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https://en.wikipedia.org/wiki/Nicholas%20C.%20Yannelis | Nicholas C. Yannelis (; born 1953) is the Henry B. Tippie Research Professor of Economics and Applied Mathematics and Computation at the University of Iowa. He is an emeritus Commerce Distinguished Alumni Professor of Economics at the University of Illinois at Urbana-Champaign. Also he was the Sir Johns Hicks Professor of Economics at the University of Manchester. His research includes the study of equilibrium concepts in games and economies with asymmetric information; equilibrium in infinite dimensional commodity spaces; equilibrium in games and economies with discontinuous preferences; and equilibrium theory and implementation under ambiguity. He has also done works in pure mathematics.
Biography
Yannelis studied undergraduate economics at the Athens University of Economics, and pursued graduate studies at the London School of Economics and the University of Rochester. He was awarded a Ph.D. in Economics at the University of Rochester under the direction of Lionel W. McKenzie.
Yannelis is the editor of Economic Theory since 2009, Economic Theory Bulletin since 2013, Studies in Economic Theory since 1991, and the associate editor of the Journal of Mathematical Economics since 1993.
Yannelis became an Economic Theory Fellow in 2011. Together with C. D. Aliprantis and Edward C. Prescott, he founded in 1991 the Society for the Advancement of Economic Theory.
Research
Nicholas C. Yannelis's early work was focused on infinite dimensional general equilibrium theory and the Aumann-Shapley value allocation. To study new problems in general equilibrium theory, Yannelis proved new mathematical results, including Caratheodory-Type Selection Theorems, the Fatou’s Lemma in infinite dimensional spaces, and the upper and lower semicontinuity of set-valued functions in Banach spaces. He subsequently focused on general equilibrium theory with asymmetric information. He proposed the notion of private core and an incentive compatible notion, and further contributed to the Aumann-Shapley values by introducing differential information. Yannelis was the first to model perfect competition in an asymmetric information economy. Yannelis has worked on games and economies with discontinuous preferences. His analysis of payoff discontinuity extends the classical results in abstract economies with non-ordered preferences. Another line of his current research focuses on the ambiguity aversion in economies and games. He has shown that there is no conflict between efficiency and incentive compatibility in the presence of maximin expected utilities, which is generally false in a model with Bayesian decision making agents.
Books
External links
University of Illinois at Urbana-Champaign
Society for the Advancement of Economic Theory
1953 births
Living people
21st-century American economists
20th-century Greek economists
University of Illinois Urbana-Champaign faculty |
https://en.wikipedia.org/wiki/Chile%20national%20football%20team%20records%20and%20statistics | This is a list of Chile national football team's competitive records. The Chile national football team represents Chile in men's international football competitions and is controlled by the Federación de Fútbol de Chile which was established in 1895.
Individual records
Player records
Players in bold are still active, at least at club level.
Most capped players
Top goalscorers
Manager records
Competition records
FIFA World Cup
Champions Runners-up Third place Fourth place
Copa América
FIFA Confederations Cup
Olympic Games
Pan American Games
Head-to-head record
This is a list of the official games played by Chile national football team. Although the team has played a number of countries around the world, some repeatedly, it has played the most games (90) against neighbouring Argentina.
This list is updated to include the match against Paraguay on 28 March 2023.
AFC
CAF
CONCACAF
CONMEBOL
OFC
UEFA
Full Confederation record
References
National association football team records and statistics |
https://en.wikipedia.org/wiki/Robert%20Remak%20%28mathematician%29 | Robert Erich Remak (14 February 1888 – 13 November 1942) was a German mathematician. He is chiefly remembered for his work in group theory (Remak decomposition). His other interests included algebraic number theory, mathematical economics and geometry of numbers. Robert Remak was the son of the neurologist Ernst Julius Remak and the grandson of the embryologist Robert Remak. He was murdered in the Holocaust.
Biography
Robert Remak was born in Berlin. He studied at Humboldt University of Berlin under Ferdinand Georg Frobenius and received his doctorate in 1911. His dissertation, Über die Zerlegung der endlichen Gruppen in indirekte unzerlegbare Faktoren ("On the decomposition of a finite group into indirect indecomposable factors") established that any two decompositions of a finite group into a direct product are related by a central automorphism. A weaker form of this statement, uniqueness, was first proved by Joseph Wedderburn in 1909. Later the theorem was generalized by Wolfgang Krull and Otto Schmidt to some classes of infinite groups and became known as the Krull–Schmidt theorem or the Krull–Remak–Schmidt theorem.
Although the dissertation was first submitted in 1911, it was rejected several times and Remak did not obtain his Habilitation until 1929. In the meantime, he wrote several papers on the geometry of numbers. Between 1929 and 1933 Remak lectured as a Privatdozent at Humboldt University. In the 1929 essay Kann die Volkwirtschaftslehre eine exakte Wissenschaft werden? ("Can economics become an exact science?"), Remak analyzed price formation in socialist and capitalist economies. He also anticipated the role played by digital computers in numerical solution of systems of linear equations. Remak's analysis may have influenced John von Neumann, who was a fellow lecturer in Berlin, but most of it has not been translated into English and it remains little known and appreciated in the English-speaking world. In 1932 Remak published a paper giving a lower bound for the regulator of an algebraic number field in terms of the numbers r1 and r2 of real embeddings and pairs of complex embeddings. He went on to investigate relations between the regulator and the discriminant of an algebraic number field, isolating an important class of CM-fields ("fields with unit defect"). His last two papers on the subject appeared in Compositio Mathematica in 1952 and 1954, more than ten years after his death.
After the Nazis seized power in 1933 and the Civil Service Law was passed a few months later, Remak, who was of Jewish ancestry, lost his right to teach in September 1933. He was arrested on Kristallnacht, 9 November 1938, and was interned at Sachsenhausen concentration camp for several weeks. After an unsuccessful campaign by his wife to secure a permission for him to emigrate to the United States, he was released and permitted to leave for Amsterdam. In 1942, however, he was arrested by the German occupational authorities in the Netherlands and de |
https://en.wikipedia.org/wiki/2005%20Russian%20Professional%20Rugby%20League%20season | This was the first season of the new Russian Professional Rugby League, replacing the former Super League.
External links
Official website
Information rugby portal
Russian rugby statistics
2005
2005 in Russian rugby union
2005 rugby union tournaments for clubs
2005–06 in European rugby union leagues
2004–05 in European rugby union leagues |
https://en.wikipedia.org/wiki/List%20of%20VFL%20debuts%20in%201955 | This is a listing of Australian rules footballers who made their senior debut for a Victorian Football League (VFL) club in 1955.
Debuts
References
Australian rules football records and statistics
Australian rules football-related lists
1955 in Australian rules football |
https://en.wikipedia.org/wiki/Holomorphic%20tangent%20bundle | In mathematics, and especially complex geometry, the holomorphic tangent bundle of a complex manifold is the holomorphic analogue of the tangent bundle of a smooth manifold. The fibre of the holomorphic tangent bundle over a point is the holomorphic tangent space, which is the tangent space of the underlying smooth manifold, given the structure of a complex vector space via the almost complex structure of the complex manifold .
Definition
Given a complex manifold of complex dimension , its tangent bundle as a smooth vector bundle is a real rank vector bundle on . The integrable almost complex structure corresponding to the complex structure on the manifold is an endomorphism with the property that . After complexifying the real tangent bundle to , the endomorphism may be extended complex-linearly to an endomorphism defined by for vectors in .
Since , has eigenvalues on the complexified tangent bundle, and therefore splits as a direct sum
where is the -eigenbundle, and the -eigenbundle. The holomorphic tangent bundle of is the vector bundle , and the anti-holomorphic tangent bundle is the vector bundle .
The vector bundles and are naturally complex vector subbundles of the complex vector bundle , and their duals may be taken. The holomorphic cotangent bundle is the dual of the holomorphic tangent bundle, and is written . Similarly the anti-holomorphic cotangent bundle is the dual of the anti-holomorphic tangent bundle, and is written . The holomorphic and anti-holomorphic (co)tangent bundles are interchanged by conjugation, which gives a real-linear (but not complex linear!) isomorphism .
The holomorphic tangent bundle is isomorphic as a real vector bundle of rank to the regular tangent bundle . The isomorphism is given by the composition of inclusion into the complexified tangent bundle, and then projection onto the -eigenbundle.
The canonical bundle is defined by .
Alternative local description
In a local holomorphic chart of , one has distinguished real coordinates defined by for each . These give distinguished complex-valued one-forms on . Dual to these complex-valued one-forms are the complex-valued vector fields (that is, sections of the complexified tangent bundle),
Taken together, these vector fields form a frame for , the restriction of the complexified tangent bundle to . As such, these vector fields also split the complexified tangent bundle into two subbundles
Under a holomorphic change of coordinates, these two subbundles of are preserved, and so by covering by holomorphic charts one obtains a splitting of the complexified tangent bundle. This is precisely the splitting into the holomorphic and anti-holomorphic tangent bundles previously described. Similarly the complex-valued one-forms and provide the splitting of the complexified cotangent bundle into the holomorphic and anti-holomorphic cotangent bundles.
From this perspective, the name holomorphic tangent bundle becomes transparent. Namely, |
https://en.wikipedia.org/wiki/Luis%20Radford | Luis Radford is professor at the School of Education Sciences at Laurentian University in Sudbury, Ontario, Canada. His research interests cover both theoretical and practical aspects of mathematics thinking, teaching, and learning. His current research draws on Lev Vygotsky's historical-cultural school of thought, as well as Evald Ilyenkov's epistemology, in a conceptual framework influenced by Emmanuel Levinas and Mikhail Bakhtin, leading to a non-utilitarian and a non-instrumentalist conception of the classroom and education.
Radford is an editor of the education journal For the Learning of Mathematics. In 2011 he was the recipient of the Hans Freudenthal Medal of the International Commission on Mathematical Instruction for his "development of a semiotic-cultural theory of learning".
He is the editor of book series "Semiotic Perspectives in the Teaching & Learning of Math" with Springer Verlag.
Publications
Luis Radford (2000) Signs and meanings in students' emergent algebraic thinking: A semiotic analysis. Educational Studies in Mathematics 42 (3).
Luis Radford (1997) On psychology, historical epistemology, and the teaching of mathematics: towards a socio-cultural history of mathematics. For the Learning of Mathematics 17 (1).
Luis Radford (2002) The seen, the spoken and the written: A semiotic approach to the problem of objectification of mathematical knowledge. For the learning of mathematics 22 (2).
References
Mathematics educators
Semioticians
Living people
Academic staff of Laurentian University
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Statistics%20%28song%29 | "Statistics" is an R&B/soul song performed and released by Chester Lyfe Jennings who also co-wrote the song with Tyler Williams. Released in 2010, it was the first track on the artists, self-proclaimed, fourth and final album,I Still Believe. On June 22, 2010, “Statistics,” was released as a single where it reached 19 on the Billboard R&B/Hip-Hop songs list on September 4, 2010.
The song was inspired by Steve Harvey’s book, "Act Like a Lady, Think Like a Man:What Men Really Think About Love, Relationships, Intimacy, and Commitment," and belts out statistics such as,
"25% of all men are unstable,
25% of all men can't be faithful
30% of them don't mean what they say
And 10% of the remaining 20 is gay
That leaves you a 10% chance of ever finding your man"
This is sung to a “lullaby-like piano melody”. The song also offers advice on keeping that good one, once he is found.
"Tell him that you're celibate
And if he wants some of your goodies he gon' have to work for it"
Promotion
"Lyfe" interviewed with Mo'Nique of "The "Mo'Nique" show. The show aired on the network BET in June 2010. Following the interview on his career and his personal life, "Lyfe" performed the song "Statistics".
"Essence" magazine was allowed a behind the scenes interview and rights to release the music video for "Statistics" on their website "Essence.com"
"Lyfe" sat down for a "round table" interview with the R&B lifestyle magazine "SingersRoom". During the interview, he discussed "unstable" and "cheating" men, as well as "Statistics" and his reason for writing the song. The interview debuted on the SingersRoom website in August 2010.
Music video
Jennings premiered the “Statistics” video on the internet as part of an interview for Essence Magazine. The exclusive, début, was uploaded on July 13, 2010 on the essence.com website. It was released for sale on July 28, 2010.
There are two different videos. Both versions are similar and include an opening scene of a close up of the face of Jennings singing in the parlando style, the words:
“Alright, alright, alright
y’all settle down settle down settle down.
If you don't know where you are this is Statistics 101
and I’m your teacher Lyfe Jennings in the flesh baby.
Books out, let’s go.”.
The second version includes an introduction, which feature eleven women talking about their prior abusive or unhealthy relationships. This introduction is the only deviation in the two videos.
Charts
Weekly charts
Year-end charts
References
2010 singles
Lyfe Jennings songs
Song recordings produced by T-Minus (record producer)
Songs written by T.I.
2009 songs
Songs written by Lyfe Jennings |
https://en.wikipedia.org/wiki/G%C3%BCnter%20Asser | Günter Asser (26 February 1926, Berlin – 23 March 2015) was a professor emeritus of logic and mathematics at the University of Greifswald. He published numerous volumes on philosophers and mathematicians. His own research was in computability theory.
In 1954, with his doctoral advisor Karl Schröter, he co-founded the journal Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, which later became Mathematical Logic Quarterly. In 1977, Günter Asser became member of the German Academy of Sciences at Berlin.
See also
Spectrum of a sentence
References
External links
Ostsee-Zeitung (German newspaper) article of 30 Mar 2015 – includes a group photograph from Greifswald University
Publication list at DBLP
1926 births
German logicians
20th-century German mathematicians
2015 deaths
German philosophers
German male writers
Members of the German Academy of Sciences at Berlin
21st-century German mathematicians |
https://en.wikipedia.org/wiki/Michael%20Benedicks | Michael Benedicks, born 1949, is a Professor of Mathematics at the Royal Institute of Technology (KTH) in Stockholm, Sweden.
He received his Ph.D. from the Royal Institute of Technology in 1980. His doctoral advisor was Professor Harold S. Shapiro. He was a visiting scholar at the Institute for Advanced Study in the summer of 1989.
He became a Professor of Mathematics at the Royal Institute of Technology in 1991.
His research interests include dynamic systems. For example, he has studied Hénon maps together with Professor Lennart Carleson.
He became a member of the Royal Swedish Academy of Sciences in 2007.
References
External links
Prof. Benedicks's website
1949 births
Swedish mathematicians
Living people
Academic staff of the KTH Royal Institute of Technology
KTH Royal Institute of Technology alumni
Members of the Royal Swedish Academy of Sciences
Institute for Advanced Study visiting scholars |
https://en.wikipedia.org/wiki/D%C3%A1vid%20Barczi | Dávid Barczi (born 1 February 1989, is a Hungarian midfielder who currently plays for III. Kerületi TVE.
Honours
Diósgyőr
Hungarian League Cup (1): 2013–14
Club statistics
Updated to games played as of 15 May 2021.
External links
Player profile at HLSZ
1989 births
Living people
People from Siófok
Hungarian men's footballers
Men's association football midfielders
Újpest FC players
Diósgyőri VTK players
Fehérvár FC players
Vasas SC players
Zalaegerszegi TE players
Mezőkövesdi SE footballers
III. Kerületi TVE footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Footballers from Somogy County |
https://en.wikipedia.org/wiki/Gda%C5%84skie%20Wydawnictwo%20O%C5%9Bwiatowe | Gdańskie Wydawnictwo Oświatowe Publishing House (GWO) is one of the first privately owned educational publishing houses in Poland. The publishing house prints textbooks for mathematics, Polish, history, physics, biology, and art.
History
Gdańskie Wydawnictwo Oświatowe was founded in 1991. Then, the book series Matematyka z plusem was created for students in elementary school, along with the "zeszyty gdańskie" and Kalendarz ósmoklasisty.
Products
Nowadays, apart from math textbook series entitled Matematyka z plusem, GWO prints books for Polish (Między nami being for elementary school and Sztuka wyrazu being for high school), history (Podróże w czasie being for elementary students, and Ślady czasu being for high schools), physics (Fizyka z plusem and To nasz świat. Fizyka for elementary school), biology (To nasz świat. Biologia for elementary school, Biologia z tangramem for high school), art (Lokomotywa. Plastyka for early elementary school), and a number of supporting books designed for teachers.
Gdańskie Wydawnictwo Oświatowe has also launched a series of online projects including online courses (Matematura.pl, Matlandia, Gimplus), interactive historical maps (History of Poland and the Roman Empire), as well as online applications for teachers (Test Composer). Moreover, GWO offers selected textbooks, tests, teacher support materials, and magazines as e-books.
Educational projects
References:
Electronic publishing
Online publishing companies
Mass media in Gdańsk
Publishing companies of Poland
Publishing companies established in 1991
Book publishing companies of Poland
1991 establishments in Poland |
https://en.wikipedia.org/wiki/Rouhollah%20Ataei | Rouhollah Ataei (born September 11, 1983 Iran – Qazvin) is an Iranian footballer. He plays for Paykan in the IPL.
Club career
Ataei has been with Paykan since 2009.
Club Career Statistics
Last Update 29 August 2010
Assist Goals
References
1983 births
Living people
Rahian Kermanshah F.C. players
Paykan F.C. players
Tractor S.C. players
Sanat Mes Kerman F.C. players
Iranian men's footballers
Men's association football forwards
People from Qazvin
21st-century Iranian people |
https://en.wikipedia.org/wiki/Mohsen%20Mirabi | Mohsen Mirabi (born 8 August 1983) is an Iranian former professional footballer who played as a midfielder.
Career
Mirabi joined Rah Ahan F.C. in 2008.
Career statistics
References
1983 births
Living people
Iranian men's footballers
Men's association football midfielders
Rah Ahan Tehran F.C. players
PAS Tehran F.C. players
Place of birth missing (living people) |
https://en.wikipedia.org/wiki/The%20Penguin%20Dictionary%20of%20Curious%20and%20Interesting%20Numbers | The Penguin Dictionary of Curious and Interesting Numbers is a reference book for recreational mathematics and elementary number theory written by David Wells. The first edition was published in paperback by Penguin Books in 1986 in the UK, and a revised edition appeared in 1997 ().
Contents
The entries are arranged in increasing order of magnitude, with the exception of the first entry on −1 and i. The book includes some irrational numbers below 10 but concentrates on integers, and has an entry for every integer up to 42. The final entry is for Graham's number.
In addition to the dictionary itself, the book includes a list of mathematicians in chronological sequence (all born before 1890), a short glossary, and a brief bibliography. The back of the book contains eight short tables "for the benefit of readers who cannot wait to look for their own patterns and properties", including lists of polygonal numbers, Fibonacci numbers, prime numbers, factorials, decimal reciprocals of primes, factors of repunits, and lastly the prime factorization and the values of the functions φ(n), d(n) and σ(n) for the first hundred integers. The book concludes with a conventional, alphabetical index.
