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Mashreghi–Ransford Inequality
In Mathematics, the Mashreghi–Ransford inequality is a bound on the growth rate of certain sequences. It is named after J. Mashreghi and T. Ransford. Let (a_n)_ be a sequence of complex numbers, and let : b_n = \sum_^n a_k, \qquad (n \geq 0), and : c_n = \sum_^n (-1)^ a_k, \qquad (n \geq 0). Here the binomial coefficients In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the t ... are defined by : = \frac. Assume that, for some \beta>1, we have b_n = O(\beta^n) and c_n = O(\beta^n) as n \to \infty. Then Mashreghi-Ransford showed that : a_n = O(\alpha^n), as n \to \infty, where \alpha=\sqrt. Moreover, there is a universal constant \kappa such that : \left( \limsup_ \frac \right) \leq \kappa \, \left( \limsup_ \frac \right)^ \left( \limsup_ \frac \right)^. The p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequences
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an ''arbitrary'' index set. For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be ''finite'', as in these examples, or ''inf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Javad Mashreghi
Javad Mashreghi is a mathematician and author working in fields of function space theory, functional analysis and complex analysis. He is a professeur titulaire at Université Laval and was the 35th President of the Canadian Mathematical Society (2020–2022). Early life and education Mashreghi was born in Kashan, Iran, in 1968. He studied electrical engineering, electronics, (B.Sc., 1991), and pure mathematics (M.Sc., 1993) at the University of Tehran. He moved to Canada in 1996 and earned his Ph.D. from the McGill University in 2001. Since then he lives in the Province of Quebec. Service to Canadian mathematical community Mashreghi is immensely involved in various aspects of North America's mathematical community, having served on numerous editorial, administrative and selection committees all across Canada and the U.S. (CMS, AMS, Fields Institute, CRM, AARMS, NSERC, FQRNT, NSF). He is the 35th President of the Canadian Mathematical Society (2020–2022), the editor-in-chie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Ransford
Thomas Ransford (born 1958) is a British-born Canadian mathematician, known for his research in spectral theory and complex analysis. He holds a Canada Research Chair in mathematics at Université Laval. Ransford earned his Ph.D. from the University of Cambridge in 1984. Career He was a fellow of Trinity College, University of Cambridge, from 1983 to 1987. In addition to over 90 research papers on mathematics, he has written a research monograph "Potential Theory in the Complex Plane" in 1995, and the graduate book "A Primer on the Dirichlet Space" with Omar El-Fallah, Karim Kellay and Javad Mashreghi in 201 He has proved results on potential theory, functional analysis, the theory of capacity, and probability. For example, with Javad Mashreghi he proved the Mashreghi–Ransford inequality. He also derived a short elementary proof of Stone–Weierstrass theorem In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a + bi, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number a+bi, is called the , and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
