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https://en.wikipedia.org/wiki/Georg%20Feigl | Georg Feigl (13 October 1890 – 20 April 1945) was a German mathematician.
Life and work
Georg Feigl started studying mathematics and physics at the University of Jena in 1909. In 1918, he obtained his doctorate under Paul Koebe. From 1928 he was editor of the Jahrbuch über die Fortschritte der Mathematik ("Yearbook on the progress of mathematics"). In 1935 he became a full professor at the University of Breslau. In 1937—1941, he was an editor of the journal Deutsche Mathematik.
Feigl's main areas of work were the foundations of geometry and topology, where he studied fixed point theorems for n-dimensional manifolds.
Feigl was one of the initial authors of the Mathematisches Wörterbuch ("Mathematical dictionary"). Because of the impending siege by the Red Army he was forced to leave Breslau in January 1945 with his family and other members of the Mathematical Institute. His wife Maria was distantly related to the lord of the manor of Wechselburg castle and prepared the castle to receive the mathematicians. Feigl brought his previously developed materials for the Mathematisches Wörterbuch and asked his students to further refine it in the castle. They did not have access to books, lecture notes, calculators, or typewriters in the castle. Johann Radon (1887–1956) and Feigl were willing and able to continue lectures started in Breslau for one hour a day at Wechselburg castle, without any documents. Feigl had a severe stomach ailment and died after a few months without medication in Wechselburg. The Mathematisches Wörterbuch did not appear until 1961, when Hermann Ludwig Schmid (1908–1956) and Joseph Naas (1906–1993) published it.
References
Siegfried Gottwald (Ed.), Lexikon bedeutender Mathematiker ("Encyclopedia of important mathematicians"), Bibliographisches Institut ("Bibliographical Institute"), Leipzig 1990, , p. 145.
Hans-Joachim Girlich, Johann Radon in Breslau. Zur Institutionalisierung der Mathematik. ("Johann Radon in Breslau. The institutionalization of Mathematics"). In M. Halub, A. Manko-Matysiak (Ed.), Schlesische Gelehrtenrepublik. ("Silesian Republic of Scholars"), Vol. 2., Wroclaw, p. 393−418. https://web.archive.org/web/20070613211747/http://www.math.uni-leipzig.de/preprint/2005/p4-2005.pdf
Josef Naas, Hermann Ludwig Schmid, Mathematisches Wörterbuch. Mit Einbeziehung der theoretischen Physik. ("Mathematical dictionary. With the inclusion of theoretical physics."), 2 Volumes, Academy Publishers, Berlin, 1961.
External links
1890 births
1945 deaths
20th-century German mathematicians
Topologists
Geometers
Scientists from Hamburg
University of Jena alumni
Academic staff of the University of Breslau |
https://en.wikipedia.org/wiki/R%C3%BCdiger%20Rehm | Rüdiger Rehm (born 22 November 1978) is a German former footballer and current coach of Waldhof Mannheim.
Managerial statistics
References
External links
1978 births
Living people
German men's footballers
Men's association football midfielders
SV Waldhof Mannheim players
1. FC Saarbrücken players
SSV Reutlingen 05 players
FC Erzgebirge Aue players
Kickers Offenbach players
FSV Oggersheim players
SG Sonnenhof Großaspach players
3. Liga managers
2. Bundesliga managers
Arminia Bielefeld managers
SV Wehen Wiesbaden managers
SG Sonnenhof Großaspach managers
FC Ingolstadt 04 managers
German football managers
SV Waldhof Mannheim managers
Sportspeople from Heilbronn
Footballers from Stuttgart (region) |
https://en.wikipedia.org/wiki/G/M/1%20queue | In queueing theory, a discipline within the mathematical theory of probability, the G/M/1 queue represents the queue length in a system where interarrival times have a general (meaning arbitrary) distribution and service times for each job have an exponential distribution. The system is described in Kendall's notation where the G denotes a general distribution, M the exponential distribution for service times and the 1 that the model has a single server.
The arrivals of a G/M/1 queue are given by a renewal process. It is an extension of an M/M/1 queue, where this renewal process must specifically be a Poisson process (so that interarrival times have exponential distribution).
Models of this type can be solved by considering one of two M/G/1 queue dual systems, one proposed by Ramaswami and one by Bright.
Queue size at arrival times
Let be a queue with arrival times that have interarrival distribution A. Define the size of the queue immediately before the nth arrival by the process . This is a discrete-time Markov chain with stochastic matrix:
where .
The Markov chain has a stationary distribution if and only if the traffic intensity is less than 1, in which case the unique such distribution is the geometric distribution with probability of failure, where is the smallest root of the equation .
In this case, under the assumption that the queue is first-in first-out (FIFO), a customer's waiting time W is distributed by:
Busy period
The busy period can be computed by using a duality between the G/M/1 model and M/G/1 queue generated by the Christmas tree transformation.
Response time
The response time is the amount of time a job spends in the system from the instant of arrival to the time they leave the system. A consistent and asymptotically normal estimator for the mean response time, can be computed as the fixed point of an empirical Laplace transform.
References
Single queueing nodes |
https://en.wikipedia.org/wiki/Pentic%207-cubes | In seven-dimensional geometry, a pentic 7-cube is a convex uniform 7-polytope, related to the uniform 7-demicube. There are 8 unique forms.
Pentic 7-cube
Cartesian coordinates
The Cartesian coordinates for the vertices of a pentic 7-cube centered at the origin are coordinate permutations:
(±1,±1,±1,±1,±1,±3,±3)
with an odd number of plus signs.
Images
Related polytopes
Penticantic 7-cube
Images
Pentiruncic 7-cube
Images
Pentiruncicantic 7-cube
Images
Pentisteric 7-cube
Images
Pentistericantic 7-cube
Images
Pentisteriruncic 7-cube
Images
Pentisteriruncicantic 7-cube
Images
Related polytopes
This polytope is based on the 7-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 95 uniform polytopes with D7 symmetry, 63 are shared by the BC7 symmetry, and 32 are unique:
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.
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
7-polytopes |
https://en.wikipedia.org/wiki/Hexic%207-cubes | In seven-dimensional geometry, a hexic 7-cube is a convex uniform 7-polytope, constructed from the uniform 7-demicube. There are 16 unique forms.
Hexic 7-cube
Cartesian coordinates
The Cartesian coordinates for the vertices of a hexic 7-cube centered at the origin are coordinate permutations:
(±1,±1,±1,±1,±1,±1,±3)
with an odd number of plus signs.
Images
Hexicantic 7-cube
Images
Hexiruncic 7-cube
Images
Hexisteric 7-cube
Images
Hexipentic 7-cube
Images
Hexiruncicantic 7-cube
Images
Hexistericantic 7-cube
Images
Hexipenticantic 7-cube
Images
Hexisteriruncic 7-cube
Images
Hexipentiruncic 7-cube
Images
Hexipentisteric 7-cube
Images
Hexisteriruncicantic 7-cube
Images
Hexipentiruncicantic 7-cube
Images
Hexipentisteriruncic 7-cube
Images
Hexipentistericantic 7-cube
Images
Hexipentisteriruncicantic 7-cube
Images
Related polytopes
This polytope is based on the 7-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 95 uniform polytopes with D7 symmetry, 63 are shared by the BC7 symmetry, and 32 are unique:
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.
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
7-polytopes |
https://en.wikipedia.org/wiki/Hexicated%207-orthoplexes | In seven-dimensional geometry, a hexicated 7-orthoplex (also hexicated 7-cube) is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-orthoplex.
There are 32 hexications for the 7-orthoplex, including all permutations of truncations, cantellations, runcinations, sterications, and pentellations. 12 are represented here, while 20 are more easily constructed from the 7-cube.
Hexitruncated 7-orthoplex
Alternate names
Petitruncated heptacross
Images
Hexicantellated 7-orthoplex
Alternate names
Petirhombated heptacross
Images
Hexicantitruncated 7-orthoplex
Alternate names
Petigreatorhombated heptacross
Images
Hexiruncitruncated 7-orthoplex
Alternate names
Petiprismatotruncated heptacross
Images
Hexiruncicantellated 7-orthoplex
In seven-dimensional geometry, a hexiruncicantellated 7-orthoplex is a uniform 7-polytope.
Alternate names
Petiprismatorhombated heptacross
Images
Hexisteritruncated 7-orthoplex
Alternate names
Peticellitruncated heptacross
Images
Hexiruncicantitruncated 7-orthoplex
Alternate names
Petigreatoprismated heptacross
Images
Hexistericantitruncated 7-orthoplex
Alternate names
Peticelligreatorhombated heptacross
Images
Hexisteriruncitruncated 7-orthoplex
Alternate names
Peticelliprismatotruncated heptacross
Images
Hexipenticantitruncated 7-orthoplex
Alternate names
Petiterigreatorhombated heptacross
Images
Hexisteriruncicantitruncated 7-orthoplex
Alternate names
Great petacellated heptacross
Images
Hexipentiruncicantitruncated 7-orthoplex
Alternate names
Petiterigreatoprismated heptacross
Images
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, PhD (1966)
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
7-polytopes |
https://en.wikipedia.org/wiki/Athletics%20abbreviations | The sports under the umbrella of athletics, particularly track and field, use a variety of statistics. In order to report that information efficiently, numerous abbreviations have grown to be common in the sport. Starting in 1948 by Bert Nelson and Cordner Nelson, Track & Field News became the leader in creating and defining abbreviations in this field. These abbreviations have also been adopted by, among others, World Athletics; the world governing body, various domestic governing bodies, the Association of Track and Field Statisticians, the Association of Road Racing Statisticians, the Associated Press, and the individual media outlets who receive their reports. These abbreviations also appear in Wikipedia.
Times and marks
Almost all races record a time. Evolving since experiments in the 1930s, to their official use at the 1968 Summer Olympics and official acceptance in 1977, fully automatic times have become common. As this evolution has occurred, the rare early times were specified as FAT times. As they are now commonplace, automatic times are now expressed using the hundredths of a second. Hand times (watches operated by human beings) are not regarded as accurate and thus are only accepted to the accuracy of a tenth of a second even when the watch displays greater accuracy. If the mark was set before 1977, a converted time to the tenth was recorded for record purposes, because they did not have a system to compare between the timing methods. Frequently in those cases there is a mark to the 100th retained for that race. Over this period of evolution, some reports show hand times also followed with an "h" or "ht" to distinguish hand times.
With two different timing methods came the inevitable desire to compare times. Track and Field News initiated adding .24 to hand times as a conversion factor. Many electronic hand stopwatches display times to the hundredth. Frequently those readings are recorded, but are not accepted as valid (leading to confused results). Some low level meets have even hand timed runners and have switched places according to the time displayed on the stopwatch. All of this is, of course, wrong. Hand times are not accurate enough to be accepted for record purposes for short races. Human reaction time is not perfectly identical between different human beings. Hand times involve human beings reacting, pushing the stopwatch button when they see the smoke or hear the sound of the starting pistol, then reacting (possibly anticipating) the runner crossing the finish line. The proper procedure for converting hand times would be to round any hundredths up to the next higher even tenth of a second and then add the .24 to get a time for comparison purposes only. But many meets displayed the converted marks accurate to the hundredth making the results look like they were taken with fully automatic timing. In these cases, some meets have displayed a 4 or a 0 in the hundredths column for all races. When detected, reports of t |
https://en.wikipedia.org/wiki/Deligne%E2%80%93Mumford%20stack | In algebraic geometry, a Deligne–Mumford stack is a stack F such that
Pierre Deligne and David Mumford introduced this notion in 1969 when they proved that moduli spaces of stable curves of fixed arithmetic genus are proper smooth Deligne–Mumford stacks.
If the "étale" is weakened to "smooth", then such a stack is called an algebraic stack (also called an Artin stack, after Michael Artin). An algebraic space is Deligne–Mumford.
A key fact about a Deligne–Mumford stack F is that any X in , where B is quasi-compact, has only finitely many automorphisms.
A Deligne–Mumford stack admits a presentation by a groupoid; see groupoid scheme.
Examples
Affine Stacks
Deligne–Mumford stacks are typically constructed by taking the stack quotient of some variety where the stabilizers are finite groups. For example, consider the action of the cyclic group on given by
Then the stack quotient is an affine smooth Deligne–Mumford stack with a non-trivial stabilizer at the origin. If we wish to think about this as a category fibered in groupoids over then given a scheme the over category is given by
Note that we could be slightly more general if we consider the group action on .
Weighted Projective Line
Non-affine examples come up when taking the stack quotient for weighted projective space/varieties. For example, the space is constructed by the stack quotient where the -action is given by
Notice that since this quotient is not from a finite group we have to look for points with stabilizers and their respective stabilizer groups. Then if and only if or and or , respectively, showing that the only stabilizers are finite, hence the stack is Deligne–Mumford.
Stacky curve
Non-Example
One simple non-example of a Deligne–Mumford stack is since this has an infinite stabilizer. Stacks of this form are examples of Artin stacks.
References
Algebraic geometry |
https://en.wikipedia.org/wiki/European%20Institute%20for%20Statistics%2C%20Probability%2C%20Stochastic%20Operations%20Research%20and%20its%20Applications | European Institute for Statistics, Probability, Stochastic Operations Research and its Applications (EURANDOM) is a research institute at the Eindhoven University of Technology, dedicated to fostering research in the stochastic sciences and their applications.
The institute was founded in 1997 at the Eindhoven University of Technology to focus on project oriented research of "stochastic problems connected to industrial and societal applications." The institute actively attracts young talent for its research and doctoral programs, facilitates research and actively seeks European cooperation.
People associated with the institute
Michel Mandjes
Onno J. Boxma, scientific director from 2005 to 2010.
Jaap Wessels
References
External links
EURANDOM at tue.nl
Eindhoven University of Technology
International scientific organizations based in Europe
Mathematical institutes
Research institutes in the Netherlands |
https://en.wikipedia.org/wiki/Jan%20Hemelrijk | Jan Hemelrijk (28 May 1918 – 16 March 2005) was a Dutch mathematician, Professor of Statistics at the University of Amsterdam, and authority in the field of stochastic processes.
Biography
Hemelrijk received his PhD in 1950 at the University of Amsterdam with a thesis entitled "Symmetry Keys and other applications of the theory of Neyman and Pearson" under supervision of David van Dantzig.
After graduation Hemelrijk started his academic career as assistant to David van Dantzig at the Centrum Wiskunde & Informatica in Amsterdam, and later Head of the Statistical Consulting Department. He was Professor at the Delft University of Technology from 1952 to 1960. In 1960, he was appointed Professor of Statistics at the University of Amsterdam as successor of David van Dantzig. Among his doctoral students were Gijsbert de Leve (1964), Willem van Zwet (1964), R. Doornbos (1966), Ivo Molenaar (1970), Robert Mokken (1970) and J. Dik (1981). Jaap Wessels in 1960 started his academic career Wessels as assistant to Jan Hemelrijk.
Hemelrijk was President of the Netherlands Society for Statistics and Operations Research, and chief editor of the Journal of the association Statistica Neerlandica. He also provided the first television course Statistics of Teleac, broadcast in 1969 and 1970.
In 1963, he was elected as a Fellow of the American Statistical Association.
Publications
1950. Symmetry Keys and other applications of the theory of Neyman and Pearson Doctoral thesis University of Amsterdam.
1957. Elementaire statistische opgaven met uitgewerkte oplossingen. Gorinchem : Noorduijn
1977. Oriënterende cursus mathematische statistiek. Amsterdam : Mathematisch Centrum
1998. Statistiek eenvoudig. With Jan Salomon Cramer. Amsterdam : Nieuwezijds
Articles, a selection:
Hemelrijk, Jan. "In memoriam prof. dr. D van Dantzig (1900-1959)." Statistica Neerlandica 13, 1954, p. 415-432
Hemelrijk, Jan. "Statistical methods applied to the mixing of solid particles, 1." Stichting Mathematisch Centrum. Statistische Afdeling S 159/54 (1954): 1-16.
Hemelrijk, Jan. "Het begrip nauwkeurigheid." Stichting Mathematisch Centrum. Statistische Afdeling S 228/58 (1958): 1-19.
References
External links
In Memoriam Prof. dr. Jan Hemelrijk (in Dutch)
1918 births
2005 deaths
Dutch mathematicians
University of Amsterdam alumni
Academic staff of the Delft University of Technology
Academic staff of the University of Amsterdam
People from Arnhem
Fellows of the American Statistical Association
Dutch resistance members
20th-century Dutch people
21st-century Dutch mathematicians |
https://en.wikipedia.org/wiki/Irreligion%20in%20the%20Philippines | In the Philippines, atheists and agnostics are not officially counted in the census of the country, although the Philippine Statistics Authority in 2020 reported that 43,931 Filipinos (or % of the total Philippine population) have no religious affiliation or have answered "none". Since 2011, the non-religious increasingly organized themselves, especially among the youth in the country. There is a stigma attached to being an atheist in the Philippines, and this necessitates many Filipino atheists to communicate with each other via the Internet, for example via the Philippine Atheism, Agnosticism and Secularism, Inc. formerly known as Philippine Atheists and Agnostics Society.
Growth
The number of atheists has risen consistently since the 1990s, as has the number of people considering it, church attendance, and overall religiously. One in eleven Filipino Catholics consider leaving the Church, only 37% attend church every week, and only 29% consider themselves strongly religious. Overall, anti-Catholic sentiment is a growing trend in the Philippines, with former president Rodrigo Duterte being an outspoken critic of the church for its sex scandals and allegations of corruption.
According to both Catholics and Atheists, belief in the Catholic Church is linked to poverty more than it is religious conviction, many go to Church out of desperation and need for hope, and some atheists, such as Miss. M, founder of HAPI, believe that starting secular outreach institutions will help Filipinos shed reliance on the Church and put their future in their own hands.
Persecution and discrimination
Filipino atheists are often harassed for their disbelief, and according to one atheist it's "how Filipinos think. They view atheists as Satanists".
Organizations
Humanist Alliance Philippines, International
Philippine Atheism, Agnosticism, and Secularism Inc.