Reviews
In a review of several books in The College Mathematics Journal, Brian Blank described it as "a charming and interesting book", and the Chicago Tribune described the revised edition as "a fascinating book on all things numerical". By contrast, Christopher Hirst called it "a volume which none but propeller-heads will find either curious or interesting" in a review of another book in The Independent.
Style
Beside the serious mathematics and number theory, Wells occasionally makes humorous or playful comments on the numbers he is discussing. For example, his entry for the number 39 largely consists of a joke involving the interesting number paradox:
39
This appears to be the first uninteresting number, which of course makes it an especially interesting number, because it is the smallest number to have the property of being uninteresting.
It is therefore also the first number to be simultaneously interesting and uninteresting. (pg. 120)
See also
List of notable numbers
On-Line Encyclopedia of Integer Sequences
References
Mathematics books
1986 books
Penguin Books books |
https://en.wikipedia.org/wiki/PCER | PCER can refer to:
Per-comparison error rate, a concept used in statistics
Partija za Celosna Emancipacija na Romite, a Macedonian political party
PCER, a type of patrol vessel of the United States Navy, derived from "Patrol Craft Escort (Rescue)" |
https://en.wikipedia.org/wiki/Minoru%20Takenaka | is a former Japanese football player.
Club statistics
Honours
A Lyga Runner-up: 2001 2002
Lithuanian Football Cup champions : 2001
References
External links
1976 births
Living people
Teikyo University alumni
Association football people from Hiroshima Prefecture
Japanese men's footballers
J2 League players
Yokohama FC players
FC Machida Zelvia players
Japanese expatriate men's footballers
Men's association football forwards |
https://en.wikipedia.org/wiki/Masataka%20Tamura | is a former Japanese football player.
Club statistics
References
External links
tochigisc.com
1988 births
Living people
Association football people from Okayama Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Japan Football League players
Kyoto Sanga FC players
Tochigi SC players
Tochigi City FC players
SC Sagamihara players
Men's association football defenders |
https://en.wikipedia.org/wiki/Junya%20Tanaka%20%28footballer%2C%20born%201983%29 | is a former Japanese football player.
Tanaka played for Vissel Kobe, JEF United Chiba, Sagan Tosu and Verspah Oita. He played in the J2 League during the 2007 season for Sagan.
Club statistics
References
External links
1983 births
Living people
Doshisha University alumni
Association football people from Osaka Prefecture
People from Takatsuki, Osaka
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Vissel Kobe players
JEF United Chiba players
Sagan Tosu players
Verspah Oita players
Men's association football defenders |
https://en.wikipedia.org/wiki/Kenji%20Tanaka%20%28footballer%2C%20born%201983%29 | is a Japanese football player.
Club statistics
Updated to 20 February 2017.
References
External links
Profile at Vanraure Hachinohe
1983 births
Living people
Association football people from Saga Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Japan Football League players
Omiya Ardija players
Sagan Tosu players
FC Machida Zelvia players
Arte Takasaki players
Zweigen Kanazawa players
AC Nagano Parceiro players
FC Ryukyu players
Vanraure Hachinohe players
Ococias Kyoto AC players
FC Kagura Shimane players
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/Kenichi%20Yagara | is a former Japanese football player.
Club statistics
References
External links
1981 births
Living people
Kansai University alumni
Association football people from Osaka Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Ehime FC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Atsushi%20Yamaguchi%20%28footballer%29 | is a former Japanese football player.
Club statistics
References
External links
1980 births
Living people
Association football people from Kanagawa Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Tokushima Vortis players
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/Atsushi%20Yoshimoto | is a former Japanese football player.
Club statistics
References
External links
Profile at output.simseed.net
1982 births
Living people
Shizuoka Sangyo University alumni
Association football people from Shizuoka Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Thespakusatsu Gunma players
V-Varen Nagasaki players
Men's association football forwards |
https://en.wikipedia.org/wiki/Satoshi%20Yoshioka | is a former Japanese football player.
Club statistics
References
External links
1987 births
Living people
Association football people from Gunma Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Yokohama FC players
Thespakusatsu Gunma players
Kataller Toyama players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Shunichiro%20Zaitsu | is a former Japanese football player.
Club statistics
References
External links
1987 births
Living people
Association football people from Fukuoka Prefecture
Japanese men's footballers
J1 League players
J2 League players
Shimizu S-Pulse players
Shonan Bellmare players
Men's association football defenders |
https://en.wikipedia.org/wiki/Abu%20as-Salt | Abū aṣ‐Ṣalt Umayya ibn ʿAbd al‐ʿAzīz ibn Abī aṣ‐Ṣalt ad‐Dānī al‐Andalusī () (October 23, 1134), known in Latin as Albuzale, was an Andalusian-Arab polymath who wrote about pharmacology, geometry, Aristotelian physics, and astronomy. His works on astronomical instruments were read both in the Islamic world and Europe. He also occasionally traveled to Palermo and worked in the court of Roger I of Sicily as a visiting physician. He became well known in Europe through translations of his works made in the Iberian Peninsula and in southern France. He is also credited with introducing Andalusi music to Tunis, which later led to the development of the Tunisian ma'luf.
Life
Abu as-Salt was born in Dénia, al-Andalus. After the death of his father while he was a child, he became a student of al‐Waqqashi (10171095) of Toledo (a colleague of Abū Ishāq Ibrāhīm az-Zarqālī). Upon completing his mathematical education in Seville, and because of the continuing conflicts during the reconquista, he set out with his family to Alexandria and then Cairo in 1096.
In Cairo, he entered the service of the Fatimid ruler Abū Tamīm Ma'add al-Mustanṣir bi-llāh and the Vizier Al-Afdal Shahanshah. His service continued until 1108, when, according to Ibn Abī Uṣaybiʿa, his attempt to retrieve a very large Felucca laden with copper, that had capsized in the Nile, ended in failure. Abu as-Salt had built a mechanical tool to retrieve the Felucca, and was close to success when the machine's silk ropes fractured. The Vizier Al-Afdal ordered Abu as-Salt's arrest, and he was imprisoned for more than three years, only to be released in 1112.
Abu al-Salt then left Egypt for Mahdia in Tunisia, the capital of the Zirids in Ifriqiya where he entered the service of king Yaḥyā ibn Tamīm as‐Ṣanhājī and where his son, ʿAbd al‐ʿAzīz was born. He also occasionally traveled to Palermo and worked in the court of Roger I of Sicily as a visiting physician. He also sent poems to the Palermitan poet Abū ḍ-Ḍawʾ. He died, probably of dropsy, in Béjaïa, Algeria. He is buried in the Ribat of Monastir, Tunisia.
Works
Abu as-Salt wrote an encyclopedic work of many treatises on the scientific disciplines known as quadrivium. This work was probably known in Arabic as Kitāb al‐kāfī fī al‐ʿulūm. His poetry is preserved in the anthology of Imad al-Din al-Isfahani. His interests also included alchemy as well as the study of medicinal plants. He was keen to discover an elixir able to transmute copper into gold and tin into silver.
Astronomy
Risāla fī al-amal bi‐l‐astrulab ("On the construction and use of the astrolabe")
A description of the three instruments known as the Andalusian equatoria.
Ṣifat ʿamal ṣafīḥa jāmiʿa taqawwama bi‐hā jamīʿ al‐kawākib al‐sabʿa ("Description of the construction and Use of a Single Plate with which the totality of the motions of the seven planets"), where the seven planets refer to Mercury, Venus, earth, Moon, Mars, Jupiter, and Saturn.
Kitāb al‐wajīz fī ʿilm al‐hayʾa (" |
https://en.wikipedia.org/wiki/O%2A-algebra | In mathematics, an O*-algebra is an algebra of possibly unbounded operators defined on a dense subspace of a Hilbert space. The original examples were described by and , who studied some examples of O*-algebras, called Borchers algebras, arising from the Wightman axioms of quantum field theory. and began the systematic study of algebras of unbounded operators.
References
Operator algebras |
https://en.wikipedia.org/wiki/Shahin%20Kheiri | Shahin Kheiri (born April 20, 1980) is an Iranian footballer who plays for Naft Tehran F.C. in the IPL.
Club career
Kheiri joined Sepahan F.C. in 2009.
Club career statistics
Assist Goals
Honours
Club
Iran's Premier Football League
Winner: 2
2005/06 with Esteghlal
2009/10 with Sepahan
References
1980 births
Living people
Esteghlal F.C. players
Zob Ahan Esfahan F.C. players
Sanat Mes Kerman F.C. players
Sepahan S.C. footballers
Naft Tehran F.C. players
Iranian men's footballers
Men's association football midfielders
Place of birth missing (living people) |
https://en.wikipedia.org/wiki/Dadhigrama | Dadhigrama was a village on the banks of Payosni river in Vidarbha where a school of mathematics and astronomy flourished during the 14th to 19th centuries CE.
Cintāmani, a Brahmana of the Devaratragotra, in the middle of the 15th century, Rama (who was patronized by a king of Vidarbha), Trimalla, and Vallala, Munisvara a grandson of Vallala, his son Rama, who wrote a commentary on the Sudhārasasāranī of Ananta (fl. 1525), Ḳrshnạ (fl. 1600–1625) etc. were some of the well-known members of this school of mathematicians. Ranganatha (fl. 1603), another astronomer of the school, wrote Gūḍhārthaprakāśikā, a commentary on the Suryasidhanta.
Known members of the Dadhigrama school of mathematics
The known members of this school include the following:
Rama (Sons: Trimalla, Gopiraja)
Trimalla (Son: Vallala)
Vallal (Sons: Rama, Krishna, Govinda, Ranganatha, Mahadeva)
Govinda (Son: Narayana)
Ranganatha (Son: Munisvara)
Schools of mathematics
Historians of mathematics have identified several schools of mathematics that flourished in different parts of India during the 14th–19th centuries CE. It has also been noted that most of the mathematical activities during this period were concentrated in these schools. The schools were at places identified by the following names:
Jambusagaranagara
Dadhigrama (Vidarbha)
Nandigrama (Maharashtra)
Parthapura (Maharashtra)
Golagrama (Maharashtra)
Kerala
References
Villages in Maharashtra |
https://en.wikipedia.org/wiki/Uncertainty%20exponent | In mathematics, the uncertainty exponent is a method of measuring the fractal dimension of a basin boundary. In a chaotic scattering system, the
invariant set of the system is usually not directly accessible because it is non-attracting and typically of measure zero. Therefore, the only way to infer the presence of members
and to measure the properties of the invariant set is through the basins of attraction. Note that in a scattering system, basins of attraction are not limit cycles therefore do not constitute members of the invariant set.
Suppose we start with a random trajectory and perturb it by a small amount,
, in a random direction. If the new trajectory ends up
in a different basin from the old one, then it is called epsilon uncertain.
If we take a large number of such trajectories,
then the fraction of them that are epsilon uncertain is the uncertainty fraction,
, and we expect it to scale exponentially
with :
Thus the uncertainty exponent, , is defined as follows:
The uncertainty exponent can be shown to approximate the box-counting dimension
as follows:
where N is the embedding dimension. Please refer to the article on chaotic mixing for an example of numerical computation of the uncertainty dimension
compared with that of a box-counting dimension.
References
C. Grebogi, S. W. McDonald, E. Ott and J. A. Yorke, Final state sensitivity: An obstruction to predictability, Phys. Letters 99A: 415-418 (1983).
Chaos theory
Fractals |
https://en.wikipedia.org/wiki/Hallade%20method | The Hallade method, devised by Frenchman Emile Hallade, is a method used in track geometry for surveying, designing and setting out curves in railway track.
It involves measuring the offset of a string line from the outside of a curve at the central point of a chord. In reality, string is too thick to provide a clear reading and breaks easily under the tension needed to minimise movement due to wind. A reel of wire may be used instead, with special holders (Hallade forks) employed to hold the wire at a fixed distance from the rail. The measurement is taken with a Hallade rule, a specialist ruler whose zero point matches the offset of the forks, thus cancelling it out. The purpose of the offset is to allow small negative measurements. Without this, surveyors would frequently have to read from both sides of the rail to determine the correct values on straight sections of track which typically feature a mix of small positive and negative versines.
A standard chord length is used: in the UK this is conventionally 30 metres, or sometimes 20 metres. Half chords, i.e. 15 metre or 10 metre intervals, are marked on the datum rail using chalk. The string, which is one full chord long, is then held taut with one end on two marks at each end of a chord, and the offset at the half chord mark measured.
The versine of the chord, which is equal to this measured offset value can be calculated using the approximation of:
which is:
where
= versine (m),
= chord length (m),
= radius of curve (m)
This formula is also true for other units of measurement such as in feet. The relationship of versine, chord and radius is derived from the Pythagorean theorem. Based on the diagram on the right:
We can replace OC with r (radius) minus v, OA with r and AC with L/2 (half a chord). Then the rearrange formula to:
Since the curved tracks are usually large, the result of v/2 is very small. To simplify the formula, the approximation is:
The following can be used to find the versine of a given constant radius curve:
The Hallade method is to use the chord to continuously measure the versine in an overlapping pattern along the curve. The versine values for the perfect circular curve would have the same number. By comparing the surveyed versine figures to the design versines, this can then be used to determine what slues should be applied to the track in order to make the curve correctly aligned. This is often done using pegs which are driven into the ground in the cess beside the track to be aligned. The process of putting the pegs in the correct positions is known as 'setting out'.
If the curve needs to be of a desired constant radius, which will usually be determined by physical obstructions and the degree of cant which is permitted, the versine can be calculated for the desired radius using this approximation. In practice, many track curves are transition curves and so have changing radii. In order to maintain a smooth transition, the differences in versines between |
https://en.wikipedia.org/wiki/Borchers%20algebra | In mathematics, a Borchers algebra or Borchers–Uhlmann algebra or BU-algebra is the tensor algebra of a vector space, often a space of smooth test functions. They were studied by , who showed that the Wightman distributions of a quantum field could be interpreted as a state, called a Wightman functional, on a Borchers algebra. A Borchers algebra with a state can often be used to construct an O*-algebra.
The Borchers algebra of a quantum field theory has an ideal called the locality ideal, generated by elements of the form ab−ba for a and b having spacelike-separated support. The Wightman functional of a quantum field theory vanishes on the locality ideal, which is equivalent to the locality axiom for quantum field theory.
References
External links
Operator algebras
Axiomatic quantum field theory |
https://en.wikipedia.org/wiki/Michigan%20Mathematics%20Prize%20Competition | The Michigan Mathematics Prize Competition (MMPC) is an annual high school mathematics competition held in Michigan. First founded in 1958, the competition has grown to include over 10,000 high school participants (although middle-schoolers may also participate through a high school). The director and host of this competition changes every three years, the most recent director being Stephanie Edwards of Hope College. This competition consists of two parts, which are added together to determine score:
Part I: A 40 question, multiple-choice exam open to all Michigan high schoolers
Part II: A 5 question, proof exam given only to the Top 1000 scorers on Part I
The Top 100 scorers on the combined score of both parts of the competition are honored at an awards banquet, usually at the host university, although recent years have seen more than 100 people being awarded due to ties.
Problem difficulty
The problems on the competition range from basic algebra to precalculus and are within the grasp of a high schooler's mathematical knowledge. The contest contains concepts from a variety of topics, including geometry and combinatorics.
Grading
Part I has 40 multiple-choice questions with five choices each. One point is awarded for each correct answer, giving a maximum score of forty points.
Part II has five ten point proof-based problems. The test is graded out of fifty points. This part is weighted x1.2, so the total number of points possible is 60.
The highest possible score on this test is 100 points (summing the Part I and Part II scores).
It is common for the winner of the competition to score anywhere from 90 to 95 points due to the difficulty of the exam. It sometimes falls even lower due to especially tough exams.
Through 2018, the only perfect scores were achieved in 2015, by Ankan Bhattacharya of International Academy East, and in 2016, by Chittesh Thavamani and Freddie Zhao, both of Troy High School. 2016 also marked the year of the highest scoring 3rd, 4th, and 5th-place winners in MMPC history with 3rd place scoring 99 points, 4th place scoring 98.8 points, and 5th place scoring 97.6 points. This changed in 2019, which saw all three winners, Maxim Li of Okemos High School, Steven Raphael of The Roeper School, and Alex Xu of Troy High School, receive a perfect score.
Awards
The Top 100 are invited to an awards banquet. Although the Top 50 are denoted as "bronze," no actual medal is awarded. Likewise, the Top 10 and Top 3 are called "silver" and "gold" (respectively) but do not receive medals.
The Lower 50 are deemed "honorable mentions" and receive a gift card/certificate/book.
Everyone in the Top 50 receives a scholarship ranging in size from $250 to $2500
In the 2012 contest, Akhil Nistala became the first winner in Novi High School history, breaking a streak of 6 consecutive top scorers for Detroit Country Day School.
Recent winners
1993: Amit Khetan, ICAE
1994: Amit Khetan, ICAE
1995: Amit Khetan, ICAE
1996: Bryant Matthew |
https://en.wikipedia.org/wiki/Banach%20bundle%20%28non-commutative%20geometry%29 | In mathematics, a Banach bundle is a fiber bundle over a topological Hausdorff space, such that each fiber has the structure of a Banach space.
Definition
Let be a topological Hausdorff space, a (continuous) Banach bundle over is a tuple , where is a topological Hausdorff space, and is a continuous, open surjection, such that each fiber is a Banach space. Which satisfies the following conditions:
The map is continuous for all
The operation is continuous
For every , the map is continuous
If , and is a net in , such that and , then , where denotes the zero of the fiber .
If the map is only upper semi-continuous, is called upper semi-continuous bundle.
Examples
Trivial bundle
Let A be a Banach space, X be a topological Hausdorff space. Define and by . Then is a Banach bundle, called the trivial bundle
See also
Banach bundles in differential geometry
References
Noncommutative geometry
Banach spaces |
https://en.wikipedia.org/wiki/Millennium%20Prize%20Problems | The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US$1 million prize for the first correct solution to each problem.
The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the Millennium Meeting held on May 24, 2000. Thus, on the official website of the Clay Mathematics Institute, these seven problems are officially called the Millennium Problems.
To date, the only Millennium Prize problem to have been solved is the Poincaré conjecture. The Clay Institute awarded the monetary prize to Russian mathematician Grigori Perelman in 2010. However, he declined the award as it was not also offered to Richard S. Hamilton, upon whose work Perelman built.
Overview
The Clay Institute was inspired by a set of twenty-three problems organized by the mathematician David Hilbert in 1900 which were highly influential in driving the progress of mathematics in the twentieth century. The seven selected problems range over a number of mathematical fields, namely algebraic geometry, arithmetic geometry, geometric topology, mathematical physics, number theory, partial differential equations, and theoretical computer science. Unlike Hilbert's problems, the problems selected by the Clay Institute were already renowned among professional mathematicians, with many actively working towards their resolution.
