|
Samuel Karlin
Samuel Karlin (June 8, 1924 – December 18, 2007) was an American mathematician at Stanford University in the late 20th century. Education and career Karlin was born in Janów, Poland and immigrated to Chicago as a child. Raised in an Orthodox Jewish household, Karlin became an atheist in his teenage years and remained an atheist for the rest of his life. Later in life he told his three children, who all became scientists, that walking down the street without a yarmulke on his head for the first time was a milestone in his life. Karlin earned his undergraduate degree from Illinois Institute of Technology; and then his doctorate in mathematics from Princeton University in 1947 (at the age of 22) under the supervision of Salomon Bochner. He was on the faculty of Caltech from 1948 to 1956, before becoming a professor of mathematics and statistics at Stanford. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lublin Province
Lublin Voivodeship ( ) is a Voivodeships of Poland, voivodeship (province) of Poland, located in the southeastern part of the country, with its capital being the city of Lublin. The region is named after its largest city and regional capital, Lublin, and its territory is made of four historical lands: the western and central part of the voivodeship, with Lublin itself, belongs to Lesser Poland, the eastern part of Lublin Area belongs to Cherven Cities/Red Ruthenia, and the northeast belongs to Polesie and Podlasie. Lublin Voivodeship borders Subcarpathian Voivodeship to the south, Świętokrzyskie Voivodeship to the south-west, Masovian Voivodeship to the west and north, Podlaskie Voivodeship along a short boundary to the north, Belarus (Brest Region) and Ukraine (Lviv Oblast, Lviv and Volyn Oblast, Volyn Regions) to the east. The region's population as of 2019 was 2,112,216. It covers an area of . History The Polish historical regions, Polish historical region that encompasse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BLAST (biotechnology)
In bioinformatics, BLAST (basic local alignment search tool) is an algorithm and program for comparing Primary structure, primary biological sequence information, such as the amino acid, amino-acid sequences of proteins or the nucleotides of DNA sequence, DNA and/or RNA sequences. A BLAST search enables a researcher to compare a subject protein or nucleotide sequence (called a query) with a library or database of sequences, and identify database sequences that resemble the query sequence above a certain threshold. For example, following the discovery of a previously unknown gene in the Mus musculus, mouse, a scientist will typically perform a BLAST search of the human genome to see if humans carry a similar gene; BLAST will identify sequences in the human genome that resemble the mouse gene based on similarity of sequence. Background BLAST is one of the most widely used bioinformatics programs for sequence searching. It addresses a fundamental problem in bioinformatics research ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Von Neumann Theory Prize
The John von Neumann Theory Prize of the Institute for Operations Research and the Management Sciences (INFORMS) is awarded annually to an individual (or sometimes a group) who has made fundamental and sustained contributions to theory in operations research and the management sciences. The Prize named after mathematician John von Neumann is awarded for a body of work, rather than a single piece. The Prize was intended to reflect contributions that have stood the test of time. The criteria include significance, innovation, depth, and scientific excellence. The award is $5,000, a medallion and a citation. The Prize has been awarded since 1975. The first recipient was George B. Dantzig for his work on linear programming. List of recipients * 2024 Jim Dai * 2023 Christos Papadimitriou and Mihalis Yannakakis * 2022 Vijay Vazirani * 2021 Alexander Shapiro * 2020 Adrian Lewis (mathematician), Adrian Lewis * 2019 Dimitris Bertsimas and Jong-Shi Pang * 2018 Dimitri Bertsekas and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Medal Of Science
The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral science, behavioral and social sciences, biology, chemistry, engineering, mathematics and physics. The twelve member presidential Committee on the National Medal of Science is responsible for selecting award recipients and is administered by the National Science Foundation (NSF). It is the highest science award in the United States. History The National Medal of Science was established on August 25, 1959, by an act of the Congress of the United States under . The medal was originally to honor scientists in the fields of the "physical, biological, mathematical, or engineering sciences". The Committee on the National Medal of Science was established on August 23, 1961, by Executive order (United States), executive order 10961 of President John F. Kennedy. O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimal Design
In the design of experiments, optimal experimental designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to Danish statistician Kirstine Smith. In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum variance. A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design. In practical terms, optimal experiments can reduce the costs of experimentation. The optimality of a design depends on the statistical model and is assessed with respect to a statistical criterion, which is related to the variance-matrix of the estimator. Specifying an appropriate model and specifying a suitable criterion function both require understanding of statistical theory and practical knowledge with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chebyshev Polynomial