Filipino Freethinkers
Prominent figures
Red Tani
Marissa Torres Langseth
Philippine religious distribution
According to the 2020 census, the religious distribution of the country's population was as follows:
Notes
See also
Hinduism in the Philippines
Buddhism in the Philippines
References
Philippines
Religion in the Philippines |
https://en.wikipedia.org/wiki/Bishop%E2%80%93Phelps%20theorem | In mathematics, the Bishop–Phelps theorem is a theorem about the topological properties of Banach spaces named after Errett Bishop and Robert Phelps, who published its proof in 1961.
Statement
Importantly, this theorem fails for complex Banach spaces.
However, for the special case where is the closed unit ball then this theorem does hold for complex Banach spaces.
See also
References
Banach spaces
Theorems in functional analysis |
https://en.wikipedia.org/wiki/Geraldine%20Claudette%20Darden | Geraldine Claudette Darden (born July 22, 1936) is an American mathematician. She was the fourteenth African American woman to earn a Ph.D. in mathematics.
Early life and education
Darden was born in Nansemond County, Virginia. Darden earned a bachelor's degrees in mathematics in 1957 from the Hampton Institute, a historically black institute, and took a teaching position at S.H. Clarke Junior High School in Portsmouth, Virginia. In the summer of 1958, Darden saw an opportunity for aspiring mathematicians created by the launch of Russian satellite Sputnik and ensuing US interest in mathematics and science a year earlier, and she applied for and received a National Science Foundation grant to attend the Summer Institute in Mathematics held at North Carolina Central University. Here she met Marjorie Lee Browne, the mathematician who directed the institute, who would encourage Darden to go on to graduate school.
Darden earned a master's degree in 1960 at the University of Illinois at Urbana–Champaign, and a second master's degree in 1965 and Ph.D. in 1967 from Syracuse University. Her dissertation was completed under the supervision of James Reid, "On the Direct Sums of Cyclic Groups".
Contributions
In addition to teaching, Darden also co-wrote Selected Papers on Pre-calculus, with textbook author Tom Apostol, Gulbank D. Chakerian, and John D. Neff.
References
Further reading
Selected Papers on Pre-calculus. Reprinted from the American Mathematical Monthly (volumes 1-81) and from the Mathematics Magazine (volumes 1-49). The Raymond W. Brink Selected Mathematical Papers, Vol. 1. The Mathematical Association of America, Washington, D.C., 1977. pp. xvii+469,
External links
Photograph of Geraldine Claudette Darden
1936 births
Living people
20th-century American mathematicians
African-American mathematicians
American women mathematicians
People from Suffolk, Virginia
Hampton University alumni
Syracuse University alumni
African-American schoolteachers
Schoolteachers from Virginia
20th-century American educators
20th-century American women educators
20th-century women mathematicians
Mathematicians from Virginia
20th-century African-American women
20th-century African-American educators
21st-century American educators
21st-century American women educators
21st-century African-American educators
21st-century African-American women
University of Illinois College of Liberal Arts and Sciences alumni |
https://en.wikipedia.org/wiki/Japan%20national%20football%20team%20records%20and%20statistics | The following is a list of the Japan national football team's competitive records and statistics.
Player records
Players in bold are still active with Japan.
Most capped players
Top goalscorers
Other records
Updated 29 March 2022
Youngest player
Daisuke Ichikawa, 17 years and 322 days old, 1 April 1998 against
Youngest goalscorer
Shinji Kagawa, 19 years and 206 days old, 9 October 2008 against
Youngest captain
Gen Shoji, 24 years and 363 days old, 9 December 2017 EAFF E-1 Championship
Oldest player
Eiji Kawashima, 39 years and 9 days old, 29 March 2022 against
Oldest goalscorer
Masashi Nakayama, 33 years and 326 days old, 15 August 2001 against
Oldest captain
Shigeo Yaegashi, 35 years and 203 days old, 13 October 1968 Summer Olympics
Most hat-trick
8, Kunishige Kamamoto
Most goal in one match
6, Kunishige Kamamoto, 27 September 1967 against
6, Kazuyoshi Miura, 22 June 1997 against
Most goal in calendar year
18, Kazuyoshi Miura, 1997
Manager records
Most appearances
Manager achievements
Team records
Updated 23 January 2015
Biggest victory
15–0 vs Philippines, 27 September 1967
Heaviest defeat
15–2 vs Philippines, 10 May 1917
Most consecutive victories
8, 8 August 1970 vs. Indonesia – 17 December 1970 vs. India
8, 14 March 1993 vs. United States – 5 May 1995 vs. Sri Lanka
8, 26 May 1996 vs. Yugoslavia – 12 December 1996 vs. China
Most consecutive matches without defeat
20, 24 June 2010 vs. Denmark – 11 November 2011 vs. Tajikistan
Most consecutive defeats
6, 10 June 1956 vs. South Korea – 28 December 1958 vs. Malaya
Most consecutive matches without victory
11, 13 August 1976 vs. Burma – 15 June 1976 vs. South Korea
Most consecutive draws
4, 13 August 1976 vs. Burma – 20 August 1976 vs. Malaysia
Most consecutive matches scoring
13, 19 December 1966 vs. Singapore – 16 October 1969 vs. Australia
13, 7 February 2004 vs. Malaysia – 24 July 2004 vs. Thailand
Most consecutive matches without scoring
6, 18 June 1989 vs. Hong Kong – 31 July 1990 vs. North Korea
Most consecutive matches conceding a goal
28, 6 November 1960 vs. South Korea – 11 December 1966 vs. Iran
Most consecutive matches without conceding a goal
7, 19 November 2003 vs. Cameroon – 18 February 2004 vs. Oman
Competitive record
Champions Runners-up Third place Fourth place
*Denotes draws includes knockout matches decided via penalty shoot-out. Red border indicates that the tournament was hosted on home soil. Gold, silver, bronze backgrounds indicate 1st, 2nd and 3rd finishes respectively. Bold text indicates best finish in tournament.
FIFA World Cup
AFC Asian Cup
Copa América
Japan is the first team from outside the Americas to participate in the Copa América, having been invited to the 1999 Copa América. Japan was also invited to the 2011 tournament and initially accepted the invitation. However, following the 2011 Tōhoku earthquake and tsunami, the JFA later withdrew on 16 May 2011, citing the difficulty of releasing |
https://en.wikipedia.org/wiki/List%20of%20works%20by%20Nicolas%20Minorsky | List of works by Nicolas Minorsky.
Books
Papers
Conferences
Patents
References
Mathematics-related lists
Bibliographies by writer |
https://en.wikipedia.org/wiki/SL2 | SL2 may refer to:
Art and entertainment
SL2 (musical group), British breakbeat hardcore group
Stuart Little 2, a 2022 film
Maths and science
Special linear Lie algebra
the mathematical structure SL2(F), a special linear group
SL2 RNA, a non-coding RNA involved in trans splicing in lower eukaryotes
Skylab 2 (SL-2), a NASA space mission
Technology and transport
Leicaflex SL2, a mechanical reflex camera
Canon EOS 200D, or Rebel SL2, a digital reflex camera
Schütte-Lanz SL2, an airship used in WWI
SL2, car in the Saturn S series
SL2 (MBTA bus), Boston bus line
Skylab 2 (SL-2), a NASA space mission
Other uses
SL postcode area, the Slough postal region covering Farnham, Great Britain
Situational Leadership II, a leadership theory developed by Paul Hersey
Super League Greece 2 Greece's 2nd Division football championship |
https://en.wikipedia.org/wiki/P%C3%A9ter%20Mihalecz | Péter Mihalecz (born 6 June 1979 in Zalaegerszeg) is a Hungarian professional footballer who plays for FC Ajka.
Club statistics
Updated to games played as of 1 June 2014.
References
MLSZ
HLSZ
1979 births
Living people
Sportspeople from Zalaegerszeg
Footballers from Zala County
Hungarian men's footballers
Men's association football forwards
Hévíz FC footballers
Büki TK Bükfürdő footballers
Szombathelyi Haladás footballers
Pécsi MFC players
FC Ajka players
Nemzeti Bajnokság I players |
https://en.wikipedia.org/wiki/%C3%81kos%20Tulip%C3%A1n | Ákos Tulipán (born 16 November 1990) is a Hungarian professional footballer who plays for Dorogi FC.
Club statistics
Updated to games played as of 1 June 2014.
References
HLSZ
1990 births
Living people
Footballers from Eger
Hungarian men's footballers
Men's association football goalkeepers
Vasas SC players
Budaörsi SC footballers
Bajai LSE footballers
Ferencvárosi TC footballers
FC Ajka players
Ceglédi VSE footballers
Dorogi FC footballers
Nemzeti Bajnokság I players |
https://en.wikipedia.org/wiki/J%C3%A1nos%20Mikl%C3%B3sv%C3%A1ri | János Miklósvári (born 10 April 1984) is a Hungarian professional footballer who plays for Ceglédi VSE.
Club statistics
Updated to games played as of 1 June 2014.
References
MLSZ
HLSZ
1984 births
Living people
Footballers from Budapest
Hungarian men's footballers
Men's association football defenders
BFC Siófok players
Ceglédi VSE footballers
BKV Előre SC footballers
Nemzeti Bajnokság I players |
https://en.wikipedia.org/wiki/L%C3%A1szl%C3%B3%20Makrai | László Makrai (born 8 January 1985) is a Hungarian professional footballer who plays for Ceglédi VSE.
Club statistics
Updated to games played as of 18 May 2014.
References
HLSZ
1985 births
Living people
Sportspeople from Vác
Hungarian men's footballers
Men's association football defenders
Vác FC players
FC Felcsút players
BKV Előre SC footballers
Gyirmót FC Győr players
FC Veszprém footballers
Ceglédi VSE footballers
FC Dabas footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Footballers from Pest County |
https://en.wikipedia.org/wiki/Willem%20Saris | Willem Egbert (Wim) Saris (born 8 July 1943) is a Dutch sociologist and Emeritus Professor of Statistics and Methodology, especially known for his work on "Causal modelling in non-experimental research" and measurement errors (for example, MTMM analyses and development of the Survey Quality Predictor (SQP) program).
Biography
Saris was born in Leiden, South Holland, Netherlands, in 1943. He finished his study of Sociology at the Utrecht University in 1968 and earned his PhD from the University of Amsterdam in 1979. He became full professor in political science, especially the methodology of the social sciences in 1983. Till 2001, he was working at the University of Amsterdam. In 1984, he created the Sociometric Research Foundation in order to improve social science research by the application of statistics. In 1998, he became member of the methodology group that facilitated the creation of the European Social Survey (ESS). As a consequence, he was also member of the Central Coordinating Team of the ESS from 2000 until 2012.
In 2001, he moved to Barcelona where he was granted a position as ICREA professor at ESADE. From 2009 to 2012, he was also director of the Research and Expertise Centre for Survey Methodology (RECSM) at the Pompeu Fabra University. He was also one of the founders and first chairman of the European Survey Research Association (ESRA).
Academic career
Studies
Political decision making
Over a long period, Saris was involved with Irmtraud Gallhofer in an applied research project studying political decision making on the basis of governmental meeting minutes and notes of advisers. After developing reliable instruments for analysis, the team applied their approach on varied decisions of the Dutch government as well as major decisions in world history, such as decisions concerning the start of the First and Second World War, the Cuban Missile Crisis and the use of the atomic bombs in 1945. The first phase of the study was directed on the argumentation of individual decision makers. In a later phase, the research was extended to the study of collective decision making by the same governmental groups. The result was that the decision makers were making relatively simple arguments with respect to serious and far-reaching outcomes of war and peace.
Statistical aspects of structural equation models (SEM)
Worried about the testing procedures of structural equation modelling, Saris worked together with Albert Satorra to improve these procedures. They together developed different procedures to evaluate structural equation models. The final product was a procedure for detecting misspecification in these models taking into account the power of the tests. A program (JRule) was developed for these tests by William van der Veld.
Improvement of measurement in survey research
Application of SEM showed how large the errors were in survey data. Therefore, he directed his research on procedures to improve the measurement instrument su |
https://en.wikipedia.org/wiki/Mittag-Leffler%20distribution | The Mittag-Leffler distributions are two families of probability distributions on the half-line . They are parametrized by a real or . Both are defined with the Mittag-Leffler function, named after Gösta Mittag-Leffler.
The Mittag-Leffler function
For any complex whose real part is positive, the series
defines an entire function. For , the series converges only on a disc of radius one, but it can be analytically extended to .
First family of Mittag-Leffler distributions
The first family of Mittag-Leffler distributions is defined by a relation between the Mittag-Leffler function and their cumulative distribution functions.
For all , the function is increasing on the real line, converges to in , and . Hence, the function is the cumulative distribution function of a probability measure on the non-negative real numbers. The distribution thus defined, and any of its multiples, is called a Mittag-Leffler distribution of order .
All these probability distributions are absolutely continuous. Since is the exponential function, the Mittag-Leffler distribution of order is an exponential distribution. However, for , the Mittag-Leffler distributions are heavy-tailed, with
Their Laplace transform is given by:
which implies that, for , the expectation is infinite. In addition, these distributions are geometric stable distributions. Parameter estimation procedures can be found here.
Second family of Mittag-Leffler distributions
The second family of Mittag-Leffler distributions is defined by a relation between the Mittag-Leffler function and their moment-generating functions.
For all , a random variable is said to follow a Mittag-Leffler distribution of order if, for some constant ,
where the convergence stands for all in the complex plane if , and all in a disc of radius if .
A Mittag-Leffler distribution of order is an exponential distribution. A Mittag-Leffler distribution of order is the distribution of the absolute value of a normal distribution random variable. A Mittag-Leffler distribution of order is a degenerate distribution. In opposition to the first family of Mittag-Leffler distribution, these distributions are not heavy-tailed.
These distributions are commonly found in relation with the local time of Markov processes.
References
Continuous distributions
Geometric stable distributions
Probability distributions with non-finite variance |
https://en.wikipedia.org/wiki/Johannes%20Runnenburg | Johannes Theodorus Runnenburg (19 February 1932 – 16 April 2008) was a Dutch mathematician and professor of probability theory and analysis at the University of Amsterdam from 1962 to 1997.
Biography
Born in Amsterdam he received his MA in Mathematics in 1956 at the University of Amsterdam, and his PhD cum laude in Mathematics and Physics in 1960 with a thesis entitled "On the Use of Markov Processes in One-server Waiting-time Problems and Renewal Theory" advised by Nicolaas Govert de Bruijn.
Runnenburg was appointed Lector in Probability theory and analysis at the University of Amsterdam in 1961. In 1962, he was promoted to Professor of Probability theory and analysis, and from 1966 to his retirement in 1997 was Professor of Pure and Applied Mathematics. Among his doctorate students were Gijsbert de Leve (1964), Laurens de Haan (1970), Fred Steutel (1971), Wim Vervaat (1972), August Balkema (1973), Frits Göbel (1974), Arie Hordijk (1974), Aegle Hoekstra (1983), Peter de Jong (1988) and Leo Klein Haneveld (1996).
Publications
Machines Served by a Patrolling Operator. 1957
On the use of Markov processes in one-server waiting-time problems and renewal theory. 1960
Einige voorbeelden van stochastische processen: openbare les Universiteit van Amsterdam. 1961.
An Example Illustrating the Possibilities of Renewal Theory and Waiting-time Theory for Markov-dependent Arrival-intervals. 1961
On K.L. Chung's problem of imbedding a time-discrete Markov chain in a time-continuous one for finitely many states. With Carel Louis Scheffer. Amsterdam : Mathematisch Centrum, 1962.
References
External links
Prof. dr. J.T. Runnenburg, 1932–2008
1932 births
2008 deaths
Dutch mathematicians
Scientists from Amsterdam
University of Amsterdam alumni
Academic staff of the University of Amsterdam |
https://en.wikipedia.org/wiki/Netherlands%20Society%20for%20Statistics%20and%20Operations%20Research | The Netherlands Society for Statistics and Operations Research (in Dutch Vereniging voor Statistiek en Operationele Research (VVS+OR)) is a Dutch professional association for Statistics and Operations Research. The society is a member of the umbrella organizations Federation of European National Statistical Societies (FENStatS), the Association of European Operational Research Societies (EURO), and of the International Federation of Operational Research Societies (IFORS).
It was founded on August 15, 1945 as "Vereniging voor Statistiek". It aims to promote the study and the correct application of statistics and operations research and closely related parts of mathematics, in order to serve science and society.
The association publishes a scientific journal, Statistica Neerlandica, as well as a magazine, STAtOR, and organizes conferences and other meetings in various fields of statistics and operations research. The society consists of nine sections, devoting to various fields of statistical science. These sections are on Biometrics, Data Science, Economics, Mathematical Statistics, Operations Research, Social Sciences, Statistics Communication, Statistics Education and one for Young Statisticians.
The president of the Society is Casper Albers. Among the previous presidents were Jaap Wessels (1993 - 1997) and Richard D. Gill (2007 - 2011), and Jacqueline J. Meulman(2011-2016).
Magazines
The association publishes the magazines "Statistica Neerlandica" and since 2000 "STAtOR". The latter replaced the Gazette "VVS-Bulletin" which was last published in 1999.
References
External links
Netherlands Society of Statistics and Operations Research VVSOR Homepage
1945 establishments in the Netherlands
Organizations established in 1945
Scientific societies based in the Netherlands
Operations research societies
Professional associations based in the Netherlands |
https://en.wikipedia.org/wiki/Jacqueline%20Meulman | Jacqueline Meulman (born 7 July 1954) is a Dutch statistician and professor emerita of Applied Statistics at the Mathematical Institute of Leiden University.
Biography
Born in The Hague, Meulman received her master's degree in mathematical psychology and data theory at Leiden University in 1981, and obtained her PhD in data theory in 1986 with the thesis entitled "A distance approach to nonlinear multivariate analysis" advised by Jan de Leeuw and John P. van de Geer. She was a consultant for Bell Telephone Laboratories in Murray Hill, NJ, from 1982 to 1983.
In addition to being an associate professor in the Department of Data Theory in Leiden, she was an adjunct professor at the University of Illinois at Urbana–Champaign from 1993 to 1999. In 1998, she was appointed Professor of Applied Data Theory at Leiden University. Since 2009 she is Professor of Applied Statistics at the Mathematical Institute in Leiden. She is currently also an adjunct professor at the Department of Statistics at Stanford University.