Grigori Perelman, who had begun work on the Poincaré conjecture in the 1990s, released his proof in 2002 and 2003. His refusal of the Clay Institute's monetary prize in 2010 was widely covered in the media. The other six Millennium Prize Problems remain unsolved, despite a large number of unsatisfactory proofs by both amateur and professional mathematicians.
Andrew Wiles, as part of the Clay Institute's scientific advisory board, hoped that the choice of US$1 million prize money would popularize, among general audiences, both the selected problems as well as the "excitement of mathematical endeavor". Another board member, Fields medalist Alain Connes, hoped that the publicity around the unsolved problems would help to combat the "wrong idea" among the public that mathematics would be "overtaken by computers".
Some mathematicians have been more critical. Anatoly Vershik characterized their monetary prize as "show business" representing the "worst manifestations of present-day mass culture", and thought that there are more meaningful ways to invest in public appreciation of mathematics. He viewed the superficial media treatments of Perelman and his work, with disproportionate attention being placed on the prize value itself, as unsurprising. By contrast, Vershik praised the Cla |
https://en.wikipedia.org/wiki/3-7%20kisrhombille | In geometry, the 3-7 kisrhombille tiling is a semiregular dual tiling of the hyperbolic plane. It is constructed by congruent right triangles with 4, 6, and 14 triangles meeting at each vertex.
The image shows a Poincaré disk model projection of the hyperbolic plane.
It is labeled V4.6.14 because each right triangle face has three types of vertices: one with 4 triangles, one with 6 triangles, and one with 14 triangles. It is the dual tessellation of the truncated triheptagonal tiling which has one square and one heptagon and one tetrakaidecagon at each vertex.
Naming
The name 3-7 kisrhombille is given by Conway, seeing it as a 3-7 rhombic tiling, divided by a kis operator, adding a center point to each rhombus, and dividing into four triangles.
Symmetry
There are no mirror removal subgroups of [7,3]. The only small index subgroup is the alternation, [7,3]+, (732).
Related polyhedra and tilings
Three isohedral (regular or quasiregular) tilings can be constructed from this tiling by combining triangles:
It is topologically related to a polyhedra sequence; see discussion. This group is special for having all even number of edges per vertex and form bisecting planes through the polyhedra and infinite lines in the plane, and are the reflection domains for the (2,3,n) triangle groups – for the heptagonal tiling, the important (2,3,7) triangle group.
See also the uniform tilings of the hyperbolic plane with (2,3,7) symmetry.
The kisrhombille tilings can be seen as from the sequence of rhombille tilings, starting with the cube, with faces divided or kissed at the corners by a face central point.
Just as the (2,3,7) triangle group is a quotient of the modular group (2,3,∞), the associated tiling is the quotient of the modular tiling, as depicted in the video at right.
References
John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)
See also
Hexakis triangular tiling
Tilings of regular polygons
List of uniform tilings
Uniform tilings in hyperbolic plane
Hyperbolic tilings
Isohedral tilings
Semiregular tilings
John Horton Conway |
https://en.wikipedia.org/wiki/Kisrhombille | In geometry, a kisrhombille is a uniform tiling of rhombic faces, divided with a center points into four triangles.
Examples:
3-6 kisrhombille – Euclidean plane
3-7 kisrhombille – hyperbolic plane
3-8 kisrhombille – hyperbolic plane
4-5 kisrhombille – hyperbolic plane
References
Uniform tilings
John Horton Conway |
https://en.wikipedia.org/wiki/Hans-J%C3%BCrgen%20Borchers | Hans-Jürgen Borchers (24 January 1926, Hamburg – 10 September 2011, Göttingen) was a mathematical physicist at the Georg-August-Universität Göttingen who worked on operator algebras and quantum field theory. He introduced Borchers algebras and the Borchers commutation relations and Borchers classes in quantum field theory. He was awarded the Max Planck Medal in 1994. Among his students is Jakob Yngvason.
Selected publications
References
External links
Department faculty list
20th-century German mathematicians
20th-century German physicists
1926 births
2011 deaths
Winners of the Max Planck Medal
Members of the Göttingen Academy of Sciences and Humanities |
https://en.wikipedia.org/wiki/4-5%20kisrhombille | In geometry, the 4-5 kisrhombille or order-4 bisected pentagonal tiling is a semiregular dual tiling of the hyperbolic plane. It is constructed by congruent right triangles with 4, 8, and 10 triangles meeting at each vertex.
The name 4-5 kisrhombille is by Conway, seeing it as a 4-5 rhombic tiling, divided by a kis operator, adding a center point to each rhombus, and dividing into four triangles.
The image shows a Poincaré disk model projection of the hyperbolic plane.
It is labeled V4.8.10 because each right triangle face has three types of vertices: one with 4 triangles, one with 8 triangles, and one with 10 triangles.
Dual tiling
It is the dual tessellation of the truncated tetrapentagonal tiling which has one square and one octagon and one decagon at each vertex.
Related polyhedra and tilings
References
John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)
See also
Hexakis triangular tiling
List of uniform tilings
Uniform tilings in hyperbolic plane
Hyperbolic tilings
Isohedral tilings
Semiregular tilings
John Horton Conway
eo:Ordo-3 dusekcita seplatera kahelaro |
https://en.wikipedia.org/wiki/Wiener%20series | In mathematics, the Wiener series, or Wiener G-functional expansion, originates from the 1958 book of Norbert Wiener. It is an orthogonal expansion for nonlinear functionals closely related to the Volterra series and having the same relation to it as an orthogonal Hermite polynomial expansion has to a power series. For this reason it is also known as the Wiener–Hermite expansion. The analogue of the coefficients are referred to as Wiener kernels. The terms of the series are orthogonal (uncorrelated) with respect to a statistical input of white noise. This property allows the terms to be identified in applications by the Lee–Schetzen method.
The Wiener series is important in nonlinear system identification. In this context, the series approximates the functional relation of the output to the entire history of system input at any time. The Wiener series has been applied mostly to the identification of biological systems, especially in neuroscience.
The name Wiener series is almost exclusively used in system theory. In the mathematical literature it occurs as the Itô expansion (1951) which has a different form but is entirely equivalent to it.
The Wiener series should not be confused with the Wiener filter, which is another algorithm developed by Norbert Wiener used in signal processing.
Wiener G-functional expressions
Given a system with an input/output pair where the input is white noise with zero mean value and power A, we can write the output of the system as sum of a series of Wiener G-functionals
In the following the expressions of the G-functionals up to the fifth order will be given:
{{Clarify}}
See also
Volterra series
System identification
Spike-triggered average
References
Itô K "A multiple Wiener integral" J. Math. Soc. Jpn. 3 1951 157–169
L.A. Zadeh On the representation of nonlinear operators. IRE Westcon Conv. Record pt.2 1957 105-113.
Mathematical series
Functional analysis |
https://en.wikipedia.org/wiki/Nadia%20Petrova%20career%20statistics | This is a list of the main career statistics of Russian professional tennis player Nadia Petrova.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup and Olympic Games are included in win–loss records.
Singles
Doubles
Significant finals
Grand Slam finals
Doubles: 2 (2 runners-up)
WTA Finals finals
Doubles: 2 (2 titles)
WTA Premier Mandatory & 5 finals
Singles: 5 (3 titles, 2 runners-up)
Doubles: 19 (9 titles, 10 runners-up)
Olympics
Doubles: 1 Bronze Medal Match (1–0)
WTA career finals
Singles: 24 (13 titles, 11 runners-up)
Doubles: 48 (24 titles, 24 runner–ups)
ITF junior results
Singles: 11 (7 titles, 4 runner–ups)
Doubles: 5 (3 titles, 2 runner–ups)
WTA Tour career earnings
Petrova earned more than 12 million dollars during her career.
Head-to-head record against other players
No. 1 wins
Record against top 10 players
Players who have been ranked World No. 1 are in boldface.
Elena Dementieva 7–8
Patty Schnyder 7–8
Li Na 6–1
Samantha Stosur 6–4
Dinara Safina 5-2
Vera Zvonareva 5–3
Ana Ivanovic 5–9
Daniela Hantuchová 4–3
Amélie Mauresmo 4–6
Nicole Vaidišová 3–1
Ai Sugiyama 3–2
Serena Williams 3–7
Elena Vesnina 2-0
Magdalena Maleeva 2–0
Alicia Molik 2–1
Conchita Martínez 2–2
Amanda Coetzer 2–2
Mary Pierce 2–2
Paola Suárez 2–2
Agnieszka Radwańska 2–3
Anastasia Myskina 2–3
Victoria Azarenka 2–4
Francesca Schiavone 2–4
Caroline Wozniacki 2–5
Svetlana Kuznetsova 2–6
Jelena Janković 2–7
Justine Henin 2–14
Martina Hingis 1–2
Kimiko Date-Krumm 1–2
Marion Bartoli 1–2
Sara Errani 1-2
Venus Williams 1–4
Kim Clijsters 1–4
Flavia Pennetta 1–5
Maria Sharapova 1–9
Anna Kournikova 0–1
Jelena Dokić 0–2
Petra Kvitová 0–2
Anna Chakvetadze 0–5
Lindsay Davenport 0–7
Top 10 wins
Notes
External links
Petrova, Nadia |
https://en.wikipedia.org/wiki/Elena%20Dementieva%20career%20statistics | Elena Dementieva is a Russian former professional tennis player. Throughout her career, Dementieva won sixteen WTA singles titles including two WTA Tier I singles titles, one WTA Premier 5 singles title and the gold medal in singles at the 2008 Beijing Olympic Games. She was also the runner-up at the 2004 French Open and 2004 US Open and a semi-finalist at the 2008 Wimbledon Championships, 2009 Australian Open and 2009 Wimbledon Championships. Dementieva was also a Silver Medallist in singles at the 2000 Sydney Olympic Games and a two-time semi-finalist at the year-ending WTA Tour Championships.
In October 2000, Dementieva reached her first career WTA singles final at the 2000 Sydney Olympic Games, where she lost in straight sets to Venus Williams and thus earned herself a silver medal. In April 2003, Dementieva rallied from a set down against Lindsay Davenport in the final of the Bausch & Lomb Championships to win her first career WTA singles title. The following year, Dementieva reached her first major singles final at the NASDAQ-100 Open where she lost in straight sets. Two months later, she reached her first grand slam singles final at the French Open but lost in straight sets to her compatriot, Anastasia Myskina in the first all-Russian grand slam final. In September of the same year, Dementieva reached her second grand slam singles final at the 2004 US Open but lost in straight sets to her compatriot, Svetlana Kuznetsova. From 2005 to 2007, the highlights of Dementieva's career were winning the 2006 Toray Pan Pacific Open and 2007 Kremlin Cup, a semi-final appearance at the 2005 US Open and quarterfinal appearances at the 2006 Wimbledon Championships and 2006 US Open.
In July 2008, Dementieva reached her first semi-final at the Wimbledon Championships but lost in straight sets to the eventual champion, Venus Williams. She rebounded by winning the gold medal in singles at the 2008 Beijing Olympics, defeating her compatriot, Dinara Safina in the final. Later that year, she reached her second consecutive grand slam semi-final at the US Open but lost in straight sets to the eventual runner-up, Jelena Janković. Dementieva finished the year by reaching the semi-finals of the WTA Tour Championships for the second time in her career where she lost in three sets to the eighth seed, Vera Zvonareva. Dementieva finished the year ranked World No. 4, which remains her best finish to date. Dementieva began the 2009 season by winning the ASB Classic and Medibank International, defeating her compatriots Elena Vesnina and Dinara Safina in the finals before reaching her first and only semi-final at the Australian Open where she lost to the eventual champion in straight sets. As a result, Dementieva has now reached the semi-finals or better at all four grand slam events. On April 3, 2009, Dementieva achieved a new career high singles ranking of World No. 3. Later that year, she reached her second consecutive semi-final at the Wimbledon Championships and won |
https://en.wikipedia.org/wiki/Fekete%20problem | In mathematics, the Fekete problem is, given a natural number N and a real s ≥ 0, to find the points x1,...,xN on the 2-sphere for which the s-energy, defined by
for s > 0 and by
for s = 0, is minimal. For s > 0, such points are called s-Fekete points, and for s = 0, logarithmic Fekete points (see ).
More generally, one can consider the same problem on the d-dimensional sphere, or on a Riemannian manifold (in which case ||xi −xj|| is replaced with the Riemannian distance between xi and xj).
The problem originated in the paper by who considered the one-dimensional, s = 0 case, answering a question of Issai Schur.
An algorithmic version of the Fekete problem is number 7 on the list of problems discussed by .
References
Mathematical analysis
Approximation theory |
https://en.wikipedia.org/wiki/Samantha%20Stosur%20career%20statistics | This is a list of the main career statistics of professional Australian tennis player Samantha Stosur. She won nine WTA singles titles, including one Grand Slam title at the 2011 US Open, while reaching the finals of 16 other WTA tournaments, including one Grand Slam final at the 2010 French Open, the 2013 WTA Tournament of Champions final, and three Premier 5 finals. Stosur also reached another three French Open semifinals (2009, 2012, 2016), two US Open quarterfinals (2010, 2012), and qualified for the WTA Tour Championships three times in a row (2010–12), reaching the semifinals in both 2010 and 2011. She reached her highest singles ranking of No. 4 in the world in February 2011.
Stosur also enjoyed a successful doubles career, in which she held the world No. 1 ranking for 61 consecutive weeks between February 2006 and April 2007, finished as the year-end world No. 1 doubles team with former partner Lisa Raymond in 2005 and 2006, and was the year-end world No. 1 doubles player in 2006. Stosur won 28 WTA doubles titles, including four Grand Slam women's doubles titles at the 2005 US Open, 2006 French Open, 2019 Australian Open, and 2021 US Open, as well as two consecutive WTA Tour Championship titles in 2005 and 2006. She reached an additional five Grand Slam finals in doubles at the 2006 Australian Open, the 2008, 2009 and 2012 Wimbledon Championships, and the 2008 US Open.
Stosur achieved notable success in mixed doubles too, winning three Grand Slam titles at the 2005 Australian Open and the 2008 and 2014 Wimbledon Championships. She would close out her playing career by reaching two more Grand Slam finals at the 2021 Australian Open and the 2022 Wimbledon Championships, both with compatriot Matthew Ebden.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Doubles
Current through the 2023 Australian Open.
Mixed doubles
Significant finals
Grand Slam tournaments
Singles: 2 (1 title, 1 runner-up)
Doubles: 9 (4 titles, 5 runner-ups)
Mixed doubles: 5 (3 titles, 2 runner-ups)
Year-end championships finals
Doubles: 2 (2 titles)
WTA 1000 finals
Singles: 3 (3 runner-ups)
Doubles: 15 (10 titles, 5 runner-ups)
WTA career finals
Singles: 25 (9 titles, 16 runner-ups)
Doubles: 43 (28 titles, 15 runner-ups)
ITF Circuit finals
Singles: 7 (4 titles, 3 runner–ups)
Doubles: 21 (11 titles, 10 runner–ups)
WTA Tour career earnings
Stosur earned more than 20 million dollars during her career.
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|width="100"|Grand Slam <br/ >titles|width="100"|WTA <br/ >titles
|width="100"|Total <br/ >titles
|width="120"|Earnings ($)
|width="100"|Money list rank
|-
|2003
|0
|0
|0
| align="right" |70,219
|140
|-
|2004
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https://en.wikipedia.org/wiki/Pitot%20theorem | The Pitot theorem in geometry states that in a tangential quadrilateral the two pairs of opposite sides have the same total length. It is named after French engineer Henri Pitot.
Statement and converse
A tangential quadrilateral is usually defined as a convex quadrilateral for which all four sides are tangent to the same inscribed circle. Pitot's theorem states that, for these quadrilaterals, the two sums of lengths of opposite sides are the same. Both sums of lengths equal the semiperimeter of the quadrilateral.
The converse implication is also true: whenever a convex quadrilateral has pairs of opposite sides with the same sums of lengths, it has an inscribed circle. Therefore, this is an exact characterization: the tangential quadrilaterals are exactly the quadrilaterals with equal sums of opposite side lengths.
Proof idea
One way to prove the Pitot theorem is to divide the sides of any given tangential quadrilateral at the points where its inscribed circle touches each side. This divides the four sides into eight segments, between a vertex of the quadrilateral and a point of tangency with the circle. Any two of these segments that meet at the same vertex have the same length, forming a pair of equal-length segments. Any two opposite sides have one segment from each of these pairs. Therefore, the four segments in two opposite sides have the same lengths, and the same sum of lengths, as the four segments in the other two opposite sides.
History
Henri Pitot proved his theorem in 1725, whereas the converse was proved by the Swiss mathematician Jakob Steiner in 1846.
Generalization
Pitot's theorem generalizes to tangential -gons, in which case the two sums of alternate sides are equal. The same proof idea applies.
References
External links
Alexander Bogomolny, "When A Quadrilateral Is Inscriptible?" at Cut-the-knot
"A generalization of Pitot's theorem"
Theorems about quadrilaterals and circles |
https://en.wikipedia.org/wiki/List%20of%20Trabzonspor%20seasons | The following table is a season-by-season summary of league performances for Trabzonspor.
Key
1960s
1970s
1980s
1990s
2000s
2010s
2020s
References
All league statistics from turkish-soccer.com
All European statistics from The Rec.Sport.Soccer Statistics Foundation
Seasons
Trabzonspor |
https://en.wikipedia.org/wiki/Jon%20Blaalid | Jon Blaalid (born 1 May 1947) is a Norwegian civil servant.
He was born in Oslo, and holds the cand.oecon. degree in economics. He worked for Statistics Norway from 1974 to 1979 and the Ministry of Trade from 1979 to 1987. From 1988 to 1990 he was deputy under-secretary of state in the Ministry of Foreign Affairs, and from 1990 to 1997 he was deputy under-secretary of state in the Ministry of Local Government. From 1997 to 2004 he was the executive director of Statskonsult, except for the period 2000 to 2001 when he was the acting director of Aetat. He succeeded Ted Hanisch who was fired with immediate effect.
References
1947 births
Living people
Norwegian civil servants
Directors of government agencies of Norway |
https://en.wikipedia.org/wiki/Inscribed%20square%20problem | The inscribed square problem, also known as the square peg problem or the Toeplitz' conjecture, is an unsolved question in geometry: Does every plane simple closed curve contain all four vertices of some square? This is true if the curve is convex or piecewise smooth and in other special cases. The problem was proposed by Otto Toeplitz in 1911. Some early positive results were obtained by Arnold Emch and Lev Schnirelmann. , the general case remains open.
Problem statement
Let C be a Jordan curve. A polygon P is inscribed in C if all vertices of P belong to C. The inscribed square problem asks:
Does every Jordan curve admit an inscribed square?
It is not required that the vertices of the square appear along the curve in any particular order.
