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Irregularity Of Distributions
The irregularity of distributions problem, stated first by Hugo Steinhaus, is a numerical problem with a surprising result. The problem is to find ''N'' numbers, x_1,\ldots,x_N, all between 0 and 1, for which the following conditions hold: * The first two numbers must be in different halves (one less than 1/2, one greater than 1/2). * The first 3 numbers must be in different thirds (one less than 1/3, one between 1/3 and 2/3, one greater than 2/3). * The first 4 numbers must be in different fourths. * The first 5 numbers must be in different fifths. * etc. Mathematically, we are looking for a sequence of real numbers :x_1,\ldots,x_N such that for every ''n'' ∈ and every ''k'' ∈ there is some ''i'' ∈ such that :\frac \leq x_i < \frac. Solution The surprising result is that there is a solution up to ''N'' = 17, but starting at ''N'' = 18 and above it is impossible. A possible solutio ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hugo Steinhaus
Hugo Dyonizy Steinhaus ( ; ; January 14, 1887 – February 25, 1972) was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the Jan Kazimierz University in Lwów (now Lviv, Ukraine), where he helped establish what later became known as the Lwów School of Mathematics. He is credited with "discovering" mathematician Stefan Banach, with whom he gave a notable contribution to functional analysis through the Banach–Steinhaus theorem. After World War II Steinhaus played an important part in the establishment of the mathematics department at Wrocław University and in the revival of Polish mathematics from the destruction of the war. Author of around 170 scientific articles and books, Steinhaus has left his legacy and contribution in many branches of mathematics, such as functional analysis, geometry, mathematical logic, and trigonometry. Notably he is regarded as one of the early found ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Number
In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and more generally in all mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers is denoted or \mathbb and is sometimes called "the reals". The adjective ''real'' in this context was introduced in the 17th century by René Descartes to distinguish real numbers, associated with physical reality, from imaginary numbers (such as the square roots of ), which seemed like a theoretical contrivance unrelated to physical reality. The real numbers include the rational numbers, such as the integer and the fraction . The rest of the real number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Irregularity Of Distributions
The irregularity of distributions problem, stated first by Hugo Steinhaus, is a numerical problem with a surprising result. The problem is to find ''N'' numbers, x_1,\ldots,x_N, all between 0 and 1, for which the following conditions hold: * The first two numbers must be in different halves (one less than 1/2, one greater than 1/2). * The first 3 numbers must be in different thirds (one less than 1/3, one between 1/3 and 2/3, one greater than 2/3). * The first 4 numbers must be in different fourths. * The first 5 numbers must be in different fifths. * etc. Mathematically, we are looking for a sequence of real numbers :x_1,\ldots,x_N such that for every ''n'' ∈ and every ''k'' ∈ there is some ''i'' ∈ such that :\frac \leq x_i < \frac. Solution The surprising result is that there is a solution up to ''N'' = 17, but starting at ''N'' = 18 and above it is impossible. A possible solutio ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mieczysław Warmus
Mieczysław Warmus (born 1 June 1918 in Dobrowlany; died 20 September 2007 in Australia) was a Polish mathematician, a pioneer of computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ... in Poland, professor, university lecturer, author of over a hundred scientific papers. ReferencesHomepage (Prof. Mieczysław Warmus (1918–2007)) Biography (Jadwiga Dutkiewicz Mieczysław Warmus Życie i praca naukowa ) [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basic Books
Basic Books is a book publisher founded in 1950 and located in New York, now an imprint of Hachette Book Group. It publishes books in the fields of psychology, philosophy, economics, science, politics, sociology, current affairs, and history. History Basic Books originated as a small Greenwich Village-based book club marketed to psychoanalysts. Arthur Rosenthal took over the book club in 1950, and under his ownership it soon began producing original books, mostly in the behavioral sciences. Early successes included Ernest Jones's ''The Life and Work of Sigmund Freud'', as well as works by Claude Lévi-Strauss, Jean Piaget and Erik Erikson. Irving Kristol joined Basic Books in 1960, and helped Basic to expand into the social sciences. Harper & Row purchased the company in 1969. In 1997, HarperCollins announced that it would merge Basic Books into its trade publishing program, effectively closing the imprint and ending its publishing of serious academic books. That same year, Bas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elwyn Berlekamp
Elwyn Ralph Berlekamp (September 6, 1940 – April 9, 2019) was a professor of mathematics and computer science at the University of California, Berkeley.Contributors, ''IEEE Transactions on Information Theory'' 42, #3 (May 1996), p. 1048. DO10.1109/TIT.1996.490574Elwyn Berlekamp listing at the Department of Mathematics, . Berlekamp was widely known for his work in computer science, and |
Ronald L
Ronald is a masculine given name derived from the Old Norse ''Rögnvaldr'', Hanks; Hardcastle; Hodges (2006) p. 234; Hanks; Hodges (2003) § Ronald. or possibly from Old English '' Regenweald''. In some cases ''Ronald'' is an Anglicised form of the Gaelic ''Raghnall'', a name likewise derived from ''Rögnvaldr''. The latter name is composed of the Old Norse elements ''regin'' ("advice", "decision") and ''valdr'' ("ruler"). ''Ronald'' was originally used in England and Scotland, where Scandinavian influences were once substantial, although now the name is common throughout the English-speaking world. A short form of ''Ronald'' is ''Ron''. Pet forms of ''Ronald'' include ''Roni'' and ''Ronnie''. ''Ronalda'' and ''Rhonda'' are feminine forms of ''Ronald''. '' Rhona'', a modern name apparently only dating back to the late nineteenth century, may have originated as a feminine form of ''Ronald''. Hanks; Hardcastle; Hodges (2006) pp. 230, 408; Hanks; Hodges (2003) § Rhona. The names ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Number Theory
The ''Journal of Number Theory'' (''JNT'') is a bimonthly peer-reviewed scientific journal covering all aspects of number theory. The journal was established in 1969 by R.P. Bambah, P. Roquette, A. Ross, A. Woods, and H. Zassenhaus (Ohio State University). It is currently published monthly by Elsevier and the editor-in-chief is Dorian Goldfeld (Columbia University). According to the ''Journal Citation Reports'', the journal has a 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... of 0.72. References External links * Number theory Mathematics journals Publications established in 1969 Elsevier academic journals Monthly journals English-language journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