Meulman has received several awards, including a five-year "fellowship" of the Royal Netherlands Academy of Arts and Sciences in 1987, de J.C. Ruigrok prijs from the Royal Holland Society of Sciences and Humanities (KHMW) in 1991, a Fulbright Award in 1992, and a PIONEER grant from the Netherlands Organization of Scientific Research (NWO) in 1994. In 2001 she was elected President of the International Psychometric Society, and since 2002 she is a member of the Royal Netherlands Academy of Arts and Sciences (KNAW). From 2011 to 2017 she was president of the Netherlands Society for Statistics and Operations Research. She is an Elected Member of the International Statistical Institute since 1996, and she was elected to the Royal Holland Society of Sciences and Humanities in 2015.
Work
Meulman's research interest are in the field of statistics and data science, and her work includes the development of new statistical methods with applications in the life and behavioral sciences.
Since the 1990s, she manages the development of software in the package CATEGORIES of IBM SPSS Statistics that includes programs for optimal scaling in regularized multiple regression analysis, principal components analysis, correspondence analysis, multidimensional scaling and unfolding. At the Mathematical Institute in Leiden, she was Program Director of the first Dutch Master in Applied Statistics and Data Science in a Faculty of Science.
She is also one of the Founding Fathers and Co-Director of the Leiden Centre of Data Science (LCDS).
Publications
Meulman has authored and co-authored many publications in the field of statistical research and its applications.
Books, a selection:
1986. A distance approach to nonlinear multivariate analysis. PhD Thesis, Leiden University: DSWO Press.
1990. Albert Gifi Nonlinear Multivariate Analysis (Eds. W.J. Heiser, J.J. Meulman, G. van der Berg). New York: Wiley.
2001. Combinatorial Data Analysis: Optimization by D |
https://en.wikipedia.org/wiki/Jerome%20H.%20Friedman | Jerome Harold Friedman (born December 29, 1939) is an American statistician, consultant and Professor of Statistics at Stanford University, known for his contributions in the field of statistics and data mining.
Biography
Friedman studied at Chico State College for two years before transferring to the University of California, Berkeley in 1959, where he received his AB in Physics in 1962, and his PhD in High Energy Particle Physics in 1967.
In 1968 he started his academic career as research physicist at the Lawrence Berkeley National Laboratory. In 1972 he started at Stanford University as leader of the Computation Research Group at the Stanford Linear Accelerator Center, where he would participate until 2003. In the year 1976–77 he was a visiting scientist at CERN in Geneva. From 1981 to 1984 he was visiting professor at the University of California, Berkeley. In 1982 he was appointed Professor of Statistics at Stanford University.
In 1984 he was elected as a Fellow of the American Statistical Association.
In 2002 he was awarded the SIGKDD Innovation Award by the Association for Computing Machinery (ACM). In 2010 he was elected as a member of the National Academy of Sciences (Applied mathematical sciences).
Publications
Friedman has authored and co-authored many publications in the field of data-mining including "nearest neighbor classification, logistical regressions, and high dimensional data analysis. His primary research interest is in the area of machine learning." A selection:
See also
Gradient boosting
LogitBoost
Multivariate adaptive regression splines
Projection pursuit regression
References
External links
Jerome H. Friedman Professor of Statistics
https://jerryfriedman.su.domains/ Homepage
1939 births
20th-century American mathematicians
21st-century American mathematicians
People associated with CERN
Living people
Machine learning researchers
Stanford University faculty
University of California, Berkeley alumni
Fellows of the American Statistical Association
People from Yreka, California
American statisticians
Data miners
Mathematical statisticians
Computational statisticians |
https://en.wikipedia.org/wiki/G%C3%A1bor%20Eperjesi | Gábor Eperjesi (born 12 January 1994) is a Hungarian professional footballer who plays for Romanian club Csíkszereda.
Career
In January 2023, Eperjesi joined Csíkszereda in Romania.
Club statistics
Updated to games played as of 10 May 2021.
Honours
Diósgyőr
Hungarian League Cup (1): 2013–14
References
External links
MLSZ
HLSZ
1994 births
Footballers from Miskolc
Living people
Hungarian men's footballers
Hungary men's youth international footballers
Hungary men's under-21 international footballers
Men's association football defenders
Diósgyőri VTK players
Mezőkövesdi SE footballers
FK Csíkszereda Miercurea Ciuc players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Liga II players
Hungarian expatriate men's footballers
Expatriate men's footballers in Romania
Hungarian expatriate sportspeople in Romania |
https://en.wikipedia.org/wiki/Emmanuel%20Rayner | Dr Emmanuel (Manny) Rayner (born 11 June 1958) is a British chess player and FIDE Master. He won the Welsh Chess Championship in 1976.
Dr Rayner studied mathematics at Trinity College, Cambridge and obtained a PhD in computer science from Stockholm University. He is currently working on Regulus-based projects at Geneva University in Switzerland.
He has stated on Goodreads that his favourite novels are Anthony Powell's saga A Dance to the Music of Time.
He has also published two humour books entitled What Pooh Might Have Said to Dante (2012) and If Research Were Romance and other Implausible Conjectures (2013), compiling book reviews originally written by him for the Goodreads.com social website. He has also written the humorous books The New Adventures of Socrates: An Extravagance and Everything You Need to Know to Write a Work of Satire in Trump's America. In addition to these, he has written two books on the Regulus Grammar Compiler, called Putting Linguistics into Speech Recognition: The Regulus Grammar Compiler (Studies in Computational Linguistics) and The Spoken Language Translator.
External links
Emmanuel (Manny) Rayner bio at the Welsh Chess Union
British chess players
1958 births
Living people
Chess FIDE Masters |
https://en.wikipedia.org/wiki/Bias%E2%80%93variance%20tradeoff | In statistics and machine learning, the bias–variance tradeoff describes the relationship between a model's complexity, the accuracy of its predictions, and how well it can make predictions on previously unseen data that were not used to train the model. In general, as we increase the number of tunable parameters in a model, it becomes more flexible, and can better fit a training data set. It is said to have lower error, or bias. However, for more flexible models, there will tend to be greater variance to the model fit each time we take a set of samples to create a new training data set. It is said that there is greater variance in the model's estimated parameters.
The bias–variance dilemma or bias–variance problem is the conflict in trying to simultaneously minimize these two sources of error that prevent supervised learning algorithms from generalizing beyond their training set:
The bias error is an error from erroneous assumptions in the learning algorithm. High bias can cause an algorithm to miss the relevant relations between features and target outputs (underfitting).
The variance is an error from sensitivity to small fluctuations in the training set. High variance may result from an algorithm modeling the random noise in the training data (overfitting).
The bias–variance decomposition is a way of analyzing a learning algorithm's expected generalization error with respect to a particular problem as a sum of three terms, the bias, variance, and a quantity called the irreducible error, resulting from noise in the problem itself.
Motivation
The bias–variance tradeoff is a central problem in supervised learning. Ideally, one wants to choose a model that both accurately captures the regularities in its training data, but also generalizes well to unseen data. Unfortunately, it is typically impossible to do both simultaneously. High-variance learning methods may be able to represent their training set well but are at risk of overfitting to noisy or unrepresentative training data. In contrast, algorithms with high bias typically produce simpler models that may fail to capture important regularities (i.e. underfit) in the data.
It is an often made fallacy to assume that complex models must have high variance; High variance models are 'complex' in some sense, but the reverse needs not be true.
In addition, one has to be careful how to define complexity: In particular, the number of parameters used to describe the model is a poor measure of complexity. This is illustrated by an example adapted from: The model has only two parameters () but it can interpolate any number of points by oscillating with a high enough frequency, resulting in both a high bias and high variance.
An analogy can be made to the relationship between accuracy and precision. Accuracy is a description of bias and can intuitively be improved by selecting from only local information. Consequently, a sample will appear accurate (i.e. have low bias) under the aforementioned sel |
https://en.wikipedia.org/wiki/Jean-Marc%20Deshouillers | Jean-Marc Deshouillers (born on September 12, 1946 in Paris) is a French mathematician, specializing in analytic number theory. He is a professor at the University of Bordeaux.
Education and career
Deshouillers attended the Paris École Polytechnique, graduating with an engineer diploma in 1968.
He received his PhD in 1972 at the University Paris VI Pierre et Marie Curie.
In the seventies, he was assistant professor in mathematics at the École Polytechnique, which moved from Paris to Palaiseau.
Deshouillers is a professor at the University of Bordeaux. In 2009 he was at the Institute for Advanced Study.
Contributions
In 1985 he showed with Ramachandran Balasubramanian and Francois Dress that, in the case of the fourth powers of Waring's problem, the least number of fourth powers that is necessary to express any positive integer as a sum of fourth powers is 19.
With Henryk Iwaniec, he improved the Kuznetsov trace formula. In 1997, with Effinger and Herman te Riele, he proved the ternary Goldbach conjecture (every odd number greater than 5 is a sum of three prime numbers) under the Generalized Riemann Hypothesis.
Among his students was Gérald Tenenbaum.
Works
Problème de Waring pour les bicarrés. Séminaire de théorie des nombres de Bordeaux, 1984/85, Online
References
20th-century French mathematicians
21st-century French mathematicians
Living people
1946 births |
https://en.wikipedia.org/wiki/Barna%20Papucsek | Barna Papucsek (born 11 October 1989) is a Hungarian professional footballer who plays for Csákvár.
Club statistics
Updated to games played as of 19 May 2019.
References
MLSZ
HLSZ
1989 births
Living people
Footballers from Budapest
Hungarian men's footballers
Men's association football defenders
Tatabányai SC players
Vasas SC players
Hévíz FC footballers
Fehérvár FC players
Puskás Akadémia FC players
Szolnoki MÁV FC footballers
Kisvárda FC players
Balmazújvárosi FC players
Nyíregyháza Spartacus FC players
Aqvital FC Csákvár players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players |
https://en.wikipedia.org/wiki/Thomas%20Craig%20%28mathematician%29 | Thomas Craig (1855–1900) was an American mathematician. He was a professor at Johns Hopkins University and a proponent of the methods of differential geometry.
Biography
Thomas Craig was born December 20, 1855, in Pittston, Pennsylvania. His father Alexander Craig immigrated from Scotland, and worked as an engineer in the mining industry.
Thomas Craig first studied civil engineering at Lafayette College in Pennsylvania, where a teacher William J. Bruce was a mentor to him. Thomas took his C.E. degree in 1875. He taught high school in Newton, New Jersey while continuing to study mathematics. He entered into correspondence with Benjamin Peirce and Peter Guthrie Tait.
Thomas Craig was one of the prime movers of Johns Hopkins University when it was launched by Daniel Coit Gilman in 1876. Craig and George Bruce Halsted were the first Hopkins Fellows in mathematics. James Joseph Sylvester had been invited to lead a graduate program in mathematics but would only be doing that. Craig was needed to teach differential calculus and integral calculus. The first year there were only fifteen students studying mathematics, but by 1883 there were 35.
In 1878 Craig took his Ph.D. degree with a dissertation The Representation of One Surface Upon Another, and Some Points in the theory of the Curvature of Surfaces. He became an instructor at Johns Hopkins that year, but also took up work at the U. S. Coast and Geodetic Survey. In that capacity he produced the text for A Treatise on Projections for workers at the Geodetic Survey. Craig and Simon Newcomb read Leo Königsberger's Theory of Functions also.
Thomas married Louise Alford, daughter of General Benjamin Alvord, on May 4, 1880. The couple raised two daughters, Alisa and Ethel.
After 1881 Craig was totally committed to Johns Hopkins, particularly anticipating Arthur Cayley's lectures on theta functions when he came over for the Spring semester of 1882. Besides the calculus courses, Craig taught differential equations, elliptic functions, elasticity, partial differential equations, calculus of variations, definite integrals, mechanics, dynamics, hydrodynamics, sound, spherical harmonics, and Bessel functions.
When the American Journal of Mathematics was launched in 1877 Craig was tasked with recording expenses, as these were underwritten by Johns Hopkins University. His report at the end of 1882 gave the total just under ten thousand dollars.
Thomas Craig died May 8, 1900. With information supplied by Luther P. Eisenhart, Simon Newcomb wrote the notice in the American Journal of Mathematics
Works
Thomas Craig wrote the following contributions to the American Journal of Mathematics:
1880: AJM 3:114 to 27: Orthomorphic projections of an ellipsoid on a sphere
1881: AJM 4: 297 to 320: On certain metric properties of surfaces
1881: AJM 4:358 to 78: The counter-pedal surface of an ellipsoid
1882: AJM 5:62 to 75: Some elliptic function formula
1882: AJM 5:76 to 8: Note on the counter-pedal surface of an e |
https://en.wikipedia.org/wiki/Kelsey%20Bone | Kelsey Renée Bone (born December 31, 1991) is an American professional basketball player who is currently a free agent.
College statistics
Source
USA Basketball
Bone was selected to play in the USA Women's Youth Development Festival. Eligible players are female basketball players who are in their sophomore or junior in high school. The 2007 event took place at the US Olympic Training Center in Colorado Springs, CO.
Bone was a member of the USA Women's U18 team which won the gold medal at the FIBA Americas Championship in Buenos Aires, Argentina. The event was held in July 2008, when the USA team defeated host Argentina to win the championship. Bone helped the team win all five games, starting all five games and scoring over ten points per game.
Bone continued on to the USA Women's U19 team which represented the US in the 2009 U19 World's Championship, held in Bangkok, Thailand in July and August 2009. Although the USA team lost the opening game to Spain, they went on to win their next seven games to earn a rematch against Spain in the finals, and won the game 81–71 to earn the gold medal. Bone started all nine games and was the team's second highest scorer, with 12.3 points per game.
WNBA career statistics
Source
Regular season
|-
| style="text-align:left;"| 2013
| style="text-align:left;"| New York
| style="background-color:#D3D3D3;"|34°||2||19.5||.460||.000||.632||5.4||0.7||0.4||0.4||1.5||6.9
|-
| style="text-align:left;"| 2014
| style="text-align:left;"| Connecticut
|style="background-color:#D3D3D3;"|34°||26||23.3||.451||.000||.662||5.3||1.4||0.6||0.5||2.0||9.3
|-
| style="text-align:left;"| 2015
| style="text-align:left;"| Connecticut
|34||33||28.3||.508||.000||.622||6.1||1.9||0.8||0.6||2.3||15.0
|-
| style="text-align:left;"| 2016
| style="text-align:left;"| Connecticut
|style="background-color:#D3D3D3;"|14° || 13 || 23.9 ||.433||.267||.667||5.4||1.3||0.7||0.2||1.9||10.7
|-
| style="text-align:left;"| 2016
| style="text-align:left;"| Phoenix
|style="background-color:#D3D3D3;"|20° || 0 || 9.7 ||.388||.000||.700||2.5||0.6||0.2||0.1||1.3||3.0
|-
| style="text-align:left;"| 2018
| style="text-align:left;"| Las Vegas
|32||10||10.8||.500||–||.500||2.2||1.2||0.1||0.1||0.9||2.8
|-
|- class="sortbottom"
| style="text-align:center;" colspan="2"| Career
| 168||84||19.6||.470||.167||.634||4.6||1.2||0.5||0.3||1.6||8.1
|}
Playoffs
|-
| style="text-align:left;"| 2016
| style="text-align:left;"| Phoenix
| 2 || 0 || 4.0 || 1.000 ||–||–||0.5||0.0||0.0||0.0||0.0||2.0
Personal life
Bone's younger half-brother, Donovan Williams, plays basketball at UNLV.
References
WNBA Biography
1991 births
Living people
All-American college women's basketball players
American expatriate basketball people in China
American expatriate basketball people in Turkey
American women's basketball players
Basketball players from Houston
Centers (basketball)
Connecticut Sun players
Galatasaray S.K. (women's basketball) players
Las Vegas Aces players
Liaoning Flying Eagles |
https://en.wikipedia.org/wiki/Michael%20Barnes%20%28motorcyclist%29 | Michael Barnes (born October 21, 1968) is an American motorcycle racer.
Career statistics
By season
Races by year
(key)
References
External links
1968 births
Living people
American motorcycle racers
MotoGP World Championship riders |
https://en.wikipedia.org/wiki/Thomas%20Mormann | Thomas Mormann (born 1951) is Professor of Philosophy at the University of the Basque Country in Donostia-San Sebastian, Spain. He obtained his PhD in Mathematics from the University of Dortmund (1978). He obtained his Habilitation from the University of Munich. He works in the philosophy of science, formal ontology, structuralism, Carnap studies, and neo-Kantianism.
Selected publications
Mormann, T. Continuous lattices and Whiteheadian theory of space. The Second German-Polish Workshop on Logic & Logical Philosophy (Żagań, 1998). Logic and Log. Philos. No. 6 (1998), 35–54.
W. Diederich, A. Ibarra, T. Mormann. Bibliography of structuralism. Erkenntnis, 1989, Springer.
T. Mormann. Rudolf Carnap. München, Beck, 2000.
T. Mormann. Ist der Begriff der Repräsentation obsolete? Zeitschrift für philosophische Forschung, 1997.
J. Echeverría, A. Ibarra, T. Mormann. The Space of Mathematics: Philosophical, Epistemological and Historical Explorations. 1992.
External links
https://facultyofphilosophyande.academia.edu/ThomasMormann
21st-century Spanish philosophers
Ontologists
Philosophers of science
Academic staff of the University of the Basque Country
1951 births
Living people |
https://en.wikipedia.org/wiki/Colin%20Mathers | Colin Mathers is Coordinator of the Mortality and Burden of Disease Unit in the Health System and Innovation at the World Health Organization (WHO) who specializes in cause of death statistics and projections, burden of disease estimates, and the measurement and reporting of population health and its determinants. He is a co-author on widely cited papers in these areas and a member of the Disease Control Priorities Project. Mathers joined the WHO in 2000 and was previously at the Australian Institute of Health and Welfare. Mathers received his PhD in theoretical physics from the University of Sydney in 1979.
He was appointed as Honorary Professor in the College of Medicine & Veterinary Medicine, by the University of Edinburgh in August 2015.