Examples
Some figures, such as circles and squares, admit infinitely many inscribed squares. If C is an obtuse triangle then it admits exactly one inscribed square; right triangles admit exactly two, and acute triangles admit exactly three.
Resolved cases
It is tempting to attempt to solve the inscribed square problem by proving that a special class of well-behaved curves always contains an inscribed square, and then to approximate an arbitrary curve by a sequence of well-behaved curves and infer that there still exists an inscribed square as a limit of squares inscribed in the curves of the sequence. One reason this argument has not been carried out to completion is that the limit of a sequence of squares may be a single point rather than itself being a square. Nevertheless, many special cases of curves are now known to have an inscribed square.
Piecewise analytic curves
showed that piecewise analytic curves always have inscribed squares. In particular this is true for polygons. Emch's proof considers the curves traced out by the midpoints of secant line segments to the curve, parallel to a given line. He shows that, when these curves are intersected with the curves generated in the same way for a perpendicular family of secants, there are an odd number of crossings. Therefore, there always exists at least one crossing, which forms the center of a rhombus inscribed in the given curve. By rotating the two perpendicular lines continuously through a right angle, and applying the intermediate value theorem, he shows that at least one of these rhombi is a square.
Locally monotone curves
Stromquist has proved that every local monotone plane simple curve admits an inscribed square. The condition for the admission to happen is that for any point , the curve should be locally represented as a graph of a function .
In more precise terms, for any given point on , there is a neighborhood and a fixed direction (the direction of the “-axis”) such that no chord of -in this neighborhood- is parallel to .
Locally monotone curves include all types of polygons, all closed convex curves, and all piecewise C1 curves without any cusps.
Curves without special trapezoids
An even weaker condition on the curve th |
https://en.wikipedia.org/wiki/Fekete%E2%80%93Szeg%C5%91%20inequality | In mathematics, the Fekete–Szegő inequality is an inequality for the coefficients of univalent analytic functions found by , related to the Bieberbach conjecture. Finding similar estimates for other classes of functions is called the Fekete–Szegő problem.
The Fekete–Szegő inequality states that if
is a univalent analytic function on the unit disk and , then
References
Inequalities |
https://en.wikipedia.org/wiki/South%20Africa%20national%20soccer%20team%20results%20%282000%E2%80%932009%29 | This page details the match results and statistics of the South Africa national soccer team from 2000 to 2009.
Results
South Africa's score is shown first in each case.
Notes
References
2000-2009
2000s in South Africa |
https://en.wikipedia.org/wiki/Gottfried%20K%C3%B6the | Gottfried Maria Hugo Köthe (born 25 December 1905 in Graz – died 30 April 1989 in Frankfurt) was an Austrian mathematician working in abstract algebra and functional analysis.
Scientific career
In 1923 Köthe enrolled in the University of Graz. He started studying chemistry, but switched to mathematics a year later after meeting the philosopher Alfred Kastil. In 1927 he submitted his thesis Beiträge zu Finslers Grundlegung der Mengenlehre ("Contributions to Finsler's foundations of set theory") and was awarded a doctorate. After spending a year in Zürich working with Paul Finsler, Köthe received a fellowship to visit the University of Göttingen, where he attended the lectures of Emmy Noether and Bartel van der Waerden on the emerging subject of abstract algebra. He began working in ring theory and in 1930 published the Köthe conjecture stating that a sum of two left nil ideals in an arbitrary ring is a nil ideal. By a recommendation of Emmy Noether, he was appointed an assistant of Otto Toeplitz in Bonn University in 1929–1930. During this time he began transition to functional analysis. He continued scientific collaboration with Toeplitz for several years afterward.
Köthe's Habilitationsschrift, Schiefkörper unendlichen Ranges über dem Zentrum ("Skew fields of infinite rank over the center"), was accepted in 1931. He became Privatdozent at University of Münster under Heinrich Behnke. During World War II he was involved in coding work. In 1946 he was appointed the director of the Mathematics Institute at the University of Mainz and he served as a dean (1948–1950) and a rector of the university (1954–1956). In 1957 he became the founding director of the Institute for Applied Mathematics at the University of Heidelberg and served as a rector of the university (1960–1961).
Köthe's best known work has been in the theory of topological vector spaces. In 1960, volume 1 of his seminal monograph Topologische lineare Räume was published (the second edition was translated into English in 1969). It was not until 1979 that volume 2 appeared, this time written in English. He also made contributions to the theory of lattices.
Awards and honors
Invited Speaker of the ICM in 1928 in Bologna, in 1932 in Zurich, and in 1936 in Oslo
Heidelberg Academy of Sciences (1960)
Gauss medal, Brunswick Academy of Sciences (1963)
German Academy of Sciences Leopoldina, Halle (1968)
Honorary degrees from University of Montpellier (1965), University of Münster (1980), University of Mainz (1981) and Saarland University (1981).
Books
References
External links
Gottfried Köthe, 1905-1989 by Joachim Weidmann, digital edition Univ. Heidelberg
Vita (in German) by Heinz Günther Tillmann, digital edition Univ. Heidelberg
20th-century German mathematicians
Scientists from Graz
1905 births
1989 deaths
Algebraists
Functional analysts
Topologists
Austrian mathematicians
Mathematicians from Austria-Hungary
University of Graz alumni
University of Bonn alumni
Academic staf |
https://en.wikipedia.org/wiki/Dinara%20Safina%20career%20statistics | This is a list of the main career statistics of retired Russian professional tennis player Dinara Safina. Throughout her career, Safina won twelve WTA Tour singles titles including three Tier I singles titles at the 2008 German Open, Rogers Cup and Pan Pacific Open, respectively; one Premier Mandatory singles title at the 2009 Madrid Open and one Premier 5 singles title at the 2009 Italian Open. She was also the runner-up at the 2008 French Open and the 2009 Australian Open and French Open as well as a silver medalist in singles at the 2008 Beijing Olympics.
Safina was also an accomplished doubles player, winning nine WTA doubles titles including one Grand Slam doubles title with Nathalie Dechy at the 2007 US Open, one Tier I-doubles title with Elena Vesnina at the 2008 Indian Wells Masters and three consecutive doubles titles at the Brisbane International from 2006 to 2008. Safina achieved her career-high doubles ranking of world No. 8 on May 12, 2008, and subsequently attained the No. 1 ranking in singles on April 20, 2009.
Career achievements
Safina made her main draw WTA debut at the 2002 Estoril Open, where she defeated third seed Martina Suchá en route to the semi-finals. In July of the same year, she won her first WTA singles title, as a qualifier, at the Warsaw Open after her opponent, Henrieta Nagyová retired whilst down a set and 4–0. As a result, Safina entered the top 100 of the WTA singles rankings for the first time in her career and became the youngest Russian tennis player to win a singles title on the WTA Tour. In October 2005, Safina scored her first win over a reigning world No. 1 by defeating Maria Sharapova in three sets en route to her first Tier I semifinal at the Kremlin Cup. She eventually finished the year ranked inside the top twenty for the first time at world No. 20. The following year, Safina reached the first two Grand Slam quarterfinals of her career in singles at the French Open and US Open respectively, defeating Sharapova in the fourth round of the former after overcoming a 5–1 third set deficit. She also reached her first Grand Slam doubles final at the latter event, where she and Katarina Srebotnik lost in straight sets to Nathalie Dechy and Vera Zvonareva. After a quarterfinal showing at the Luxembourg Open, Safina cracked the top ten of the WTA rankings for the first time in her career on October 2, 2006. Highlights of Safina's 2007 season were singles and doubles titles at the Brisbane International, a finals appearance at the Tier I Family Circle Cup and winning her maiden grand slam doubles title at the US Open with Dechy, after a straight sets win over Chan Yung-jan and Chuang Chia-jung in the final.
Safina enjoyed a breakthrough season in 2008. She compiled a disappointing singles win–loss record of 11–10 to start the season but won her third consecutive doubles title at the Brisbane International with Ágnes Szávay and her first and only Tier I doubles title at the Pacific Life Open with compatriot, |
https://en.wikipedia.org/wiki/John%20Newsome%20Crossley | John Newsome Crossley (born 28 September 1937, Yorkshire, England) is a British-Australian mathematician and logician who writes in the field of logic in computer science, history of mathematics and medieval history. He is involved in the field of mathematical logic in Australia and South East Asia.
As of 2010, Crossley is Emeritus Professor of Logic at Monash University, Australia, to which he has been connected since 1968.
Biography
Crossley was educated at Queen Elizabeth Grammar School, Wakefield, and then went up to St John's College, Oxford. He was a Harmsworth Senior Scholar at Merton College from 1960 to 1962, before taking up a one-year Junior Research Fellowship there; he received his DPhil and MA (Mathematics) in 1963. His early career was spent at Oxford where he was the first university lecturer in mathematical logic and was a Fellow of All Souls College, Oxford. He is still a Quondam Fellow there. He was offered a Readership position and following a lecturing visit to Monash University in 1968, he was elected to a Chair in Pure Mathematics. He accepted this position and as of 2010, Crossley continues to be active at Monash University where he serves through its Faculty of Information Technology.
Crossley has written books in logic, mathematics and computer science. He is known as the lead author of the book What is Mathematical Logic. Co-written with some of his students, the book popularized the subject to the interested layman. Many of Crossley's doctoral students have gone on to be professors themselves and have written books in the field of mathematics or computing, including Peter Aczel, Wilfrid Hodges, John Lane Bell and Rod Downey.
Crossley is also an avid photographer. In 1974 he first exhibited his photographs in Melbourne and again in 2005 he exhibited Composition and Context, a collection of photographs shot by Crossley around the world that illustrates the title and theme of the exhibition. A number of these photographs since have appeared in publications in Australia, Britain and the Philippines.
Publications
Books
Constructive Order Types John N. Crossley North-Holland Publishing Company, Amsterdam, 1969
What is Mathematical Logic John N. Crossley et al. Oxford University Press, 1972
Combinatorial Functors John N. Crossley and Anil Nerode, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer, Berlin, 1974
The emergence of number John Newsome Crossley, World Scientific, Singapore, 1987
Nine Chapters on the Mathematical Art -- Companion & Commentary, Shen Kangshen, John N. Crossley and Anthony W.-C. Lun. Oxford University Press, 1999
Adapting proofs-as-programs: The Curry-Howard Protocol, Iman Hafiz Poernomo, John Newsome Crossley and Martin Wirsing, Springer Monographs in Computer Science, Springer, New York, 2005
Growing ideas of number John N. Crossley Australian Council for Educational Research, Camberwell, 2007
Ars musice Constant J. Mews, John N. Crossley, Catherine Jeffreys, Leigh McKinnon, and Ca |
https://en.wikipedia.org/wiki/Nicod%27s%20axiom | In logic, Nicod's axiom (named after the French logician and philosopher Jean Nicod) is a formula that can be used as the sole axiom of a semantically complete system of propositional calculus. The only connective used in the formulation of Nicod's axiom is the Sheffer's stroke.
The axiom has the following form:
((φ | (χ | ψ)) | ((τ | (τ | τ)) | ((θ | χ) | ((φ | θ) | (φ | θ)))))
Nicod showed that the whole propositional logic of Principia Mathematica could be derived from this axiom alone by using one inference rule, called "Nicod's modus ponens":
1. φ
2. (φ | (χ | ψ))
∴ ψ
In 1931, the Polish logician Mordechaj Wajsberg discovered an equally powerful and easier-to-work-with alternative:
((φ | (ψ | χ)) | (((τ | χ) | ((φ | τ) | (φ | τ))) | (φ | (φ | ψ))))
References
External links
Propositional calculus
Theorems in propositional logic
pl:aksjomat Nicoda-Łukasiewicza |
https://en.wikipedia.org/wiki/Meertens%20number | In number theory and mathematical logic, a Meertens number in a given number base is a natural number that is its own Gödel number. It was named after Lambert Meertens by Richard S. Bird as a present during the celebration of his 25 years at the CWI, Amsterdam.
Definition
Let be a natural number. We define the Meertens function for base to be the following:
where is the number of digits in the number in base , is the -prime number, and
is the value of each digit of the number. A natural number is a Meertens number if it is a fixed point for , which occurs if . This corresponds to a Gödel encoding.
For example, the number 3020 in base is a Meertens number, because
.
A natural number is a sociable Meertens number if it is a periodic point for , where for a positive integer , and forms a cycle of period . A Meertens number is a sociable Meertens number with , and a amicable Meertens number is a sociable Meertens number with .
The number of iterations needed for to reach a fixed point is the Meertens function's persistence of , and undefined if it never reaches a fixed point.
Meertens numbers and cycles of Fb for specific b
All numbers are in base .
See also
Arithmetic dynamics
Dudeney number
Factorion
Happy number
Kaprekar's constant
Kaprekar number
Narcissistic number
Perfect digit-to-digit invariant
Perfect digital invariant
Sum-product number
References
External links
Arithmetic dynamics
Base-dependent integer sequences |
https://en.wikipedia.org/wiki/Playerhistory.com | Playerhistory.com is an internet association football statistics database, founded in April 2002 by former footballer Håkon André Winther (born 15 September 1969 in Tromsø).
Maintained by a team of volunteers from all over the world, it is one of the largest websites of its kind. As of August 2009, when Football DataCo threatened legal action in a dispute over fixtures, the site contains more than 340,000 player profiles, 40,000 club details and more than 1,600,000 match results.
Playerhistory.com's material has been reproduced in media sources including Aftenposten, and Bladet Tromsø.
References
External links
List of archived Playerprofiles on Playerhistory.com at Wayback Machine.
Online person databases
Association football websites
Sport Internet forums
Internet properties established in 2002 |
https://en.wikipedia.org/wiki/Huzihiro%20Araki | was a Japanese mathematical physicist and mathematician who worked on the foundations of quantum field theory, on quantum statistical mechanics, and on the theory of operator algebras.
Biography
Araki is the son of the University of Kyoto physics professor Gentarō Araki, with whom he studied and with whom in 1954 he published his first physics paper. He earned his diploma under Hideki Yukawa and in 1960 he attained his doctorate at Princeton University with thesis advisors Rudolf Haag and Arthur Wightman. He was a professor at the University of Kyoto starting in 1966, and became the director of the Research Institute for Mathematical Sciences (RIMS).
Araki died on 16 December 2022.
Research
Araki worked on axiomatic quantum field theory, statistical mechanics, and in particular on applications of operator algebras like von Neumann algebras and C*-algebras. At the beginning of the 1960s, in Princeton, he made important contributions to local quantum physics and to the scattering theories of Haag and David Ruelle. He also supplied important contributions in the mathematical theory of operator algebras, classifying the type-III factors of von Neumann algebras. Araki originated the concept of relative entropy of states of von Neumann algebras. In the 1970s he showed the equivalence in quantum thermodynamics of, on the one hand, the KMS condition (named after Ryogo Kubo, Paul C. Martin, and Julian Schwinger) for the characterization of quantum mechanical states in thermodynamic equilibrium with, on the other hand, the variational principle for quantum mechanical spin systems on lattices. With Yanase he worked on the foundations of quantum mechanics, i.e. the Wigner-Araki-Yanase theorem, which describes restrictions that conservation laws impose upon the physical measuring process. Stated in more precise terms, they proved that an exact measurement of an operator, which additively replaces the operator with a conserved size, is impossible. However, Yanase did prove that the uncertainty of the measurement can be made arbitrarily small, provided that the measuring apparatus is sufficiently large.
Honors and awards
Huzihiro Araki was an invited speaker at the International Congress of Mathematicians in 1970 in Nice and in 1978 in Helsinki. He was the second president of the International Association of Mathematical Physics, during the period 1979–1981. In 2003 he received, together with Oded Schramm and Elliott Lieb, the Henri Poincaré Prize. In 1990 he was the chief organizer of the International Congress of Mathematicians in Kyoto. He was editor of the scientific journal Communications in Mathematical Physics and founder of Reviews in Mathematical Physics. In 2012 he became a fellow of the American Mathematical Society.
Selected works
See also
Araki–Sucher correction
Algebraic quantum field theory
C*-algebra
KMS state
Local quantum physics
Quantum field theory
Quantum thermodynamics
Von Neumann algebra
References
Further reading
Ext |
https://en.wikipedia.org/wiki/2010%E2%80%9311%20F.C.%20Copenhagen%20season | This article shows 2010–11 statistics of individual players for the football club F.C. Copenhagen. It also lists all matches that F.C. Copenhagen played in the 2010–11 season.
Players
Squad information
This section show the squad as currently, considering all players who are confirmedly moved in and out (see section Players in / out).
Squad stats
Starting 11
This section shows the most used players for each position considering a 4-4-2 formation.
Players in / out
In
Out
Club
Coaching staff
Kit
|
|
|
|
|
Other information
Competitions
Overall
Danish Superliga
Classification
Results summary
Results by round
UEFA Champions League
Third qualifying round
Play-off round
Group D
Classification
Results by round
Round of 16
Results summary
Matches
Competitive
References
External links
F.C. Copenhagen official website
2010-11
Danish football clubs 2010–11 season
2010–11 UEFA Champions League participants seasons |
https://en.wikipedia.org/wiki/Dean%20Hooper | Dean Raymond Hooper (born 13 April 1971) is an English retired professional footballer who played as a full back for Swindon Town and Peterborough United in the Football League.
Career statistics
Honours
Kingstonian
Isthmian League Premier Division: 1997–98
Surrey Senior Cup: 1997–98
Aldershot Town
Isthmian League Premier Division: 2002–03
References
External links
1971 births
Living people
People from Harefield
Footballers from the London Borough of Hillingdon
English men's footballers
Brentford F.C. players
Yeading F.C. players
Hayes F.C. players
Swindon Town F.C. players
Peterborough United F.C. players
Stevenage F.C. players
Kingstonian F.C. players
Dagenham & Redbridge F.C. players
Aldershot Town F.C. players
St Albans City F.C. players
Lewes F.C. players
Cambridge United F.C. players
English Football League players
Chalfont St Peter A.F.C. players
Marlow F.C. players
Isthmian League players
National League (English football) players
Men's association football fullbacks |
https://en.wikipedia.org/wiki/Quantile%20normalization | In statistics, quantile normalization is a technique for making two distributions identical in statistical properties. To quantile-normalize a test distribution to a reference distribution of the same length, sort the test distribution and sort the reference distribution. The highest entry in the test distribution then takes the value of the highest entry in the reference distribution, the next highest entry in the reference distribution, and so on, until the test distribution is a perturbation of the reference distribution.
To quantile normalize two or more distributions to each other, without a reference distribution, sort as before, then set to the average (usually, arithmetic mean) of the distributions. So the highest value in all cases becomes the mean of the highest values, the second highest value becomes the mean of the second highest values, and so on.
Generally a reference distribution will be one of the standard statistical distributions such as the Gaussian distribution or the Poisson distribution. The reference distribution can be generated randomly or from taking regular samples from the cumulative distribution function of the distribution. However, any reference distribution can be used.
