References == == External links == Jean Giraud, 1936– at Library of Congress Authorities – with 4 catalogue records
|
Wikipedia:Jean Jacques Bret#0
|
Jean Jacques Bret (25 September 1781 – 29 January 1819) was a French professor of mathematics at the University of Grenoble. He worked on analytical geometry, polynomial roots, and the theory of conics and quadrics. Bret was born in Mercuriol, Drôme, where his father was a notary. He went to study civil engineering at the École Polytechnique in 1800 but was unable to complete studies due to poor health. In 1804 he became a professor of mathematics at the lycée in Grenoble. In 1811 he became a professor at the faculty of science at the University of Grenoble and received a doctorate in 1812. Bret's work was in coordinate geometry, both on the plane and in 3-dimensions. He was among the first to use a parametric form for the line in space. Bret suggested a rule for the superior limits of the roots of polynomial in 1815. The rule has been stated as: "if we add to unity a series of fractions whose numerators are the successive negative coefficients, taken positively, and whose denominators are the sums of the positive coefficients, including that of the first term, the greatest of the resulting values will be a superior limit of the roots of the equation." He also contributed to the study of continued fractions. == References ==
|
Wikipedia:Jean Mawhin#0
|
Jean L. Mawhin (born 11 December 1942 in Verviers) is a Belgian mathematician and historian of mathematics. Mawhin received his PhD in 1969 (Le problème des solutions périodiques en mécanique non linéaire) under Paul Ledoux at the University of Liège, where he had studied since 1962 and received his licentiate in mathematics in 1964. He was assistant professor at Liège from 1964 and maitre de conferences (lecturer) from 1969 to 1973. From 1970 he was assistant professor (chargé de cours) and from 1974 professor of mathematics at the Université catholique de Louvain (with full professorship from 1977). In 2008 he retired. He was a visiting professor at various US and Canadian universities (University of Michigan, Brown University, University of Utah, Colorado State University, University of Alberta, Centre de Recherches Mathématiques in Montreal, Rutgers University), at the University of Paris, in Strasbourg, Rome, Turin, Trieste, Brisbane, Graz, Brazil, Florence, Darmstadt, Karlsruhe and Würzburg. He worked on (nonlinear) ordinary differential equations and the topological methods used there (fixed-point theorems, Leray-Schauder theory) and methods of nonlinear functional analysis. As a historian of mathematics, he dealt with Henri Poincaré, among others. He received the Bolzano Medal of the Czech Academy of Sciences. In 2012, he was awarded the first Juliusz Schauder Prize. In 1986 he became a corresponding member and in 1992 a full member of the Royal Academy of Science, Letters and Fine Arts of Belgium, of which he was president in 2002, and director of the Class of Sciences. In 1992 he became an honorary member of the Grand Ducal Institute. He has been married since 1966 and has three children. == Selected works == with Michel Willem, Critical point theory and hamiltonian systems, Springer 1989 with Robert E. Gaines, Coincidence degree and nonlinear differential equations, Springer 1977 Topological degree methods in nonlinear boundary value problems, American Mathematical Society 1979 Points fixes, points critiques et problèmes aux limites, Presses de l’Université de Montreal, 1985 with Nicolas Rouche, Equations differentielles ordinaires, Paris, Masson 1973 (english translation Ordinary differential equations: stability and periodic solutions, Boston, Pitman, 1980) Boundary value problems for nonlinear ordinary differential equations: from successive approximations to topology, in Jean-Paul Pier Development of Mathematics 1900-1950, Birkhäuser 1994 Topological fixed point theory and nonlinear differential equations, in R. F. Brown et.al. (eds.) Handbook of Topological Fixed Point Theory, Springer 2005, p. 867–904 Leray-Schauder degree, a half century of extensions and applications, Topological Methods in Nonlinear Analysis, Journal of the Juliusz Schauder Center, Vol. 14, 1999, p. 195–228 The centennial legacy of Poincaré and Lyapunov in ordinary differential equations, Rend. Circolo Math. Palermo, Suppl. 34, 1994, S. 9–46 Poincaré’s early use of Analysis Situs in nonlinear differential equations, Philos. Sci., Vol. 4, 2000, p. 103–143 Nonlinear oscillations: a hundred years after Poincaré and Liapunov, Journal of Applied Mathematics and Mechanics, Vol. 73, 1993, T 53-T62 Les mathématiques, in: Robert Halleux, Geert Vanpaemel, Jan Vandersmissen, Andrée Despy-Meyer (eds.), Histoire des sciences en Belgique, 1815-2000, Brussels: Dexia/La Renaissance du livre, 2001, Vol. 1 == References == M. Delgado et.al. (eds.) The first 60 years of nonlinear analysis of Jean Mawhin (Sevilla Conference 2003), World Scientific 2004
|
Wikipedia:Jean Serra#0
|
Jean Paul Frédéric Serra (born 1940 in Algeria) is a French mathematician and engineer, and known as one of the co-founders (together with Georges Matheron) of mathematical morphology. == Biography == === Education === Serra received a scientific baccalauréat in 1957, and an engineering degree from the École Nationale Supérieure des Mines de Nancy in 1962. He also obtained a Bachelor's degree in philosophy/psychology, from the University of Nancy, in 1965. He obtained a PhD in Mathematical Geology from the University of Nancy in 1967, and a doctorat d'etat in Mathematics, from the Pierre and Marie Curie University, Paris, in 1986. He speaks French, Russian, English, and Spanish. === Mathematical morphology === From 1962 to 1966, while a research engineer at the Institut de recherche de la sidérurgie, France, Serra was a PhD student under the supervision of Georges Matheron. The subject of his thesis was "stochastic modeling of the iron deposit of Lorraine, at various scales," one of the goals of which was to quantify petrographic characteristics of its iron orebody. During that period, Serra came up with the idea of using structuring elements for transforming images of cross sections of the ore, in order to gain information about it. The result was a device called "Texture Analyser", which was patented in 1965. This work also lead to the concept of hit-or-miss transform, which evolved into the concepts of erosion, dilation, opening and closing due to Matheron. Granulometry and other concepts followed. In the Winter of 1966, in a pub of Nancy, Matheron, Philippe Formery, and Serra decided to give a name to this body of works: "Mathematical morphology". The new theory and method has since evolved to be applied in a variety of image processing problems and tasks, and is researched worldwide (main article: Mathematical morphology). In 1968, the Centre of Mathematical Morphology (CMM) of the École des Mines de Paris was created (after 1979, it was called Centre of Geostatistics and Mathematical Morphology). Matheron was named director, and Serra was hired as master of research ("Maître de Recherches") and assistant director. In 1986, upon the split of the Centre of Geostatistics and Mathematical Morphology into two separate centers, Serra became director of research ("Directeur de Recherches") and the director of the new CMM. Serra has continued to contribute to mathematical morphology over the years; In fact, some of the most important theoretical developments are due to him: Generalization of mathematical morphology to complete lattices Theory for morphological filtering, with Matheron Connections === Additional highlights === 1979–1983: Vice-president of the International Society for Stereology. 1983–: Member of the editorial board of Acta Stereologica. 1988–1991: Member of the scientific board of the French T.V. cultural program. 1989–: Member of the editorial board of the Journal of Visual Communication and Image Representation. 1990–: Member of the editorial board of the Journal of Mathematical Imaging and Vision. 1991–1993 : Chairman of the "Image Algebra and Morphological Processing Conference" in SPIE annual meeting, San Diego, California, USA. 1993: Chairman of the first Int. Conf. in Mathematical Morphology, Barcelona, Spain. 1994: Chairman of the second Int. Conf. in Mathematical Morphology, Fontainebleau, France. == Honors and awards == 1982 : ESCLANGON prize, awarded by the French Society of Physics. 1988 : First award of the great prize of the AFCET Society. 1989 : Chevalier of the National Order of Merit. 1993 : Doctor Honoris Causa of the Autonomous University of Barcelona, Spain. 1993 : Founder of the International Society for Mathematical Morphology, and first president of this society. 2006 : First recipient of Georges Matheron Lectureship Award of International Association for Mathematical Geosciences == Main publications == Image Analysis and Mathematical Morphology, ISBN 0-12-637240-3 (1982) Image Analysis and Mathematical Morphology, Volume 2: Theoretical Advances, ISBN 0-12-637241-1 (1988) == Notes == == References == Serra's curriculum vitae Serra's web page at the Centre de Morphologie Mathématique, École des Mines de Paris History of Mathematical Morphology Archived 4 March 2011 at the Wayback Machine, by Georges Matheron and Jean Serra Mathematical Morphology and its Application to Signal Processing, J. Serra and Ph. Salembier (Eds.), proceedings of the 1st international symposium on mathematical morphology (ISMM'93), ISBN 84-7653-271-7 (1993) Mathematical Morphology and Its Applications to Image Processing, J. Serra and P. Soille (Eds.), proceedings of the 2nd international symposium on mathematical morphology (ISMM'94), ISBN 0-7923-3093-5 (1994) Mathematical Morphology: 40 Years On, Christian Ronse, Laurent Najman, and Etienne Decencière (Eds.), ISBN 1-4020-3442-3 (2005) Mathematical Morphology and its Applications to Signal and Image Processing, Gerald J.F. Banon, Junior Barrera, Ulisses M. Braga-Neto (Eds.), proceedings of the 8th international symposium on mathematical morphology (ISMM'07), ISBN 978-85-17-00032-4 (2007) Special Issue on 'Spatial Information Retrieval, Analysis, Reasoning and Modelling, B. S. Daya Sagar and Jean Serra (Eds.), International Journal of Remote Sensing, v. 31, no. 22, pp. 5747–6032 (2010) Special Issue on 'Filtering and Segmentation in Mathematical Morphology, Laurent Najman, Junior Barrera, B. S. Daya Sagar, Petros Maragos and Dan Schonfeld (Eds.), IEEE Journal of Selected Topics in Signal Processing, v. 6, no. 7, pp. 737–886 (2012)
|
Wikipedia:Jean Trenchant#0
|
