High Quality Content by WIKIPEDIA articles! In coding theory, a standard array (or Slepian array) is a qn ? k by qk array that lists all elements of a particular mathbb{F}_q^n vector space. Standard arrays are used to decode linear codes; i.e. to find the corresponding codeword for any received vector. Note that the above is only one possibility for the standard array; had 00011 been chosen as the first coset leader of weight two, another standard array representing the code would have been constructed. Note that the first row contains the 0 vector and the codewords of C3 (0 itself being a codeword). Also, the leftmost column contains the vectors of minimum weight enumerating vectors of weight 1 first and then using vectors of weight 2....

ISBN: 978-6-1312-4152-9
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High Quality Content by WIKIPEDIA articles! In mathematics, the standard conjectures about algebraic cycles is a term applied to a package of several conjectures describing the relationship of algebraic cycles and Weil cohomology theories. One of the original applications envisaged by Alexander Grothendieck was to prove that his construction of pure motives gave an abelian category that is semisimple. Moreover, as he pointed out, the standard conjectures also imply the hardest part of the Weil conjectures, namely the "Riemann hypothesis" conjecture that remained open at the end of the 1960s and was proved later by Pierre Deligne; for details on the link between Weil and standard conjectures, see Kleiman (1968). The standard conjectures...

ISBN: 978-6-1312-5089-7
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High Quality Content by WIKIPEDIA articles! A standard normal deviate (or standard normal variable) is a normally distributed random variable with expected value 0 and variance 1. A fuller term is standard normal random variable. Where collections of such random variables are used, there is often an associated (possibly unstated) assumption that members of such collections are statistically independent. Standard normal variables play a major role in theoretical statistics in the description of many types of model, particularly in regression analysis, the analysis of variance and time series analysis. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1312-5178-8
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High Quality Content by WIKIPEDIA articles! In probability theory, a standard probability space (called also Lebesgue–Rokhlin probability space or just Lebesgue space; the latter term is ambiguous) is a probability space satisfying certain assumptions introduced by Vladimir Rokhlin in 1940. He showed that the unit interval endowed with the Lebesgue measure has important advantages over general probability spaces, and can be used as a probability space for all practical purposes in probability theory. The dimension of the unit interval is not a concern, which was clear already to Norbert Wiener. He constructed the Wiener process (also called Brownian motion) in the form of a measurable map from the unit interval to the space of...

ISBN: 978-6-1304-9894-8
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High Quality Content by WIKIPEDIA articles! In non-standard analysis, the standard part function "st" is the key ingredient in Abraham Robinson's resolution of the paradox of Leibniz's definition of the derivative as the ratio of two infinitesimals. The standard part of any infinitesimal is 0. Thus if N is a hypernatural, then N is infinitesimal, and st =0. The existence of the standard part function is a consequence of the completeness of the reals or the fact that finite closed intervals of the reals are compact. The standard part function "st" is not an internal object. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд...

ISBN: 978-6-1303-6114-3
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High Quality Content by WIKIPEDIA articles! In elementary arithmetic, a standard algorithm or method is a specific method of computation which is conventionally taught for solving particular mathematical problems. These methods vary somewhat by nation and time, but generally include carrying, borrowing, long division, and long multiplication using a standard notation, and standard formulas for average, area, and volume. Similar methods also exist for procedures such as square root and even more sophisticated functions, but have fallen out of the general mathematics curriculum in favor of calculators (or tables and slide rules before them). Данное издание не является оригинальным. Книга...

ISBN: 978-6-1312-4108-6
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High Quality Content by WIKIPEDIA articles! In statistics, a standard score indicates how many standard deviations an observation or datum is above or below the mean. It is a dimensionless quantity derived by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This conversion process is called standardizing or normalizing; however, "normalizing" can refer to many types of ratios; see normalization (statistics) for more. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-3544-1
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High Quality Content by WIKIPEDIA articles! In modal logic, standard translation is a way of transforming formulas of modal logic into formulas of first-order logic which capture the meaning of the modal formulas. Standard translation is defined inductively on the structure of the formula. In short, atomic formulas are mapped onto unary predicates and the objects in the first-order language are the accessible worlds. The logical connectives from propositional logic remain untouched and the modal operators are transformed into first-order formulas according to their semantics. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд...