Quantile normalization is frequently used in microarray data analysis. It was introduced as quantile standardization and then renamed as quantile normalization.
Example
A quick illustration of such normalizing on a very small dataset:
Arrays 1 to 3, genes A to D
A 5 4 3
B 2 1 4
C 3 4 6
D 4 2 8
For each column determine a rank from lowest to highest and assign number i-iv
A iv iii i
B i i ii
C ii iii iii
D iii ii iv
These rank values are set aside to use later.
Go back to the first set of data. Rearrange that first set of column values so each column is in order going lowest to highest value. (First column consists of 5,2,3,4. This is rearranged to 2,3,4,5. Second Column 4,1,4,2 is rearranged to 1,2,4,4, and column 3 consisting of 3,4,6,8 stays the same because it is already in order from lowest to highest value.) The result is:
A 5 4 3 becomes A 2 1 3
B 2 1 4 becomes B 3 2 4
C 3 4 6 becomes C 4 4 6
D 4 2 8 becomes D 5 4 8
Now find the mean for each row to determine the ranks
A (2 + 1 + 3)/3 = 2.00 = rank i
B (3 + 2 + 4)/3 = 3.00 = rank ii
C (4 + 4 + 6)/3 = 4.67 = rank iii
D (5 + 4 + 8)/3 = 5.67 = rank iv
Now take the ranking order and substitute in new values
A iv iii i
B i i ii
C ii iii iii
D iii ii iv
becomes:
A 5.67 4.67 2.00
B 2.00 2.00 3.00
C 3.00 4.67 4.67
D 4.67 3.00 5.67
These are the new normalized values.
However, note that when, as in column two, values are tied in rank, they should instead be assigned the mean of the values corresponding to the ranks they would normally represent if they were different. I |
https://en.wikipedia.org/wiki/Morton%20Brown | Morton Brown (born August 12, 1931, in New York City, New York) is an American mathematician, who specializes in geometric topology.
In 1958 Brown earned his Ph.D. from the University of Wisconsin-Madison under R. H. Bing. From 1960 to 1962 he was at the Institute for Advanced Study. Afterwards he became a professor at the University of Michigan at Ann Arbor.
With Barry Mazur in 1965 he won the Oswald Veblen prize for their independent and nearly simultaneous proofs of the generalized Schoenflies hypothesis in geometric topology. Brown's short proof was elementary and fully general. Mazur's proof was also elementary, but it used a special assumption which was removed via later work of Morse.
In 2012 he became a fellow of the American Mathematical Society.
References
External links
20th-century American mathematicians
21st-century American mathematicians
Fellows of the American Mathematical Society
Institute for Advanced Study visiting scholars
University of Michigan faculty
University of Wisconsin–Madison alumni
1931 births
Living people
Topologists
Mathematicians from New York (state)
Scientists from New York City |
https://en.wikipedia.org/wiki/Nef%20polygon | In mathematics Nef polygons and Nef polyhedra are the sets of polygons and polyhedra which can be obtained from a finite set of halfplanes (halfspaces) by Boolean operations of set intersection and set complement. The objects are named after the Swiss mathematician Walter Nef (1919–2013), who introduced them in his 1978 book on polyhedra.
Since other Boolean operations, such as union or difference, may be expressed via intersection and complement operations, the sets of Nef polygons (polyhedra) are closed with respect to these operations as well.
In addition, the class of Nef polyhedra is closed with respect to the topological operations of taking closure, interior, exterior, and boundary. Boolean operations, such as difference or intersection, may produce non-regular sets. However the class of Nef polyhedra is also closed with respect to the operation of regularization.
Convex polytopes are a special subclass of Nef polyhedra, being the set of polyhedra which are the intersections of a finite set of half-planes.
Terminology
In the language of Nef polyhedra you can refer to various objects as 'faces' with different dimensions. What would normally be called a 'corner' or 'vertex' of a shape is called a 'face' with dimension of 0. An 'edge' or 'segment' is a face with dimension 1. A flat shape in 3D space, like a triangle, is called a face with dimension 2 – or a 'facet'. A shape in 3D space, like a cube, is called a face with dimension 3 – or a 'volume'.
Implementations
The Computational Geometry Algorithms Library, or CGAL, represents Nef Polyhedra by using two main data structures. The first is a 'Sphere map' and the second is a 'Selective Nef Complex' (or SNC). The 'sphere map' stores information about the polyhedron by creating an imaginary sphere around each vertex, and painting it with various points and lines representing how the polyhedron divides space. The SNC basically stores and organizes the sphere maps. Each face contains a 'label' or 'mark' telling whether it is part of the object or not.
See also
CGAL
References
Types of polygons
Polyhedra |
https://en.wikipedia.org/wiki/Heinrich-Wolfgang%20Leopoldt | Heinrich-Wolfgang Leopoldt (22 August 1927 – 28 July 2011) was a German mathematician who worked on algebraic number theory.
Leopoldt earned his Ph.D. in 1954 at the University of Hamburg under Helmut Hasse with the thesis Über Einheitengruppe und Klassenzahl reeller algebraischer Zahlkörper (On group of unity and class number of real algebraic number fields). As a postdoc, he was from 1956 to 1958 at the Institute for Advanced Study. In 1959, he obtained his habilitation degree at the University of Erlangen and was then at the University of Tübingen. From 1964, he was ordentlicher Professor at the University of Karlsruhe, where he was also Director of the Mathematics Institute.
Leopoldt and Tomio Kubota introduced and investigated p-adic L-functions (now named after them). These functions are a component of Iwasawa theory and are a p-adic version of the Dirichlet L-functions. With Hans Zassenhaus he also worked on computer algebra and its applications in number theory.
Leopoldt and Peter Roquette edited the collected works of Hasse.
In 1979, Leopoldt became a member of the Heidelberger Akademie der Wissenschaften.
See also
Leopoldt's conjecture
References
20th-century German mathematicians
1927 births
2011 deaths
University of Hamburg alumni
Academic staff of the University of Erlangen-Nuremberg
Academic staff of the Karlsruhe Institute of Technology |
https://en.wikipedia.org/wiki/Comparison%20of%20linear%20algebra%20libraries | The following tables provide a comparison of linear algebra software libraries, either specialized or general purpose libraries with significant linear algebra coverage.
Dense linear algebra
General information
Matrix types and operations
Matrix types (special types like bidiagonal/tridiagonal are not listed):
Real – general (nonsymmetric) real
Complex – general (nonsymmetric) complex
SPD – symmetric positive definite (real)
HPD – Hermitian positive definite (complex)
SY – symmetric (real)
HE – Hermitian (complex)
BND – band
Operations:
TF – triangular factorizations (LU, Cholesky)
OF – orthogonal factorizations (QR, QL, generalized factorizations)
EVP – eigenvalue problems
SVD – singular value decomposition
GEVP – generalized EVP
GSVD – generalized SVD
References
External links
Comparison of linear algebra libraries
Numerical analysis
Numerical linear algebra
Linear algebra libraries |
https://en.wikipedia.org/wiki/Morphism | In mathematics, particularly in category theory, a morphism is a structure-preserving map from one mathematical structure to another one of the same type. The notion of morphism recurs in much of contemporary mathematics. In set theory, morphisms are functions; in linear algebra, linear transformations; in group theory, group homomorphisms; in analysis and topology, continuous functions, and so on.
In category theory, morphism is a broadly similar idea: the mathematical objects involved need not be sets, and the relationships between them may be something other than maps, although the morphisms between the objects of a given category have to behave similarly to maps in that they have to admit an associative operation similar to function composition. A morphism in category theory is an abstraction of a homomorphism.
The study of morphisms and of the structures (called "objects") over which they are defined is central to category theory. Much of the terminology of morphisms, as well as the intuition underlying them, comes from concrete categories, where the objects are simply sets with some additional structure, and morphisms are structure-preserving functions. In category theory, morphisms are sometimes also called arrows.
Definition
A category C consists of two classes, one of and the other of . There are two objects that are associated to every morphism, the and the . A morphism from to is a morphism with source and target ; it is commonly written as or the latter form being better suited for commutative diagrams.
For many common categories, objects are sets (often with some additional structure) and morphisms are functions from an object to another object. Therefore, the source and the target of a morphism are often called and respectively.
Morphisms are equipped with a partial binary operation, called . The composition of two morphisms f and g is defined precisely when the target of f is the source of g, and is denoted g ∘ f (or sometimes simply gf). The source of g ∘ f is the source of f, and the target of g ∘ f is the target of g. The composition satisfies two axioms:
For every object X, there exists a morphism idX : X → X called the identity morphism on X, such that for every morphism we have idB ∘ f = f = f ∘ idA.
Associativity h ∘ (g ∘ f) = (h ∘ g) ∘ f whenever all the compositions are defined, i.e. when the target of f is the source of g, and the target of g is the source of h.
For a concrete category (a category in which the objects are sets, possibly with additional structure, and the morphisms are structure-preserving functions), the identity morphism is just the identity function, and composition is just ordinary composition of functions.
The composition of morphisms is often represented by a commutative diagram. For example,
The collection of all morphisms from X to Y is denoted HomC(X,Y) or simply Hom(X, Y) and called the hom-set between X and Y. Some authors write MorC(X,Y), Mor(X, Y) or C(X, Y). The ter |
https://en.wikipedia.org/wiki/Stuart%20Pocock | Stuart J. Pocock is a British medical statistician. He has been professor of medical statistics at the London School of Hygiene and Tropical Medicine since 1989. His research interests include statistical methods for the design, monitoring, analysis and reporting of randomized clinical trials. He also collaborates on major clinical trials, particularly in cardiovascular disease.
In 2003, the Royal Statistical Society awarded him the Bradford Hill Medal "for his development of clinical trials methodology, including group sequential methods, his extensive applied work, notably in the epidemiology and treatment of heart disease, and his exposition of good practice nationally and internationally, especially through his book Clinical Trials: a Practical Approach and through his service on influential government committees."
Books
External links
References
British statisticians
Academics of the London School of Hygiene and Tropical Medicine
Living people
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Paris%20Institute%20of%20Statistics | Institut de Statistiques de l'Université de Paris (ISUP, roughly translated as "Paris Institute of Statistics" or literally to "Institute of Statistics of the University of Paris") is a graduate school of statistics based in Paris, in the fifth arrondissement. It offers specializations in actuarial sciences (finance and insurance), biostatistics as well as industry and services. The ISUP is considered one of the most prestigious centers of learning of statistics in France, reflected in the number of job offers received regularly, the strength of its alumni network, and wages offered to its students out of school, which place it in the "top 15-ranked" French Grandes Ecoles
Founded in 1922 by the mathematician Émile Borel, is the oldest and one of the most prestigious schools for statistics in France. Since 2018, the institute is affiliated to Sorbonne University and located on the campus of Jussieu.
History
Origin
The ISUP is the oldest training statistics in France: it was founded in 1922 (by the mathematician Émile Borel) 20 years before the ENSAE and 72 years before the ENSAI.
At the end of the Great War, Émile Borel, one of the greatest mathematicians of his time, was appointed to the Chair of Probability and Mathematical Physics at the University of Paris. So at this time, there is almost no teaching of statistics and the idea of applying mathematics to any specific field arouses contempt "real" mathematicians. Borel is confident that in economy - in Insurance, in particular - there is a demand. This intuition is the basis for the creation of the ISUP 1922. During the thirty years that followed, under the leadership of mathematical leaders, ISUP will initiate the introduction in France, the teaching of statistics and industrial applications, management or Operational Research.
Notable people from ISUP
Émile Borel, Academician, fondator and first director
Maurice Allais, Nobel Prize for Economics 1988, professor at l'ISUP during 21 years
Georges Darmois, Academician, former director
Daniel Dugué, Academician, former director, author for Encyclopædia Universalis (Calculation of probability)
Jean-Paul Benzécri, Normalien, professor at ISUP, initiator of Data analysis
Gérard Calot, Polytechnician, then student at ISUP, director of l'INED
Paul Deheuvels, Academician, currently professor
Dominique Strauss-Kahn, former Director of International Monetary Fund, former student.
Éric Le Boucher, Director of economy magazine Enjeux-Les Echos.
Nicholas Georgescu-Roegen, Romanian mathematician, statistician and economist, progenitor of Ecological economics, former student.
The ISUP today
The current headmaster is Olivier Lopez. Among teachers, traditionally shared with the University of Paris VI or with some ESSEC (partner school) or Dauphine (other actuarial school), several have a worldwide reputation for their research. These include Jean Jacod (the Franco-German Science Award 2008), Paul Deheuvels (a member of the Academy of Sciences) |
https://en.wikipedia.org/wiki/List%20of%20St%20Helens%20R.F.C.%20statistics%20and%20records | The following is a list of St Helens R.F.C.'s honours and records, both personal of individuals and of the team as a whole, that have been set over the 137-year history of the club.
Team honours
Titles
Biggest win
Heaviest defeat
Largest Attendance
Record attendance in Super League era
Player honours
Century of tries
Below is a list of players who have scored 100 or more tries for St Helens:
All-Time Records
Below are the all-time scoring and in-game records achieved by St Helens
Tries in a game
Goals in a game
Most points in a game
Most tries in a season
Most goals in a season
Most points in a season
Most career tries
Most career goals
Most career points
Most career appearances
List of coaches
St Helens R.F.C. |
https://en.wikipedia.org/wiki/Gareth%20Loy | Gareth Loy is an American author, composer, musician and mathematician. Loy is the author of the two volume series about the intersection of music and mathematics titled Musimathics. Loy was an early practitioner of music synthesis at Stanford, and wrote the first software compiler for the Systems Concepts Digital Synthesizer (Samson Box). More recently, Loy has published the freeware music programming language Musimat, designed specifically for subjects covered in Musimathics, available as a free download. Although Musimathics was first published in 2006 and 2007, the series continues to evolve with updates by the author and publishers. The texts are being used in numerous math and music classes at both the graduate and undergraduate level, with more current reviews noting that the originally targeted academic distribution is now reaching a much wider audience. Music synthesis pioneer Max Mathews stated that Loy's books are a "guided tour-de-force of the mathematics of physics and music... Loy has always been a brilliantly clear writer. In Musimathics, he is also an encyclopedic writer. He covers everything needed to understand existing music and musical instruments, or to create new music or new instruments. Loy's book and John R. Pierce's famous The Science of Musical Sound belong on everyone's bookshelf, and the rest of the shelf can be empty." John Chowning states, in regard to Nekyia and the Samson Box, "After completing the (Samson Box) software, Loy composed Nekyia, a beautiful and powerful composition in four channels that fully exploited the capabilities of the Samson Box. As an integral part of the (original Stanford) community, Loy has paid back many times over all that he learned, by conceiving the (Samson) system with maximal generality such that it could be used for research projects in psychoacoustics as well as for hundreds of compositions by a host of composers having diverse compositional strategies."
Biographical background
Loy was born in Los Angeles in 1945. He was an early employee at Apple Computer, and is the brother of the late Tom Loy, a renowned molecular archaeologist, and member of the team that researched Oetzi the Iceman.
In the 1960s and 1970s, CCRMA – the Center for Research in Music and Acoustics at Stanford University – which was then a research project at the Stanford Artificial Intelligence Laboratory (SAIL), developed fundamental technologies later used extensively in the digital synthesizer and digital audio industries. Dr. Loy was a grad student at CCRMA in the mid-70s, and wrote the compiler software for the original Samson Box, which was the original and most powerful and complex digital synthesizer/processor of the day. Since Dr. Loy is both a mathematician and a composer, in addition to the mathematics, engineering and software code for the Samson Box, Loy also composed Nekyia, a dynamic and powerful four channel composition, to fully demonstrate the capabilities of the Samson Box. Nekyia still stand |
https://en.wikipedia.org/wiki/Computational%20Statistics%20%28journal%29 | Computational Statistics is a quarterly peer-reviewed scientific journal that publishes applications and research in the field of computational statistics, as well as reviews of hardware, software, and books. According to the Journal Citation Reports, the journal has a 2012 impact factor of 0.482. It was established in 1986 as Computational Statistics Quarterly and obtained its current title in 1992. The journal is published by Springer Science+Business Media and the editor-in-chief is Yuichi Mori (Okayama University of Science).
See also
List of statistics journals
References
External links
Computational statistics journals
Quarterly journals
English-language journals |
https://en.wikipedia.org/wiki/Indian%20Mathematical%20Society | Indian Mathematical Society (IMS) is the oldest organization in India devoted to the promotion of study and research in mathematics. The Society was founded in April 1907 by V. Ramaswami Aiyar with its headquarters at Pune. The Society started its activities under the tentatively proposed name Analytic Club and the name was soon changed to Indian Mathematical Club. After the adoption of a new constitution in 1910, the society acquired its present name, namely, the Indian Mathematical Society. The first president of the Society was B. Hanumantha Rao.
Publications
The Society publishes two periodicals both of which are quarterly:
The Journal of the Indian Mathematical Society (JIMS: ISSN 0019-5839)
The Mathematics Student (Math Student: )
The 1911 volume of the Journal contains one of the earliest contributions of the Indian mathematician Srinivasa Ramanujan. It was in the form of a set of questions. A fifteen page paper entitled Some properties of Bernoulli Numbers contributed by Srinivasa Ramanujan also appeared in the same 1911 volume of the Journal.
The Mathematics Student usually contains the texts of addresses, talks and lectures delivered at the Annual Conferences of the Society, the abstracts of research papers presented at the Annual Conferences, and the Proceedings of the Society's Annual Conferences, as well as research papers, expository and popular articles, and book reviews.
Annual Conferences
The first Annual Conference of the Society was held at Madras in 1916. The second conference was held at Bombay in 1919. From that time on, a conference was held every two years until 1951 when it was decided to hold the conferences annually. The twenty-fifth Conference was held at Allahabad in 1959 which was inaugurated by Jawaharlal Nehru, the first Prime Minister of India.
Memorial Award Lectures
During every Annual Conference, the following Memorial Award Lectures are arranged as a part of the Academic Programme:
P.L. Bhatnagar Memorial Award Lecture (instituted in 1987).
Srinivasa Ramanujan Memorial Award Lecture (instituted in 1990).
V. Ramaswamy Aiyer Memorial Award Lecture (instituted in 1990).
Hansraj Gupta Memorial Award Lecture (instituted in 1990).
Ganesh Prasad Memorial Award Lecture (instituted in 1993 and delivered every alternate year).
IMS Prizes
Professor A. K. Agarwal Award
Award of INR 10,000 for the best publication in any journal in the world. The first Professor A. K. Agarwal Award for best publication awarded to Dr. Neena Gupta.
P.L. Bhatnagar Memorial Prize
This Prize is awarded annually to the top scorer of the Indian team at the International Mathematical Olympiad. It consists of a cash of Rs. 1000/- and a Certificate. The award is presented during the Inaugural Session of the Annual Conference of the Indian Mathematical Society.