References
University of Sydney alumni
World Health Organization officials
Australian officials of the United Nations |
https://en.wikipedia.org/wiki/Pietro%20Saporetti | Pietro Saporetti (Bagnacavallo, Emilia-Romagna, 1832 – 1893) was an Italian painter.
In Bagnacavallo his father was a teacher of Physics and mathematics at the Lyceum. He took his first lesson in Bagnacavallo, under Antonio Moni. In 1851, he went to study painting in Florence. In 1854, he studied at the Academy of Fine Arts in Venice under Luigi Ferrari, professor of sculpture. In 1855, he returned to Florence, where he painted Christ exorcises a demon. Finally he moved to Rome. The political events of 1859 exiled him back to Bagnacavallo, until 1867 he was hired as an instructor of design at the Technical Institute and Academy of Fine Arts of Ravenna.
Among his paintings are: Lavoro e Carità (small size); Un vecchio cacciatore (life-size and found in the Galleria Rasponi of Ravenna); Una finita ai carcerati (life-size and exhibited in 1873 at Vienna); La buona sorellina (small size and once in the Galleria Sollian of Trieste); Un novello Atteone (1877 exhibited at Naples); Castelli in aria (life-size, 1878); Una emancipata (life-size and exhibited at Turin in 1880); Un sequestro nell ' educandato (half-size); Preghiera del mattino (half size); Pensiero giovanile (small size and once found in galleria Sollian of Trieste).
He was the father of the painter Edgardo Saporetti.
References
19th-century Italian painters
Italian male painters
1832 births
1893 deaths
19th-century Italian male artists |
https://en.wikipedia.org/wiki/Estimation%20statistics | Estimation statistics, or simply estimation, is a data analysis framework that uses a combination of effect sizes, confidence intervals, precision planning, and meta-analysis to plan experiments, analyze data and interpret results. It complements hypothesis testing approaches such as null hypothesis significance testing (NHST), by going beyond the question is an effect present or not, and provides information about how large an effect is. Estimation statistics is sometimes referred to as the new statistics.
The primary aim of estimation methods is to report an effect size (a point estimate) along with its confidence interval, the latter of which is related to the precision of the estimate. The confidence interval summarizes a range of likely values of the underlying population effect. Proponents of estimation see reporting a P value as an unhelpful distraction from the important business of reporting an effect size with its confidence intervals, and believe that estimation should replace significance testing for data analysis.
History
Starting in 1929, physicist Raymond Thayer Birge published review papers in which he used weighted-averages methods to calculate estimates of physical constants, a procedure that can be seen as the precursor to modern meta-analysis.
In the 1960s, estimation statistics was adopted by the non-physical sciences with the development of the standardized effect size by Jacob Cohen.
In the 1970s, modern research synthesis was pioneered by Gene V. Glass with the first systematic review and meta-analysis for psychotherapy. This pioneering work subsequently influenced the adoption of meta-analyses for medical treatments more generally.
In the 1980s and 1990s, estimation methods were extended and refined by biostatisticians including Larry Hedges, Michael Borenstein, Doug Altman, Martin Gardner, and many others, with the development of the modern (medical) meta-analysis.
Starting in the 1980s, the systematic review, used in conjunction with meta-analysis, became a technique widely used in medical research. There are over 200,000 citations to "meta-analysis" in PubMed.
In the 1990s, editor Kenneth Rothman banned the use of p-values from the journal Epidemiology; compliance was high among authors but this did not substantially change their analytical thinking.
In the 2010s, Geoff Cumming published a textbook dedicated to estimation statistics, along with software in Excel designed to teach effect-size thinking, primarily to psychologists. Also in the 2010s, estimation methods were increasingly adopted in neuroscience.
In 2013, the Publication Manual of the American Psychological Association recommended to use estimation in addition to hypothesis testing. Also in 2013, the Uniform Requirements for Manuscripts Submitted to Biomedical Journals document made a similar recommendation: "Avoid relying solely on statistical hypothesis testing, such as P values, which fail to convey important information about effect size."
|
https://en.wikipedia.org/wiki/Legendre%27s%20three-square%20theorem | In mathematics, Legendre's three-square theorem states that a natural number can be represented as the sum of three squares of integers
if and only if is not of the form for nonnegative integers and .
The first numbers that cannot be expressed as the sum of three squares (i.e. numbers that can be expressed as ) are
7, 15, 23, 28, 31, 39, 47, 55, 60, 63, 71 ... .
History
Pierre de Fermat gave a criterion for numbers of the form 8a + 1 and 8a + 3 to be sums of a square plus twice another square, but did not provide a proof. N. Beguelin noticed in 1774 that every positive integer which is neither of the form 8n + 7, nor of the form 4n, is the sum of three squares, but did not provide a satisfactory proof. In 1796 Gauss proved his Eureka theorem that every positive integer n is the sum of 3 triangular numbers; this is equivalent to the fact that 8n + 3 is a sum of three squares. In 1797 or 1798 A.-M. Legendre obtained the first proof of his 3 square theorem. In 1813, A. L. Cauchy noted that Legendre's theorem is equivalent to the statement in the introduction above. Previously, in 1801, C. F. Gauss had obtained a more general result, containing Legendre's theorem of 1797–8 as a corollary. In particular, Gauss counted the number of solutions of the expression of an integer as a sum of three squares, and this is a generalisation of yet another result of Legendre, whose proof is incomplete. This last fact appears to be the reason for later incorrect claims according to which Legendre's proof of the three-square theorem was defective and had to be completed by Gauss.
With Lagrange's four-square theorem and the two-square theorem of Girard, Fermat and Euler, the Waring's problem for k = 2 is entirely solved.
Proofs
The "only if" of the theorem is simply because modulo 8, every square is congruent to 0, 1 or 4. There are several proofs of the converse (besides Legendre's proof). One of them is due to J. P. G. L. Dirichlet in 1850, and has become classical. It requires three main lemmas:
the quadratic reciprocity law,
Dirichlet's theorem on arithmetic progressions, and
the equivalence class of the trivial ternary quadratic form.
Relationship to the four-square theorem
This theorem can be used to prove Lagrange's four-square theorem, which states that all natural numbers can be written as a sum of four squares. Gauss pointed out that the four squares theorem follows easily from the fact that any positive integer that is 1 or 2 mod 4 is a sum of 3 squares, because any positive integer not divisible by 4 can be reduced to this form by subtracting 0 or 1 from it.
However, proving the three-square theorem is considerably more difficult than a direct proof of the four-square theorem that does not use the three-square theorem. Indeed, the four-square theorem was proved earlier, in 1770.
See also
Fermat's two-square theorem
Sum of two squares theorem
Notes
Additive number theory
Squares in number theory
Theorems in number theory |
https://en.wikipedia.org/wiki/Tetrahedrally%20diminished%20dodecahedron | In geometry, a tetrahedrally diminished dodecahedron (also tetrahedrally stellated icosahedron or propello tetrahedron) is a topologically self-dual polyhedron made of 16 vertices, 30 edges, and 16 faces (4 equilateral triangles and 12 identical quadrilaterals).
A canonical form exists with two edge lengths at 0.849 : 1.057, assuming that the radius of the midsphere is 1. The kites remain isosceles.
It has chiral tetrahedral symmetry, and so its geometry can be constructed from pyritohedral symmetry of the pseudoicosahedron with 4 faces stellated, or from the pyritohedron, with 4 vertices diminished. Within its tetrahedral symmetry, it has geometric varied proportions. By Dorman Luke dual construction, a unique geometric proportion can be defined. The kite faces have edges of length ratio ~ 1:0.633.
Topologically, the triangles are always equilateral, while the quadrilaterals are irregular, although the two adjacent edges that meet at the vertices of a tetrahedron are equal.
As a self-dual hexadecahedron, it is one of 302404 forms, 1476 with at least order 2 symmetry, and the only one with tetrahedral symmetry.
As a diminished regular dodecahedron, with 4 vertices removed, the quadrilaterals faces are trapezoids.
As a stellation of the regular icosahedron it is one of 32 stellations defined with tetrahedral symmetry. It has kite faces.
In Conway polyhedron notation, it can represented as pT, applying George W. Hart's propeller operator to a regular tetrahedron.
Related polytopes and honeycombs
This polyhedron represents the vertex figure of a hyperbolic uniform honeycomb, the partially diminished icosahedral honeycomb, pd{3,5,3}, with 12 pentagonal antiprisms and 4 dodecahedron cells meeting at every vertex.
Vertex figure projected as Schlegel diagram
Notes
References
External links
tetrahedrally truncated dodecahedron and stellated icosahedron
Generation of an icosahedron by the intersection of five tetrahedra: geometrical and crystallographic features of the intermediate polyhedra
VRML model as truncated regular dodecahedron
VRML model as tetrahedrally stellated icosahedron
Polyhedra |
https://en.wikipedia.org/wiki/Bedtime%20Math | Bedtime Math is a non-profit organization focused on mathematics education for young children, launched by Laura Overdeck in February 2012.
History
Bedtime Math was founded in February 2012, initially as a website. In March 2014, Bedtime Math launched Crazy 8s, a free nationwide after-school recreational math club.
In 2018, researchers at Johns Hopkins University released results of a study that found its Crazy 8s math club significantly reduced children's feelings of math anxiety after eight weeks of participation. The effect was more pronounced among students in the kindergarten through second grade club.
In 2019, Bedtime Math created Fun Factor, a new K-5 curriculum developed in consultation with Teachers College, Columbia University. It features dynamic math activities that aligns with standards and address key concepts, paired with teacher professional development.
Products
Nightly math problem: Bedtime Math's core offering is daily math problems for elementary school-age kids, broadcast by email and posted daily on the website's homepage and Facebook page.
Apps: The organization delivers the same daily riddles via a free mobile application for Android and iPhone OS.
Books: Overdeck has also published four children's books (100% of her book royalties are donated toward Bedtime Math's programming).
Bedtime Math: A Fun Excuse to Stay up Late (Macmillan Children's Publishing Group, June 2013)
Bedtime Math: This Time It's Personal (Macmillan Children's Publishing Group, March 2014)
Bedtime Math: The Truth Comes Out (Macmillan Children's Publishing Group, March 2015)
How Many Guinea Pigs Can Fit on a Plane? (Macmillan Children's Publishing Group, June 2016)
Crazy 8s after-school math club: The free program provides a free kit of materials to help host eight sessions of a weekly math club. As of 2019, there were 10,000 schools and libraries across the country who have participated.
Fun Factor in-school offering: In contrast to Crazy 8s, Fun Factor activities are standards-aligned for grades K-5 and geared towards small-group differentiated instruction.
Summer of Numbers: A summer math incentive program for libraries, in which kids track their daily math using gold star stickers on a calendar. The program, once offered through the Collaborative Summer Library Program, is now exclusively offered by Bedtime Math.
Videos: For Math Awareness Month in April 2013, Bedtime Math produced four short math comedies.
Reception
Bedtime Math has been featured in The New York Times parenting blog, USA Today, and National Public Radio (NPR); its books have been featured on NPR's Science Friday and reviewed in The Wall Street Journal. Time described it as "heartening news for educators who bemoan the state of science, technology, engineering and math (STEM) education in the U.S."
In 2015, an article in the journal Science reported on a randomized trial that found use of the Bedtime Math iPad app improved performance of first-graders in math at schoo |
https://en.wikipedia.org/wiki/Dinesh%20Thakur%20%28mathematician%29 | Dinesh S. Thakur is an Indian mathematician and a professor of mathematics at University of Rochester. Before moving to Rochester, Thakur was a professor at University of Arizona. His main research interest is number theory.
Early life
Thakur was born in Mumbai, India. He attended Balmohan Vidyamandir School in Bombay and completed his undergraduate education at Ruia College, University of Bombay. He got his Ph.D in 1987 at Harvard University under the guidance of Professor John Tate.
Career
Thakur has spent three and half years at Institute for Advanced Study, Princeton and three years at Tata Institute of Fundamental Research, Bombay. He held positions at University of Minnesota and University of Michigan. He moved to University of Arizona in 1993. He joined University of Rochester in July
2013. Thakur wrote a research monograph Function Field Arithmetic. Thakur has been serving on the editorial boards of Journal of Number Theory, International Journal of Number Theory, and P-adic Numbers, Ultrametric Analysis and Applications. Thakur is a founding member of-and for 15 years a participant in-the NSF-funded Southwest Center for Arithmetic Geometry and the Arizona Winter School.
He was elected as a member of the 2017 class of Fellows of the American Mathematical Society "for contributions to the arithmetic of function fields, exposition, and service to the mathematical community".
Work
His main work has been in number theory, where he has been instrumental in developing various aspects of function field arithmetic and arithmetic geometry.
References
External links
Home Page at University of Rochester
Function Field Arithmetic
Mathematics Genealogy
Rochester Faculty
List of publications
1961 births
Living people
21st-century Indian mathematicians
Fellows of the American Mathematical Society
Harvard Graduate School of Arts and Sciences alumni
Indian expatriates in the United States
Indian number theorists
Scientists from Maharashtra
University of Michigan faculty
University of Mumbai alumni
University of Rochester faculty |
https://en.wikipedia.org/wiki/Smith%20space | In functional analysis and related areas of mathematics, a Smith space is a complete compactly generated locally convex topological vector space having a universal compact set, i.e. a compact set which absorbs every other compact set (i.e. for some ).
Smith spaces are named after
Marianne Ruth Freundlich Smith, who introduced them as duals to Banach spaces in some versions of duality theory for topological vector spaces. All Smith spaces are stereotype and are in the stereotype duality relations with Banach spaces:
for any Banach space its stereotype dual space is a Smith space,
and vice versa, for any Smith space its stereotype dual space is a Banach space.
Smith spaces are special cases of Brauner spaces.
Examples
As follows from the duality theorems, for any Banach space its stereotype dual space is a Smith space. The polar of the unit ball in is the universal compact set in . If denotes the normed dual space for , and the space endowed with the -weak topology, then the topology of lies between the topology of and the topology of , so there are natural (linear continuous) bijections
If is infinite-dimensional, then no two of these topologies coincide. At the same time, for infinite dimensional the space is not barreled (and even is not a Mackey space if is reflexive as a Banach space).
If is a convex balanced compact set in a locally convex space , then its linear span possesses a unique structure of a Smith space with as the universal compact set (and with the same topology on ).
If is a (Hausdorff) compact topological space, and the Banach space of continuous functions on (with the usual sup-norm), then the stereotype dual space (of Radon measures on with the topology of uniform convergence on compact sets in ) is a Smith space. In the special case when is endowed with a structure of a topological group the space becomes a natural example of a stereotype group algebra.
A Banach space is a Smith space if and only if is finite-dimensional.
See also
Stereotype space
Brauner space
Notes
References
Functional analysis
Topological vector spaces |
https://en.wikipedia.org/wiki/Marie%20Diener-West | Marie Diener-West is the Helen Abbey and Margaret Merrell Professor of Biostatistics and the chair of the Master of Public Health Program at Johns Hopkins Bloomberg School of Public Health. Diener-West is an editor for the Cochrane Eyes and Vision Group and a member of the American Public Health Association, American Statistical Association, Association for Research in Vision and Ophthalmology, and the Society for Clinical Studies.
Education and career
Diener-West earned a B.S., magna cum laude, degree in both Mathematics and Biology from Loyola University Chicago in 1977, earning the "Best Biology Student Award." While working on her Ph.D., she worked as a Teaching and Research Assistant in the Departments of Biostatistics and Epidemiology at Johns Hopkins University (1978-1981) and as a Senior Statistician in the Radiation Therapy and Oncology Group at the American College of Radiology in Philadelphia (1983-1986). Diener-West went on to earn her Ph.D. in Biostatistics from the Johns Hopkins School of Hygiene and Public Health.
In 1986, Diener-West was awarded a joint appointment at Johns Hopkins University as an assistant professor in both the department of Biostatistics at Johns Hopkins School of Hygiene and Public Health and the department of ophthalmology at the Johns Hopkins School of Medicine. During her joint appointment, Diener-West became the Study Statistician and Deputy Director of the Coordinating Center for the Collaborative Ocular Melanoma Study (COMS) at Johns Hopkins School of Medicine, a position she held from 1986–2005. In 1989, she worked for the Save the Children Federation as a statistician in Kathmandu, Nepal. In 1990, Diener-West returned to her joint appointment at Johns Hopkins University, while also becoming a faculty member at the Johns Hopkins Center for Clinical Trials, a position she holds to this day. During her second term as a joint associate professor, Diener-West became a member of the editorial board of the American Journal of Ophthalmology, a position she held from 1998–2004.
In 2000, Diener-West was given another joint appointment at Johns Hopkins University, however, this time, she was appointed as a full professor in the departments of Biostatistics and Epidemiology at Johns Hopkins Bloomberg School of Public Health.
In 2004, Diener-West was appointed as the Inaugural Helen Abbey and Margaret Merrell Professor of Biostatistics Education, a position she has held to this day. In 2008, Diener-West was named as the chair of the Johns Hopkins Bloomberg School of Public Health's Master of Public Health program
Research area
Diener-West states that her "research interests have focused on the design, conduct, and analysis of clinical trials." While working as the Study Statistician and Deputy Director of the Coordinating Center for the Collaborative Ocular Melanoma Study (COMS) at Johns Hopkins School of Medicine Diener-West co-published several articles concerning the project. The subject of these articles |
https://en.wikipedia.org/wiki/Ramsey%20class | In the area of mathematics known as Ramsey theory, a Ramsey class is one which satisfies a generalization of Ramsey's theorem.
Suppose , and are structures and is a positive integer. We denote by the set of all subobjects of which are isomorphic to . We further denote by the property that for all partitions of there exists a and an such that .
Suppose is a class of structures closed under isomorphism and substructures. We say the class has the A-Ramsey property if for ever positive integer and for every there is a such that holds. If has the -Ramsey property for all then we say is a Ramsey class.
Ramsey's theorem is equivalent to the statement that the class of all finite sets is a Ramsey class.
References
Ramsey theory |
https://en.wikipedia.org/wiki/Integration%20along%20fibers | In differential geometry, the integration along fibers of a k-form yields a -form where m is the dimension of the fiber, via "integration". It is also called the fiber integration.