ISBN: 978-6-1312-5219-8
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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Stanis?aw Ruziewicz (b. August 29, 1889 in Podstaje - July 12, 1941 in Lviv, Ukraine, then Soviet Union) was a Polish mathematician and one of the founders of the Lviv School of Mathematics. He was a former student of Wac?aw Sierpi?ski, a professor at the Lviv University and Lviv Academy of Foreign Trade. During the Second World War, he was arrested and murdered by the Gestapo on July 12, 1941 in Lviv, during the Massacre of Lviv professors. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1311-6518-4
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Stanis?aw Saks (December 30, 1897 — November 23, 1942) was a Polish mathematician and university tutor, known primarily for his membership in the Scottish Cafe circle, an extensive monograph on the Theory of Integrals, his works on measure theory and the Vitali-Hahn-Saks theorem. Stanis?aw Saks was born December 30, 1897 in Kalisz, Congress Poland, to an assimilated Polish-Jewish family. In 1915 he graduated from a local gymnasium and joined the newly-recreated Warsaw University. In 1922 he received a doctorate of his alma mater with a prestigious award Cum Maxima Laude. Soon afterwards he also passed his habilitation and received the Rockefeller scholarship, which allowed him to travel to...

ISBN: 978-6-1311-6534-4
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High Quality Content by WIKIPEDIA articles! Stanis?aw P. Radziszowski (born June 7, 1953) is a Polish-American mathematician and computer scientist. Radziszowski was born in Gda?sk, Poland, and received his PhD from the Institute of Informatics of the University of Warsaw in 1980. His thesis topic was "Logic and Complexity of Synchronous Parallel Computations". From 1976 to 1980 he worked as a visiting professor in various universities in Mexico City. In 1984, he moved to the United States, where he took up a position in the Department of Computer Science at the Rochester Institute of Technology. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1311-0911-9
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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Stanis?aw Zaremba (October 3, 1863 – November 23, 1942) was a Polish mathematician. His research in differential equations, applied mathematics, classical analysis, particularly on harmonic analysis, was widely recognized. He was a mathematician who contributed to the success of the Polish School of Mathematics through his teaching and organizational skills as well as through his research. Zaremba wrote a number of university textbooks and monographies. He was a professor of the Jagiellonian University (since 1900), member of Academy of Learning (since 1903), co-founder and president of the Polish Mathematical Society (1919). Данное...

ISBN: 978-6-1311-5258-0
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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Stanis?aw Mazur (born 1 January 1905, Lviv - 5 November 1981, Warsaw) was a Polish mathematician and a member of the Polish Academy of Sciences. Mazur was a student of Stefan Banach at Lwow (now Lviv, Ukraine). His doctorate, under Banach's supervision, was awarded in 1935. From 1948 Mazur worked at the University of Warsaw. Mazur was a close collaborator with Banach at Lwow and was a member of the Lwow School of Mathematics, where he participated in the mathematical activities at the Scottish Cafe. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1311-5201-6
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High Quality Content by WIKIPEDIA articles! In mathematics, a Stanley–Reisner ring is a quotient of a polynomial algebra over a field by a square-free monomial ideal. Such ideals are described more geometrically in terms of finite simplicial complexes. The Stanley–Reisner ring construction is a basic tool within algebraic combinatorics and combinatorial commutative algebra. Its properties were investigated by Richard Stanley, Melvin Hochster, and Gerald Reisner in the early 1970s. Given an abstract simplicial complex on the vertex set {x1,…,xn} and a field k, the corresponding Stanley–Reisner ring, or face ring, denoted k[ ], is obtained from the polynomial ring k[x1,…,xn] by quotienting out the ideal I generated by the...

ISBN: 978-6-1312-4951-8
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High Quality Content by WIKIPEDIA articles! In combinatorial mathematics, Stanley's reciprocity theorem, named after MIT mathematician Richard P. Stanley, states that a certain functional equation is satisfied by the generating function of any rational cone (defined below) and the generating function of the cone's interior. A rational cone is the set of all d-tuples (a1, ..., ad) of nonnegative integers satisfying a system of inequalities Mleft[begin{matrix}a_1 vdots a_dend{matrix}right] geq left[begin{matrix}0 vdots 0end{matrix}right] where M is a matrix of integers. A d-tuple satisfying the corresponding strict inequalities, i.e., with ">" rather than ">=", is in the interior of the cone. The generating function of such a cone is...