Prizes for research paper presentations
The Society holds, during its Annual Conferences, a Special Session of Paper Presentation Competition and Prizes are awarded to |
https://en.wikipedia.org/wiki/Kirsti | Kirsti is a feminine given name. Related names include Kersti, Kirsten, Kjersti. Notable people with the name include:
Kirsti Andersen (born 1941), Danish historian of mathematics
Kirsti Bergstø (born 1981), Norwegian politician
Kirsti Biermann (born 1950), Norwegian speed skater
Kirsti Blom (born 1953), Norwegian author
Kirsti Coward (born 1940), Norwegian judge
Kirsti Eskelinen (born 1948), Finnish diplomat
Kirsti Huke (born 1977), Norwegian singer and composer
Kirsti Ilvessalo (1920–2019), Finnish textile artist
Kirsti Kauppi (born 1957), Finnish diplomat
Kirsti Koch Christensen (born 1940), Norwegian linguist
Kirsti Kolle Grøndahl (born 1943), Norwegian politician
Kirsti Lay (born 1988), Canadian cyclist and speed skater
Kirsti Leirtrø (born 1963), Norwegian politician
Kirsti Lintonen (born 1945), Finnish politician
Kirsti Lyytikäinen (1926–2008), Finnish businesswoman and journalist
Kirsti Manninen (born 1952), Finnish writer and screenwriter
Kirsti Paltto (born 1947), Finnish writer
Kirsti Saxi (born 1953), Norwegian politician
Kirsti Sparboe (born 1946), Norwegian singer
Kirsti Strøm Bull (born 1945), Norwegian professor of law
See also
Kirsty, a given name
References
Danish feminine given names
Estonian feminine given names
Feminine given names
Finnish feminine given names
Norwegian feminine given names |
https://en.wikipedia.org/wiki/Abdus%20Salam%20Award | The Abdus Salam Award (sometimes called the Salam Prize), is a most prestigious award that is awarded annually to Pakistani nationals to the field of chemistry, mathematics, physics, biology. The award is awarded to the scientists who are resident in Pakistan, below 35 years of age on 31 December of the year for which the Prize was to be awarded. It is to consist of a certificate giving a citation and a cash award of US$1,000. It is to be awarded on the basis of the collected research and/or a technical essay written specially for the Prize
The Award is a brainchild of Professor Abdus Salam's students Dr. Riazuddin, Dr. Fayyazuddin and Dr. Asghar Qadir who first presented the idea to Abdus Salam in 1979. Abdus Salam, who felt that he had no right to use the Prize money for personal purposes but that it must be used to further his mission of development of Science in the Third World. Abdus Salam specially put aside money to help Pakistan and Pakistani students. In 1980, Prof. Salam asked Prof. Fayyazuddin and Dr. Asghar Qadir to formulate the rules and procedures for a Prize to be awarded to young Pakistani scientists for their research in the basic sciences. Professor Asghar Qadir is currently the Secretary of Salam Prize Committee at School of Natural Sciences (SNS) in National University of Sciences and Technology (NUST).
Recipients
1981: Dr. Nazma Ikram (Maiden name: Dr. Nazma Masud) – (Physics)
No award was given by Abdus Salam in 1982. According to him none of the nominations came close to the 1981 award winner Dr. Nazma Ikram.
1984: Dr. Pervaiz Amirali Hoodbhoy – (Mathematics)
1985: Dr. Mujahid Kamran - (Physics)
1985: Dr. Mujaddid Ahmed Ijaz – (Physics)
1986: Dr. Muhammad Suhail Zubairy – (Physics)
1986: Dr. Bina S. Siddiqui – (Chemistry)
1987: Dr. Qaiser Mushtaq – (Mathematics)
1990: Dr. M. Iqbal Choudhry– (Chemistry)
1991: Dr. Ashfaque H. Bokhari – (Mathematics)
1994: Dr. Anwar-ul Hassan Gilani – (Biology)
1997: Dr. Asghar Qadir - (Mathematics)
1998: Dr. Naseer Shahzad – (Mathematics)
1999: Dr. Tasawar Hayat – (Mathematics)
2000: Dr. Rabia Hussain – (Biology)
2001: Dr. Farhan Saif – (Physics)
2002: Dr. Muhammad Arif Malik - (Chemistry)
2003: Dr. Ghulam Shabbir - (Mathematics)
2009: Dr. Naseer-Ud-Din Shams – (Physics)
2009: Dr. Tayyab Kamran – (Mathematics)
2010: Dr. Muhammad Tahir - (Biology)
2012: Dr. Amer Iqbal — (Physics)
2012: Dr. Hafiz Zia-ur-Rehman - (Chemistry), Department of Chemistry, Quaid-i-Azam University, Islamabad.
2013: Dr. Rahim Umar - (Mathematics), Faculty of Engineering Sciences, Ghulam Ishaq Khan Institute of Engineering Sciences and Technology.
See also
List of biology awards
List of chemistry awards
List of mathematics awards
List of physics awards
Resources
Physics awards
Mathematics awards
Chemistry awards
Biology awards
Pakistani science and technology awards
Civil awards and decorations of Pakistan
Awards established in 1980
Abdus Salam |
https://en.wikipedia.org/wiki/Durfee%20square | In number theory, a Durfee square is an attribute of an integer partition. A partition of n has a Durfee square of size s if s is the largest number such that the partition contains at least s parts with values ≥ s. An equivalent, but more visual, definition is that the Durfee square is the largest square that is contained within a partition's Ferrers diagram. The side-length of the Durfee square is known as the rank of the partition.
The Durfee symbol consists of the two partitions represented by the points to the right or below the Durfee square.
Examples
The partition 4 + 3 + 3 + 2 + 1 + 1:
{|
|- style="vertical-align:top; text-align:left;"
|
|}
has a Durfee square of side 3 (in red) because it contains 3 parts that are ≥ 3, but does not contain 4 parts that are ≥ 4. Its Durfee symbol consists of the 2 partitions 1 and 2+1+1.
History
Durfee squares are named after William Pitt Durfee, a student of English mathematician James Joseph Sylvester. In a letter to Arthur Cayley in 1883, Sylvester wrote:
Properties
It is clear from the visual definition that the Durfee square of a partition and its conjugate partition have the same size. The partitions of an integer n contain Durfee squares with sides up to and including .
See also
h-index
References
Number theory
Integer partitions |
https://en.wikipedia.org/wiki/R%C3%BAben%20Br%C3%ADgido | Rúben Luís Maurício Brígido (born 23 June 1991 in Leiria) is a Portuguese professional footballer who plays as a central midfielder.
Career statistics
References
External links
1991 births
Living people
People from Leiria
Portuguese men's footballers
Footballers from Leiria District
Men's association football midfielders
Primeira Liga players
Liga Portugal 2 players
C.D. Fátima players
U.D. Leiria players
C.S. Marítimo players
Liga I players
ASC Oțelul Galați players
Cypriot First Division players
Cypriot Second Division players
Ermis Aradippou FC players
Othellos Athienou FC players
Anagennisi Deryneia FC players
Nea Salamis Famagusta FC players
First Professional Football League (Bulgaria) players
PFC Beroe Stara Zagora players
Kazakhstan Premier League players
FC Ordabasy players
FC Tobol players
FC Caspiy players
Portugal men's youth international footballers
Portuguese expatriate men's footballers
Expatriate men's footballers in Romania
Expatriate men's footballers in Cyprus
Expatriate men's footballers in Bulgaria
Expatriate men's footballers in Kazakhstan
Portuguese expatriate sportspeople in Romania
Portuguese expatriate sportspeople in Cyprus
Portuguese expatriate sportspeople in Bulgaria
Portuguese expatriate sportspeople in Kazakhstan |
https://en.wikipedia.org/wiki/Christophe%20Ajas | Christophe Ajas (born 23 May 1972) is a French former professional footballer who played as a forward. He played nine matches in Ligue 1 for FC Gueugnon.
References
Christophe Ajas career statistics
1972 births
Living people
French men's footballers
FC Gueugnon players
AS Muret players
LB Châteauroux players
Angoulême Charente FC players
ÉFC Fréjus Saint-Raphaël players
FC Martigues players
Ligue 1 players
Ligue 2 players
Balma SC players
Men's association football forwards
Footballers from Toulouse |
https://en.wikipedia.org/wiki/Ambroz%20Hara%C4%8Di%C4%87 | Ambroz Haračić (born Mali Lošinj, 5 December 1855, died Mali Lošinj, 1 October 1916), was a Croatian botanist.
Haračić studied mathematics and natural sciences in Vienna. In 1879 he started teaching at Mali Lošinj nautical school, and in 1897 he was transferred to Trieste. He spent 18 years in his hometown conducting meteorological measurements and observations, and based on the results of the research, the Austro-Hungarian government declared Mali Lošinj to be a health resort, which resulted in development of tourism on the island.
Haračić studied vegetation of Lošinj and several smaller nearby islands like Ilovik, Susak, Unije, Male Srakane, Vele Srakane, Murtar, Oruda, always connecting the island climate with the flora of the island. He also helped with forestation of the island of Lošinj. His rich collection of herbs is preserved in Botanics department of Faculty of Natural sciences and Mathematics of the University in Zagreb. He published many works based on his research. Complete bibliography of his work can be found in Zbornik radova o prirodoslovcu Ambrozu Haračiću (Proceedings of the natural scientist Ambroz Haračić).
For his efforts, a statue was erected on the south part of the Čikat cove.
Sources
"Enciklopedija Jugoslavije" (Encyclopedia of Jugoslavia) (4 E-Hrv), Zagreb, 1986.
1855 births
1916 deaths
Botanists from Austria-Hungary
Croatian botanists
Croatian meteorologists
19th-century botanists
People from Mali Lošinj
Botanists active in Europe |
https://en.wikipedia.org/wiki/Erik%20van%20Rossum | Erik van Rossum (born 27 March 1963, in Nijmegen) is a former Dutch football player.
He runs a pub in Nijmegen.
Club statistics
References
External links
Neil Brown
1963 births
Living people
Dutch men's footballers
Men's association football central defenders
Plymouth Argyle F.C. players
English Football League players
NEC Nijmegen players
FC Twente players
Willem II (football club) players
Eredivisie players
Belgian Pro League players
J1 League players
Tokyo Verdy players
Expatriate men's footballers in Belgium
Expatriate men's footballers in England
Expatriate men's footballers in Japan
Dutch expatriate men's footballers
Dutch expatriate sportspeople in Japan
Footballers from Nijmegen
Dutch expatriate sportspeople in England
Dutch expatriate sportspeople in Belgium |
https://en.wikipedia.org/wiki/Anderson%20Batatais | Anderson Luis da Silva (born 22 December 1972), known as Anderson Silva or Anderson Batatais, is a Brazilian football coach and former player who played as a central defender.
Club statistics
References
External links
1972 births
Living people
Campeonato Brasileiro Série A managers
Brazilian men's footballers
Brazilian football managers
Expatriate men's footballers in Japan
J1 League players
J2 League players
Brazilian expatriate men's footballers
Paulista Futebol Clube players
Albirex Niigata players
Clube Atlético Sorocaba players
Coritiba Foot Ball Club players
Associação Atlética Ponte Preta players
Ceará Sporting Club managers
Mirassol Futebol Clube managers
FC Atlético Cearense managers
Ferroviário Atlético Clube (CE) managers
Men's association football defenders
People from Batatais
Footballers from São Paulo (state) |
https://en.wikipedia.org/wiki/Rodrigo%20Riep | Rodrigo Sebastián Riep (born 20 February 1976) is a former Argentine football player.
Personal life
He is the father of the professional footballer .
Club statistics
Post-retirement
He works as a football agent.
References
External links
Rodrigo Riep at PlaymakerStats
1976 births
Living people
Footballers from Buenos Aires
Argentine men's footballers
Argentine expatriate men's footballers
Club Atlético River Plate footballers
Everton de Viña del Mar footballers
Avispa Fukuoka players
C.D. Cobreloa footballers
Olympiacos Volos F.C. players
Caracas FC players
C.D. Cobresal footballers
Deportes La Serena footballers
Coquimbo Unido footballers
UA Maracaibo players
Barcelona S.C. footballers
Carabobo F.C. players
Independiente Medellín footballers
Atlético Junior footballers
Argentine Primera División players
Primera B de Chile players
Chilean Primera División players
J1 League players
Football League (Greece) players
Venezuelan Primera División players
Ecuadorian Serie A players
Categoría Primera A players
Argentine expatriate sportspeople in Chile
Argentine expatriate sportspeople in Japan
Argentine expatriate sportspeople in Greece
Argentine expatriate sportspeople in Venezuela
Argentine expatriate sportspeople in Ecuador
Argentine expatriate sportspeople in Colombia
Expatriate men's footballers in Chile
Expatriate men's footballers in Japan
Expatriate men's footballers in Greece
Expatriate men's footballers in Venezuela
Expatriate men's footballers in Ecuador
Expatriate men's footballers in Colombia
Men's association football midfielders |
https://en.wikipedia.org/wiki/Sorana%20C%C3%AErstea%20career%20statistics | This is a list of the main career statistics of the Romanian professional tennis player Sorana Cîrstea. Cirstea has won two singles titles (2008 Tashkent Open and 2021 İstanbul Cup) and five doubles titles on the WTA Tour. She was also the runner-up at the 2013 Rogers Cup.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Current through the 2023 Canadian Open.
Doubles
Current through the 2023 Canadian Open.
Significant finals
WTA 1000 tournaments
Singles: 1 (runner-up)
WTA Tour career finals
Singles: 6 (2 titles, 4 runner-ups)
Doubles: 10 (5 titles, 5 runner-ups)
WTA 125 finals
Singles: 1 (title)
ITF Circuit finals
Singles: 16 (9 titles, 7 runner–ups)
Doubles: 16 (9 titles, 7 runner–ups)
WTA Tour career earnings
Current after the 2022 US Open
Career Grand Slam statistics
Seedings
The tournaments won by Cîrstea are in boldface, and advanced into finals by Cîrstea are in italics.
Best Grand Slam results details
Head-to-head records
Record against top 10 players
She has a 20–52 () record against players who were, at the time the match was played, ranked in the top 10.
Double bagel matches (6–0, 6–0)
Notes
References
External links
Cirstea, Sorana |
https://en.wikipedia.org/wiki/Elliott%20Mendelson | Elliott Mendelson (May 24, 1931 – May 7, 2020) was an American logician. He was a professor of mathematics at Queens College of the City University of New York, and the Graduate Center, CUNY. He was Jr. Fellow, Society of Fellows, Harvard University, 1956–58.
Career
Mendelson earned his BA from Columbia University and PhD from Cornell University.
Mendelson taught mathematics at the college level for more than 30 years, and is the author of books on logic, philosophy of mathematics, calculus, game theory and mathematical analysis.
His Introduction to Mathematical Logic, first published in 1964, was reviewed by Dirk van Dalen who noted that it included "a large variety of subjects that should be part of the education of any mathematics student with an interest in foundational matters."
Books
Sole author
Co-author
Editor
Journal articles
P. C. Gilmore, Donald A. Martin & Elliott Mendelson (1975). Meeting of the Association for Symbolic Logic. Journal of Symbolic Logic 40 (2):299-304.
Hugues Leblanc, Elliott Mendelson & Alex Orenstein (1984). Preface. Synthese 60 (1).
Elliott Mendelson (2005). Book Review: Igor Lavrov, Larisa Maksimova, Problems in Set Theory, Mathematical Logic and the Theory of Algorithms, Edited by Giovanna Corsi, Kluwer Academic / Plenum Publishers, 2003, Us$141.00, Pp. XII + 282, , Hardbound. Studia Logica 79 (3).
Elliott Mendelson (2000). Critical Studies/Book Reviews. Philosophia Mathematica 8 (3).
Elliott Mendelson (2007). Graham Oppy. Philosophical Perspectives on Infinity. Philosophia Mathematica 15 (3).
Elliott Mendelson (1956) "Some Proofs of Independence in Axiomatic Set Theory", Journal of Symbolic Logic 21(3): 291–303.
Elliott Mendelson (1990) "Second Thoughts About Church's Thesis and Mathematical Proofs", Journal of Philosophy 87(5): 225–233.
Elliott Mendelson (1956) "The Independence of a Weak Axiom of Choice", Journal of Symbolic Logic 21(4): 350–366.
Sidney Morgenbesser & Elliott Mendelson (1966) "Annual Meeting of the Association for Symbolic Logic", Journal of Symbolic Logic 31(4):682-696.
Notes
American logicians
Philosophers of mathematics
20th-century American philosophers
Queens College, City University of New York faculty
2020 deaths
1931 births
Columbia College (New York) alumni
Cornell University alumni |
https://en.wikipedia.org/wiki/Robert%20Blanch%C3%A9 |
Robert Blanché (1898–1975) was an associate professor of philosophy at the University of Toulouse. He wrote many books addressing the philosophy of mathematics.
About Structures intellectuelles
Robert Blanché died in 1975. Nine years before, in 1966, he published with Vrin: Structures intellectuelles. Therein, he deals with the logical hexagon. Whereas the logical square or square of Apuleius represents four values: A,E,I,O , the logical hexagon represents six, that is to say, not only A,E,I,O but also two new values: Y and U. It is advisable to read the article: logical hexagon as well what concerns Indian logic.
In La Logique et son histoire d' Aristote à Russell, published with Armand Colin in 1970, Robert Blanché, the author of Structures intellectuelles (Vrin, 1966) mentions that Józef Maria Bocheński speaks of a sort of Indian logical triangle to be compared with the square of Aristotle (or square of Apuleius), in other words with the square of opposition.
Works
La Notion de fait psychique, essai sur les rapports du physique et du mental – 1934, ed. PUF.
Le Rationalisme de Whewell – 1935, ed. PUF.
Whewell : de la construction de la science – 1938, ed. J. Vrin
La Science physique et la réalité : réalisme, positivisme, mathématisme - 1948, ed. PUF
Les Attitudes idéalistes – 1949, ed. PUF
L’Axiomatique – 1955, ed. P.U.F. coll. Quadrige, 112p.
Introduction à la logique contemporaine - 1957, ed. Armand Colin, coll Cursus, 205p.
Structures intellectuelles, essai sur l’organisation systématique des concepts - 1966, ed. J. Vrin
Raison et discours, défense de la logique réflexive – 1967, ed. J. Vrin
La science actuelle et le rationalisme - 1967, Ed. PUF.
La Méthode expérimentale et la philosophie de la physique – 1969, ed. Armand Collin, 384p
La logique et son histoire d’Aristote à Russell, ed. Amand Colin, coll. U, Paris, 1970, 366p.