Definition
Let be a fiber bundle over a manifold with compact oriented fibers. If is a k-form on E, then for tangent vectors wi's at b, let
where is the induced top-form on the fiber ; i.e., an -form given by: with lifts of to ,
(To see is smooth, work it out in coordinates; cf. an example below.)
Then is a linear map . By Stokes' formula, if the fibers have no boundaries(i.e. ), the map descends to de Rham cohomology:
This is also called the fiber integration.
Now, suppose is a sphere bundle; i.e., the typical fiber is a sphere. Then there is an exact sequence , K the kernel,
which leads to a long exact sequence, dropping the coefficient and using :
,
called the Gysin sequence.
Example
Let be an obvious projection. First assume with coordinates and consider a k-form:
Then, at each point in M,
From this local calculation, the next formula follows easily (see Poincaré_lemma#Direct_proof): if is any k-form on
where is the restriction of to .
As an application of this formula, let be a smooth map (thought of as a homotopy). Then the composition is a homotopy operator (also called a chain homotopy):
which implies induce the same map on cohomology, the fact known as the homotopy invariance of de Rham cohomology. As a corollary, for example, let U be an open ball in Rn with center at the origin and let . Then , the fact known as the Poincaré lemma.
Projection formula
Given a vector bundle π : E → B over a manifold, we say a differential form α on E has vertical-compact support if the restriction has compact support for each b in B. We write for the vector space of differential forms on E with vertical-compact support.
If E is oriented as a vector bundle, exactly as before, we can define the integration along the fiber:
The following is known as the projection formula. We make a right -module by setting .
Proof: 1. Since the assertion is local, we can assume π is trivial: i.e., is a projection. Let be the coordinates on the fiber. If , then, since is a ring homomorphism,
Similarly, both sides are zero if α does not contain dt. The proof of 2. is similar.
See also
Transgression map
Notes
References
Michele Audin, Torus actions on symplectic manifolds, Birkhauser, 2004
Differential geometry |
https://en.wikipedia.org/wiki/Segal%E2%80%93Bargmann%20space | In mathematics, the Segal–Bargmann space (for Irving Segal and Valentine Bargmann), also known as the Bargmann space or Bargmann–Fock space, is the space of holomorphic functions F in n complex variables satisfying the square-integrability condition:
where here dz denotes the 2n-dimensional Lebesgue measure on It is a Hilbert space with respect to the associated inner product:
The space was introduced in the mathematical physics literature separately by Bargmann and Segal in the early 1960s; see and . Basic information about the material in this section may be found in and . Segal worked from the beginning in the infinite-dimensional setting; see and Section 10 of for more information on this aspect of the subject.
Properties
A basic property of this space is that pointwise evaluation is continuous, meaning that for each there is a constant C such that
It then follows from the Riesz representation theorem that there exists a unique Fa in the Segal–Bargmann space such that
The function Fa may be computed explicitly as
where, explicitly,
The function Fa is called the coherent state (applied in mathematical physics) with parameter a, and the function
is known as the reproducing kernel for the Segal–Bargmann space. Note that
meaning that integration against the reproducing kernel simply gives back (i.e., reproduces) the function F, provided, of course that F is an element of the space (and in particular is holomorphic).
Note that
It follows from the Cauchy–Schwarz inequality that elements of the Segal–Bargmann space satisfy the pointwise bounds
Quantum mechanical interpretation
One may interpret a unit vector in the Segal–Bargmann space as the wave function for a quantum particle moving in In this view, plays the role of the classical phase space, whereas is the configuration space. The restriction that F be holomorphic is essential to this interpretation; if F were an arbitrary square-integrable function, it could be localized into an arbitrarily small region of the phase space, which would go against the uncertainty principle. Since, however, F is required to be holomorphic, it satisfies the pointwise bounds described above, which provides a limit on how concentrated F can be in any region of phase space.
Given a unit vector F in the Segal–Bargmann space, the quantity
may be interpreted as a sort of phase space probability density for the particle. Since the above quantity is manifestly non-negative, it cannot coincide with the Wigner function of the particle, which usually has some negative values. In fact, the above density coincides with the Husimi function of the particle, which is obtained from the Wigner function by smearing with a Gaussian. This connection will be made more precise below, after we introduce the Segal–Bargmann transform.
The canonical commutation relations
One may introduce annihilation operators and creation operators on the Segal–Bargmann space by setting
and
These operators satisfy the |
https://en.wikipedia.org/wiki/Serial%20subgroup | In the mathematical field of group theory, a subgroup H of a given group G is a serial subgroup of G if there is a chain C of subgroups of G extending from H to G such that for consecutive subgroups X and Y in C, X is a normal subgroup of Y. The relation is written H ser G or H is serial in G.
If the chain is finite between H and G, then H is a subnormal subgroup of G. Then every subnormal subgroup of G is serial. If the chain C is well-ordered and ascending, then H is an ascendant subgroup of G; if descending, then H is a descendant subgroup of G. If G is a locally finite group, then the set of all serial subgroups of G form a complete sublattice in the lattice of all normal subgroups of G.
See also
Characteristic subgroup
Normal closure
Normal core
References
Subgroup properties |
https://en.wikipedia.org/wiki/2013%20Swedish%20Football%20Division%202 | Statistics of Swedish football Division 2 for the 2013 season.
League standings
Norrland 2013
Norra Svealand 2013
Södra Svealand 2013
Norra Götaland 2013
Västra Götaland 2013
Södra Götaland 2013
Player of the year awards
Ever since 2003 the online bookmaker Unibet have given out awards at the end of the season to the best players in Division 2. The recipients are decided by a jury of sportsjournalists, coaches and football experts. The names highlighted in green won the overall national award.
References
Swedish Football Division 2 seasons
4
Sweden
Sweden |
https://en.wikipedia.org/wiki/Henry%20Ogilvie | Henry Ogilvie (born 2 November 1941) is a former Australian rules footballer who played with Carlton in the Victorian Football League (VFL).
Notes
External links
Henry Ogilvie's playing statistics from The VFA Project
Henry Ogilvie's profile at Blueseum
1941 births
Carlton Football Club players
Ararat Football Club players
Werribee Football Club players
Australian rules footballers from Victoria (state)
Living people |
https://en.wikipedia.org/wiki/Bence%20Sipos | Bence Sipos (born 7 April 1994) is a Hungarian professional footballer who plays for MTK Budapest FC.
Club statistics
Updated to games played as of 1 March 2014.
References
MLSZ
HLSZ
1994 births
Living people
Footballers from Eger
Hungarian men's footballers
Men's association football midfielders
MTK Budapest FC players
Szigetszentmiklósi TK footballers
Nemzeti Bajnokság I players |
https://en.wikipedia.org/wiki/Bagplot | A bagplot, or starburst plot, is a method in robust statistics for visualizing two- or three-dimensional statistical data, analogous to the one-dimensional box plot. Introduced in 1999 by Rousseuw et al., the bagplot allows one to visualize the location, spread, skewness, and outliers of a data set.
Construction
The bagplot consists of three nested polygons, called the "bag", the "fence", and the "loop".
The inner polygon, called the bag, is constructed on the basis of Tukey depth, the smallest number of observations that can be contained by a half-plane that also contains a given point. It contains at most 50% of the data points
The outermost of the three polygons, called the fence is not drawn as part of the bagplot, but is used to construct it. It is formed by inflating the bag by a certain factor (usually 3). Observations outside the fence are flagged as outliers.
The observations that are not marked as outliers are surrounded by a loop, the convex hull of the observations within the fence.
An asterisk symbol (*) near the center of the graph is used to mark the depth median, the point with the highest possible Tukey depth. The observations between the bag and fence are marked by line segments, on a line to the depth median, connecting them to the bag.
The three-dimensional version consists of an inner and outer bag. The outer bag must be drawn in transparent colors so that the inner bag remains visible.
Properties
The bagplot is invariant under affine transformations of the plane, and robust against outliers.
References
Robust statistics
Statistical charts and diagrams
Statistical outliers |
https://en.wikipedia.org/wiki/T%C5%A1oanelo%20Koetle | Tšoanelo Koetle (born 22 November 1992) is Mosotho international footballer who plays for Lioli as a right-back. He played at the 2014 FIFA World Cup qualification.
Career statistics
Scores and results list Lesotho's goal tally first.
References
External links
1992 births
Living people
Lesotho men's footballers
Lesotho men's international footballers
Men's association football midfielders
Lioli FC players
Matlama FC players |
https://en.wikipedia.org/wiki/Benjamin%20Kindsvater | Benjamin Kindsvater (born 8 February 1993) is a German professional footballer who plays as a left midfielder for VfR Aalen.
Career statistics
References
External links
1993 births
Living people
Men's association football midfielders
German men's footballers
SV Wacker Burghausen players
TSV 1860 Munich players
FC Nitra players
VfR Aalen players
3. Liga players
Regionalliga players
Slovak First Football League players
German expatriate men's footballers
German expatriate sportspeople in Slovakia
Expatriate men's footballers in Slovakia |
https://en.wikipedia.org/wiki/Trapezoidal%20distribution | In probability theory and statistics, the trapezoidal distribution is a continuous probability distribution whose probability density function graph resembles a trapezoid. Likewise, trapezoidal distributions also roughly resemble mesas or plateaus.
Each trapezoidal distribution has a lower bound and an upper bound , where , beyond which no values or events on the distribution can occur (i.e. beyond which the probability is always zero). In addition, there are two sharp bending points (non-differentiable discontinuities) within the probability distribution, which we will call and , which occur between and , such that .
The image to the right shows a perfectly linear trapezoidal distribution. However, not all trapezoidal distributions are so precisely shaped. In the standard case, where the middle part of the trapezoid is completely flat, and the side ramps are perfectly linear, all of the values between and will occur with equal frequency, and therefore all such points will be modes (local frequency maxima) of the distribution. On the other hand, though, if the middle part of the trapezoid is not completely flat, or if one or both of the side ramps are not perfectly linear, then the trapezoidal distribution in question is a generalized trapezoidal distribution, and more complicated and context-dependent rules may apply. The side ramps of a trapezoidal distribution are not required to be symmetric in the general case, just as the sides of trapezoids in geometry are not required to be symmetric.
The non-central moments of the trapezoidal distribution are
Special cases of the trapezoidal distribution include the uniform distribution (with and ) and the triangular distribution (with ). Trapezoidal probability distributions seem to not be discussed very often in the literature. The uniform, triangular, Irwin-Hall, Bates, Poisson, normal, bimodal, and multimodal distributions are all more frequently discussed in the literature. This may be because these other (non-trapezoidal) distributions seem to occur more frequently in nature than the trapezoidal distribution does. The normal distribution in particular is especially common in nature, just as one would expect from the central limit theorem.
See also
Trapezoid
Probability distribution
Central limit theorem
Uniform distribution (continuous)
Triangular distribution
Irwin–Hall distribution
Bates distribution
Normal distribution
Multimodal distribution
Poisson distribution
References
Continuous distributions |
https://en.wikipedia.org/wiki/Jim%20Cooke | Jim Cooke is a retired science teacher from Dublin, Ireland. He taught primarily physics, but also maths, science and applied maths.
He was educated at Synge Street CBS, and taught there for nearly 40 years. During his time there, he achieved unrivalled acclaim for his mentoring of students through the Young Scientist competition including two overall winners and three 2nd places. He also mentored Abdusalam Abubakar to a First in Mathematics at the European Union Contest for Young Scientists in 2007.
In 2009 he mentored his student Andrei Triffio to winning the Intel Student Award in Physics, Chemistry and Mathematics at the Young Scientists Exhibition. The prize for the award was an all-expenses paid trip to Intel International Science and Engineering Fair in Nevada to represent Ireland in the event, where he was placed third in the world overall.
Cooke retired from teaching in 2009.
Awards
2012 - European Union Special Recognition of Achievement for Inspiring Students in Science
2009 - Engineers Ireland Annual Award for Science, Engineering and Technology Awareness
2005 - Victor W Graham Perpetual Trophy Winner for outstanding achievement in Applied Mathematics
References
Irish educators
Staff of Synge Street school
Young Scientist and Technology Exhibition
20th-century births
Living people
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Ferdinand%20Rudio | Ferdinand Rudio (born 2 August 1856 in Wiesbaden, died 21 June 1929 in Zurich) was a German and Swiss mathematician and historian of mathematics.
Education and career
Rudio's father and maternal grandfather were both public officials in the independent Duchy of Nassau, which was annexed by Prussia when Rudio was 10. He was educated at the local gymnasium and Realgymnasium in Wiesbaden, and then in 1874 began studying at ETH Zurich, then known as the Eidgenössische Polytechnikum Zürich. His initial courses in Zurich were in civil engineering, but in his second year (under the influence of Karl Geiser) he switched to mathematics and physics. Finishing at Zurich in 1877, he went on to graduate studies at the University of Berlin from 1877 to 1880, earning his Ph.D. under the joint supervision of Ernst Kummer and Karl Weierstrass.
Next, Rudio returned to ETH Zurich, earning his habilitation in 1881 and becoming at that time a privatdozent. He became an extraordinary professor at Zurich in 1885, and a full professor in 1889.
Rudio was one of the organizers of the first International Congress of Mathematicians (ICM) in 1897. He served as General Secretary of the congress, and as editor of the proceedings of the congress. He was the editor of the quarterly journal of the Zürich Natural Sciences Society from 1893 until 1912, and was also president of the society.
In 1919, the University of Zurich gave Rudio an honorary doctorate. By 1928, he was in poor health, and retired from his position at Zurich. He died a year later.
Contributions
Rudio's research ranged over group theory, abstract algebra, and geometry. His
thesis research concerned the use of differential equations to characterize surface by the properties of their sets of centers of curvature, and he was also known for the first proof of convergence of Viète's infinite product for π. He also authored the textbook Die Elemente Der Analytischen Geometrie, in analytic geometry, published in 1908.
Beginning in 1883, with a speech Rudio gave at a celebration of the centennial of Leonhard Euler's death, Rudio became interested in Euler's life and works. At the first ICM and again at a celebration in 1907 of Euler's 200th birthday, Rudio urged the compilation of a set of Euler's complete works. In 1909 the Swiss Society of Natural Sciences took up the project and appointed Rudio as editor. He finished two volumes of this project, and assisted in the editing of the next three. He gave a talk Mitteilungen über die Eulerausgabe (news about the Euler edition) at the fifth ICM in Cambridge, England in August 1912. By the time he retired as general editor of the series in 1928, 20 volumes of the series had been published of what would eventually be over 80 volumes.
Other work in the history of mathematics by Rudio included the book Der Bericht des Simplicius über die Quadraturen des Antiphon und des Hippokrates (1902) on the ancient problem of squaring the circle, and a collection of biographies of mat |
https://en.wikipedia.org/wiki/Notre%20Dame%20Journal%20of%20Formal%20Logic | The Notre Dame Journal of Formal Logic is a quarterly peer-reviewed scientific journal covering the foundations of mathematics and related fields of mathematical logic, as well as philosophy of mathematics. It was established in 1960 and is published by Duke University Press on behalf of the University of Notre Dame. The editors-in-chief are Curtis Franks and Anand Pillay (University of Notre Dame).
Abstracting and indexing
The journal is abstracted and indexed in:
According to the Journal Citation Reports, the journal has a 2012 impact factor of 0.431.
References
External links
Journal page at Notre Dame University
Journal page at Project Euclid
Mathematical logic
Mathematics journals
Logic journals
Philosophy of mathematics literature
Duke University Press academic journals
Quarterly journals
Academic journals established in 1960
University of Notre Dame academic journals |
https://en.wikipedia.org/wiki/Point%20process%20notation | In probability and statistics, point process notation comprises the range of mathematical notation used to symbolically represent random objects known as point processes, which are used in related fields such as stochastic geometry, spatial statistics and continuum percolation theory and frequently serve as mathematical models of random phenomena, representable as points, in time, space or both.
The notation varies due to the histories of certain mathematical fields and the different interpretations of point processes, and borrows notation from mathematical areas of study such as measure theory and set theory.
Interpretation of point processes
The notation, as well as the terminology, of point processes depends on their setting and interpretation as mathematical objects which under certain assumptions can be interpreted as random sequences of points, random sets of points or random counting measures.
Random sequences of points
In some mathematical frameworks, a given point process may be considered as a sequence of points with each point randomly positioned in d-dimensional Euclidean space Rd as well as some other more abstract mathematical spaces. In general, whether or not a random sequence is equivalent to the other interpretations of a point process depends on the underlying mathematical space, but this holds true for the setting of finite-dimensional Euclidean space Rd.
Random set of points
A point process is called simple if no two (or more points) coincide in location with probability one. Given that often point processes are simple and the order of the points does not matter, a collection of random points can be considered as a random set of points The theory of random sets was independently developed by David Kendall and Georges Matheron. In terms of being considered as a random set, a sequence of random points is a random closed set if the sequence has no accumulation points with probability one
A point process is often denoted by a single letter, for example , and if the point process is considered as a random set, then the corresponding notation:
is used to denote that a random point is an element of (or belongs to) the point process . The theory of random sets can be applied to point processes owing to this interpretation, which alongside the random sequence interpretation has resulted in a point process being written as:
which highlights its interpretation as either a random sequence or random closed set of points. Furthermore, sometimes an uppercase letter denotes the point process, while a lowercase denotes a point from the process, so, for example, the point (or ) belongs to or is a point of the point process , or with set notation, .
Random measures
To denote the number of points of located in some Borel set , it is sometimes written
where is a random variable and is a counting measure, which gives the number of points in some set. In this mathematical expression the point process is denoted by:
.
On |
https://en.wikipedia.org/wiki/One%20in%20ten%20rule | In statistics, the one in ten rule is a rule of thumb for how many predictor parameters can be estimated from data when doing regression analysis (in particular proportional hazards models in survival analysis and logistic regression) while keeping the risk of overfitting and finding spurious correlations low. The rule states that one predictive variable can be studied for every ten events. For logistic regression the number of events is given by the size of the smallest of the outcome categories, and for survival analysis it is given by the number of uncensored events.