Jean Trenchant (... – 15th-century) was a French mathematician L'aritmetique departie en trois livres was used as a reference by Simon Stevin in the preface of Tafelen van Interest. == Works == Trenchant, Jean (1561). L'aritmetique de Jan Trenchant departie en trois livres, ensemble un petit discours des changes. Avec l'art de calculet aux Getons (in French). Lyon: Jove. Trenchant, Jean (1571). Arithmetique (in French). A Lyon: Michel Jouve, Pierre Roussin. == References ==
|
Wikipedia:Jean-Baptiste Leblond#0
|
Jean-Baptiste Leblond (born 21 May 1957 in Boulogne-Billancourt) is a French materials scientist, member of the Mechanical Modelling Laboratory of the Pierre-et-Marie-Curie University (MISES) and professor at the same university. == Biography == Leblond attended his scientific preparatory classes, notably in the special M' mathematics class at the Lycée Louis-le-Grand and was admitted to the École normale supérieure de la rue d'Ulm, mathematics option, in 1976. He then joined the Corps des mines and became a doctor of physical sciences. Since 2005, he has been a member of the French Academy of Sciences and a founding member of the French Academy of Technologies (2000). He is a senior member of the Institut universitaire de France. == Scientific fields covered == Modeling of solid-state transformation kinetics in steels and alloys. Leblond's classical model is essentially based on the notion of phase proportions at thermodynamic equilibrium, and the deviation from these proportions. Theoretical analysis and modelling of the transformation plasticity of steels and alloys, based on the mechanism proposed by Greenwood and Johnson in 1965. The first classical approach to Leblond's problem has recently been taken up again by combining the theories of homogenization and boundary analysis. Numerical simulation of thermomechanical treatments of steels and alloys (welding, quenching, etc.). Initially limited to the solid part of the structure, these simulations have been extended to the modelling of fluid flow and heat in the molten bath, including in particular the effects of surface tension. Crack propagation paths in linear mechanics of brittle fracture, 2D and 3D. One of the most difficult issues examined by Leblond is that of interpreting and explaining the fragmentation of crack fronts in brittle materials under partial I+III or general I+II+III mixed mode loading. Ductile failure of metals. The problems examined include the shape effects of cavities and the theoretical analysis and modelling of their coalescence, a prelude to the formation or propagation of a macroscopic crack. Reference provides a summary of the work. Diffusion/reaction phenomena in solids, with particular application to the internal oxidation of metal plates. A major advance consists in an ab initio prediction, without adjustable parameters, of the transition from internal to external oxidation (limited to the surface of the material). Advanced numerical methods in solid mechanics and metallurgy. Special efforts have been devoted to the development of Gaussian pointless finite element methods, including a nodal integration technique with various advantages. == Leblond's kinetic theory == This is an approach established by Leblond in his work on phase transformations. The theory proposes an evolutionary model to quantify the composition of the different phases of a crystalline material during heat treatment. The method is based on experimentally established CRT (Continuous Cooling Transformation) diagrams to compose TTT (Time-Temperature-Transformation) diagrams, which are widely used for numerical simulation or for the manufacture of industrial parts. The theory posits the equivalent volume fraction of a constituent yeq as the stationary solution of the evolution equations describing the phase change kinetics: y ˙ = f ( y , T ) e t f ( y e q , T ) = 0 → {\displaystyle {\dot {y}}=f(y,T)\quad et\quad f(y_{eq},T)=0\,\rightarrow } stationnart phase We then suppose in anisothermal condition that the real fraction y is close to yeq, it is then possible to approximate the real value Y by a Taylor development at order 1: f ( y , T ) = f ( y e q , T ) + ∂ f ( y e q , T ) ∂ y ( y − y e q ) {\displaystyle f(y,T)=f(y_{eq},T)+{\frac {\partial f(y_{eq},T)}{\partial y}}(y-y_{eq})} The evolution is given by : y ˙ = y − y e q τ ( T ) e t 1 τ = − ∂ f ( y e q , T ) ∂ y {\displaystyle {\dot {y}}={\frac {y-y_{eq}}{\tau (T)}}\quad et\quad {\frac {1}{\tau }}=-{\frac {\partial f(y_{eq},T)}{\partial y}}} τ is determined on the one hand by the incubation period (critical time) and on the other hand by the cooling rates T. There are also other formalisms such as the theory of Kirkaldy, Johnson-Mehl-Avrami or Waeckel. One of the most classical, quite old, is that of Johnson-Mehl-Avrami. The model proposed by Jean-Baptiste Leblod is in fact based on this classical model by generalizing it on two points: 1) it considers any number of phases and transformations between these phases, and not just two phases and a single transformation; 2) the transformations can remain, after an infinitely long time, partial, and not necessarily complete as in the Johnson-Mehl-Avrami model (this is linked to the existence, in the new model, of fractions "at equilibrium" of the phases towards which the system evolves after an infinite time, not necessarily equal to 0 or 1 but which can take any value between these limits). The Leblond model is designed for applications in the thermometallurgical treatment of steels; this explains its success with the modellers of these treatments. == References ==
|
Wikipedia:Jean-Charles Faugère#0
|
Jean-Charles Faugère is the head of the POLSYS project-team (Solvers for Algebraic Systems and Applications) of the Laboratoire d'Informatique de Paris 6 (LIP6) and Paris–Rocquencourt center of INRIA, in Paris. The team was formerly known as SPIRAL and SALSA. Faugère obtained his Ph.D. in mathematics in 1994 at the University of Paris VI, with the dissertation "Résolution des systemes d’équations algébriques" (Solving systems of algebraic equations), under the supervision of Daniel Lazard. He works on Gröbner bases and their applications, in particular, in cryptology. With his collaborators, he has devised the FGLM algorithm for computing Gröbner bases; he has also introduced the F4 and F5 algorithms for calculating Gröbner bases. In particular, his F5 algorithm allowed him to solve various problems in cryptography such as HFE; he also introduced a new type of cryptanalysis, called algebraic cryptanalysis. == Notes == == External links == POLSYS web site The old SPIRAL web site The old SALSA web site Jean-Charles Faugère's page
|
Wikipedia:Jean-Claude Falmagne#0
|
Jean-Claude Falmagne (French pronunciation: [ʒɑ̃ klod falmaɲ]; born February 4, 1934, in Brussels, Belgium) is a mathematical psychologist whose scientific contributions deal with problems in reaction time theory, psychophysics, philosophy of science, measurement theory, decision theory, and educational technology. Together with Jean-Paul Doignon, he developed knowledge space theory, which is the mathematical foundation for the ALEKS software for the assessment of knowledge in various academic subjects, including K-12 mathematics, chemistry, and accounting. == Early life and career == After finishing high school, Falmagne spent two years in the Belgian army, where he became an officer. Military service was mandatory in Belgium at the time. In 1954, he enrolled at the University of Brussels (Université libre de Bruxelles) as a student in the psychology department. He received his undergraduate degree in 1959 and was hired as an assistant at the University of Brussels, which is a faculty position in the Belgian system. He obtained his Ph.D. degree in 1965 from the same institution. While working on his doctoral dissertation, which dealt with reaction times, Falmagne became interested in the applications of mathematics to the cognitive sciences. In 1964, he was invited by Patrick Suppes to spend the summer at Stanford University. He presented the results of his dissertation at a conference there and met several prominent mathematical psychologists, including Bill Estes, Dick Atkinson, and Duncan Luce, and the mathematician János Aczél. Suppes, Luce, and Aczél had a strong influence on Falmagne's choice of scientific career and on his approach to solving scientific problems. His visit to Stanford convinced him that he needed to continue his education in the United States. With the support of Fulbright and FNRS fellowships, Falmagne held post-doctoral positions at the University of Pennsylvania, the University of Wisconsin-Madison, and the University of Michigan between 1966 and 1969. His interests grew to include psychophysics, measurement theory, and probabilistic models of ordering and algebraic measurement. After short teaching stints back in Europe at the University of Brussels and the University of Paris, he returned to the United States in 1971 as a Professor of Psychology at New York University. In 1989, he joined the faculty of University of California, Irvine, accepting an appointment at the Department of Cognitive Sciences and the Institute for Mathematical Behavioral Sciences. He remained there until his retirement in 2004. Until 2013, Falmagne was Chairman of ALEKS Corporation, a web-based educational software company that he founded with some of his graduate students. He is currently a Research Professor at the University of California, Irvine. == Research == In 1978, Falmagne solved a well-known problem, posed in 1960 by the economists H.D. Block and Jacob Marschak in their article "Random Orderings and Stochastic Theories of Responses", concerning the representation of choice probabilities by random variables and published his findings in the Journal of Mathematical Psychology.[F78] === Knowledge spaces, media theory, learning spaces and the ALEKS software === In 1985, Falmagne, along with Jean-Paul Doignon, wrote “Spaces for the Assessment of Knowledge”.[DF85] In this article, they presented a formal framework for the assessment of knowledge in various academic subjects, such as arithmetic, algebra, and chemistry. This early framework was combinatoric in character, and as such insufficient for a practical assessment, which is unavoidably plagued by careless errors on the part of the test takers. In time, they created a stochastic framework for the description of the evolution of an assessment, question by question.