La Logique et son histoire, (avec Jacques Dubucs), ed. Amand Colin, coll. U, Paris, 1996, 396p. (édition revue de 1970)
L’Épistémologie - 1972 ; ed. PUF
Le Raisonnement – 1973, ed. PUF
L’Induction scientifique et les lois naturelles – 1975, ed. PUF
References
Biography on Larousse
1898 births
1975 deaths
Philosophers of mathematics
Academic staff of the University of Toulouse
French male non-fiction writers
20th-century French philosophers
20th-century French male writers |
https://en.wikipedia.org/wiki/Studia%20Logica | Studia Logica (full name: Studia Logica, An International Journal for Symbolic Logic), is a scientific journal publishing papers employing formal tools from Mathematics and Logic. The scope of papers published in Studia Logica covers all scientific disciplines; the key criterion for published papers is not their topic but their method: they are required to contain significant and original results concerning formal systems and their properties. The journal offers papers on topics in general logic and on applications of logic to methodology of science, linguistics, philosophy, and other branches of knowledge. The journal is published by the Institute of Philosophy and Sociology of the Polish Academy of Sciences and Springer publications.
History
The name Studia Logica appeared for the first time in 1934, but only one volume (edited by Jan Łukasiewicz) has been published that time. It had been published continuously since December 1953 in changing frequency by the Polish Academy of Sciences. Articles used to appear in Polish, Russian, German, English or French, and their summaries or full translations in at least two of the languages. Kazimierz Ajdukiewicz was chief editor until his death in 1963. The position was later taken by Jerzy Słupecki (1963-1970), Klemens Szaniawski (1970-1974). Under the editorship of Ryszard Wójcicki (1975-1980), who later headed the journal as chairman of the editorial board, Studia Logica moved to publish in English only, and partnered with a Dutch international distributor. Jacek Malinowski runs Studia Logica as Editor-in-Chief from 2006.
Conferences
In 2003, to celebrate the 50 years of Studia Logica, two conferences were organized: in Warsaw/Mądralin (Poland) and in Roskilde (Denmark). They started a series of scientific conferences in collaboration with Studia Logica under the name "Trends in Logic". More than 20 Trends in Logic conferences have been organized, in different countries in Europe, Asia and South America. Full list of Trends in Logic conferences can be found at http://studialogica.org/past.events.html
Bookseries Studia Logica Library
Studia Logica Library was founded by Ryszard Wójcicki. First book in the series, The Is-Ought Problem by Gerhard Schurz, was published in 1997. Originally, these volumes were published by Kluwer Academic Publishers, and starting in September 2005 (on Trends in Logic volume 24), they began publishing with Springer.
Currently Studia Logica Library consist of three subseries:
Trends in Logic run by Heinrich Wansing;
Outstanding contributions run by Sven Ove Hansson;
Logic in Asia run by Fenrong Liu and Hiroakira Ono.
References
External links
Studia Logica website
Studia Logica at Springer
50 years of Studia Logica, October 2003
Logic journals
Polish Academy of Sciences academic journals
Academic journals established in 1953 |
https://en.wikipedia.org/wiki/Log-polar%20coordinates | In mathematics, log-polar coordinates (or logarithmic polar coordinates) is a coordinate system in two dimensions, where a point is identified by two numbers, one for the logarithm of the distance to a certain point, and one for an angle. Log-polar coordinates are closely connected to polar coordinates, which are usually used to describe domains in the plane with some sort of rotational symmetry. In areas like harmonic and complex analysis, the log-polar coordinates are more canonical than polar coordinates.
Definition and coordinate transformations
Log-polar coordinates in the plane consist of a pair of real numbers (ρ,θ), where ρ is the logarithm of the distance between a given point and the origin and θ is the angle between a line of reference (the x-axis) and the line through the origin and the point. The angular coordinate is the same as for polar coordinates, while the radial coordinate is transformed according to the rule
.
where is the distance to the origin. The formulas for transformation from Cartesian coordinates to log-polar coordinates are given by
and the formulas for transformation from log-polar to Cartesian coordinates are
By using complex numbers (x, y) = x + iy, the latter transformation can be written as
i.e. the complex exponential function. From this follows that basic equations in harmonic and complex analysis will have the same simple form as in Cartesian coordinates. This is not the case for polar coordinates.
Some important equations in log-polar coordinates
Laplace's equation
Laplace's equation in two dimensions is given by
in Cartesian coordinates. Writing the same equation in polar coordinates gives the more complicated equation
or equivalently
However, from the relation it follows that so Laplace's equation in log-polar coordinates,
has the same simple expression as in Cartesian coordinates. This is true for all coordinate systems where the transformation to Cartesian coordinates is given by a conformal mapping. Thus, when considering Laplace's equation for a part of the plane with rotational symmetry, e.g. a circular disk, log-polar coordinates is the natural choice.
Cauchy–Riemann equations
A similar situation arises when considering analytical functions. An analytical function written in Cartesian coordinates satisfies the Cauchy–Riemann equations:
If the function instead is expressed in polar form , the Cauchy–Riemann equations take the more complicated form
Just as in the case with Laplace's equation, the simple form of Cartesian coordinates is recovered by changing polar into log-polar coordinates (let ):
The Cauchy–Riemann equations can also be written in one single equation as
By expressing and in terms of and this equation can be written in the equivalent form
Euler's equation
When one wants to solve the Dirichlet problem in a domain with rotational symmetry, the usual thing to do is to use the method of separation of variables for partial differential equations for Lap |
https://en.wikipedia.org/wiki/Scatterplot%20smoothing | In statistics, several scatterplot smoothing methods are available to fit a function through the points of a scatterplot to best represent the relationship between the variables.
Scatterplots may be smoothed by fitting a line to the data points in a diagram. This line attempts to display the non-random component of the association between the variables in a 2D scatter plot. Smoothing attempts to separate the non-random behaviour in the data from the random fluctuations, removing or reducing these fluctuations, and allows prediction of the response based value of the explanatory variable.
Smoothing is normally accomplished by using any one of the techniques mentioned below.
A straight line (simple linear regression)
A quadratic or a polynomial curve
Local regression
Smoothing splines
The smoothing curve is chosen so as to provide the best fit in some sense, often defined as the fit that results in the minimum sum of the squared errors (a least squares criterion).
See also
Additive model
Generalized additive model
Smoothing
References
Regression analysis
Statistical charts and diagrams |
https://en.wikipedia.org/wiki/Balanced%20matrix | In mathematics, a balanced matrix is a 0-1 matrix (a matrix where every entry is either zero or one) that does not contain any square submatrix of odd order having all row sums and all column sums equal to 2.
Balanced matrices are studied in linear programming. The importance of balanced matrices comes from the fact that the solution to a linear programming problem is integral if its matrix of coefficients is balanced and its right hand side or its objective vector is an all-one vector. In particular, if one searches for an integral solution to a linear program of this kind, it is not necessary to explicitly solve an integer linear program, but it suffices to find an optimal vertex solution of the linear program itself.
As an example, the following matrix is a balanced matrix:
Characterization by forbidden submatrices
Equivalent to the definition, a 0-1 matrix is balanced if and only if it does not contain a submatrix that is the incidence matrix of any odd cycle (a cycle graph of odd order).
Therefore, the only three by three 0-1 matrix that is not balanced is (up to permutation of the rows and columns) the following incidence matrix of a cycle graph of order 3:
The following matrix is the incidence matrix of a cycle graph of order 5:
The above characterization implies that any matrix containing or (or the incidence matrix of any other odd cycle) as a submatrix, is not balanced.
Connection to other matrix classes
Every balanced matrix is a perfect matrix.
More restricting than the notion of balanced matrices is the notion of totally balanced matrices. A 0-1 matrix is called totally balanced if it does not contain a square submatrix having no repeated columns and all row sums and all column sums equal to 2. Equivalently, a matrix is totally balanced if and only if it does not contain a submatrix that is the incidence matrix of any cycle (no matter if of odd or even order). This characterization immediately implies that any totally balanced matrix is balanced.
Moreover, any 0-1 matrix that is totally unimodular is also balanced. The following matrix is a balanced matrix as it does not contain any submatrix that is the incidence matrix of an odd cycle:
Since this matrix is not totally unimodular (its determinant is -2), 0-1 totally unimodular matrices are a proper subset of balanced matrices.
For example, balanced matrices arise as the coefficient matrix in special cases of the set partitioning problem.
An alternative method of identifying some balanced matrices is through the subsequence count, where the subsequence count SC of any row s of matrix A is
SC = |{t | [asj = 1, aij = 0 for s < i < t, atj = 1], j = 1, ..., n}|
If a 0-1 matrix A has SC(s) ≤ 1 for all rows s = 1, ..., m, then A has a unique subsequence, is totally unimodular and therefore also balanced. Note that this condition is sufficient but not necessary for A to be balanced. In other words, the 0-1 matrices with SC(s) ≤ 1 for all rows s = 1, ..., m are a proper sub |
https://en.wikipedia.org/wiki/Truncated%207-simplexes | In seven-dimensional geometry, a truncated 7-simplex is a convex uniform 7-polytope, being a truncation of the regular 7-simplex.
There are unique 3 degrees of truncation. Vertices of the truncation 7-simplex are located as pairs on the edge of the 7-simplex. Vertices of the bitruncated 7-simplex are located on the triangular faces of the 7-simplex. Vertices of the tritruncated 7-simplex are located inside the tetrahedral cells of the 7-simplex.
Truncated 7-simplex
In seven-dimensional geometry, a truncated 7-simplex is a convex uniform 7-polytope, being a truncation of the regular 7-simplex.
Alternate names
Truncated octaexon (Acronym: toc) (Jonathan Bowers)
Coordinates
The vertices of the truncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,0,1,2). This construction is based on facets of the truncated 8-orthoplex.
Images
Bitruncated 7-simplex
Alternate names
Bitruncated octaexon (acronym: bittoc) (Jonathan Bowers)
Coordinates
The vertices of the bitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,1,2,2). This construction is based on facets of the bitruncated 8-orthoplex.
Images
Tritruncated 7-simplex
Alternate names
Tritruncated octaexon (acronym: tattoc) (Jonathan Bowers)
Coordinates
The vertices of the tritruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,2,2,2). This construction is based on facets of the tritruncated 8-orthoplex.
Images
Related polytopes
These three polytopes are from a set of 71 uniform 7-polytopes with A7 symmetry.
See also
List of A7 polytopes
Notes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
Norman Johnson Uniform Polytopes, Manuscript (1991)
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
x3x3o3o3o3o3o - toc, o3x3x3o3o3o3o - roc, o3o3x3x3o3o3o - tattoc
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
7-polytopes |
https://en.wikipedia.org/wiki/Rectified%207-simplexes | In seven-dimensional geometry, a rectified 7-simplex is a convex uniform 7-polytope, being a rectification of the regular 7-simplex.
There are four unique degrees of rectifications, including the zeroth, the 7-simplex itself. Vertices of the rectified 7-simplex are located at the edge-centers of the 7-simplex. Vertices of the birectified 7-simplex are located in the triangular face centers of the 7-simplex. Vertices of the trirectified 7-simplex are located in the tetrahedral cell centers of the 7-simplex.
Rectified 7-simplex
The rectified 7-simplex is the edge figure of the 251 honeycomb. It is called 05,1 for its branching Coxeter-Dynkin diagram, shown as .
E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as S.
Alternate names
Rectified octaexon (Acronym: roc) (Jonathan Bowers)
Coordinates
The vertices of the rectified 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,0,1,1). This construction is based on facets of the rectified 8-orthoplex.
Images
Birectified 7-simplex
E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as S. It is also called 04,2 for its branching Coxeter-Dynkin diagram, shown as .
Alternate names
Birectified octaexon (Acronym: broc) (Jonathan Bowers)
Coordinates
The vertices of the birectified 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,1,1,1). This construction is based on facets of the birectified 8-orthoplex.
Images
Trirectified 7-simplex
The trirectified 7-simplex is the intersection of two regular 7-simplexes in dual configuration.
E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as S.
This polytope is the vertex figure of the 133 honeycomb. It is called 03,3 for its branching Coxeter-Dynkin diagram, shown as .
Alternate names
Hexadecaexon (Acronym: he) (Jonathan Bowers)
Coordinates
The vertices of the trirectified 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,1,1,1). This construction is based on facets of the trirectified 8-orthoplex.
The trirectified 7-simplex is the intersection of two regular 7-simplices in dual configuration. This characterization yields simple coordinates for the vertices of a trirectified 7-simplex in 8-space: the 70 distinct permutations of (1,1,1,1,−1,−1,−1,-1).
Images
Related polytopes
Related polytopes
These polytopes are three of 71 uniform 7-polytopes with A7 symmetry.
See also
List of A7 polytopes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S. |
https://en.wikipedia.org/wiki/Sri%20Lanka%20cricket%20lists | This is a list of Sri Lanka Cricket lists, an article with a collection of lists relating to the Sri Lankan Cricket team.
Teams
Stadiums
Cricketers
Player statistics
Batting
List of international cricket centuries by Aravinda de Silva
List of international cricket centuries by Kumar Sangakkara
List of international cricket centuries by Mahela Jayawardene
List of international cricket centuries by Marvan Atapattu
List of international cricket centuries by Sanath Jayasuriya
List of international cricket centuries by Tillakaratne Dilshan
Bowling
List of international cricket five-wicket hauls by Muttiah Muralitharan
List of international cricket five-wicket hauls by Rangana Herath
Records
Test
List of Sri Lankan Test cricket records
100 Runs Test Cricket Partnerships by Sri Lanka
One-day International
List of Sri Lanka One Day International cricket records
Twenty20
List of Sri Lanka Twenty20 International cricket records
By ground
centuries
List of international cricket centuries at the Colombo Cricket Club Ground
List of international cricket centuries at the Paikiasothy Saravanamuttu Stadium
List of international cricket centuries at the R. Premadasa Stadium
List of international cricket centuries at the Sinhalese Sports Club Ground
List of international cricket centuries at the Tyronne Fernando Stadium
five-wicket hauls
List of international cricket five-wicket hauls at the Mahinda Rajapaksa International Stadium
List of international cricket five-wicket hauls at the Paikiasothy Saravanamuttu Stadium
List of international cricket five-wicket hauls at the Sinhalese Sports Club Ground
See also
2009 attack on the Sri Lanka national cricket team
External links
Cricinfo
Sri Lanka in international cricket
Cricket |
https://en.wikipedia.org/wiki/Wales%20national%20football%20team%20records%20and%20statistics | This page details Wales national football team records; the most capped players, the players with the most goals, Wales's match record by opponent and decade.
Player records
Most capped players
Top goalscorers
Age records
Youngest player to make debut: Harry Wilson – 16 years and 207 days
Oldest player to play a game: Billy Meredith – 45 years and 229 days
Youngest player to play at World Cup finals: Roy Vernon – 21 years and 42 days
Oldest player to play at World Cup finals: Dave Bowen – 30 years and 1 day
Youngest player to score a goal: Gareth Bale – 17 years and 83 days
Other
Longest serving player: Billy Meredith – 25 years (1895–1920)
Games and results
Firsts
First International: 26 March 1876 vs
First home international: 5 March 1877 vs
First win: 26 February 1881 vs
First overseas opponent: , 25 May 1933
First win over an overseas opponent: 23 November 1949 vs
Biggest
Biggest Win: 11–0 vs , 3 March 1888
Biggest Loss: 0–9 vs , 23 March 1878
Longest
Longest winning streak: 6, 2 June 1980 – 16 May 1981
Longest losing streak: 5, 25 March 1876 – 27 March 1880
Goals
First Welsh goal: William Davies, 18 January 1879 vs
Youngest player to score: Gareth Bale – 17 years and 83 days, 7 October 2006 v
Most goals scored in one game by a player: 4
John Price, 12 Feb 1882 vs
Jack Doughty, 3 Mar 1888 vs
Mel Charles, 11 Apr 1962 vs
Ian Edwards, 25 October 1978 vs
Hat-tricks
First hat-trick: John Price, 12 February 1882 vs
International tournaments
FIFA World Cup
Qualification
First match: 15 October 1949 vs
First goal: Mal Griffiths vs , 15 October 1949
Finals
First finals: Sweden 1958
Total number of times qualified for the finals: 2 (1958, 2022)
First game: 8 June 1958 vs
First goal: John Charles vs , 8 June 1958
Most successful finals: 1958 – Quarter-finals
World Cup top goalscorer: 2
Ivor Allchurch (1958)
UEFA European Championship
Finals
First finals: France 2016
Total number of times qualified for the finals: 2 (2016, 2020)
First game: 11 June 2016 vs
First goal: Gareth Bale vs , 11 June 2016
Most successful finals: 2016 – Semi-finals
European Championship top goalscorer: 3
Gareth Bale (2016)
Rankings
Highest FIFA Rank: 8 (October 2015)
Lowest FIFA Rank: 117 (August 2011)
Highest Elo Rank: 3 (1876–1885)
Lowest Elo Rank: 75 (September 2000)
Team records
Head to head
P – Played; W – Won; D – Drawn; L – Lost
Statistics include official FIFA recognised matches only
Up to date as of 15 October 2023
By decade
P – Played,
W – Won,
D – Drawn,
L – Lost,
GF – Goals For,
GA – Goals Against,
GD – Goal Difference
Statistics include official FIFA recognised matches only
Up to date as of 15 October 2023
Notes
Only clubs played for while receiving caps are listed.
See also
British Home Championship
1954 FIFA World Cup qualification
1958 FIFA World Cup qualification
1958 FIFA World Cup
References
Bibliography
Notes
External links
RSSSF: Wales – International Results
Wales nati |
https://en.wikipedia.org/wiki/Rigid%20transformation | In mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points.
The rigid transformations include rotations, translations, reflections, or any sequence of these. Reflections are sometimes excluded from the definition of a rigid transformation by requiring that the transformation also preserve the handedness of objects in the Euclidean space. (A reflection would not preserve handedness; for instance, it would transform a left hand into a right hand.) To avoid ambiguity, a transformation that preserves handedness is known as a proper rigid transformation, or rototranslation. Any proper rigid transformation can be decomposed into a rotation followed by a translation, while any improper rigid transformation can be decomposed into an improper rotation followed by a translation, or into a sequence of reflections.
Any object will keep the same shape and size after a proper rigid transformation.
All rigid transformations are examples of affine transformations. The set of all (proper and improper) rigid transformations is a mathematical group called the Euclidean group, denoted for -dimensional Euclidean spaces. The set of proper rigid transformations is called special Euclidean group, denoted .
In kinematics, proper rigid transformations in a 3-dimensional Euclidean space, denoted SE(3), are used to represent the linear and angular displacement of rigid bodies. According to Chasles' theorem, every rigid transformation can be expressed as a screw displacement.
Formal definition
A rigid transformation is formally defined as a transformation that, when acting on any vector , produces a transformed vector of the form
where (i.e., is an orthogonal transformation), and is a vector giving the translation of the origin.