For example, if a sample of 200 patients is studied and 20 patients die during the study (so that 180 patients survive), the one in ten rule implies that two pre-specified predictors can reliably be fitted to the total data. Similarly, if 100 patients die during the study (so that 100 patients survive), ten pre-specified predictors can be fitted reliably. If more are fitted, the rule implies that overfitting is likely and the results will not predict well outside the training data. It is not uncommon to see the 1:10 rule violated in fields with many variables (e.g. gene expression studies in cancer), decreasing the confidence in reported findings.
Improvements
A "one in 20 rule" has been suggested, indicating the need for shrinkage of regression coefficients, and a "one in 50 rule" for stepwise selection with the default p-value of 5%. Other studies, however, show that the one in ten rule may be too conservative as a general recommendation and that five to nine events per predictor can be enough, depending on the research question.
More recently, a study has shown that the ratio of events per predictive variable is not a reliable statistic for estimating the minimum number of events for estimating a logistic prediction model. Instead, the number of predictor variables, the total sample size (events + non-events) and the events fraction (events / total sample size) can be used to calculate the expected prediction error of the model that is to be developed. One can then estimate the required sample size to achieve an expected prediction error that is smaller than a predetermined allowable prediction error value.
Alternatively, three requirements for prediction model estimation have been suggested: the model should have a global shrinkage factor of ≥ .9, an absolute difference of ≤ .05 in the model's apparent and adjusted Nagelkerke R2, and a precise estimation of the overall risk or rate in the target population. The necessary sample size and number of events for model development are then given by the values that meet these requirements.
Literature
David A. Freedman (1983) A Note on Screening Regression Equations, The American Statistician, 37:2, 152-155,
References
Rules of thumb
Regression variable selection |
https://en.wikipedia.org/wiki/Point%20process%20operation | In probability and statistics, a point process operation or point process transformation is a type of mathematical operation performed on a random object known as a point process, which are often used as mathematical models of phenomena that can be represented as points randomly located in space. These operations can be purely random, deterministic or both, and are used to construct new point processes, which can be then also used as mathematical models. The operations may include removing or thinning points from a point process, combining or superimposing multiple point processes into one point process or transforming the underlying space of the point process into another space. Point process operations and the resulting point processes are used in the theory of point processes and related fields such as stochastic geometry and spatial statistics.
One point process that gives particularly convenient results under random point process operations is the Poisson point process, The Poisson point process often exhibits a type of mathematical closure such that when a point process operation is applied to some Poisson point process, then provided some conditions on the point process operation, the resulting process will be often another Poisson point process operation, hence it is often used as a mathematical model.
Point process operations have been studied in the mathematical limit as the number of random point process operations applied approaches infinity. This had led to convergence theorems of point process operations, which have their origins in the pioneering work of Conny Palm in 1940s and later Aleksandr Khinchin in the 1950s and 1960s who both studied point processes on the real line, in the context of studying the arrival of phone calls and queueing theory in general. Provided that the original point process and the point process operation meet certain mathematical conditions, then as point process operations are applied to the process, then often the resulting point process will behave stochastically more like a Poisson point process if it has a non-random mean measure, which gives the average number of points of the point process located in some region. In other words, in the limit as the number of operations applied approaches infinity, the point process will converge in distribution (or weakly) to a Poisson point process or, if its measure is a random measure, to a Cox point process. Convergence results, such as the Palm-Khinchin theorem for renewal processes, are then also used to justify the use of the Poisson point process as a mathematical of various phenomena.
Point process notation
Point processes are mathematical objects that can be used to represent collections of points randomly scattered on some underlying mathematical space. They have a number of interpretations, which is reflected by the various types of point process notation. For example, if a point belongs to or is a member of a point process, denoted by , then t |
https://en.wikipedia.org/wiki/UMBC%20College%20of%20Natural%20and%20Mathematical%20Sciences | The University of Maryland, Baltimore County College of Natural and Mathematical Sciences focuses in the areas of life science, including Biology, Chemistry, Biochemistry, Mathematics, Statistics, Marine Biology, and Physics.
Departments
Biological Sciences
Chemistry and Biochemistry
Mathematics and Statistics
Marine Biotechnology
Physics
Centers and Institutes
Center for Space Science and Technology (CSST)
Institute of Fluorescence
Joint Center for Earth Systems Technology (JCET)
Goddard Earth Sciences and Technology Center (GEST)
Center for Advanced Study of Photonics Research (CASPR)
Joint Center for Astrophysics (JCA)
References
External links
College of Natural and Mathematical Sciences Homepage
Departmental Directory
University of Maryland, Baltimore County Homepage
College of Natural and Mathematical Sciences
Natural and Mathematical Sciences
Educational institutions established in 1966 |
https://en.wikipedia.org/wiki/Homotopy%20excision%20theorem | In algebraic topology, the homotopy excision theorem offers a substitute for the absence of excision in homotopy theory. More precisely, let be an excisive triad with nonempty, and suppose the pair is ()-connected, , and the pair is ()-connected, . Then the map induced by the inclusion ,
,
is bijective for and is surjective for .
A geometric proof is given in a book by Tammo tom Dieck.
This result should also be seen as a consequence of the most general form of the Blakers–Massey theorem, which deals with the non-simply-connected case.
The most important consequence is the Freudenthal suspension theorem.
References
Bibliography
J. Peter May, A Concise Course in Algebraic Topology, Chicago University Press.
Theorems in homotopy theory |
https://en.wikipedia.org/wiki/Complex-oriented%20cohomology%20theory | In algebraic topology, a complex-orientable cohomology theory is a multiplicative cohomology theory E such that the restriction map is surjective. An element of that restricts to the canonical generator of the reduced theory is called a complex orientation. The notion is central to Quillen's work relating cohomology to formal group laws.
If E is an even-graded theory meaning , then E is complex-orientable. This follows from the Atiyah–Hirzebruch spectral sequence.
Examples:
An ordinary cohomology with any coefficient ring R is complex orientable, as .
Complex K-theory, denoted KU, is complex-orientable, as it is even-graded. (Bott periodicity theorem)
Complex cobordism, whose spectrum is denoted by MU, is complex-orientable.
A complex orientation, call it t, gives rise to a formal group law as follows: let m be the multiplication
where denotes a line passing through x in the underlying vector space of . This is the map classifying the tensor product of the universal line bundle over . Viewing
,
let be the pullback of t along m. It lives in
and one can show, using properties of the tensor product of line bundles, it is a formal group law (e.g., satisfies associativity).
See also
Chromatic homotopy theory
References
M. Hopkins, Complex oriented cohomology theory and the language of stacks
J. Lurie, Chromatic Homotopy Theory (252x)
Algebraic topology
Cohomology theories |
https://en.wikipedia.org/wiki/Homotopy%20colimit%20and%20limit | In mathematics, especially in algebraic topology, the homotopy limit and colimitpg 52 are variants of the notions of limit and colimit extended to the homotopy category . The main idea is this: if we have a diagramconsidered as an object in the homotopy category of diagrams , (where the homotopy equivalence of diagrams is considered pointwise), then the homotopy limit and colimits then correspond to the cone and coconewhich are objects in the homotopy category , where is the category with one object and one morphism. Note this category is equivalent to the standard homotopy category since the latter homotopy functor category has functors which picks out an object in and a natural transformation corresponds to a continuous function of topological spaces. Note this construction can be generalized to model categories, which give techniques for constructing homotopy limits and colimits in terms of other homotopy categories, such as derived categories. Another perspective formalizing these kinds of constructions are derivatorspg 193 which are a new framework for homotopical algebra.
Introductory examples
Homotopy pushout
The concept of homotopy colimitpg 4-8 is a generalization of homotopy pushouts, such as the mapping cylinder used to define a cofibration. This notion is motivated by the following observation: the (ordinary) pushout
is the space obtained by contracting the n-1-sphere (which is the boundary of the n-dimensional disk) to a single point. This space is homeomorphic to the n-sphere Sn. On the other hand, the pushout
is a point. Therefore, even though the (contractible) disk Dn was replaced by a point, (which is homotopy equivalent to the disk), the two pushouts are not homotopy (or weakly) equivalent.
Therefore, the pushout is not well-aligned with a principle of homotopy theory, which considers weakly equivalent spaces as carrying the same information: if one (or more) of the spaces used to form the pushout is replaced by a weakly equivalent space, the pushout is not guaranteed to stay weakly equivalent. The homotopy pushout rectifies this defect.
The homotopy pushout of two maps of topological spaces is defined as
,
i.e., instead of glueing B in both A and C, two copies of a cylinder on B are glued together and their ends are glued to A and C.
For example, the homotopy colimit of the diagram (whose maps are projections)
is the join .
It can be shown that the homotopy pushout does not share the defect of the ordinary pushout: replacing A, B and / or C by a homotopic space, the homotopy pushout will also be homotopic. In this sense, the homotopy pushouts treats homotopic spaces as well as the (ordinary) pushout does with homeomorphic spaces.
Composition of maps
Another useful and motivating examples of a homotopy colimit is constructing models for the homotopy colimit of the diagramof topological spaces. There are a number of ways to model this colimit: the first is to consider the spacewhere is the equivalence relation |
https://en.wikipedia.org/wiki/Bousfield%20localization | In category theory, a branch of mathematics, a (left) Bousfield localization of a model category replaces the model structure with another model structure with the same cofibrations but with more weak equivalences.
Bousfield localization is named after Aldridge Bousfield, who first introduced this technique in the context of localization of topological spaces and spectra.
Model category structure of the Bousfield localization
Given a class C of morphisms in a model category M the left Bousfield localization is a new model structure on the same category as before. Its equivalences, cofibrations and fibrations, respectively, are
the C-local equivalences
the original cofibrations of M
and (necessarily, since cofibrations and weak equivalences determine the fibrations)
the maps having the right lifting property with respect to the cofibrations in M which are also C-local equivalences.
In this definition, a C-local equivalence is a map which, roughly speaking, does not make a difference when mapping to a C-local object. More precisely, is required to be a weak equivalence (of simplicial sets) for any C-local object W. An object W is called C-local if it is fibrant (in M) and
is a weak equivalence for all maps in C. The notation is, for a general model category (not necessarily enriched over simplicial sets) a certain simplicial set whose set of path components agrees with morphisms in the homotopy category of M:
If M is a simplicial model category (such as, say, simplicial sets or topological spaces), then "map" above can be taken to be the derived simplicial mapping space of M.
This description does not make any claim about the existence of this model structure, for which see below.
Dually, there is a notion of right Bousfield localization, whose definition is obtained by replacing cofibrations by fibrations (and reversing directions of all arrows).
Existence
The left Bousfield localization model structure, as described above, is known to exist in various situations, provided that C is a set:
M is left proper (i.e., the pushout of a weak equivalence along a cofibration is again a weak equivalence) and combinatorial
M is left proper and cellular.
Combinatoriality and cellularity of a model category guarantee, in particular, a strong control over the cofibrations of M.
Similarly, the right Bousfield localization exists if M is right proper and cellular or combinatorial and C is a set.
Universal property
The localization of an (ordinary) category C with respect to a class W of morphisms satisfies the following universal property:
There is a functor which sends all morphisms in W to isomorphisms.
Any functor that sends W to isomorphisms in D factors uniquely over the previously mentioned functor.
The Bousfield localization is the appropriate analogous notion for model categories, keeping in mind that isomorphisms in ordinary category theory are replaced by weak equivalences. That is, the (left) Bousfield localization is such tha |
https://en.wikipedia.org/wiki/List%20of%20European%20Union%20regions%20by%20GDP | This is a list of European Union regions (NUTS2 regions) sorted by their gross domestic product (GDP). Eurostat calculates the GDP based on the information provided by national statistics institutes affiliated to Eurostat.
The list presents statistics for 2021 from Eurostat, . The figures are in millions of nominal euros, purchasing power standards and purchasing power standard per capita.
2021 list
See also
Economy of the European Union
List of EU metropolitan areas by GDP
List of NUTS regions in the European Union by GDP
References
Sources
Eurostat news release, retrieved 18 March 2018
External links
Press release: Regional GDP per capita in the EU in 2010
Press release: Twenty-one regions below half of the EU average……and five regions over double the average
Economy of Europe-related lists |
https://en.wikipedia.org/wiki/List%20of%20Azerbaijani%20inventions%20and%20discoveries | Azerbaijani inventions and discoveries are inventions and discoveries by Azerbaijani scientists and researchers, both locally and while working at overseas research institutes.
Science
Mathematics
Fuzzy Logic. Lutfali Aliaskerzadeh (1965).
Physics
Gas Laser. Ali Javan (1960)
Astronomy
Topographic map of Mars. Nadir Ibrahimov (1971)
Asteroid belt theory. Hajibey Sultanov
Biology
Buffalo breeding. Aghakhan Aghabeyli (1932)
Medicine
Analgesic. Mustafa Topchubashov (1938).
Plague of Jusitinian vaccine. Latif Valiyev (1934)
Oil industry
Oil in Russia. Farman Salmanov (1961).
Oil in India. Eyyub Taghiyev (1958)
Oil in Brazil. Eyyub Taghiyev (1961)
Offshore oil platform. Agha Aliyev (1949)
Weapons
Molotov cocktail. Yusif Mammadaliyev (1939-1940)
S-300 (Favorit). Igor Ashurbeyli
S-400 (Triumf). Igor Ashurbeyli
Tectonic weapon. Ikram Karimov (1970)
F-1 (nuclear reactor). Abbas Chaykhorski (1946)
Istiglal – a recoil-operated, semi-automatic anti-material sniper rifle.
Yalguzag – a bolt-action sniper rifle that fires the 7.62×51mm NATO round used by the Azerbaijani Land Forces.
Art
Shabaka (window) – stained glass windows made by national Azerbaijani masters, without glue or nails.
Folk music
Ashiqs of Azerbaijan
Jazz-Mugham. Vagif Mustafazadeh (1960).
Meykhana – literary and folk rap tradition, consisting of an unaccompanied song performed by one or more people improvising on a particular subject.
Mugham – folk musical composition from Azerbaijan.
Musical Instruments
Balaban – a cylindrical-bore, double-reed wind instrument.
Nagara (drum) – folk drum with double head that is played on one side with the bare hands.
Tar – Mirza Sadig (1870).
Language and literature
Persian sign language. Jabbar Asgarzadeh.
School for Muslim girls. Zeynalabdin Taghiyev (1904)
Foods
Dovga
Doymenj
Dushbara – a sort of dumplings of dough filled with ground meat and flavor.
Qutab – a thinly rolled dough that may be cooked briefly on a convex griddle.
Shekarbura – Azerbaijani dessert. There are still several of deserts and popular foods of Azerbaijan.
References
Azerbaijani
Azer
Inventions and discoveries |
https://en.wikipedia.org/wiki/Derived%20scheme | In algebraic geometry, a derived scheme is a pair consisting of a topological space X and a sheaf either of simplicial commutative rings or of commutative ring spectra on X such that (1) the pair is a scheme and (2) is a quasi-coherent -module. The notion gives a homotopy-theoretic generalization of a scheme.
A derived stack is a stacky generalization of a derived scheme.
Differential graded scheme
Over a field of characteristic zero, the theory is closely related to that of a differential graded scheme. By definition, a differential graded scheme is obtained by gluing affine differential graded schemes, with respect to étale topology. It was introduced by Maxim Kontsevich "as the first approach to derived algebraic geometry." and was developed further by Mikhail Kapranov and Ionut Ciocan-Fontanine.
Connection with differential graded rings and examples
Just as affine algebraic geometry is equivalent (in categorical sense) to the theory of commutative rings (commonly called commutative algebra), affine derived algebraic geometry over characteristic zero is equivalent to the theory of commutative differential graded rings. One of the main example of derived schemes comes from the derived intersection of subschemes of a scheme, giving the Koszul complex. For example, let , then we can get a derived scheme
where
is the étale spectrum. Since we can construct a resolution
the derived ring is the koszul complex . The truncation of this derived scheme to amplitude provides a classical model motivating derived algebraic geometry. Notice that if we have a projective scheme
where we can construct the derived scheme where
with amplitude
Cotangent complex
Construction
Let be a fixed differential graded algebra defined over a field of characteristic . Then a -differential graded algebra is called semi-free if the following conditions hold:
The underlying graded algebra is a polynomial algebra over , meaning it is isomorphic to
There exists a filtration on the indexing set where and for any .
It turns out that every differential graded algebra admits a surjective quasi-isomorphism from a semi-free differential graded algebra, called a semi-free resolution. These are unique up to homotopy equivalence in a suitable model category. The (relative) cotangent complex of an -differential graded algebra can be constructed using a semi-free resolution : it is defined as
Many examples can be constructed by taking the algebra representing a variety over a field of characteristic 0, finding a presentation of as a quotient of a polynomial algebra and taking the Koszul complex associated to this presentation. The Koszul complex acts as a semi-free resolution of the differential graded algebra where is the graded algebra with the non-trivial graded piece in degree 0.
Examples
The cotangent complex of a hypersurface can easily be computed: since we have the dga representing the derived enhancement of , we can compute the cotangent comp |
https://en.wikipedia.org/wiki/Commutative%20ring%20spectrum | In the mathematical field of algebraic topology, a commutative ring spectrum, roughly equivalent to a -ring spectrum, is a commutative monoid in a good category of spectra.
The category of commutative ring spectra over the field of rational numbers is Quillen equivalent to the category of differential graded algebras over .
Example: The Witten genus may be realized as a morphism of commutative ring spectra MString →tmf.
See also: simplicial commutative ring, highly structured ring spectrum and derived scheme.
Terminology
Almost all reasonable categories of commutative ring spectra can be shown to be Quillen equivalent to each other. Thus, from the point view of the stable homotopy theory, the term "commutative ring spectrum" may be used as a synonymous to an -ring spectrum.
Notes
References
Algebraic topology |
https://en.wikipedia.org/wiki/Derived%20algebraic%20geometry | Derived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local charts, are replaced by either differential graded algebras (over ), simplicial commutative rings or -ring spectra from algebraic topology, whose higher homotopy groups account for the non-discreteness (e.g., Tor) of the structure sheaf. Grothendieck's scheme theory allows the structure sheaf to carry nilpotent elements. Derived algebraic geometry can be thought of as an extension of this idea, and provides natural settings for intersection theory (or motivic homotopy theory) of singular algebraic varieties and cotangent complexes in deformation theory (cf. J. Francis), among the other applications.