[FD88] With extensive financial support from the National Science Foundation, their work on the stochastic framework led to the creation of the web-based system ALEKS for the assessment and learning of mathematics and science. Falmagne and Doignon's 2011 book, Learning Spaces,[FD11] contains the most current presentation and development of the stochastic framework for the assessment of knowledge. Learning spaces are specific kinds of knowledge spaces, whose best applications are to situations where assessments guide efficient learning. Learning spaces are a part of the concept of Media Theory,[EFO07] which explores the modeling of knowledge structures and knowledge states. More generally, these lines of research are collectively called Knowledge Space Theory and are being pursued by many investigators, mostly in Austria, Germany, and the Netherlands. === The meaningfulness of scientific laws === A common practice in the statement of scientific laws ensures that the mathematical expression of the law is invariant with respect to changes of units of its variables—except for the values of dimensional constants. In dimensional analysis, this invariance is implicit and captured by the concept of "quantities". In "Scales and Meaningfulness of Quantitative Laws", Falmagne and Louis Narens argue that the requirement of invariance, which they call "meaningfulness" should be part of the axioms or theory establishing the law, rather than result from them.[FN83] They proposed a more powerful framework making this invariance explicit in the notation. This approach was generalized by Falmagne in "Meaningfulness and Order Invariance: Two Fundamental Principles for Scientific Laws",[F04] and applied to several exemplary laws of physics. === Other work === The monograph Elements of Psychophysical Theory[F85] presents the mathematical foundation of psychophysics and includes an introduction to measurement theory and functional equations. Falmagne's work in philosophy of science concerns foundational issues in algebraic measurement[DF69][F75] and in probabilistic measurement.[F76] A distinctive feature of his research lies in the use of functional equations in order to achieve generality.[F80][AF99][AF00][FD10] == Awards and honors == Falmagne is the recipient of Fulbright and Guggenheim Fellowships and of a von Humboldt Award. In 1994, he was recognized as a "Friend of NSERC" by the Natural Sciences and Engineering Research Council of Canada and János D. Aczél . That same year, he was elected as a member of the New York Academy of Sciences. He is also a fellow of the Society of Experimental Psychologists. He received an Innovation Award from the University of California, Irvine in 2004 and a doctoris honoris causa degree in science from the University of Graz in 2005. In celebration of Falmagne's 70th birthday in 2004, a "Falmagne Symposium" was held at the annual meeting of the European Mathematical Psychology Group in Ghent, Belgium, and a "Falmagne Festschrift Meeting" was held at the University of Michigan, Ann Arbor. Two special issues of the Journal of Mathematical Psychology were published in 2005 with the papers presented at two meetings organized to honor his 70th birthday. In 2014, a conference on meaningfulness and learning spaces was held in Irvine in honor of his 80th birthday. In 2015 the UC Irvine Alumni Association gave him their highest honor, the Extraordinarius award. == Selected publications == == References == == External links == ALEKS Corporation Falmagne's Profile and Bibliography at University of California, Irvine John Simon Guggenheim Memorial Foundation Bibliography of Knowledge Spaces - Maintained by Cord Hockemeyer at the University of Graz Archived 2016-12-20 at the Wayback Machine 2011 Meeting of the European Mathematical Psychology Group
|
Wikipedia:Jean-Claude Sikorav#0
|
Jean-Claude Sikorav (born 21 June 1957) is a French mathematician. He is professor at the École normale supérieure de Lyon. He is specialized in symplectic geometry. == Main contributions == Sikorav is known for his proof, joint with François Laudenbach, of the Arnold conjecture for Lagrangian intersections in cotangent bundles, as well as for introducing generating families in symplectic topology. == Selected publications == Sikorav is one of fifteen members of a group of mathematicians who published the book Uniformisation des surfaces de Riemann under the pseudonym of Henri Paul de Saint-Gervais. He has written the survey Sikorav, Jean-Claude (1994), "Some properties of holomorphic curves in almost complex manifolds", Holomorphic curves in symplectic geometry, Progress in Mathematics, vol. 117, Basel: Birkhäuser, pp. 165–189, MR 1274929. and research papers Hofer, Helmut; Lizan, Véronique; Sikorav, Jean-Claude (1997), "On genericity for holomorphic curves in four-dimensional almost-complex manifolds", Journal of Geometric Analysis, 7 (1): 149–159, doi:10.1007/BF02921708, MR 1630789, S2CID 119936346. Laudenbach, François; Sikorav, Jean-Claude (1985), "Persistance d'intersection avec la section nulle au cours d'une isotopie hamiltonienne dans un fibré cotangent", Inventiones Mathematicae, 82 (2): 349–357, Bibcode:1985InMat..82..349L, doi:10.1007/BF01388807, MR 0809719, S2CID 122242002. == Honors == Sikorav is a Knight of the Ordre des Palmes Académiques. == References == == External links == Jean-Claude Sikorav at the Mathematics Genealogy Project Home page at the École Normale Supérieure de Lyon
|
Wikipedia:Jean-Dominique Lebreton#0
|
Jean-Dominique Lebreton (born February 19, 1950, in Saint-Étienne) is a biomathematician and a member of the French Academy of Sciences. == Course == Jean-Dominique Lebreton obtained a university degree in Mathematics and Physics in 1969, then a Certificate of Master of Mathematics and Fundamental Applications and a Master of Computer Science in 1971. He obtained his Diploma of Advanced Studies in Applied Biology in 1972, his Doctorate of Specialty in Lyon in 1974 and his Doctor of Science in 1981. He was Assistant and then Assistant Professor at the University of Lyon before becoming Director of Research at the CNRS (CEFE) in Montpellier in 1990. Since 2014, he has been Director of Research Emeritus. == Scientific work == Computer scientist and mathematician by training, naturalist by family tradition (younger brother of Philippe Lebreton), Jean-Dominique Lebreton is a biomathematician, mainly specialized in modelling in ecology and population dynamics. Animal and plant population dynamics result from multiple mechanisms, such as feedback from populations on demographic performance or environmental variability. On an evolutionary scale, the diversification of demographic strategies raises many questions. Only modelling can therefore shed light on population dynamics, both at the ecological and evolutionary level. It is one of the main international actors in the development of population dynamics models. First, it contributed to the launch of matrix models of population dynamics, producing formal sensitivity results and original stochastic generalizations, and applying these models to various vertebrates. He then demonstrated the key role of generation time in the diversity of demographic strategies and in the sensitivity of populations to demographic impacts. Jean-Dominique Lebreton was then one of the driving forces behind the renewal of demographic capture-recapture methods. First, it was necessary to shift their focus from a focus on numbers to estimating individual flows and then to introduce ideas from generalized linear models, thus making it possible to analyze probabilities of survival according to age, gender or environment. His work, by bridging the gap between capture-recapture models and analysis of variance, has contributed to a real revolution, with a wide range of applications in evolutionary ecology and conservation biology. In recent years, he has been involved in the development of various types of models in which individuals move between several states, for example, to study dispersion and reproductive achievement. At the same time, he developed a long-term program on the Forézian population of Black-legged Kittiwake Chroicocephalus ridibundus, which highlighted the importance of dispersal behaviour in colonial birds in the face of spatial and temporal heterogeneity in the environments. He has also relaunched theoretical and practical studies in the context of the biology of exploited populations. The integration of the dynamic and statistical models he developed, both by himself and in the team he created in Montpellier, has enabled him to shed light on the conservation and management of the populations subject to sampling: Hunting, especially ducks and geese; Involuntary removals, such as incidental catches of Albatrosses by longline fishing lines; Levies to limit numbers, with the elaboration for the Ministry of the Environment of a management plan for large cormorants wintering in France. Both personally and through the team he created, but also through the development of close collaborations with the French vertebrate population biology teams (LBBE Lyon, Paris VI, MNHN, Chizé, Strasbourg, Tour du Valat), he and various colleagues have contributed to the creation of a "French school" for the dynamics and biology of vertebrate populations with high international visibility. The development and distribution of flexible and user-friendly software (Biomeco; U-CARE; SURGE, M-SURGE, E-SURGE) to support his team's research production have greatly contributed to this visibility. As in his research administration activities, he was able to focus on "social utility" and collective construction in his international research and collaborations – there was a full choice in his generation. He has established long-term collaborations with colleagues such as J.D. Nichols and H. Caswell in the United States, B.J.T. Morgan in Great Britain, G. Gauthier in Canada. The population dynamics workshops he has launched for more than 20 years, after similar workshops in statistical ecology, have brought together hundreds of colleagues, many of whom have remained in contact for data processing, visits to CEFE, or long-term collaborations. These workshops have been organized on several occasions in foreign countries (Great Britain, Canada, New Zealand, Spain, Morocco, United States...). He recently organized a workshop on "Matrix models for population management and conservation", from March 5 to 10, 2017 at the University of Florida (Gainesville). He is regularly invited to international conferences in his field. Since 2009 he has been a Member of the Academia Europaea. == Pedagogical activity == Jean-Dominique Lebreton has taught in the first, second and third cycles. He has also been asked for occasional courses and ongoing training. == Other institutional responsibilities == Deputy Director of CEFE, UMR 5175, December 2001 – December 2005 Director of CEFE, UMR 5175, January 2006-December 2010 Deputy Director of IFR 119 "Montpellier-Environnement-Biodiversity", 2006–2010 Acting Director of this RFI, 2009–2010. Founder and Director of LABEX CeMEB, 2011–2013 Secretary (1974–1980), and President (1981) of the Rhône-Alpes Ornithological Centre Member of the "Ecological Methodology" working group associated with the "Management of Renewable Natural Resources" committee, D.G.R.S.T., 1976–1979 Secretary of the Scientific Council of the U.E.R. des Sciences de la Nature, University of Lyon I, 1977 Member of the Board of Directors of the Société Française de Biométrie, 1979–1986; 1990 to date; Secretary, 1983–1986, and President, 1990–1992, of this company Member of the Board of the International Biometric Society, 2000–2003 Member of the French Bird Certification Committee, 1983–1987 Representative of the CNRS on the Scientific Council of the Camargue National Reserve (SNPN), 1995–95 Alternate member, representative of the CNRS, on the Conseil National de la Chasse et de la Faune Sauvage (CNCFS), 1996– Member of the Scientific Council of the National Office for Hunting and Wildlife (ONCFS), 1996–96 Scientific Advisor, Tour du Valat Foundation, 1990– Member of the Scientific Committee of the URA CNRS 367, "Écologie des Eaux Douces", 1990–1993 Member of the Scientific Committee of the Centre d'Études Biologiques de Chizé, 1998–2001 Chairman of various UMR evaluation committees. == Distinctions == First prize, first researcher's film festival, Nancy, March 1996, "Glaros, Biologie d'une population de Mouettes rieuses". Video Film (26''), L'Esplanade Saint-Étienne Vidéo. Saint-Étienne. (Director: J.C. PARAYRE, Scientific Advisor, J.