The Chebyshev polynomials are two sequences of orthogonal polynomials related to the trigonometric functions, cosine and sine functions, notated as T_n(x) and U_n(x). They can be defined in several equivalent ways, one of which starts with trigonometric functions: The Chebyshev polynomials of the first kind T_n are defined by T_n(\cos \theta) = \cos(n\theta). Similarly, the Chebyshev polynomials of the second kind U_n are defined by U_n(\cos \theta) \sin \theta = \sin\big((n + 1)\theta\big). That these expressions define polynomials in \cos\theta is not obvious at first sight but can be shown using de Moivre's formula (see #Trigonometric definition, below). The Chebyshev polynomials are polynomials with the largest possible leading coefficient whose absolute value on the interval (mathematics), interval is bounded by 1. They are also the "extremal" polynomials for many other properties. In 1952, Cornelius Lanczos showed that the Chebyshev polynomials are important in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Total Positivity
In mathematics, a totally positive matrix is a square matrix in which all the minors are positive: that is, the determinant of every square submatrix is a positive number. A totally positive matrix has all entries positive, so it is also a positive matrix; and it has all principal minors positive (and positive eigenvalues). A symmetric totally positive matrix is therefore also positive-definite. A totally non-negative matrix is defined similarly, except that all the minors must be non-negative (positive or zero). Some authors use "totally positive" to include all totally non-negative matrices. Definition Let \mathbf = (A_)_ be an ''n'' × ''n'' matrix. Consider any p\in\ and any ''p'' × ''p'' submatrix of the form \mathbf = (A_)_ where: : 1\le i_1 < \ldots < i_p \le n,\qquad 1\le j_1 <\ldots < j_p \le n. Then A is a totally positive matrix if: [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Aumann
Robert John Aumann (Yisrael Aumann, ; born June 8, 1930) is an Israeli-American mathematician, and a member of the United States National Academy of Sciences. He is a professor at the Center for the Study of Rationality in the Hebrew University of Jerusalem. He also holds a visiting position at Stony Brook University, and is one of the founding members of the Stony Brook Center for Game Theory. Aumann received the Nobel Memorial Prize in Economic Sciences in 2005 for his work on conflict and cooperation through game theory analysis. He shared the prize with Thomas Schelling. Early life and education Aumann was born in Frankfurt am Main, Germany, and fled to the United States with his family in 1938, two weeks before the Kristallnacht pogrom. He attended the Rabbi Jacob Joseph School, a yeshiva high school in New York City. Aumann graduated from the City College of New York in 1950 with a B.S. in mathematics. He received his M.S. in 1952, and his Ph.D. in Mathematics in 1955, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Festschrift
In academia, a ''Festschrift'' (; plural, ''Festschriften'' ) is a book honoring a respected person, especially an academic, and presented during their lifetime. It generally takes the form of an edited volume, containing contributions from the honoree's colleagues, former pupils, and friends. ''Festschriften'' are often titled something like ''Essays in Honour of...'' or ''Essays Presented to... .'' Terminology The term, borrowed from German, and literally meaning "celebration writing" (cognate with ''feast-script''), might be translated as "celebration publication" or "celebratory (piece of) writing". An alternative Latin term is (literally: "book of friends"). A comparable book presented posthumously is sometimes called a (, "memorial publication"), but this term is much rarer in English. A ''Festschrift'' compiled and published by electronic means on the internet is called a (pronounced either or ), a term coined by the editors of the late Boris Marshak's , ''Eran ud Ane ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lloyd Shapley
Lloyd Stowell Shapley (; June 2, 1923 – March 12, 2016) was an American mathematician and Nobel Memorial Prize-winning economist. He contributed to the fields of mathematical economics and especially game theory. Shapley is generally considered one of the most important contributors to the development of game theory since the work of von Neumann and Morgenstern. With Alvin E. Roth, Shapley won the 2012 Nobel Memorial Prize in Economic Sciences "for the theory of stable allocations and the practice of market design." Life and career Lloyd Shapley was born on June 2, 1923, in Cambridge, Massachusetts, one of the sons of astronomers Harlow Shapley and Martha Betz Shapley, both from Missouri. He attended Phillips Exeter Academy and was a student at Harvard when he was drafted in 1943. He served in the United States Army Air Corps in Chengdu, China and received the Bronze Star decoration for breaking the Soviet weather code. After the war, Shapley returned to Harvard and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment Problem
In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure \mu to the sequence of moments :m_n = \int_^\infty x^n \,d\mu(x)\,. More generally, one may consider :m_n = \int_^\infty M_n(x) \,d\mu(x)\,. for an arbitrary sequence of functions M_n. Introduction In the classical setting, \mu is a measure on the real line, and M is the sequence \. In this form the question appears in probability theory, asking whether there is a probability measure having specified mean, variance and so on, and whether it is unique. There are three named classical moment problems: the Hamburger moment problem in which the support of \mu is allowed to be the whole real line; the Stieltjes moment problem, for ,\infty); and the Hausdorff moment problem for a bounded interval, which without loss of generality may be taken as ,1/math>. The moment problem also extends to complex analysis as the trigonometric moment problem in which the Hankel matric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
