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Keith Martin Ball
Keith Martin Ball FRS FRSE (born 26 December 1960) is a mathematician and professor at the University of Warwick. He was scientific director of the International Centre for Mathematical Sciences (ICMS) from 2010 to 2014. Education Ball was educated at Berkhamsted School and Trinity College, Cambridge where he studied the Cambridge Mathematical Tripos and was awarded a Bachelor of Arts degree in mathematics in 1982 and a PhD in 1987 for research supervised by Béla Bollobás. Research Keith Ball's research is in the fields of functional analysis, high-dimensional and discrete geometry and information theory. He is the author of ''Strange Curves, Counting Rabbits, & Other Mathematical Explorations''. Awards and honours Ball was elected a Fellow of the American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and internatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Definition, norm, Topological space#Definition, topology, etc.) and the linear transformation, linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of function space, spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous function, continuous, unitary operator, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential equations, differential and integral equations. The usage of the word ''functional (mathematics), functional'' as a noun goes back to the calculus of variati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Definition, norm, Topological space#Definition, topology, etc.) and the linear transformation, linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of function space, spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous function, continuous, unitary operator, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential equations, differential and integral equations. The usage of the word ''functional (mathematics), functional'' as a noun goes back to the calculus of variati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1960 Births
Year 196 ( CXCVI) was a leap year starting on Thursday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Dexter and Messalla (or, less frequently, year 949 ''Ab urbe condita''). The denomination 196 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Emperor Septimius Severus attempts to assassinate Clodius Albinus but fails, causing Albinus to retaliate militarily. * Emperor Septimius Severus captures and sacks Byzantium; the city is rebuilt and regains its previous prosperity. * In order to assure the support of the Roman legion in Germany on his march to Rome, Clodius Albinus is declared Augustus by his army while crossing Gaul. * Hadrian's wall in Britain is partially destroyed. China * First year of the '' Jian'an era of the Chinese Han Dynasty. * Emperor Xian o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second Law Of Thermodynamics
The second law of thermodynamics is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unless energy in some form is supplied to reverse the direction of heat flow. Another definition is: "Not all heat energy can be converted into Work (thermodynamics), work in a cyclic process."Young, H. D; Freedman, R. A. (2004). ''University Physics'', 11th edition. Pearson. p. 764. The second law of thermodynamics in other versions establishes the concept of entropy as a physical property of a thermodynamic system. It can be used to predict whether processes are forbidden despite obeying the requirement of conservation of energy as expressed in the first law of thermodynamics and provides necessary criteria for spontaneous processes. The second law may be formulated by the observation that the entropy of isolated systems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assaf Naor
Assaf Naor (born May 7, 1975) is an Israeli American and Czech mathematician, computer scientist, and a professor of mathematics at Princeton University. Academic career Naor earned a baccalaureate from Hebrew University of Jerusalem in 1996 and a doctorate from the same university in 2002, under the supervision of Joram Lindenstrauss.Curriculum vitae retrieved 2019-06-15. He worked at from 2002 until 2007, with an affiliated faculty position at the , and joined the NYU faculty in 2006. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Franck Barthe
Franck Barthe is a French mathematician. He was awarded the European Congress of Mathematics (ECM) prize in 2004. He is working as a professor of mathematics at Paul Sabatier University. Work Franck Barthe is known for his reverse form of the Brascamp-Lieb inequality. With Keith M. Ball, Shiri Artstein, and Assaf Naor, he solved Shannon's problem of the monotonic entropy increase of sums of random variables. Awards In 2004, he received the EMS Prize (prize presentation: isoperimetric inequalities, probability measures and convex geometry In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbe ...) for his leading role in the application of mass-theoretical transport techniques. In 2005, he received the Grand Prix Jacques Herbrand. References Living people 20th-century ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shiri Artstein
Shiri Artstein-Avidan ( he, שירי ארטשטיין-אבידן, born 28 September 1978) is an Israeli mathematician who in 2015 won the Erdős Prize. She specializes in convex geometry and asymptotic geometric analysis, and is a professor of mathematics at Tel Aviv University. Education and career Artstein was born in Jerusalem, the daughter of mathematician Zvi Artstein. She graduated summa cum laude from Tel Aviv University in 2000, with a bachelor's degree in mathematics, and completed her PhD at Tel Aviv University in 2004 under the supervision of Vitali Milman, with a dissertation on ''Entropy Methods''. She worked from 2004 to 2006 as a Veblen Research Instructor in Mathematics at Princeton University and as a researcher at the Institute for Advanced Study before returning to Tel Aviv as a faculty member in 2006. Recognition Artstein won the Haim Nessyahu Prize in Mathematics, an annual dissertation award of the Israel Mathematical Union, in 2006. In 2008 she won the Kri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann Zeta Function
The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for \operatorname(s) > 1 and its analytic continuation elsewhere. The Riemann zeta function plays a pivotal role in analytic number theory, and has applications in physics, probability theory, and applied statistics. Leonhard Euler first introduced and studied the function over the reals in the first half of the eighteenth century. Bernhard Riemann's 1859 article "On the Number of Primes Less Than a Given Magnitude" extended the Euler definition to a complex variable, proved its meromorphic continuation and functional equation, and established a relation between its zeros and the distribution of prime numbers. This paper also contained the Riemann hypothesis, a conjecture about the distribution of complex zeros of the Riemann zeta function that is consid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Boundedness Principle
In mathematics, the uniform boundedness principle or Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with the Hahn–Banach theorem and the open mapping theorem, it is considered one of the cornerstones of the field. In its basic form, it asserts that for a family of continuous linear operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm. The theorem was first published in 1927 by Stefan Banach and Hugo Steinhaus, but it was also proven independently by Hans Hahn. Theorem The completeness of X enables the following short proof, using the Baire category theorem. There are also simple proofs not using the Baire theorem . Corollaries The above corollary does claim that T_n converges to T in operator norm, that is, uniformly on bounded sets. However, since \left\ is bounded in operator norm, and the limit operator T is continuous ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lipschitz Continuity
In mathematical analysis, Lipschitz continuity, named after German mathematician Rudolf Lipschitz, is a strong form of uniform continuity for functions. Intuitively, a Lipschitz continuous function is limited in how fast it can change: there exists a real number such that, for every pair of points on the graph of this function, the absolute value of the slope of the line connecting them is not greater than this real number; the smallest such bound is called the ''Lipschitz constant'' of the function (or '' modulus of uniform continuity''). For instance, every function that has bounded first derivatives is Lipschitz continuous. In the theory of differential equations, Lipschitz continuity is the central condition of the Picard–Lindelöf theorem which guarantees the existence and uniqueness of the solution to an initial value problem. A special type of Lipschitz continuity, called contraction, is used in the Banach fixed-point theorem. We have the following chain of strict inclus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