-D. LEBRETON). "Visiting Professor", University of Kent (Canterbury, Great Britain), 1996–2001. CNRS Silver medal, 1990. Chevalier in the Ordre national du Mérite, on the proposal of the Minister of Regional Planning and the Environment, November 1998 Member of the French Academy of sciences (elected on 28 November 2005). Grand Prize of the French Society of Ecology and Evolution. == Few Bibliographic references == Lebreton, J.-D., Burnham, K. P., Clobert, J. & Anderson, D. R. Modeling survival and testing biological hypotheses using marked animals: a unified approach with case studies. Ecological Monographs, 1992, 62: 67–118. (4028 citations) Lebreton, J.-D. & Pradel, R. Multistate recapture models: modelling incomplete individual histories. Journal of Applied Statistics. 2002, 29: 353–369. (311 citations) Lebreton, J.-D., Nichols, J.D., Barker, R.J. Pradel, R. & Spendelow, J.A. Modeling individual animal histories with multistate capture-recapture models. Advances in Ecological Research, 2009, 41: 87–173. (186 citations) Choquet, R., Lebreton, J.-D., Gimenez, O., Reboulet A.-M., Pradel, R. -U-CARE: Utilities for performing goodness of fit tests and manipulating CApture-REcapture data. Ecography, 2009, 32: 1071–1074. (449 citations) Lebreton, J.-D. & Gimenez O. Detecting and estimating Density-Dependence in wildlife populations. Journal of Wildlife Management, 2013, 77: 12–23 (Published on line27 AUG 2012 | DOI: 10.1002/jwmg.425) (45 citations) Niel, C. & Lebreton, J.-D. Using demographic invariants to detect overharvested bird populations from incomplete data. Conservation Biology, 2005, 19: 826–835. (125 citations) Lebreton J.-D. Dynamical and Statistical models for exploited populations. Australian and New-Zealand Journal of Statistics, 2005, 47: 49–63. (103 citations) Henaux, V., Bregnballe, T. & Lebreton, J.-D. Dispersal and recruitment during population growth in a colonial bird, the Great Cormorant. Journal of Avian Biology, 2007, 38: 44–57. (90 citations) Lebreton, J.-D. Demographic models for subdivided populations: the renewal equation approach. Theoretical Population Biology, 1996, 49: 291–313. (113 citations) == References ==
|
Wikipedia:Jean-François Mertens#0
|
Jean-François Mertens (11 March 1946 – 17 July 2012) was a Belgian game theorist and mathematical economist. Mertens contributed to economic theory in regards to order-book of market games, cooperative games, noncooperative games, repeated games, epistemic models of strategic behavior, and refinements of Nash equilibrium (see solution concept). In cooperative game theory he contributed to the solution concepts called the core and the Shapley value. Regarding repeated games and stochastic games, Mertens 1982 and 1986 survey articles, and his 1994 survey co-authored with Sylvain Sorin and Shmuel Zamir, are compendiums of results on this topic, including his own contributions. Mertens also made contributions to probability theory and published articles on elementary topology. == Epistemic models == Mertens and Zamir implemented John Harsanyi's proposal to model games with incomplete information by supposing that each player is characterized by a privately known type that describes his feasible strategies and payoffs as well as a probability distribution over other players' types. They constructed a universal space of types in which, subject to specified consistency conditions, each type corresponds to the infinite hierarchy of his probabilistic beliefs about others' probabilistic beliefs. They also showed that any subspace can be approximated arbitrarily closely by a finite subspace, which is the usual tactic in applications. == Repeated games with incomplete information == Repeated games with incomplete information, were pioneered by Aumann and Maschler. Two of Jean-François Mertens's contributions to the field are the extensions of repeated two person zero-sum games with incomplete information on both sides for both (1) the type of information available to players and (2) the signalling structure. (1) Information: Mertens extended the theory from the independent case where the private information of the players is generated by independent random variables, to the dependent case where correlation is allowed. (2) Signalling structures: the standard signalling theory where after each stage both players are informed of the previous moves played, was extended to deal with general signalling structure where after each stage each player gets a private signal that may depend on the moves and on the state. In those set-ups Jean-François Mertens provided an extension of the characterization of the minmax and maxmin value for the infinite game in the dependent case with state independent signals. Additionally with Shmuel Zamir, Jean-François Mertens showed the existence of a limiting value. Such a value can be thought either as the limit of the values v n {\displaystyle v_{n}} of the n {\displaystyle n} stage games, as n {\displaystyle n} goes to infinity, or the limit of the values v λ {\displaystyle v_{\lambda }} of the λ {\displaystyle {\lambda }} -discounted games, as agents become more patient and λ → 1 {\displaystyle {\lambda }\to 1} . A building block of Mertens and Zamir's approach is the construction of an operator, now simply referred to as the MZ operator in the field in their honor. In continuous time (differential games with incomplete information), the MZ operator becomes an infinitesimal operator at the core of the theory of such games. Unique solution of a pair of functional equations, Mertens and Zamir showed that the limit value may be a transcendental function unlike the maxmin or the minmax (value in the complete information case). Mertens also found the exact rate of convergence in the case of game with incomplete information on one side and general signalling structure. A detailed analysis of the speed of convergence of the n-stage game (finitely repeated) value to its limit has profound links to the central limit theorem and the normal law, as well as the maximal variation of bounded martingales. Attacking the study of the difficult case of games with state dependent signals and without recursive structure, Mertens and Zamir introduced new tools on the introduction based on an auxiliary game, reducing down the set of strategies to a core that is 'statistically sufficient.' Collectively Jean-François Mertens's contributions with Zamir (and also with Sorin) provide the foundation for a general theory for two person zero sum repeated games that encompasses stochastic and incomplete information aspects and where concepts of wide relevance are deployed as for example reputation, bounds on rational levels for the payoffs, but also tools like splitting lemma, signalling and approachability. While in many ways Mertens's work here goes back to the von Neumann original roots of game theory with a zero-sum two person set up, vitality and innovations with wider application have been pervasive. == Stochastic games == Stochastic games were introduced by Lloyd Shapley in 1953. The first paper studied the discounted two-person zero-sum stochastic game with finitely many states and actions and demonstrates the existence of a value and stationary optimal strategies. The study of the undiscounted case evolved in the following three decades, with solutions of special cases by Blackwell and Ferguson in 1968 and Kohlberg in 1974. The existence of an undiscounted value in a very strong sense, both a uniform value and a limiting average value, was proved in 1981 by Jean-François Mertens and Abraham Neyman. The study of the non-zero-sum with a general state and action spaces attracted much attention, and Mertens and Parthasarathy proved a general existence result under the condition that the transitions, as a function of the state and actions, are norm continuous in the actions. == Market games: limit price mechanism == Mertens had the idea to use linear competitive economies as an order book (trading) to model limit orders and generalize double auctions to a multivariate set up. Acceptable relative prices of players are conveyed by their linear preferences, money can be one of the goods and it is ok for agents to have positive marginal utility for money in this case (after all agents are really just orders!). In fact this is the case for most order in practice. More than one order (and corresponding order-agent) can come from same actual agent. In equilibrium good sold must have been at a relative price compared to the good bought no less than the one implied by the utility function. Goods brought to the market (quantities in the order) are conveyed by initial endowments. Limit order are represented as follows: the order-agent brings one good to the market and has non zero marginal utilities in that good and another one (money or numeraire). An at market sell order will have a zero utility for the good sold at market and positive for money or the numeraire. Mertens clears orders creating a matching engine by using the competitive equilibrium – in spite of most usual interiority conditions being violated for the auxiliary linear economy. Mertens's mechanism provides a generalization of Shapley–Shubik trading posts and