Introduction
Basic objects of study in the field are derived schemes and derived stacks. The oft-cited motivation is Serre's intersection formula. In the usual formulation, the formula involves the Tor functor and thus, unless higher Tor vanish, the scheme-theoretic intersection (i.e., fiber product of immersions) does not yield the correct intersection number. In the derived context, one takes the derived tensor product , whose higher homotopy is higher Tor, whose Spec is not a scheme but a derived scheme. Hence, the "derived" fiber product yields the correct intersection number. (Currently this is hypothetical; the derived intersection theory has yet to be developed.)
The term "derived" is used in the same way as derived functor or derived category, in the sense that the category of commutative rings is being replaced with a ∞-category of "derived rings." In classical algebraic geometry, the derived category of quasi-coherent sheaves is viewed as a triangulated category, but it has natural enhancement to a stable ∞-category, which can be thought of as the ∞-categorical analogue of an abelian category.
Definitions
Derived algebraic geometry is fundamentally the study of geometric objects using homological algebra and homotopy. Since objects in this field should encode the homological and homotopy information, there are various notions of what derived spaces encapsulate. The basic objects of study in derived algebraic geometry are derived schemes, and more generally, derived stacks. Heuristically, derived schemes should be functors from some category of derived rings to the category of sets
which can be generalized further to have targets of higher groupoids (which are expected to be modelled by homotopy types). These derived stacks are suitable functors of the form
Many authors model such functors as functors with values in simplicial sets, since they model homotopy types and are well-studied. Differing definitions on these derived spaces depend on a choice of what the derived rings are, and what the homotopy types should look like. Some examples of derived rings include commutative differential graded algebras, simplicial rings, and -rings.
Derived geometry over characteristic 0
Over characte |
https://en.wikipedia.org/wiki/Ditrigonal%20polyhedron | In geometry, there are seven uniform and uniform dual polyhedra named as ditrigonal.
Ditrigonal vertex figures
There are five uniform ditrigonal polyhedra, all with icosahedral symmetry.
The three uniform star polyhedron with Wythoff symbol of the form 3 | p q or | p q are ditrigonal, at least if p and q are not 2. Each polyhedron includes two types of faces, being of triangles, pentagons, or pentagrams. Their vertex configurations are of the form p.q.p.q.p.q or (p.q)3 with a symmetry of order 3. Here, term ditrigonal refers to a hexagon having a symmetry of order 3 (triangular symmetry) acting with 2 rotational orbits on the 6 angles of the vertex figure (the word ditrigonal means "having two sets of 3 angles").
Other uniform ditrigonal polyhedra
The small ditrigonal dodecicosidodecahedron and the great ditrigonal dodecicosidodecahedron are also uniform.
Their duals are respectively the small ditrigonal dodecacronic hexecontahedron and great ditrigonal dodecacronic hexecontahedron.
See also
Small complex icosidodecahedron
Great complex icosidodecahedron
References
Notes
Bibliography
Coxeter, H.S.M., M.S. Longuet-Higgins and J.C.P Miller, Uniform Polyhedra, Phil. Trans. 246 A (1954) pp. 401–450.
Har'El, Z. Uniform Solution for Uniform Polyhedra., Geometriae Dedicata 47, 57–110, 1993. Zvi Har’El, Kaleido software, Images, dual images
Further reading
Johnson, N.; The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
Polyhedra |
https://en.wikipedia.org/wiki/Mike%20Bukta | Mike Bukta (born June 1, 1967) is a Canadian former ice hockey player who played two seasons in the ECHL for the Nashville Knights.
Career statistics
References
External links
1967 births
Living people
Canadian ice hockey defencemen
Calgary Wranglers (WHL) players
Seattle Breakers players
Seattle Thunderbirds players
Saskatoon Blades players
Nashville Knights players
Ice hockey people from Calgary |
https://en.wikipedia.org/wiki/Rytz%27s%20construction | The Rytz’s axis construction is a basic method of descriptive geometry to find the axes, the semi-major axis and semi-minor axis and the vertices of an ellipse, starting from two conjugated half-diameters. If the center and the semi axis of an ellipse are determined the ellipse can be drawn using an ellipsograph or by hand (see ellipse).
Rytz’s construction is a classical construction of Euclidean geometry, in which only compass and ruler are allowed as aids. The design is named after its inventor David Rytz of Brugg (1801–1868).
Conjugate diameters appear always if a circle or an ellipse is projected parallelly (the rays are parallel) as images of orthogonal diameters of a circle (see second diagram) or as images of the axes of an ellipse. An essential property of two conjugate diameters is: The tangents at the ellipse points of one diameter are parallel to the second diameter (see second diagram).
Problem statement and solution
The parallel projection (skew or orthographic) of a circle that is in general an ellipse (the special case of a line segment as image is omitted). A fundamental task in descriptive geometry is to draw such an image of a circle. The diagram shows a military projection of a cube with 3 circles on 3 faces of the cube. The image plane for a military projection is horizontal. That means the circle on the top appears in its true shape (as circle). The images of the circles at the other two faces are obviously ellipses with unknown axes. But one recognizes in any case the images of two orthogonal diameters of the circles. These diameters of the ellipses are no more orthogonal but as images of orthogonal diameters of the circle they are conjugate (the tangents at the end points of one diameter are parallel to the other diameter !). This is a standard situation in descriptive geometry:
From an ellipse the center and two points on two conjugate diameters are known.
Task: find the axes and semi-axes of the ellipse.
Steps of the construction
(1) rotate point around by 90°.
(2) Determine the center of the line segment .
(3) Draw the line and the circle with center through . Intersect the circle and the line. The intersection points are .
(4) The lines and are the of the ellipse.
(5) The line segment can be considered as a paperstrip of length (see ellipse) generating point . Hence and are the . (If then is the semi- axis.)
(6) The vertices and co-vertices are known and the ellipse can be drawn by one of the drawing methods.
If one performs a left turn of point , then the configuration shows the 2nd paper strip method (see second diagram in next section) and and is still true.
Proof of the statement
The standard proof is performed geometrically. An alternative proof uses analytic geometry:
The proof is done, if one is able to show that
the intersection points of the line with the axes of the ellipse lie on the circle through with center , hence and , and
Proof
(1): Any ellipse can be represented |
https://en.wikipedia.org/wiki/Simplicial%20commutative%20ring | In algebra, a simplicial commutative ring is a commutative monoid in the category of simplicial abelian groups, or, equivalently, a simplicial object in the category of commutative rings. If A is a simplicial commutative ring, then it can be shown that is a ring and are modules over that ring (in fact, is a graded ring over .)
A topology-counterpart of this notion is a commutative ring spectrum.
Examples
The ring of polynomial differential forms on simplexes.
Graded ring structure
Let A be a simplicial commutative ring. Then the ring structure of A gives the structure of a graded-commutative graded ring as follows.
By the Dold–Kan correspondence, is the homology of the chain complex corresponding to A; in particular, it is a graded abelian group. Next, to multiply two elements, writing for the simplicial circle, let be two maps. Then the composition
,
the second map the multiplication of A, induces . This in turn gives an element in . We have thus defined the graded multiplication . It is associative because the smash product is. It is graded-commutative (i.e., ) since the involution introduces a minus sign.
If M is a simplicial module over A (that is, M is a simplicial abelian group with an action of A), then the similar argument shows that has the structure of a graded module over (cf. Module spectrum).
Spec
By definition, the category of affine derived schemes is the opposite category of the category of simplicial commutative rings; an object corresponding to A will be denoted by .
See also
E_n-ring
References
What is a simplicial commutative ring from the point of view of homotopy theory?
What facts in commutative algebra fail miserably for simplicial commutative rings, even up to homotopy?
Reference request - CDGA vs. sAlg in char. 0
A. Mathew, Simplicial commutative rings, I.
B. Toën, Simplicial presheaves and derived algebraic geometry
P. Goerss and K. Schemmerhorn, Model categories and simplicial methods
Commutative algebra
Ring theory
Algebraic structures |
https://en.wikipedia.org/wiki/Sheaf%20of%20spectra | In algebraic topology, a presheaf of spectra on a topological space X is a contravariant functor from the category of open subsets of X, where morphisms are inclusions, to the good category of commutative ring spectra. A theorem of Jardine says that such presheaves form a simplicial model category, where F →G is a weak equivalence if the induced map of homotopy sheaves is an isomorphism. A sheaf of spectra is then a fibrant/cofibrant object in that category.
The notion is used to define, for example, a derived scheme in algebraic geometry.
References
External links
Algebraic topology |
https://en.wikipedia.org/wiki/EMF%20EURO | The EMF EURO is the main small-sided football competition for men's national teams, governed by the European Minifootball Federation. The tournament is six-a-side.
Results
Statistics
Performance by nations
Medal count
Participation details
GS - Group Stage
KS - Knockout Stage
QF - Quarterfinals
See also
WMF World Cup
References
External links
EMF EURO 2022
Minifootball competitions
European championships in association football
2010 establishments in Europe
Recurring sporting events established in 2010 |
https://en.wikipedia.org/wiki/Symmetric%20spectrum | In algebraic topology, a symmetric spectrum X is a spectrum of pointed simplicial sets that comes with an action of the symmetric group on such that the composition of structure maps
is equivariant with respect to . A morphism between symmetric spectra is a morphism of spectra that is equivariant with respect to the actions of symmetric groups.
The technical advantage of the category of symmetric spectra is that it has a closed symmetric monoidal structure (with respect to smash product). It is also a simplicial model category. A symmetric ring spectrum is a monoid in ; if the monoid is commutative, it's a commutative ring spectrum. The possibility of this definition of "ring spectrum" was one of motivations behind the category.
A similar technical goal is also achieved by May's theory of S-modules, a competing theory.
References
Introduction to symmetric spectra I
M. Hovey, B. Shipley, and J. Smith, “Symmetric spectra”, Journal of the AMS 13 (1999), no. 1, 149 – 208.
Algebraic topology
Simplicial sets
Symmetry |
https://en.wikipedia.org/wiki/Kenji%20Fukaya | Kenji Fukaya (Japanese: 深谷賢治, Fukaya Kenji) is a Japanese mathematician known for his work in symplectic geometry and Riemannian geometry. His many fundamental contributions to mathematics include the discovery of the Fukaya category. He is a permanent faculty member at the Simons Center for Geometry and Physics and a professor of mathematics at Stony Brook University.
Biography
Fukaya was both an undergraduate and a graduate student in mathematics at the University of Tokyo, receiving his BA in 1981, and his PhD in 1986. In 1987, he joined the University of Tokyo faculty as an associate professor. He then moved to Kyoto University as a full professor in 1994. In 2013, he then moved to the United States in order to join the faculty of the Simons Center for Geometry and Physics at Stony Brook.
The Fukaya category, meaning the category of whose objects are Lagrangian submanifolds of a given symplectic manifold, is named after him, and is intimately related to Floer homology. Other contributions to symplectic geometry include his proof (with Kaoru Ono) of a weak version of the Arnold conjecture and a construction of general Gromov-Witten invariants. His many other mathematical contributions include important theorems in Riemannian geometry and work on physics-related topics such as gauge theory and mirror symmetry.
Fukaya was awarded the Japanese Mathematical Society's Geometry Prize in 1989 and Spring Prize in 1994. He also received the Inoue Prize in 2002, the Japan Academy Prize in 2003, the Asahi Prize in 2009, and the Fujihara Award in 2012. He has served on the governing board of the Japanese Mathematical Society and on the Mathematical Committee of the Science Council of Japan.
Fukaya was an invited speaker at the 1990 International Congress of Mathematicians in Kyoto, where he gave a talk entitled, Collapsing Riemannian Manifolds and its Applications.
Selected publications
with T. Yamaguchi The fundamental group of almost non negatively curved manifolds, Annals of Mathematics 136, 1992, pp. 253 – 333
with Kaoru Ono Arnold conjecture and Gromov-Witten invariant, Topology, 38, 1999, pp. 933–1048
with Y. Oh, H. Ohta, K. Ono Lagrangian intersection Floer theory- anomaly and obstruction, 2007
Morse homotopy, -Category, and Floer homologies, in H. J. Kim (editor) Proceedings of Workshop on Geometry and Topology, Seoul National University, 1994, pp. 1 – 102
Floer homology and mirror symmetry. II. Minimal surfaces, geometric analysis and symplectic geometry, Adv. Stud. Pure Math. 34, Math. Soc. Japan, Tokyo, 2002, pp. 31–127
Multivalued Morse theory, asymptotic analysis and mirror symmetry in Graphs and patterns in mathematics and theoretical physics, Proc. Sympos.Pure Math. 73, American Mathematical Society, 2005, pp. 205–278
Editor: Topology, Geometry and Field Theory, World Scientific 1994
Editor: Symplectic geometry and mirror symmetry (Korea Institute for Advanced Study conference, Seoul 2000), World Scientific 2001
Gauge Theory |
https://en.wikipedia.org/wiki/Equation%20%28disambiguation%29 | An equation in mathematics is a formula stating that two expressions have the same value.
Equation may also refer to:
Chemical equation, a symbolic representation of a chemical reaction
Equation of time, the difference between solar time, as shown by a sundial, and mean time, as shown by a clock that runs at constant speed
Equation clock, a clock that contains a mechanism that embodies the equation of time, so the clock shows solar time
Equation of state, a relationship between physical conditions and the state of a material
Equation (band), an English folk band formed in 1996
Equation Group, a computer espionage group
"The Equation", a 2008 episode of Fringe
"[Equation]" (ΔMi−1 = −αΣn=1NDi[n] [Σj∈C[i]Fji[n − 1] + Fexti[n−1]]), the first B-side of "Windowlicker" by Aphex Twin, also known as "[Formula]"
See also
List of equations |
https://en.wikipedia.org/wiki/Abdullah%20Al-Qasabi | Abdullah Mohammed Al-Qasabi (; born 28 April 1986), commonly known as Abdullah Al-Qasabi, is an Omani footballer who plays for Fanja SC in Oman Professional League.
Club career statistics
International career
Abdullah was selected for the national team for the first time in 2012. He made his first appearance for Oman on 8 November 2012 in a friendly match against Estonia. He has represented the national team in the 2014 FIFA World Cup qualification.
Honours
Club
With Fanja
Oman Professional League (0): Runner-up 2012-13, 2013-14
Sultan Qaboos Cup (1): 2013-14
Oman Professional League Cup (1): 2014-15
Oman Super Cup (1): 2012, Runners-up 2013, 2014
References
External links
Abdullah Al-Qasabi at Goal.com
1986 births
Living people
Omani men's footballers
Oman men's international footballers
Men's association football defenders
Fanja SC players
Oman Professional League players |
https://en.wikipedia.org/wiki/%C3%81lex%20Mari%C3%B1elarena | Alejandro Mariñelarena Mutiloa is a former Grand Prix motorcycle racer from Spain. He was forced to retire from racing after a serious crash on Circuit Paul Ricard.
Career statistics
By season
Races by year
(key)
References
External links
1992 births
Living people
Spanish motorcycle racers
Moto2 World Championship riders |
https://en.wikipedia.org/wiki/Grace%20Bates | Grace Elizabeth Bates (13 August 1914 – 19 November 1996) was an American mathematician and one of few women in the United States to be granted a Ph.D. in mathematics in the 1940s. She became an emeritus professor at Mount Holyoke College. Bates specialized in algebra and probability theory, and she co-authored two textbooks: The Real Number System and Modern Algebra, Second Course. Throughout her own education, Bates overcame obstructions to her pursuit of knowledge, opening the way for future women learners.
Early life and education
She was born on 13 August 1914. Interested in mathematics from a very young age, Bates was encouraged to pursue her interest by her family. Bates maintained a close relationship with her brother, reinforced by the early death of their mother. Upon completing high school, her brother used his salary to help her continue her education through high school and college.
During her studies, Bates petitioned several times to take more advanced math courses than were typically available to female students. She attended the Cazenovia Seminary for high school, where she petitioned to take intermediate algebra. She pursued her undergraduate studies at Middlebury College, which was segregated by sex at this time. For her senior year, Bates petitioned to take differential equations, which was only offered to male students. After completing her B.S. in mathematics in 1935, she continued in her studies to obtain a master's degree from Brown University in 1938.
Bates entered her doctoral program at the University of Illinois at Urbana-Champaign in 1944. Initially interested in geometry, Bates instead decided to pursue algebra and work under Reinhold Baer. She completed her doctoral thesis, titled "Free Loops and Nets and their Generalizations", in 1946.
Professional life and continuing education
Bates taught briefly at Sweet Briar College before joining the faculty of Mount Holyoke College. After discussing her interest in probability and statistics with colleague Antoni Zygmund, Zygmund referred her to Jerzy Neyman at the University of California, Berkeley. Consequently, Bates obtained an assistantship at the Berkeley Statistical Laboratory and spend several summers working with Neyman in the 1950s. Together they wrote a number of research articles on probability theory.
Bates advanced to become a full and emeritus professor at Mount Holyoke College and taught until her retirement in 1979. She died on 19 November 1996.
References
1914 births
1996 deaths
20th-century American mathematicians
Brown University alumni
Middlebury College alumni
Mount Holyoke College faculty
American women mathematicians
20th-century women mathematicians
20th-century American women academics
University of Illinois College of Liberal Arts and Sciences alumni |
https://en.wikipedia.org/wiki/Anna%20Lubiw | Anna Lubiw is a computer scientist
known for her work in computational geometry and graph theory. She is currently a professor at the University of Waterloo.
Education
Lubiw received her Ph.D from the University of Toronto in 1986 under the joint supervision of Rudolf Mathon and Stephen Cook.
Research
At Waterloo, Lubiw's students have included both Erik Demaine and his father Martin Demaine, with whom she published the first proof of the fold-and-cut theorem in mathematical origami. In graph drawing, Hutton and Lubiw found a polynomial time algorithm for upward planar drawing of graphs with a single source vertex. Other contributions of Lubiw include proving the NP-completeness of finding permutation patterns, and of finding derangements in permutation groups.
Awards
Lubiw was named an ACM Distinguished Member in 2009.