A proper rigid transformation has, in addition,
which means that R does not produce a reflection, and hence it represents a rotation (an orientation-preserving orthogonal transformation). Indeed, when an orthogonal transformation matrix produces a reflection, its determinant is −1.
Distance formula
A measure of distance between points, or metric, is needed in order to confirm that a transformation is rigid. The Euclidean distance formula for is the generalization of the Pythagorean theorem. The formula gives the distance squared between two points and as the sum of the squares of the distances along the coordinate axes, that is
where and , and the dot denotes the scalar product.
Using this distance formula, a rigid transformation has the property,
Translations and linear transformations
A translation of a vector space adds a vector to every vector in the space, which means it is the transformation
It is easy to show that this is a rigid transformation by showing that the distance between translated vectors equal the distance between the original vectors:
A linear |
https://en.wikipedia.org/wiki/Rectified%208-simplexes | In eight-dimensional geometry, a rectified 8-simplex is a convex uniform 8-polytope, being a rectification of the regular 8-simplex.
There are unique 3 degrees of rectifications in regular 8-polytopes. Vertices of the rectified 8-simplex are located at the edge-centers of the 8-simplex. Vertices of the birectified 8-simplex are located in the triangular face centers of the 8-simplex. Vertices of the trirectified 8-simplex are located in the tetrahedral cell centers of the 8-simplex.
Rectified 8-simplex
E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as S. It is also called 06,1 for its branching Coxeter-Dynkin diagram, shown as .
Coordinates
The Cartesian coordinates of the vertices of the rectified 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,0,0,1,1). This construction is based on facets of the rectified 9-orthoplex.
Images
Birectified 8-simplex
E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as S. It is also called 05,2 for its branching Coxeter-Dynkin diagram, shown as .
The birectified 8-simplex is the vertex figure of the 152 honeycomb.
Coordinates
The Cartesian coordinates of the vertices of the birectified 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,0,1,1,1). This construction is based on facets of the birectified 9-orthoplex.
Images
Trirectified 8-simplex
E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as S. It is also called 04,3 for its branching Coxeter-Dynkin diagram, shown as .
Coordinates
The Cartesian coordinates of the vertices of the trirectified 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,1,1,1,1). This construction is based on facets of the trirectified 9-orthoplex.
Images
Related polytopes
This polytope is the vertex figure of the 9-demicube, and the edge figure of the uniform 261 honeycomb.
It is also one of 135 uniform 8-polytopes with A8 symmetry.
Notes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
Norman Johnson Uniform Polytopes, Manuscript (1991)
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
o3x3o3o3o3o3o3o - rene, o3o3x3o3o3o3o3o - brene, o3o3o3x3o3o3o3o - trene
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
8-polytopes |
https://en.wikipedia.org/wiki/Spatial%20distribution | A spatial distribution in statistics is the arrangement of a phenomenon across the Earth's surface and a graphical display of such an arrangement is an important tool in geographical and environmental statistics. A graphical display of a spatial distribution may summarize raw data directly or may reflect the outcome of a more sophisticated data analysis. Many different aspects of a phenomenon can be shown in a single graphical display by using a suitable choice of different colours to represent differences.
One example of such a display could be observations made to describe the geographic patterns of features, both physical and human across the earth.
The information included could be where units of something are, how many units of the thing there are per units of area, and how sparsely or densely packed they are from each other.
Patterns of spatial distribution
Usually, for a phenomenon that changes in space, there is a pattern that determines the location of the subject of the phenomenon and its intensity or size, in X and Y coordinates. The scientific challenge is trying to identify the variables that affect this pattern. The issue can be demonstrated with several simple examples:
The spatial distribution of the human population
The spatial distribution of the population and development are closely related to each other, especially in the context of sustainability. The challenges related to the spatial spread of a population include: rapid urbanization and population concentration, rural population, urban management and poverty housing, displaced persons and refugees. Migration is a basic element in the spatial distribution of a population, and it may remain a key driver in the coming decades, especially as an element of urbanization in developing countries.
The spatial distribution of economic activity in the world
In a pair of studies from Brown University by urban economist J. Vernon Henderson, with co-authors Adam Storeygard and David Weil, the spatial distribution of the economic activity in the world was examined by mapping the artificial lights at night from space over 250,000 grid cells, the average area of each of which is 560 square kilometers. They found that 50% of the variation in this activity can be explained through a system of physical geographic features.
The spatial distribution of the seismic intensities of an earthquake
The seismic intensityies of an earthquake are distributed across space with an elementary regularity, so that in towns located close to the epicenter of the earthquake, high seismic intensities are observed and vice versa; Low intensities were observed in settlements far from the epicenter. The distance of each settlement from the epicenter is marked with XY coordinates, a variable that affects the seismic intensity observed there. But there are other variables that affect these intensities, such as the geological structure of each settlement, its topography, and more. All these make the simple |
https://en.wikipedia.org/wiki/Robert%20B.%20Lisek | Robert B. Lisek is a Polish artist and mathematician who focuses on systems and processes, conducts a research in the area theory of ordered sets in relation with logic, algebra and combinatorics; his artistic practice draws upon conceptual art, radical art strategies, hacktivism, bioart, software art.
Works
Lisek is an artist whose work is focused on systems and processes (computer, biological and social), disrupting the language of these systems, including rules, commands, errors and by using worms and computer viruses. Lisek is currently researching problems of security, privacy and identity in networked societies. He built NEST – Citizens Intelligent Agency, a piece of software for searching hidden patterns and links between people, groups, events, objects and places.
Lisek is also a scientist focused on the computational complexity theory, graph theory and order theory. He studied at the Department of Logic of Wroclaw University, at the Fine Art Academy in Wroclaw and the PWSTiTV film school in Łódź.
His research interest is also artificial general intelligence (AGI). He examines, among others: problem of self-reference, mathematical induction, probabilistic techniques and recurrent AI self-improvement.
He is also working on human enhancement: extensions through the use of radical transgressive methods that arise at the intersection of disciplines such as AGI, bioengineering, and political and social sciences. He has prepared an anthology entitled Transhuman.
Lisek is a founder of Institute for Research in Science and Art, Fundamental Research Lab and an ACCESS art symposium.
Exhibitions
Lisek exhibits, lectures, and conducts workshops worldwide. His projects include among others:
NEST – FILE Electronic Language International Festival, São Paulo
NEST – ARCO International Contemporary Art Fair, Madrid
FLOAT – Lower Manhattan Cultural Council, NY
FLOAT – Harvestworks Digital Media Art Center, NY
SPECTRUM – Leto Gallery, Warsaw
WWAI – SIGGRAPH 2005, Los Angeles
Falsecodes – Red Gate Gallery & Planetary Collegium, Beijing
GENGINE – Zacheta National Gallery, Warsaw
FLEXTEXT – CiberArt Bilbao
FLEXTEXT – Medi@terra – Byzantine Museum, Athens
FXT – ACA Japan Media Festival, Tokyo
STACK – ISEA 02, Nagoya
SSSPEAR – 17th Meridian, WRO Art Center, Wroclaw
The New Art Fest (2020), digital art festival, Lisbon
References
External links
http://turbulence.org/blog/2008/11/10/gespenst-widmo-spectre-warsaw/
http://www.recyklingidei.pl/vitcheva_wypadek_laboratorium
http://portal.acm.org/citation.cfm?id=1186796.1186804
http://music.columbia.edu/organism/?s=robert+lisek
http://knowledgetoday.org/wiki/index.php/ICCS07/72
http://fundamental.art.pl/
http://lisek.art.pl/gespenst.html
Polish scientists
Polish contemporary artists
Polish conceptual artists
BioArtists
Living people
Year of birth missing (living people)
University of Wrocław alumni
Polish mathematicians |
https://en.wikipedia.org/wiki/Jan%20Kmenta | Jan Kmenta (January 3, 1928 – July 24, 2016) was a Czech-American economist. He was the Professor Emeritus of Economics and Statistics at the University of Michigan and Visiting Professor at CERGE-EI in Prague, until summer 2016.
Academic positions and awards
After earning his PhD in Economics with a minor in Statistics from Stanford under Kenneth Arrow in 1964, Kmenta held academic positions at the University of Wisconsin 1964–65, Michigan State University 1965–73, and the University of Michigan 1973-93 (emeritus 1993-2016) and was a visiting faculty member at universities in five countries. Kmenta received 24 academic honors, awards, and prizes during his career, beginning with being made a fellow of the American Statistical Association in 1970 and a fellow of the Econometric Society in 1980, and stretching through 2010 when he received the NEURON Award for Lifetime Achievement in Economics.
Econometric work
Kmenta wrote extensively on econometric model building as well as econometric methods. He edited two books with James B. Ramsey: Evaluation of Econometric Models and Large Scale Macro-Econometric Models: Theory and Practice and is the author of at least 34 published econometrics papers. A wide-ranging econometrician, his papers analyze topics as disparate as small sample properties of estimators, missing observations, estimation of production function parameters, and ridge regression among many others. Much of his published research is focused on econometric issues that are relevant in areas far beyond economics. As a result, his work is referenced in publications in medicine, political science, insurance underwriting, antitrust litigation, and energy issues, to list but a few. For example, the early (1966) "Specification and Estimation of Cobb-Douglas Production Function Models" with Arnold Zellner and Jacques Drèze has been cited by research as different as family involvement effects on firm productivity and devising fishing gears with reduced environmental effects.
Kmenta's "General Procedure for Obtaining Maximum Likelihood Estimates in Generalized Regression Models" (with W. Oberhofer) formally established conditions for validity of the iterative estimation method most widely used in econometrics today, while his simplified estimation of the constant elasticity of substitution constant elasticity of substitution production function both gave "the nascent field of industrial organization a new set of powerful tools for studying firm efficiency" and has been used to analyze the cost of network infrastructure, among many other applications.
Kmenta has made multiple other contributions incorporated into the core of econometrics.
Elements of Econometrics
Jan Kmenta is best known to the general economics profession around the world for his internationally acclaimed textbook, Elements of Econometrics (titled after Euclid's Elements) which was first published in 1971 and extensively revised in a 1986 second edition. Having been publis |
https://en.wikipedia.org/wiki/Mandelbox | In mathematics, the mandelbox is a fractal with a boxlike shape found by Tom Lowe in 2010. It is defined in a similar way to the famous Mandelbrot set as the values of a parameter such that the origin does not escape to infinity under iteration of certain geometrical transformations. The mandelbox is defined as a map of continuous Julia sets, but, unlike the Mandelbrot set, can be defined in any number of dimensions. It is typically drawn in three dimensions for illustrative purposes.
Simple definition
The simple definition of the mandelbox is this: repeatedly transform a vector z, according to the following rules:
First, for each component c of z (which corresponds to a dimension), if c is greater than 1, subtract it from 2; or if c is less than -1, subtract it from −2.
Then, depending on the magnitude of the vector, change its magnitude using some fixed values and a specified scale factor.
Generation
The iteration applies to vector z as follows:
function iterate(z):
for each component in z:
if component > 1:
component := 2 - component
else if component < -1:
component := -2 - component
if magnitude of z < 0.5:
z := z * 4
else if magnitude of z < 1:
z := z / (magnitude of z)^2
z := scale * z + c
Here, c is the constant being tested, and scale is a real number.
Properties
A notable property of the mandelbox, particularly for scale −1.5, is that it contains approximations of many well known fractals within it.
For the mandelbox contains a solid core. Consequently, its fractal dimension is 3, or n when generalised to n dimensions.
For the mandelbox sides have length 4 and for they have length .
See also
Mandelbulb
Buddhabrot
Lichtenberg figure
References
External links
Gallery and description
Images of some Mandelbox cubes
Video : zoom in the Mandelbox cube
Fractals |
https://en.wikipedia.org/wiki/Isaac%20Greenwood | Isaac Greenwood (11 May 1702 – 22 October 1745) was an American mathematician. He was the first Hollisian Professor of Mathematics and Natural Philosophy at Harvard College.
Biography
He graduated at Harvard in 1721, and was instrumental in the smallpox inoculation controversy of that year, speaking out in favour of inoculation. He travelled to London, where he lodged with John Theophilus Desaguliers and attended his lectures on Newtonian Experimental Philosophy. He later introduced the subject in the American Colonies and his book An Experimental Course of Mechanical Philosophy, published in Boston in 1726, owed much to Desaguliers. In London Greenwood met with Thomas Hollis, who wished to endow a chair at Harvard College for him. Hollis later fell out with Greenwood, over his financial imprudence. However, back in Boston, Greenwood was eventually appointed to the new Hollis Chair in 1727.
During his tenure, he wrote anonymously the first natively-published American book on mathematics – the Greenwood Book, published in 1729. This book made the first published statement of the short scale value for billion in the United States, which eventually became the value used in most English-speaking countries.
Greenwood married Sara Shrimpton Clarke, daughter of Dr John Clarke, on 31 July 1729, and had five children, of whom the eldest, Isaac, became a noted dentist.
He was removed from the chair for intemperance in 1737. Unable to support his family, he joined the Royal Navy as a chaplain aboard in 1742, transferring to in 1744. He was released from service in Charleston, South Carolina, on 22 May 1744 and died from the effects of alcohol on 22 October 1745.
References
1702 births
1745 deaths
People from Boston
Harvard College alumni
Harvard University Department of Mathematics faculty
Harvard University faculty
Hollis Chair of Mathematics and Natural Philosophy
18th-century American mathematicians
Royal Navy chaplains
Alcohol-related deaths in South Carolina |
https://en.wikipedia.org/wiki/Svante%20Janson | Carl Svante Janson (born 21 May 1955) is a Swedish mathematician. A member of the Royal Swedish Academy of Sciences since 1994, Janson has been the chaired professor of mathematics at Uppsala University since 1987.
In mathematical analysis, Janson has publications in functional analysis (especially harmonic analysis) and probability theory. In mathematical statistics, Janson has made contributions to the theory of U-statistics. In combinatorics, Janson has publications in probabilistic combinatorics, particularly random graphs and in the analysis of algorithms: In the study of random graphs, Janson introduced U-statistics and the Hoeffding decomposition.
Janson has published four books and over 300 academic papers (). He has an Erdős number of 1.
Biography
Svante Janson has already had a long career in mathematics, because he started research at a very young age.
From prodigy to docent
A child prodigy in mathematics, Janson took high-school and even university classes while in primary school. He was admitted in 1968 to Gothenburg University at age 12. After his 1968 matriculation at Uppsala University at age 13, Janson obtained the following degrees in mathematics: a "candidate of philosophy" (roughly an "honours" B.S. with a thesis) at age 14 (in 1970) and a doctor of philosophy at age 21–22 (in 1977). Janson's Ph.D. was awarded on his 22nd birthday. Janson's doctoral dissertation was supervised by Lennart Carleson, who had himself received his doctoral degree when he was 22 years old.
After having earned his doctorate, Janson was a postdoc with the Mittag-Leffler Institute from 1978 to 1980. Thereafter he worked at Uppsala University. Janson's ongoing research earned him another PhD from Uppsala University in 1984 – this second doctoral degree being in mathematical statistics; the supervisor was Carl-Gustav Esseen.
In 1984, Janson was hired by Stockholm University as docent (roughly associate professor in the USA).
Professorships
In 1985 Janson returned to Uppsala University, where he was named the chaired professor in mathematical statistics. In 1987 Janson became the chaired professor of mathematics at Uppsala university. Traditionally in Sweden, the chaired professor has had the role of a "professor ordinarius" in a German university (roughly combining the roles of research professor and director of graduate studies at a research university in the USA).
Awards
Besides being a member of the Royal Swedish Academy of Sciences (KVA), Svante Janson is a member of the Royal Society of Sciences in Uppsala. His thesis received the 1978 Sparre Award from the KVA. He received the 1994 Swedish medal for the best young mathematical scientist, the Göran Gustafsson Prize. Janson's former doctoral student, Ola Hössjer, received the Göran Gustafsson prize in 2009, becoming the first statistician so honored.
In December 2009, Janson received the Eva & Lars Gårding prize from the Royal Physiographic Society in Lund.
In 2021, Janson received the Fla |
https://en.wikipedia.org/wiki/Mark%20Mahowald | Mark Edward Mahowald (December 1, 1931 – July 20, 2013) was an American mathematician known for work in algebraic topology.
Life
Mahowald was born in Albany, Minnesota in 1931. He received his Ph.D. from the University of Minnesota in 1955 under the direction of Bernard Russell Gelbaum with a thesis on Measure in Groups. In the sixties, he became professor at Syracuse University and around 1963 he went to Northwestern University in Evanston, Illinois.
Work
Much of Mahowald's most important works concerns the homotopy groups of spheres, especially using the Adams spectral sequence at the prime 2. He is known for constructing one of the first known infinite families of elements in the stable homotopy groups of spheres by showing that the classes survive the Adams spectral sequence for . In addition, he made extensive computations of the structure of the Adams spectral sequence and the 2-primary stable homotopy groups of spheres up to dimension 64 together with Michael Barratt, Martin Tangora, and Stanley Kochman. Using these computations, he could show that a manifold of Kervaire invariant 1 exists in dimension 62.
In addition, he contributed to the chromatic picture of the homotopy groups of spheres: His earlier work contains much on the image of the J-homomorphism and recent work together with Paul Goerss, Hans-Werner Henn, Nasko Karamanov, and Charles Rezk does computations in stable homotopy localized at the Morava K-theory .
Besides the work on the homotopy groups of spheres and related spaces, he did important work on Thom spectra. This work was used heavily in the proof of the nilpotence theorem by Ethan Devinatz, Michael J. Hopkins, and Jeffrey Smith.
Awards and honors
In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. In 2012 he became a fellow of the American Mathematical Society.
Selected publications
Mark E. Mahowald and Martin C. Tangora, Some differentials in the Adams spectral sequence, Topology 6 (1967) 349–369.
Michael G. Barratt, Mark E. Mahowald, and Martin C. Tangora, Some differentials in the Adams spectral sequence II, Topology 9 (1970) 309–316.
Stanley O. Kochman and Mark E. Mahowald, On the computation of stable stems in The Čech centennial: a Conference on Homotopy Theory, June 22–26, 1993, pp. 299–316.
Mark E. Mahowald, A new infinite family in , Topology 16 (1977) 249–256.
Paul Goerss, Hans-Werner Henn, Mark E. Mahowald, and Charles Rezk, A resolution of the K(2)-local sphere at the prime 3, Annals of Mathematics 162 (2005), 777–822.
Prasit Bhattacharya, Philip Egger and Mark E. Mahowald, On the periodic v2-self-map of A1, Algebraic and Geometric Topology 17 (2017) 657–692. doi:10.2140/agt.2017.17.657
References
External links
Homepage at Northwestern University
(294 kB)
1931 births
20th-century American mathematicians
21st-century American mathematicians
University of Minnesota alumni
Northwestern University faculty
Fellows of the American Mathematical Societ |
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