has the potential of a real life implementation with limit orders across markets rather than with just one specialist in one market. == Shapley value == The diagonal formula in the theory of non-atomic cooperatives games elegantly attributes the Shapley value of each infinitesimal player as his marginal contribution to the worth of a perfect sample of the population of players when averaged over all possible sample sizes. Such a marginal contribution has been most easily expressed in the form of a derivative—leading to the diagonal formula formulated by Aumann and Shapley. This is the historical reason why some differentiability conditions have been originally required to define Shapley value of non-atomic cooperative games. But first exchanging the order of taking the "average over all possible sample sizes" and taking such a derivative, Jean-François Mertens uses the smoothing effect of such an averaging process to extend the applicability of the diagonal formula. This trick alone works well for majority games (represented by a step function applied on the percentage of population in the coalition). Exploiting even further this commutation idea of taking averages before taking derivative, Jean-François Mertens expends by looking at invariant transformations and taking averages over those, before taking the derivative. Doing so, Mertens expends the diagonal formula to a much larger space of games, defining a Shapley value at the same time. == Refinements and Mertens-stable equilibria == Solution concepts that are refinements of Nash equilibrium have been motivated primarily by arguments for backward induction and forward induction. Backward induction posits that a player's optimal action now anticipates the optimality of his and others' future actions. The refinement called subgame perfect equilibrium implements a weak version of backward induction, and increasingly stronger versions are sequential equilibrium, perfect equilibrium, quasi-perfect equilibrium, and proper equilibrium, where the latter three are obtained as limits of perturbed strategies. Forward induction posits that a player's optimal action now presumes the optimality of others' past actions whenever that is consistent with his observations. Forward induction is satisfied by a sequential equilibrium for which a player's belief at an information set assigns probability only to others' optimal strategies that enable that information to be reached. In particular since completely mixed Nash equilibrium are sequential – such equilibria when they exist satisfy both forward and backward induction. In his work Mertens manages for the first time to select Nash equilibria that satisfy both forward and backward induction. The method is to let such feature be inherited from perturbed games that are forced to have completely mixed strategies—and the goal is only achieved with Mertens-stable equilibria, not with the simpler Kohlberg Mertens equilibria. Elon Kohlberg and Mertens emphasized that a solution concept should be consistent with an admissible decision rule. Moreover, it should satisfy the invariance principle that it should not depend on which among the many equivalent representations of the strategic situation as an extensive-form game is used. In particular, it should depend only on the reduced normal form of the game obtained after elimination of pure strategies that are redundant because their payoffs for all players can be replicated by a mixture of other pure strategies. Mertens emphasized also the importance of the small worlds principle that a solution concept should depend only on the ordinal properties of players' preferences, and should not depend on whether the game includes extraneous players whose actions have no effect on the original players' feasible strategies and payoffs. Kohlberg and Mertens defined tentatively a set-valued solution concept called stability for games with finite numbers of pure strategies that satisfies admissibility, invariance and forward induction, but a counterexample showed that it need not satisfy backward induction; viz. the set might not include a sequential equilibrium. Subsequently, Mertens defined a refinement, also called stability and now often called a set of Mertens-stable equilibria, that has several desirable properties: Admissibility and Perfection: All equilibria in a stable set are perfect, hence admissible. Backward Induction and Forward Induction: A stable set includes a proper equilibrium of the normal form of the game that induces a quasi-perfect and sequential equilibrium in every extensive-form game with perfect recall that has the same normal form. A subset of a stable set survives iterative elimination of weakly dominated strategies and strategies that are inferior replies at every equilibrium in the set. Invariance and Small Worlds: The stable sets of a game are the projections of the stable sets of any larger game in which it is embedded while preserving the original players' feasible strategies and payoffs. Decomposition and Player Splitting. The stable sets of the product of two independent games are the products of their stable sets. Stable sets are not affected by splitting a player into agents such that no path through the game tree includes actions of two agents. For two-player games with perfect recall and generic payoffs, stability is equivalent to just three of these properties: a stable set uses only undominated strategies, includes a quasi-perfect equilibrium, and is immune to embedding in a larger game. A stable set is defined mathematically by (in brief) essentiality of the projection map from a closed connected neighborhood in the graph of the Nash equilibria over the space of perturbed games obtained by perturbing players' strategies toward completely mixed strategies. This definition entails more than the property that every nearby game has a nearby equilibrium. Essentiality requires further that no deformation of the projection maps to the boundary, which ensures that perturbations of the fixed point problem defining Nash equilibria have nearby solutions. This is apparently necessary to obtain all the desirable properties listed above. == Social choice theory and relative utilitarianism == A social welfare function (SWF) maps profiles of individual preferences to social preferences over a fixed set of alternatives. In a seminal paper Arrow (1950) showed the famous "Impossibility Theorem", i.e. there does not exist an SWF that satisfies a very minimal system of axioms: Unrestricted Domain, Independence of Irrelevant Alternatives, the Pareto criterion and Non-dictatorship. A large literature documents various ways to relax Arrow's axioms to get possibility results. Relative Utilitarianism (RU) (Dhillon and Mertens, 1999) is a SWF that consists of normalizing individual utilities between 0 and 1 and adding them, and is a "possibility" result that is derived from a system of axioms that are very close to Arrow's original ones but modified for the space of preferences over lotteries. Unlike classical Utilitarianism, RU does not assume cardinal utility or interpersonal comparability. Starting from individual preferences over lotteries, which are assumed to satisfy the von-Neumann–Morgenstern axioms (or equivalent), the axiom system uniquely fixes the interpersonal comparisons. The theorem can be interpreted as providing an axiomatic foundation for the "right" interpersonal comparisons, a problem that has plagued social choice theory for a long time. The axioms are: Individualism: If all individuals are indifferent between all alternatives then so is society, Non Triviality: The SWF is not constantly totally indifferent between all alternatives, No Ill will: It is not true that when all individuals but one are totally indifferent then society's preferences are opposite to his, Anonymity: A permutation of all individuals leaves the social preferences unchanged. Independence of Redundant Alternatives: This axiom restricts Arrow's Independence of Irrelevant Alternatives (IIA) to the case where both before and after the change, the "irrelevant" alternatives are lotteries on the other alternatives. Monotonicity is much weaker than the following "good will axiom": Consider two lotteries p {\displaystyle p} and q {\displaystyle q} and two preference profiles which coincide for all individuals except i {\displaystyle i} , i {\displaystyle i} is indifferent between p {\displaystyle p} and q {\displaystyle q} on the first profile but strictly prefers p {\displaystyle p} to q {\displaystyle q} in the second profile, then society strictly prefers p {\displaystyle p} to q {\displaystyle q} in the second profile as well. Finally the Continuity axiom is basically a closed graph property taking the strongest possible convergence for preference profiles. The main theorem shows that RU satisfies all the axioms and if the number of individuals is bigger than three, number of candidates is bigger than 5 then any SWF satisfying the above axioms is equivalent to RU, whenever there exist at least 2 individuals who do not have exactly the same or exactly the opposite preferences. == Intergenerational equity in policy evaluation == Relative utilitarianism can serve to rationalize using 2% as an intergenerationally fair social discount rate for cost-benefit analysis. Mertens and Rubinchik show that a shift-invariant welfare function defined on a rich space of (temporary) policies, if differentiable, has as a derivative a discounted sum of the policy (change), with a fixed discount rate, i.e., the induced social discount rate. (Shift-invariance requires a function evaluated on a shifted policy to return an affine transformation of the value of the original policy, while the coefficients depend on the time-shift only.) In an overlapping generations model with exogenous growth (with time being the whole real line), relative utilitarian function is shift-invariant when evaluated on (small temporary) policies around a balanced growth equilibrium (with capital stock growing exponentially). When policies are represented as changes in endowments of individuals (transfers or taxes), and utilities of all generations are weighted equally, the social discount rate induced by relative utilitarianism is the growth rate of per capita GDP (2% in the U.S.). This is also consistent with the current practices described in the Circular A-4 of the US Office of Management and Budget, stating: If your rule will have important intergenerational benefits or costs you might consider a further sensitivity analysis using a lower but positive discount rate in addition to calculating net benefits using discount rates of 3 and 7 percent. == References ==
|
Wikipedia:Jean-Louis Loday#0
|
