|
Tamás Erdélyi (mathematician)
Tamás Erdélyi is a Hungarian-born mathematician working at Texas A&M University. His main areas of research are related to polynomials and their approximations, although he also works in other areas of applied mathematics. Life, education and positions Tamás Erdélyi was born on September 13, 1961, in Budapest, Hungary. From 1980 to 1985 he studied mathematics at the ELTE in Budapest, where he received his diploma. After graduation, he worked for two years as a research assistant at the Mathematics Institute of the Hungarian Academy of Sciences. He later pursued his graduate studies at the University of South Carolina (1987–88) and the Ohio State University (1988–89). He received his Ph.D. from the University of South Carolina in 1989. He was a postdoctoral fellow at the Ohio State University (1989–92), Dalhousie University (1992–93), Simon Fraser University (1993–95), and finally at the University of Copenhagen (1996–97). In 1995, he started to work at the Texa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hungary
Hungary ( hu, Magyarország ) is a landlocked country in Central Europe. Spanning of the Carpathian Basin, it is bordered by Slovakia to the north, Ukraine to the northeast, Romania to the east and southeast, Serbia to the south, Croatia and Slovenia to the southwest, and Austria to the west. Hungary has a population of nearly 9 million, mostly ethnic Hungarians and a significant Romani minority. Hungarian, the official language, is the world's most widely spoken Uralic language and among the few non-Indo-European languages widely spoken in Europe. Budapest is the country's capital and largest city; other major urban areas include Debrecen, Szeged, Miskolc, Pécs, and Győr. The territory of present-day Hungary has for centuries been a crossroads for various peoples, including Celts, Romans, Germanic tribes, Huns, West Slavs and the Avars. The foundation of the Hungarian state was established in the late 9th century AD with the conquest of the Carpathian Basin by Hungar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dalhousie University
Dalhousie University (commonly known as Dal) is a large public research university in Nova Scotia Nova Scotia ( ; ; ) is one of the thirteen provinces and territories of Canada. It is one of the three Maritime provinces and one of the four Atlantic provinces. Nova Scotia is Latin for "New Scotland". Most of the population are native Eng ..., Canada, with three campuses in Halifax, a fourth in Bible Hill, Nova Scotia, Bible Hill, and a second medical school campus in Saint John, New Brunswick. Dalhousie offers more than 4,000 courses, and over 200 degree programs in 13 undergraduate, graduate, and professional faculties. The university is a member of the U15 Group of Canadian Research Universities, U15, a group of research-intensive universities in Canada. The institution was established as ''Dalhousie College'', a nonsectarian institution established in 1818 by the eponymous Lieutenant Governor of Nova Scotia, George Ramsay, 9th Earl of Dalhousie, with education reforme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Sum
In mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually expressed by means of the function :e(x) = \exp(2\pi ix).\, Therefore, a typical exponential sum may take the form :\sum_n e(x_n), summed over a finite sequence of real numbers ''x''''n''. Formulation If we allow some real coefficients ''a''''n'', to get the form :\sum_n a_n e(x_n) it is the same as allowing exponents that are complex numbers. Both forms are certainly useful in applications. A large part of twentieth century analytic number theory was devoted to finding good estimates for these sums, a trend started by basic work of Hermann Weyl in diophantine approximation. Estimates The main thrust of the subject is that a sum :S=\sum_n e(x_n) is ''trivially'' estimated by the number ''N'' of terms. That is, the absolute value :, S, \le N\, by the triangle inequality, since each summand has absolute va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newman's Product Problem
Newman's was an American department store chain based out of Joplin, Missouri. Newman Mercantile Company was started by Jewish entrepreneur Joseph Newman, a German immigrant, in the mid 19th century. Joseph Newman's son Albert and son in law Gabe Newburger opened the first Newman's dry goods store in Joplin in 1898. In 1910 Newman's relocated their Joplin store to the newly built Newman Brothers Building located at the corner of 6th & Main in downtown Joplin. Newman's department store operated out of that building until 1972, when they relocated to the newly completed Northpark Mall. Newman's co-developed the mall with Enterprise Development. Newman's filed for chapter 11 bankruptcy in 1987 closing some of their locations, and closing the last of their stores in 1988. The Joplin store located at the mall was bought by Heer's department stores of Springfield, Missouri Springfield is the third largest city in the U.S. state of Missouri and the county seat of Greene County. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lebesgue Measure
In measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of ''n''-dimensional Euclidean space. For ''n'' = 1, 2, or 3, it coincides with the standard measure of length, area, or volume. In general, it is also called ''n''-dimensional volume, ''n''-volume, or simply volume. It is used throughout real analysis, in particular to define Lebesgue integration. Sets that can be assigned a Lebesgue measure are called Lebesgue-measurable; the measure of the Lebesgue-measurable set ''A'' is here denoted by ''λ''(''A''). Henri Lebesgue described this measure in the year 1901, followed the next year by his description of the Lebesgue integral. Both were published as part of his dissertation in 1902. Definition For any interval I = ,b/math>, or I = (a, b), in the set \mathbb of real numbers, let \ell(I)= b - a denote its length. For any subset E\subseteq\mathbb, the Lebesgue oute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compact Space
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space by making precise the idea of a space having no "punctures" or "missing endpoints", i.e. that the space not exclude any ''limiting values'' of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval ,1would be compact. Similarly, the space of rational numbers \mathbb is not compact, because it has infinitely many "punctures" corresponding to the irrational numbers, and the space of real numbers \mathbb is not compact either, because it excludes the two limiting values +\infty and -\infty. However, the ''extended'' real number line ''would'' be compact, since it contains both infinities. There are many ways to make this heuristic notion precise. These ways usually agree in a metric space, but may not be equivalent in other topologic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Remez Inequality
In mathematics, the Remez inequality, discovered by the Soviet mathematician Evgeny Yakovlevich Remez , gives a bound on the sup norms of certain polynomials, the bound being attained by the Chebyshev polynomials. The inequality Let ''σ'' be an arbitrary fixed positive number. Define the class of polynomials Ï€''n''(''σ'') to be those polynomials ''p'' of the ''n''th degree for which :, p(x), \le 1 on some set of measure ≥ 2 contained in the closed interval ˆ’1, 1+''σ'' Then the Remez inequality states that :\sup_ \left\, p\right\, _\infty = \left\, T_n\right\, _\infty where ''T''''n''(''x'') is the Chebyshev polynomial of degree ''n'', and the supremum norm is taken over the interval ˆ’1, 1+''σ'' Observe that ''T''''n'' is increasing on , +\infty/math>, hence : \, T_n\, _\infty = T_n(1+\sigma). The R.i., combined with an estimate on Chebyshev polynomials, implies the following corollary: If ''J'' ⊂ R is a finite interval, and ''E'' ⊂&nb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inequality (mathematics)
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size. There are several different notations used to represent different kinds of inequalities: * The notation ''a'' ''b'' means that ''a'' is greater than ''b''. In either case, ''a'' is not equal to ''b''. These relations are known as strict inequalities, meaning that ''a'' is strictly less than or strictly greater than ''b''. Equivalence is excluded. In contrast to strict inequalities, there are two types of inequality relations that are not strict: * The notation ''a'' ≤ ''b'' or ''a'' ⩽ ''b'' means that ''a'' is less than or equal to ''b'' (or, equivalently, at most ''b'', or not greater than ''b''). * The notation ''a'' ≥ ''b'' or ''a'' ⩾ ''b'' means that ''a'' is greater than or equal to ''b'' (or, equivalently, at least ''b'', or not less than ''b''). The re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernstein's Inequality (mathematical Analysis)
Bernstein's theorem is an inequality relating the maximum modulus of a complex polynomial function on the unit disk with the maximum modulus of its derivative on the unit disk. It was proven by Sergei Bernstein while he was working on approximation theory. Statement Let \max_ , f(z), denote the maximum modulus of an arbitrary function f(z) on , z, =1, and let f'(z) denote its derivative. Then for every polynomial P(z) of degree n we have : \max_ , P'(z), \le n \max_ , P(z), . The inequality is best possible with equality holding if and only if : P(z) = \alpha z^n,\ , \alpha, = \max_ , P(z), . Proof Let P(z) be a polynomial of degree n, and let Q(z) be another polynomial of the same degree with no zeros in , z, \ge 1. We show first that if , P(z), < , Q(z), on , then on . By |
Markov Inequality
In probability theory, Markov's inequality gives an upper bound for the probability that a non-negative function (mathematics), function of a random variable is greater than or equal to some positive Constant (mathematics), constant. It is named after the Russian mathematician Andrey Markov, although it appeared earlier in the work of Pafnuty Chebyshev (Markov's teacher), and many sources, especially in Mathematical analysis, analysis, refer to it as Chebyshev's inequality (sometimes, calling it the first Chebyshev inequality, while referring to Chebyshev's inequality as the second Chebyshev inequality) or Irénée-Jules Bienaymé, Bienaymé's inequality. Markov's inequality (and other similar inequalities) relate probabilities to expected value, expectations, and provide (frequently loose but still useful) bounds for the cumulative distribution function of a random variable. Statement If is a nonnegative random variable and , then the probability that is at least is at most th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