Personal life
As well her academic work, Lubiw is an amateur violinist, and chairs the volunteer council in charge of the University of Waterloo orchestra. She is married to Jeffrey Shallit, also a computer scientist.
Selected publications
.
. First presented at the 2nd ACM-SIAM Symposium on Discrete Algorithms, 1991.
. First presented at WADS 1993.
.
References
External links
Home page at U. Waterloo
Year of birth missing (living people)
Living people
Canadian computer scientists
Canadian women computer scientists
Researchers in geometric algorithms
Graph drawing people
University of Toronto alumni
Academic staff of the University of Waterloo |
https://en.wikipedia.org/wiki/Crime%20in%20Hong%20Kong | Crime in Hong Kong is present in various forms. The most common crimes are thefts, assaults, vandalism, burglaries, drug offenses, sex trafficking, and triad-related crimes.
Statistics
In the year 2018, crime dropped to a 39-year low for Hong Kong. There were 8,884 reported incidents of violent crimes in Hong Kong at that time. In 2018, Hong Kong had 48 homicides, 4,593 incidents of wounding and serious assaults, 147 robberies, 1,575 burglaries, and 63 rapes. After 2018, crime rate are increasing every year (as of 2023). In the 2000s, the number and rate of murders were the highest in 2002. 2011 had the lowest rate and number of murders, at 17 (0.2 murders per 100,000 people). The homicide rate increased 129.6% in 2013 from 2012 though this was due to the inclusion of 39 deaths from the Lamma Island ferry collision.
The most common forms of crime in Hong Kong are non-violent crimes. There were 27,512 reports of theft in Hong Kong in 2015. The most common forms of theft were miscellaneous thefts, shoplifting, pick-pocketing, and vehicle theft. Criminal damage is also a common crime in Hong Kong, with 5,920 reports in 2015. Fraud and deception has significant increase since 2022. Since late 2022, there are increasing public concern on increasing knife crime and knife attack in the city.
Organised crime
Crimes committed by triads occur in Hong Kong. Common triad-related offenses include extortion, illegal gambling, drug trafficking, and racketeering. One of the world's largest triads, Sun Yee On, was founded in Hong Kong in 1919 and is reported to have 55,000 members worldwide. Sun Yee On's rival organisation, 14K Triad, was formed in Guangzhou, Guangdong, China in 1945, and relocated to Hong Kong in 1949. According to British criminal Colin Blaney in his autobiography Undesirables, British organised crime groups known as the Wide Awake Firm and the Inter City Jibbers that specialise in jewelry thefts and picking pockets have also been known to operate in Hong Kong.
Human trafficking
Hong Kong is a known transit city for human trafficking; victims are often coerced into forced labour or sexual exploitation.
Sex trafficking
Domestic and transnational criminal organizations carry out sex trafficking in Hong Kong. Victims of forced prostitution are often assaulted in brothels, homes, and businesses in the city. Many mainland Chinese prostitutes in Hong Kong are victims of sexual trafficking. There is no comprehensive anti-human trafficking law in Hong Kong.
Racism
There have been reports of systematic racism in Hong Kong against non-Chinese or "dark-skinned" citizens.
Knife attacks
Knife crime and knife attacks in Hong Kong is an issue. In 2022, local media in Hong Kong coined the term "", which can be translated literally as "international knife metropolis", to describe a spike in knife attacks in the city.
Fraud
In 2022, fraud cases rose 45 percent compared to the previous year. The first five months of 2023 saw an almost 60 percen |
https://en.wikipedia.org/wiki/John%20Marshall%20%28jockey%29 | John Marshall (c. 1958 – 23 December 2018) was an Australian jockey from Perth, who was best known for riding Rogan Josh to victory in the 1999 Melbourne Cup.
Career statistics
Career Winners: 2,000
Career Group 1 (G1) Wins: 36
Career Group 2 (G2) Wins: 36
Career Group 3 (G3) Wins: 30
Career Listed (LR) Wins: 68
Total Stakes (Group/Listed) Wins: 170
Marshall won the Sydney Jockey Premiership in the 1987/88 season with 86 wins, beating Jim Cassidy with 65 wins.
He also finished 2nd in the Sydney Jockey's Premiership 3 times:
1982/83 season - 52 wins (won by Ron Quinton: 90 wins),
1986/87 season - 85 1/2 wins (won by Malcolm Johnston: 92 1/2 wins),
1989/90 season - 67 wins (won by Mick Dittman: 75 wins).
Group 1 wins
1982
AJC Oaks (2400m): Sheraco
1983
Epsom Handicap (1600m): Cool River
1984
AJC Derby (2400m): Prolific
Sydney Cup (3200m): Trissaro
1985
Randwick Guineas (1600m): Spirit Of Kingston
Rosehill Guineas (2000m): Spirit Of Kingston
1986
Doomben 10,000 (1350m): Between Ourselves
Toorak Handicap (1600m): Canny Lass
1987
Champagne Stakes (1600m): Sky Chase
Spring Champion Stakes (2000m): Beau Zam
Rosehill Guineas (2000m): Ring Joe
The Galaxy (1100m) Princely Heart
Doomben 10,000 (1350m): Broad Reach
George Main Stakes (1600m) : Campaign King
1988
Rosehill Guineas (2000m): Sky Chase
George Ryder Stakes (1500m): Campaign King
Caulfied Stakes (2000m): Sky Chase
Ranvet Stakes (2000m): Beau Zam
Tancred Stakes (2400m): Beau Zam
AJC Derby (2400m): Beau Zam
Queen Elizabeth Stakes (2000m): Beau Zam
Doomben 10,000 (1350m): Campaign King
Stradbroke Handicap (1400m): Campaign King
1989
Ranvet Stakes (2000m): Beau Zam
AJC Sires Produce Stakes (1400m): Reganza
Queensland Sires Produce Stakes (1400m): Zamoff
Stradbroke Handicap (1400m): Robian Steel
1990
Rosehill Guineas (2000m): Solar Circle
George Main Stakes (1600m): Shaftesbury Avenue
1991
All Aged Stakes (1600m): Shaftesbury Avenue
1996
Coolmore Classic (1500m): Chlorophyll
1997
Ranvet Stakes (2000m): Arkady
1998
AJC Oaks (2400m): On Air
1999
Epsom Handicap (1600m): Allez Suez
Mackinnon Stakes (2000m): Rogan Josh
Melbourne Cup (3200m): Rogan Josh
Marshall died of cancer at age 60 on 23 December 2018.
References
1950s births
2018 deaths
Australian jockeys
Sportspeople from Perth, Western Australia
Deaths from cancer in Western Australia
Year of birth missing |
https://en.wikipedia.org/wiki/Karel%20Hrb%C3%A1%C4%8Dek | Karel Hrbáček (born 1944) is professor emeritus of mathematics at City College of New York. He specializes in mathematical logic, set theory, and non-standard analysis.
Early life and education
Karel studied at Charles University with Petr Vopěnka, looking at large cardinal numbers. He was awarded the degree RNDr. Before his appointment at CCNY he was an exchange fellow at University of California, Berkeley and a research associate at Rockefeller University. In 1980 he received an award from the Mathematical Association of America for his article on Non-standard Set Theory.
Selected publications
1999: (with Thomas Jech) Introduction to Set Theory, Third edition. Monographs and Textbooks in Pure and Applied Mathematics, 220. Marcel Dekker
1992: (with David Ballard) "Standard foundations for nonstandard analysis", Journal of Symbolic Logic 57(2): 741–748
1979: "Nonstandard set theory", American Mathematical Monthly 86(8): 659–677
1978: "Axiomatic foundations for nonstandard analysis", Fundamenta Mathematicae 98(1): 1–19
References
Mathematical logicians
Set theorists
City College of New York faculty
1944 births
Living people |
https://en.wikipedia.org/wiki/Egypt%20national%20football%20team%20all-time%20record | The lists shown below shows the Egypt national football team all-time record against opposing nations. The statistics are composed of all men's A matches only. Olympic games are not included.
All-time records
The following table shows Egypt's all-time international record, correct as of 18 June 2023.
References
Egypt national football team |
https://en.wikipedia.org/wiki/PROSE%20modeling%20language | PROSE was the mathematical 4GL virtual machine that established the holistic modeling paradigm known as Synthetic Calculus (AKA MetaCalculus). A successor to the SLANG/CUE simulation and optimization language developed at TRW Systems, it was introduced in 1974 on Control Data supercomputers. It was the first commercial language to employ automatic differentiation (AD), which was optimized to loop in the instruction-stack of the CDC 6600 CPU.
Although PROSE was a rich block-structured procedural language, its focus was the blending of simultaneous-variable mathematical systems such as:
implicit non-linear equations systems, ordinary differential-equations systems, and multidimensional optimization.
Each of these kinds of system models were distinct and had operator templates to automate and solve them, added to the procedural syntax. These automated system problems were considered "holistic" because their unknowns were simultaneous, and they could not be reduced in formulation to solve piecewise, or by algebra manipulation (e.g. substitution), but had to be solved as wholes. And wholeness also pertained to algorithmic determinacy or mathematical "closure", which made solution convergence possible and certain in principle, if not corrupted by numerical instability.
Holarchies of Differential Propagation
Since these holistic problem models could be independently automated and solved due to this closure, they could be blended into higher wholes by nesting one inside of another, in the manner of subroutines. Users could regard them as if they were ordinary subroutines.
Yet semantically, this mathematical blending was considerably more complex than the mechanics of subroutines because an iterative solution engine was attached to each problem model by its calling operator template above it in the program hierarchy. In its numerical solution process, this engine would take control and would call the problem model subroutine iteratively, not returning to the calling template until its system problem was solved. During some or maybe all of the iterative model-subroutine calls, the engine would invoke automatic differentiation of the formulas in the model holarchy with respect to the model's input-unknowns (arguments) defined in the calling template. Additional mechanisms were performed in the semantics to accommodate ubiquitous nesting of these holistic models.
Differentiation of Prediction Processes
If the nested solution was a prediction (e.g. numerical integration), then its solution algorithm, in addition to the model formulas, would also be automatically differentiated. Since this differentiation propagated (via the chain rule) throughout the integration from initial conditions to boundary conditions, the differentiation of boundary conditions with respect to initial conditions (so called Fréchet derivatives) would be performed. This enabled the routine solution of boundary-value problems by iterative "shooting" methods using Newton-method |
https://en.wikipedia.org/wiki/Svetlana%20Katok | Svetlana Katok (born May 1, 1947) is a Russian-American mathematician and a professor of mathematics at Pennsylvania State University.
Education and career
Katok grew up in Moscow, and earned a master's degree from Moscow State University in 1969; however, due to the anti-Semitic and anti-intelligentsia policies of the time, she was denied admission to the doctoral program there and instead worked for several years in the area of early and secondary mathematical education. She immigrated to the US in 1978,
and earned her doctorate from the University of Maryland, College Park in 1983 under the supervision of Don Zagier. She joined the Pennsylvania State University faculty in 1990.
Katok founded the Electronic Research Announcements of the American Mathematical Society in 1995; it was renamed in 2007 to the Electronic Research Announcements in Mathematical Sciences, and she remains its managing editor.
Katok was an American Mathematical Society (AMS) Council member at large.
Books
Katok is the author of:
Fuchsian Groups, Chicago Lectures in Mathematics, University of Chicago Press, 1992. Russian edition, Faktorial Press, Moscow, 2002.
p-adic Analysis Compared with Real, Student Mathematical Library, vol. 37, American Math. Soc., 2007. Russian edition, MCCME Press, Moscow, 2004.
Additionally, she coedited the book MASS Selecta: Teaching and learning advanced undergraduate mathematics (American Math. Soc., 2003).
Awards and honors
Katok was the 2004 Emmy Noether Lecturer of the Association for Women in Mathematics. In 2012 she and her husband, mathematician Anatole Katok, both became fellows of the American Mathematical Society.
References
1947 births
Living people
20th-century American mathematicians
21st-century American mathematicians
Russian mathematicians
Russian women mathematicians
American women mathematicians
Moscow State University alumni
University of Maryland, College Park alumni
Pennsylvania State University faculty
Fellows of the American Mathematical Society
20th-century women mathematicians
21st-century women mathematicians
20th-century American women
21st-century American women |
https://en.wikipedia.org/wiki/Cocycle%20category | In category theory, a branch of mathematics, the cocycle category of objects X, Y in a model category is a category in which the objects are pairs of maps and the morphisms are obvious commutative diagrams between them. It is denoted by . (It may also be defined using the language of 2-category.)
One has: if the model category is right proper and is such that weak equivalences are closed under finite products,
is bijective.
References
Algebraic topology |
https://en.wikipedia.org/wiki/Nonabelian%20cohomology | In mathematics, a nonabelian cohomology is any cohomology with coefficients in a nonabelian group, a sheaf of nonabelian groups or even in a topological space.
If homology is thought of as the abelianization of homotopy (cf. Hurewicz theorem), then the nonabelian cohomology may be thought of as a dual of homotopy groups.
Nonabelian Poincaré duality
See: Nonabelian Poincare Duality (Lecture 8)
See also
Stacks
Group cohomology
References
Cohomology theories |
https://en.wikipedia.org/wiki/Julia%20F.%20Knight | Julia Frandsen Knight is an American mathematician, specializing in model theory and computability theory. She is the Charles L. Huisking Professor of Mathematics at the University of Notre Dame and director of the graduate program in mathematics there.
Education
Knight did her undergraduate studies at Utah State University, graduating in 1964, and earned her Ph.D. from the University of California, Berkeley in 1972 under the supervision of Robert Lawson Vaught.
Honors and awards
In 2012, she became a fellow of the American Mathematical Society and she was elected to be the 30th president of the Association for Symbolic Logic. She was named MSRI Simons Professor for Fall 2020.
In 2014, Knight held the Gödel Lecture, titled Computable structure theory and formulas of special forms.
References
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
American women mathematicians
Utah State University alumni
University of California, Berkeley alumni
University of Notre Dame faculty
Model theorists
Fellows of the American Mathematical Society
20th-century women mathematicians
21st-century women mathematicians
20th-century American women
21st-century American women |
https://en.wikipedia.org/wiki/Reshetnyak%20gluing%20theorem | In metric geometry, the Reshetnyak gluing theorem gives information on the structure of a geometric object built by using as building blocks other geometric objects, belonging to a well defined class. Intuitively, it states that a manifold obtained by joining (i.e. "gluing") together, in a precisely defined way, other manifolds having a given property inherit that very same property.
The theorem was first stated and proved by Yurii Reshetnyak in 1968.
Statement
Theorem: Let be complete locally compact geodesic metric spaces of CAT curvature , and convex subsets which are isometric. Then the manifold , obtained by gluing all along all , is also of CAT curvature .
For an exposition and a proof of the Reshetnyak Gluing Theorem, see .
Notes
References
, translated in English as:
.
.
Theorems in geometry
Metric geometry |
https://en.wikipedia.org/wiki/Statistica%20%28journal%29 | Statistica is a quarterly peer-reviewed open access scientific journal dealing with methodological and technical aspects of statistics and statistical analyses in the various scientific fields.
It was established in 1931 as the Supplemento statistico ai nuovi problemi di Politica, Storia ed Economia (English: Statistical Supplement to the New Problems of Politics, History and Economics) and obtained its current title in 1941. It is published by the University of Bologna and is an historical Italian journal in the field of statistics. The founding editor-in-chief was Paolo Fortunati and Italo Scardovi was editor from 1981 till 2004. The current editor-in-chief is Christian Hennig (University of Bologna).
Famous scholars collaborated to Statistica as members of Scientific Board or simply as authors of papers. Among them there are Corrado Gini, Bruno De Finetti, Carlo E. Bonferroni, Marcel Fréchet, Samuel Kotz, Camilo Dagum, Estelle Bee Dagum, Italo Scardovi.
Abstracting and indexing
The journal is abstracted and indexed in Web of Science Core Collection – Emerging Sources Citation Index, a Clarivate Analytics database and Repec.
References
External links
Statistics journals
Creative Commons Attribution-licensed journals
Academic journals established in 1931
Quarterly journals
University of Bologna
English-language journals
Academic journals published by universities and colleges |
https://en.wikipedia.org/wiki/Functor%20%28disambiguation%29 | A functor, in mathematics, is a map between categories.
Functor may also refer to:
Predicate functor in logic, a basic concept of predicate functor logic
Function word in linguistics
In computer programming:
Functor (functional programming)
Function object used to pass function pointers along with state information
for use of the term in Prolog language, see Prolog syntax and semantics
In OCaml and Standard ML, a functor is a higher-order module (a module parameterized by one or more other modules), often used to define type-safe abstracted algorithms and data structures.
See also
Function (disambiguation) |
https://en.wikipedia.org/wiki/Steric%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the steric tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Alternate names
Small diprismatodemitesseractic tetracomb (siphatit)
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
16-cell honeycomb
24-cell honeycomb
Rectified 24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
Notes
References
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 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
x3o3o *b3o4x - siphatit - O108
Honeycombs (geometry)
5-polytopes |
https://en.wikipedia.org/wiki/Steriruncic%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the steriruncic tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Alternate names
Prismatorhombated demitesseractic tetracomb (pirhatit)
Great prismatodemitesseractic tetracomb
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
16-cell honeycomb
24-cell honeycomb
Rectified 24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
Notes
References
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 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
x3o3o *b3x4x - pirhatit - O110
Honeycombs (geometry)
5-polytopes |
https://en.wikipedia.org/wiki/Stericantic%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the stericantic tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Alternate names
Prismatotruncated demitesseractic tetracomb (pithatit)
Small prismatodemitesseractic tetracomb
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
16-cell honeycomb
24-cell honeycomb
Rectified 24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
Notes
References
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 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
x3x3o *b3o4x - pithatit - O109
Honeycombs (geometry)
5-polytopes |
https://en.wikipedia.org/wiki/Steriruncicantic%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the steriruncicantic tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Alternate names
great prismated demitesseractic tetracomb (giphatit)
great diprismatodemitesseractic tetracomb
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
16-cell honeycomb
24-cell honeycomb
Rectified 24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
Notes
References
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 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
x3x3o *b3x4x - giphatit - O111
Honeycombs (geometry)
5-polytopes |
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