Jean-Louis Loday (12 January 1946 – 6 June 2012) was a French mathematician who worked on cyclic homology and who introduced Leibniz algebras (sometimes called Loday algebras) and Zinbiel algebras. He occasionally used the pseudonym Guillaume William Zinbiel, formed by reversing the last name of Gottfried Wilhelm Leibniz. == Education and career == Loday studied at Lycée Louis-le-Grand and at École Normale Supérieure in Paris. He completed his Ph.D. at the University of Strasbourg in 1975 under the supervision of Max Karoubi, with a dissertation titled K-Théorie algébrique et représentations de groupes. He went on to become a senior scientist at CNRS and a member of the Institute for Advanced Mathematical Research (IRMA) at the University of Strasbourg. == Publications == Loday, Jean-Louis (1998), Cyclic homology, Grundlehren der Mathematischen Wissenschaften, vol. 301 (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-3-540-63074-6, MR 1600246 Loday, Jean-Louis & Pirashvili, Teimuraz (1993). "Universal enveloping algebras of Leibniz algebras and (co)homology". Mathematische Annalen. 296 (1): 139–158. CiteSeerX 10.1.1.298.1142. doi:10.1007/BF01445099. S2CID 16865683. Loday, Jean-Louis; Vallette, Bruno (2012), Algebraic Operads (PDF), Grundlehren der Mathematischen Wissenschaften, vol. 346, Berlin, New York: Springer-Verlag, ISBN 978-3-642-30361-6, archived from the original (PDF) on 2011-08-23, retrieved 2012-06-20 Zinbiel, Guillaume William (2012), "Encyclopedia of types of algebras 2010", in Guo, Li; Bai, Chengming; Loday, Jean-Louis (eds.), Operads and universal algebra, Nankai Series in Pure, Applied Mathematics and Theoretical Physics, vol. 9, pp. 217–298, arXiv:1101.0267, Bibcode:2011arXiv1101.0267Z, ISBN 9789814365116, Zinbiel is a pseudonym of Jean-Louis Loday == See also == Associahedron Blakers–Massey theorem Loday functor == References == Obituary Home page Archived 2017-07-04 at the Wayback Machine Jean-Louis Loday at the Mathematics Genealogy Project == External links == Loday's biography of Guillaume William Zinbiel Archived 2011-08-23 at the Wayback Machine
|
Wikipedia:Jean-Marie Souriau#0
|
Jean-Marie Souriau (3 June 1922, Paris – 15 March 2012, Aix-en-Provence) was a French mathematician. He was one of the pioneers of modern symplectic geometry. == Education and career == Souriau started studying mathematics in 1942 at École Normale Supérieure in Paris. In 1946 he was a research fellow of CNRS and an engineer at ONERA. His PhD thesis, defended in 1952 under the supervision of Joseph Pérès and André Lichnerowicz, was entitled "Sur la stabilité des avions" (On the stability of planes). Between 1952 and 1958 he worked at Institut des Hautes Études in Tunis, and since 1958 he was Professor of Mathematics at the University of Provence in Marseille. In 1981 he was awarded the Prix Jaffé of the French Academy of Sciences. == Research == Souriau contributed to the introduction and the development of many important concepts in symplectic geometry, arising from classical and quantum mechanics. In particular, he introduced the notion of moment map, gave a classification of the homogeneous symplectic manifolds (now known as the Kirillov–Kostant–Souriau theorem), and investigated the coadjoint action of a Lie group, which led to the first geometric interpretation of spin at a classical level. He also suggested a program of geometric quantization and developed a more general approach to differentiable manifolds by means of diffeologies. Souriau published more than 50 papers in peer-review scientific journals, as well as three monographs, on linear algebra, on relativity and on geometric mechanics. He supervised 9 PhD students. == References == == External links == Jean-Marie Souriau official website (the website hosts copies of many of Souriau's works) Ray F. Streater: Souriau Patrick Iglesias-Zemmour: Souriau (in French) In Memoriam Conference 2012: Web site "Structure des Systèmes Dynamiques" Anniversary Conference 2019 Interview of Jean-Marie Souriau by Laurence Honnorat on YouTube (in French)
|
Wikipedia:Jean-Michel Coron#0
|
Jean-Michel Coron (born August 8, 1956) is a French mathematician. He first studied at École Polytechnique, where he worked on his PhD thesis advised by Haïm Brezis. Since 1992, he has studied the control theory of partial differential equations, and which includes both control and stabilization. His results concern partial differential equations related to fluid dynamics, with emphasis on nonlinear phenomena, and part of them found applications to control channels. He had previously worked in the field of non-linear functional analysis, where he also obtained significant results. Jean-Michel Coron was awarded numerous prizes, such as the Fermat prize in 1993, the Peccot lecture in 1987, the Jaffé prize in 1995 by the Académie des Sciences, and the Dargelos prize in 2002. He was invited at the 1990 International Congress of Mathematicians (Kyoto) in the section Partial Differential Equations, and he was also invited as a plenary speaker at the 2010 International Congress of Mathematicians, Hyderabad, India. He is an emeritus Professor at Sorbonne University in Paris, and was a Senior member of the Institut Universitaire de France between 2003 and 2013. He is also a member of the Académie des Sciences and the Academia Europaea. Jean-Michel Coron is the husband of Claire Voisin who was also plenary speaker at the 2010 International Congress of Mathematicians and who is the 2016 recipient of the Gold medal of the French National Centre for Scientific Research, the highest scientific research award in France. They have five children. == Notable publications == Haïm Brezis and Jean-Michel Coron. Multiple solutions of H-systems and Rellich's conjecture. Comm. Pure Appl. Math. 37 (1984), no. 2, 149–187. Jean-Michel Coron. Topologie et cas limite des injections de Sobolev. C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), no. 7, 209–212. H. Brezis and J.-M. Coron. Convergence of solutions of H-systems or how to blow bubbles. Arch. Rational Mech. Anal. 89 (1985), no. 1, 21–56. Haïm Brezis, Jean-Michel Coron, and Elliott H. Lieb. Harmonic maps with defects. Comm. Math. Phys. 107 (1986), no. 4, 649–705. doi:10.1007/BF01205490 A. Bahri and J.-M. Coron. On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain. Comm. Pure Appl. Math. 41 (1988), no. 3, 253–294. A. Bahri and J.-M. Coron. The scalar-curvature problem on the standard three-dimensional sphere. J. Funct. Anal. 95 (1991), no. 1, 106–172. Jean-Michel Coron. Global asymptotic stabilization for controllable systems without drift. Math. Control Signals Systems 5 (1992), no. 3, 295–312. doi:10.1007/BF01211563 Jean-Michel Coron, Brigitte d'Andréa-Novel, and Georges Bastin. A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws. IEEE Trans. Autom. Control 52 (2007), no. 1, 2–11. doi:10.1109/TAC.2006.887903 == References == == External links == fr:Institut universitaire de France Institut Universitaire de France (IUF) "Personal page of Jean-Michel Coron at Laboratoire Jacques-Louis Lions". Archived from the original on September 9, 2009. "Coron: List of publications (with links to several videos)". Université Pierre-et-Marie-Curie (UPMC). Jean-Michel Coron at the Mathematics Genealogy Project
|
Wikipedia:Jean-Michel Salanskis#0
|
Jean-Michel Emmanuel Salanskis (born 5 April 1951 in Paris) is a French philosopher and mathematician, professor of science and philosophy at the University of Paris X Nanterre. == Life == Originally gaining a Diplôme d'études approfondies in pure mathematics, he went on to study philosophy with Luis Puig and Jean-Francois Lyotard from 1974 to 1983. In 1986 he completed a doctoral dissertation on Le continu et le discret (the continuous and the discrete). == Work == He is an important interpreter of continental philosophers such as Jacques Derrida, Emmanuel Levinas, Edmund Husserl, Martin Heidegger, and Gilles Deleuze, and he has published widely in English and French. He has also written about Judaism and the philosophy of mathematics. In his book La gauche et l'égalité he argues that the left is structured by a “critique of power taking the form of a critique of man’s humiliation at the hands of transcendence" (p. 22), and that it is therefore necessary "to eliminate entirely the communist episode from the left,” for this episode partakes of the crushing of the people by one man who can “become the keystone of the world, restoring the attributes and the aura of royalty" (p. 37). In his 2010 book Derrida, he presents the philosophy of Jacques Derrida in an accessible manner for the lay reader, showing how Derrida's work related to the fields of psychoanalysis, radical politics, and literature. In Les temps du sens he embarks on a project to devise a mathematical hermeneutics that can be applied to fields such as philosophy of science, cognitive sciences and philosophy of religion. == Bibliography == 1991 - "L'herméneutique formelle" Éditions du CNRS. 1997 - "Heidegger" Belles Lettres. 1997 - "Le Temps du Sens" (English: The times of the senses). Hyx. 1998 - "Husserl". Belles Lettres. 1999 - "Le constructivisme non standard" Presses universitaires du Septentrion. 2000 - "Modèles et pensées de l'action"(Paris : L'harmattan). 2001 - "Sens et philosophie du sens"(Paris : Desclée de Brouwer). 2003 - 'Extermination, loi, Israël. Ethanalyse du fait juif" (English: Extermination, law, Israel: Eth-Analysis of the Jewish Fact) Paris, Les Belles Lettres. 2003 - "Herméneutique et cognition" Presses universitaires du Septentrion. 2004 - "Talmud, science et philosophie (English: Talmud, science and philosophy) Paris Les Belles Lettres. 2006 - "Lévinas vivant" (English: Lévinas alive) Paris, Les Belles Lettres. 2007 - "Territoires de sens" (English: Territories of the senses) Librairie Philosophique Vrin. 2008 - "Usages contemporains de la phénoménologie" (avec F.-D. Sebbah) Paris, Sens et Tonka. 2008 - "Philosophie des mathématiques" (English: Philosophy of Mathematics) Librairie Philosophique Vrin. 2009 - "Heidegger, le mal et la science. (English: Heidegger, Evil and Science) Paris, Klincksieck. 2009 - "Vivre avec les mathématiques" (English: Life with Mathematics) Seuil. 2009 - "La Gauche et L'égalité. (English: The Left and Equality) Presses Universitaires de France. 2010 - "Derrida". Belles Lettres. 2011 - "Le monde du computationnel" (English: the World of the Computational) Paris, Encre Marine. 2011 - "L'émotion éthique (Levinas vivant I)", Paris, Klincksieck. 2011 - "L'humanité de l'homme (Levinas vivant II)", Paris, Klincksieck. 2013 - "L'herméneutique formelle" (second edition), Paris, Klincksieck. 2014 - "Partages du sens", Nanterre, Presses Universitaires de Paris Nanterre. 2015 - "Le concret et l'idéal (Levinas vivant III)", Paris, Klincksieck. 2015 - "De la série à l'ethos", Nanterre, Presses Universitaires de Paris Nanterre. 2016 - "Crépuscule du théorique?" Paris, Encre Marine. 2016 - "Philosophie française et philosophie analytique au XXe siècle Presses Universitaires de France. 2016 - "L'humain impensé", (avec A. Piette) Nanterre, Presses Universitaires de Paris Nanterre. 2017 - "Le fait juif" (English: The Jewish Fact) Paris, Les Belles Lettres. 2019 - "La voie idéale Paris, Presses Universitaires de France. 2020 - "Itinerarium Jeana François Lyotarda. Wprowadzenie do filizofii XX wieku, Warsaw, Semper. 2020 - "Versions du politique", Nanterre, Presses Universitaires de Paris Nanterre. === Articles in English === 1994 - "Continuity, cognition, linguistics", in The Continuum in Semantical Linguistics, C. Fuchs and B. Victorri (Ed.), Amsterdam/Philadelphia, J. Benjamins, 127-153. 1995 - "Die Wissenschaft denkt nicht", in Tekhnema n° 2, trad. G. Collins, Paris, 60-84. 1996 - "Idea and Destination" in Deleuze : A Critical Reader, P. Patton ed., Oxford-Cambridge, Blackwell, 1996, 57-80. 1997 - "Analysis, Hermeneutics, Mathematics", in Otte, M., & Panza, M. (eds), Analysis and Synthesis in Mathematics, Kluwer Academic Publishers, 227-241. 2000- "Sense and Continuum in Husserl", in Petitot, J., Varela, F.J., Pachoud, B., & Roy, J.-M., Naturalizing Phenomenology, Standford, Stanford University Press, 490-507. 2002 - "Some Figures of Matter", in What is Materialism ?, Plì The Warwick Journal of Philosophy, Brassier, R. & Toscano, A. eds, vol. 12, Warwick, 2001, 5-13. 2006- "Mathematics, Metaphysics, Philosophy", in Duffy, S., (ed.)Virtual Mathematics, Manchester, Clinamen Press, 46-64. 2010- "The Early Levinas and Heidegger", in Levinas Studies, vol. 5, Pittsburgh, Duquenne University Press, pp. 43–64. 2012- "Honneth, Lyotard, Levinas", in Recognition theory and contemporary French moral and political philosophy, Manchester, Manchester University Press, pp. 191–207. 2014- "Some notions of action", in Science After the Practice Turn in Philosophy, History and the Social Studies of Science, Routledge, pp. 44–57. 2015- "Freedom of Framework", in Science as it Could Have Been, L. Soler, E. Trizio and A. Pickering (ed.), Pittsburgh, University of Pittsburgh Press, pp. 240–261. 2019- "Violence, a Slippery Notion", in Murawska, M. and Sosnowska, P. (eds), Eidos A Journal for Philosophy of Culture, Volume 3: No. 2 (8)/2019, Labyrinths of Violence, pp. 5–12. 2021- "Truth, Practice and Philosophy of Culture", in Eidos A Journal for Philosophy of Culture, vol.4 n°4, pp. 7–16. == References == == External links == Official page at University of Paris, Nanterre
|
Wikipedia:Jean-Paul Bergeron#0
|
Jean-Paul Bergeron (born October 21, 1947) is a Quebec politician. He previously served as the member for Iberville in the Quebec National Assembly as a member of the Parti Québécois from 1998 until 2003. == Biography == Bergeron was born in Saint-Alexandre, Quebec. He earned his bachelor's degree in pedagogy from the Université de Montréal in 1969. He holds a certificate in computer science, a master's degree in education and a Doctorate in mathematics from the Université du Québec à Montréal. Bergeron was a high school mathematics teacher from and a lecturer at TÉLUQ. == Political career == Bergeron ran in the 1998 Quebec provincial election for the seat of Iberville that was left open by the decision of former Cabinet Minister Richard Le Hir to not run. He won easily. He served as a backbench supporter in the governments of Lucien Bouchard and Bernard Landry. He was defeated in the 2003 election by Jean Rioux of the Quebec Liberal Party by less than 1,000 votes. Bergeron attempted to run again for Iberville in 2007 election but lost the PQ nomination to Marie Bouillé 168–156. == Electoral record == === Provincial === == References ==
|
Wikipedia:Jean-Paul Delahaye#0
|
Jean-Paul Delahaye (born 29 June 1952 in Saint-Mandé Seine) is a French computer scientist and mathematician. == Career == Delahaye has been a professor of computer science at the Lille University of Science and Technology since 1988 and a researcher in the school's computer sciences lab since 1983. Since 1991 he has written a monthly column in Pour la Science, the French version of Scientific American, dealing with mathematical games and recreations, logic, and computer science. He is a contributing author of the online scientific journal Interstices and a science and mathematics advisor to the Encyclopædia Britannica. Delahaye won the 1998 d'Alembert prize from the Société mathématique de France for his books and articles popularizing mathematics, especially for the book Le fascinant nombre Pi. == Works == Delahaye, J.-P. (1981). "Automatic selection of sequence transformations". Math. Comp. 37 (155): 197–204. doi:10.1090/S0025-5718-1981-0616372-5. Formal Methods in Artificial Intelligence, North-Oxford Academic, 1987, ISBN 0470208260 Le fascinant nombre pi, Paris: Bibliothèque Pour la Science, 1997, ISBN 2902918259 == References == == External links == Media related to Jean-Paul Delahaye at Wikimedia Commons Jean-Paul Delahaye at the Mathematics Genealogy Project Jean-Paul Delahaye's home page
|
Wikipedia:Jean-Paul Pier#0
|
Jean-Paul Pier (July 5, 1933 – December 14, 2016) was a Luxembourgish mathematician, specializing in harmonic analysis and the history of mathematics, particularly mathematical analysis in the 20th century. == Education and career == Jean-Paul Pier was a graduate student in Luxembourg and at the universities of Paris and Nancy. He earned a University of Luxembourg doctorate in mathematical sciences and a French doctorate in pure mathematics. He also spent six months at the Grenoble Nuclear Research Center (1961) and a year at the University of Oregon (1966-1967). He taught mathematics at the Lycée de Garçons in Esch-sur-Alzette from 1956 to 1980. In 1971 he created the Séminaire de mathématiques at the Centre universitaire de Luxembourg (now the University of Luxembourg). He was a professor at the Centre from its creation in 1974 until 1998, when he retired as professor emeritus. Pier was primarily responsible for the creation in January 1989 of the Luxembourg Mathematical Society, of which he was president from 1989 to 1993 and again from 1995 to 1998. He was during the academic year 1994–1995 a visiting professor at the Université catholique de Louvain. Pier was the editor of two scholarly anthologies, which are standard works on the history of 20th-century mathematics. He organized several colloquia and conferences in Luxembourg. He was active internationally in various scientific bodies, including NATO Science for Peace and Security and UNESCO. == Selected publications == Amenable locally compact groups, Wiley, 1984. Amenable Banach algebras, Longman, 1988. L'Analyse harmonique. Son développement historique, Masson, 1990. Histoire de l'intégration, vingt-cinq siècles de mathématiques, Masson, 1996. Mathematical Analysis during the 20th century, Oxford University Press, 2001 Mathématiques entre savoir et connaissance, Vuibert, 2006. Development of Mathematics 1900-1950, edited by Jean-Paul Pier, Birkhäuser, 1994. Development of Mathematics 1950-2000, edited by Jean-Paul Pier, Birkhäuser, 2000. Gabriel Lippmann. Commémoration par la section des sciences naturelles, physiques et mathématiques de l’Institut grand-ducal de Luxembourg du 150e anniversaire du savant né au Luxembourg lauréat du prix Nobel en 1908, J.-P. Pier et J. A. Massard, éditeurs, 1997. Le Choix de la parole, Lethielleux/DDB, 2009. == References == == External links == Bibliothèque nationale de France Bibliothèque du Congrès
|
Wikipedia:Jean-Pierre Serre#0
|
Jean-Pierre Serre (French: [sɛʁ]; born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inaugural Abel Prize in 2003. == Biography == === Personal life === Born in Bages, Pyrénées-Orientales, to pharmacist parents, Serre was educated at the Lycée de Nîmes. Then he studied at the École Normale Supérieure in Paris from 1945 to 1948. He was awarded his doctorate from the Sorbonne in 1951. From 1948 to 1954 he held positions at the Centre National de la Recherche Scientifique in Paris. In 1956 he was elected professor at the Collège de France, a position he held until his retirement in 1994. His wife, Professor Josiane Heulot-Serre, was a chemist; she also was the director of the Ecole Normale Supérieure de Jeunes Filles. Their daughter is the former French diplomat, historian and writer Claudine Monteil. The French mathematician Denis Serre is his nephew. He practices skiing, table tennis, and rock climbing (in Fontainebleau). === Career === From a very young age he was an outstanding figure in the school of Henri Cartan, working on algebraic topology, several complex variables and then commutative algebra and algebraic geometry, where he introduced sheaf theory and homological algebra techniques. Serre's thesis concerned the Leray–Serre spectral sequence associated to a fibration. Together with Cartan, Serre established the technique of using Eilenberg–MacLane spaces for computing homotopy groups of spheres, which at that time was one of the major problems in topology. In his speech at the Fields Medal award ceremony in 1954, Hermann Weyl gave high praise to Serre, and also made the point that the award was for the first time awarded to a non-analyst. Serre subsequently changed his research focus. ==== Algebraic geometry ==== In the 1950s and 1960s, a fruitful collaboration between Serre and the two-years-younger Alexander Grothendieck led to important foundational work, much of it motivated by the Weil conjectures. Two major foundational papers by Serre were Faisceaux Algébriques Cohérents (FAC, 1955), on coherent cohomology, and Géométrie Algébrique et Géométrie Analytique (GAGA, 1956). Even at an early stage in his work Serre had perceived a need to construct more general and refined cohomology theories to tackle the Weil conjectures. The problem was that the cohomology of a coherent sheaf over a finite field could not capture as much topology as singular cohomology with integer coefficients. Amongst Serre's early candidate theories of 1954–55 was one based on Witt vector coefficients. Around 1958 Serre suggested that isotrivial principal bundles on algebraic varieties – those that become trivial after pullback by a finite étale map – are important. This acted as one important source of inspiration for Grothendieck to develop the étale topology and the corresponding theory of étale cohomology. These tools, developed in full by Grothendieck and collaborators in Séminaire de géométrie algébrique (SGA) 4 and SGA 5, provided the tools for the eventual proof of the Weil conjectures by Pierre Deligne. ==== Other work ==== From 1959 onward Serre's interests turned towards group theory, number theory, in particular Galois representations and modular forms. Amongst his most original contributions were: his "Conjecture II" (still open) on Galois cohomology; his use of group actions on trees (with Hyman Bass); the Borel–Serre compactification; results on the number of points of curves over finite fields; Galois representations in ℓ-adic cohomology and the proof that these representations have often a "large" image; the concept of p-adic modular form; and the Serre conjecture (now a theorem) on mod-p representations that made Fermat's Last Theorem a connected part of mainstream arithmetic geometry. In his paper FAC, Serre asked whether a finitely generated projective module over a polynomial ring is free. This question led to a great deal of activity in commutative algebra, and was finally answered in the affirmative by Daniel Quillen and Andrei Suslin independently in 1976. This result is now known as the Quillen–Suslin theorem. == Honors and awards == Serre, at twenty-seven in 1954, was and still is the youngest person ever to have been awarded the Fields Medal. He went on to win the Balzan Prize in 1985, the Steele Prize in 1995, the Wolf Prize in Mathematics in 2000, and was the first recipient of the Abel Prize in 2003. He has been awarded other prizes, such as the Gold Medal of the French National Scientific Research Centre (Centre National de la Recherche Scientifique, CNRS). He is a foreign member of several scientific Academies (US, Norway, Sweden, Russia, the Royal Society, Royal Netherlands Academy of Arts and Sciences (1978), American Academy of Arts and Sciences, National Academy of Sciences, the American Philosophical Society) and has received many honorary degrees (from Cambridge, Oxford, Harvard, Oslo and others). In 2012 he became a fellow of the American Mathematical Society. Serre has been awarded the highest honors in France as Grand Cross of the Legion of Honour (Grand Croix de la Légion d'Honneur) and Grand Cross of the Legion of Merit (Grand Croix de l'Ordre National du Mérite). == See also == Multiplicity (mathematics) Bourbaki group — Serre joined it in the late 1940s == Bibliography == A list of corrections, and updating, of these books can be found on his home page at Collège de France. == Notes == == External links == O'Connor, John J.; Robertson, Edmund F., "Jean-Pierre Serre", MacTutor History of Mathematics Archive, University of St Andrews Jean-Pierre Serre at the Mathematics Genealogy Project Jean-Pierre Serre, Collège de France, biography and publications. Jean-Pierre Serre Archived 11 June 2007 at the Wayback Machine at the French Academy of Sciences, in French. Interview with Jean-Pierre Serre in Notices of the American Mathematical Society. An Interview with Jean-Pierre Serre by C.T. Chong and Y.K. Leong, National University of Singapore. How to write mathematics badly a public lecture by Jean-Pierre Serre on writing mathematics. Biographical page Archived 11 June 2007 at the Wayback Machine (in French)
|
Wikipedia:Jean-Yves Girard#0
|
Jean-Yves Girard (French: [ʒiʁaʁ]; born 1947) is a French logician working in proof theory. He is a research director (emeritus) at the mathematical institute of University of Aix-Marseille, at Luminy. == Biography == Jean-Yves Girard is an alumnus of the École normale supérieure de Saint-Cloud. He made a name for himself in the 1970s with his proof of strong normalization in a system of second-order logic called System F. This result gave a new proof of Takeuti's conjecture, which was proven a few years earlier by William W. Tait, Motō Takahashi and Dag Prawitz. For this purpose, he introduced the notion of "reducibility candidate" ("candidat de réducibilité"). He is also credited with the discovery of Girard's paradox, linear logic, the geometry of interaction, ludics, and (satirically) the mustard watch. He obtained the CNRS Silver Medal in 1983 and is a member of the French Academy of Sciences. == Bibliography == Ernest Nagel; James R. Newman; Kurt Gödel; Jean-Yves Girard (1989). Le théorème de Gödel. Éditions du Seuil. Jean-Yves Girard; P. Taylor; Yves Lafont (1989). Proofs and Types. Cambridge University Press. Jean-Yves Girard (2007). Le Point Aveugle, Cours de Logique. Hermann. Jean-Yves Girard (2011). The Blind Spot: Lectures on Logic Jean-Yves Girard (2016). Le fantôme de la transparence. Éditions Allia. == See also == Affine logic Linear logic == References == == External links == Official website Jean-Yves Girard at the Mathematics Genealogy Project Jean-Yves Girard at DBLP Bibliography Server Journées Jean-Yves Girard web site of 2007 conference in honour of Girard's 60th birthday
|
Wikipedia:Jean-Yves Jaffray#0
|
Jean-Yves Jaffray (1939–2009) was a French mathematician and economist who made influential contributions in the fields of decision theory and mathematical statistics. He pioneered methods in decision theory such as linear utility theory for belief functions, bridging the gap between expected utility and the maximin rule by using subjective probability to encompass belief functions. == References ==
|
Wikipedia:Jean-Éric Pin#0
|
Jean-Éric Pin is a French mathematician and theoretical computer scientist known for his contributions to the algebraic automata theory and semigroup theory. He is a CNRS research director. == Biography == Pin earned his undergraduate degree from ENS Cachan in 1976 and his doctorate (Doctorat d'état) from the Pierre and Marie Curie University in 1981. Since 1988 he has been a CNRS research director at Paris Diderot University. In the years 1992–2006 he was a professor at École Polytechnique. Pin is a member of the Academia Europaea (2011) and an EATCS fellow (2014). In 2018, Pin became the first recipient of the Salomaa Prize in Automata Theory, Formal Languages, and Related Topics. == Notable Work == Pin is the author of the prominent textbook Varieties of Formal Languages on automata theory and formal language theory. == References == == External links == Personal page
|
Wikipedia:Jeanne Peiffer#0
|
Jeanne Peiffer (born 20 August 1948 in Mersch) is a Luxembourgish historian of mathematics. She is Emeritus Research Director at the CNRS, at the Center Alexandre Koyré of the CNRS, and at the École des hautes études en sciences sociales (EHESS). == Biography == Peiffer studied at the University of Luxembourg where she was a professor after being a student of René Taton. She was co-editor (with Pierre Costabel) of the correspondence of Johann Bernoulli (Birkhäuser 1988, 1992) and published a French translation of the geometry of Albrecht Dürer. With Amy Dahan, she wrote a popular French-language history of mathematics that was translated into English and German. From 1995 to 2015 she was co-editor of the Revue d'histoire des mathématiques and co-editor of Historia Mathematica. She deals with scientific journals in the 17th and 18th centuries, also from a scientific sociological point of view and with the aspect of the history of the specialization of mathematics journals, with perspective in the Renaissance in connection with geometry and optics, and the letter as a communication tool of mathematics in the 18th century. == Publications == Dahan-Dalmédico, Amy; Peiffer, Jeanne (1986). Une histoire des mathématiques: routes et dédales (in French). Paris: Editions du Seuil. ISBN 978-2-02-009138-1. (English translation) Dahan-Dalmedico, Amy; Pieffer, Jeanne (3 August 2020). History of Mathematics: Highways and Byways. American Mathematical Soc. ISBN 978-1-4704-5746-4. Herausgeberin und Übersetzerin: Albrecht Dürer, Géométrie, Ed. du Seuil 1995 (also translated into Spanish) Faire des mathématiques par lettres, Revue d'histoire des mathématiques IV/1, 1998, pp. 143–157 Peiffer, Jeanne; Vitu, Jean-Pierre (2008). "Les journaux savants, formes de la communication et agents de la construction des savoirs (17e -18e siècles)". Dix-Huitième Siècle (in German). 40: 281–300. doi:10.3917/dhs.040.0281. ISSN 0070-6760. Constructing perspective in sixteenth-century Nuremberg, in: Mario Carpo, Frédérique Lemerle (publisher), Perspective, Projections & Design. Technologies of Architectural Representation, London & New York : Routledge, 2007, pp. 65–76 == References == == External links == Publications by Jeanne Peiffer on CAIRN
|
Wikipedia:Jeannette Janssen#0
|
Jeannette Catharina Maria Janssen is a Dutch and Canadian mathematician whose research concerns graph theory and the theory of complex networks. She is a professor of mathematics at Dalhousie University, the chair of the Dalhousie Department of Mathematics and Statistics, and the chair of the Activity Group on Discrete Mathematics of the Society for Industrial and Applied Mathematics. == Education and career == Janssen earned a master's degree at the Eindhoven University of Technology in 1988. She completed her Ph.D. at Lehigh University in 1993. Her dissertation, Even and Odd Latin Squares, concerned Latin squares and was supervised by Edward F. Assmus Jr. From 1988 to 1990 Janssen was a lecturer at the Universidad de Guanajuato in Mexico. After completing her Ph.D., she became a postdoctoral researcher jointly at the Laboratoire de Combinatoire et d’Informatique Mathématique of Université du Québec à Montréal and at Concordia University. She took a position as a lecturer and research associate at the London School of Economics in 1995, and moved to Acadia University in 1997 before taking her present position at Dalhousie University. At Dalhousie, she was named department chair in 2016, becoming the first female chair of the mathematics department. == Service == Janssen directed the Atlantic Association for Research in the Mathematical Sciences from 2011 to 2016, and chairs its board of directors. She was elected as chair of the Activity Group on Discrete Mathematics (SIAG-DM) of the Society for Industrial and Applied Mathematics (SIAM) for the 2021–2022 term. == Research == In a 1993 paper, Janssen solved the unbalanced case of the Dinitz conjecture, showing that any partial Latin rectangle could be extended to a full rectangle. The problem is equivalent to list edge-coloring of complete bipartite graphs, and her solution was based on earlier work on list coloring by Noga Alon and Michael Tarsi. Janssen's work "surprised even many of the experts", and was considered to be "great progress" on the Dinitz conjecture. The remaining case of the conjecture for squares (balanced complete bipartite graphs) was proven a year later by Fred Galvin. == References == == External links == Home page Jeannette Janssen publications indexed by Google Scholar
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.