ISBN: 978-6-1312-4957-0
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In combinatorial mathematics, the theory of Stanley–Reisner rings is a basic tool that supports the use of commutative algebra by defining a polynomial algebra for any abstract simplicial complex. Definition. An (augmented abstract) simplicial complex ? on a vertex set V? is a collection (possibly empty) of finite subsets ?, the simplices, of V? satisfying: mbox{(a)}text{ If } vin V_{Sigma}, text{ then } {v}in Sigma. mbox{(b)} text{ If } sigmain Sigma text{ and } tausubset sigma, text{ then } tauin Sigma. Define the simplicial join Sigma_1astSigma_2, of two simplicial complexes ?1 and ?2 with disjoint vertex sets, to be: Sigma_1astSigma_2:={sigma_1cupsigma_2 mid sigma_iinSigma_i (i=1,2) }....

ISBN: 978-6-1312-4941-9
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Stanton number, St or CH, is a dimensionless number which measures the ratio of heat transferred into a fluid to the thermal capacity of fluid. It is used to characterize heat transfer in forced convection flows. mathrm{St} = frac{h}{c_pcdotrhocdot V} where * h = convection heat transfer coefficient * ? = density of the fluid * cp = specific heat of the fluid * V = velocity of the fluid Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-6130-3
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High Quality Content by WIKIPEDIA articles! In mathematics, a set S in the Euclidean space Rn is called a star domain (or star-convex set) if there exists x0 in S such that for all x in S the line segment from x0 to x is in S. This definition is immediately generalizable to any real or complex vector space. Intuitively, if one thinks of S as of a region surrounded by a fence, S is a star domain if one can find a vantage point x0 in S from which any point x in S is within line-of-sight. Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. Данное издание не...

ISBN: 978-6-1312-4979-2
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the star product of two graded posets (P,le_P) and (Q,le_Q), where P has a unique maximal element widehat{1} and Q has a unique minimal element widehat{0}, is a poset P * Q on the set (Psetminuswidehat{1})cup(Qsetminuswidehat{0}). We define the partial order le_{P*Q} by xle y if and only if: 1. {x,y}subset P, and xle_P y; 2. {x,y}subset Q, and xle_Q y; or 3. xin P and yin Q. In other words, we pluck out the top of P and the bottom of Q, and require that everything in P be smaller than everything in Q. For example, suppose P and Q are the Boolean algebra on two elements. Данное издание не является оригинальным. Книга печатается...

ISBN: 978-6-1312-5008-8
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High Quality Content by WIKIPEDIA articles! n graph-theoretic mathematics, a star coloring of a graph G is a (proper) vertex coloring in which every path on four vertices uses at least three distinct colors. Equivalently, in a star coloring, the induced subgraphs formed by the vertices of any two colors has connected components that are star graphs. The star chromatic number s(G) of G is the least number of colors needed to star color G. One generalization of star coloring is the closely-related concept of acyclic coloring, where it is required that every cycle uses at least three colors, so the two-color induced subgraphs are forests. If we denote the acyclic chromatic number of a graph G by a(G), we have that chi_a(G) leq chi_s(G), and...

ISBN: 978-6-1312-4975-4
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, specifically in the study of topology and open covers of a topological space X, a star refinement is a particular kind of refinement of an open cover of X. Given x in X and an open cover {Ui} of X with index set I, the star of x with respect to the cover is the set of i in I such that x is in Ui. That is, x^* = {i in I ;|; x in U_i} ., For each x we can take the union of the sets in its star; this is also called the star of x. That is, U^*(x) = bigcup_{i in x^*} U_i ., Then this open cover is a star refinement of some other open cover {Vj}, with index set J, if 1. each Ui is contained in some Vj (the refinement condition), and 2. each star U*(x) is contained in a Vj (star...

ISBN: 978-6-1312-5012-5
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The star transform, or starred transform is a discrete-time variation of the Laplace transform that represents an ideal sampler with period of time T. The star transform is similar to the Z transform with a simple change of variables, but the star transform explicitly identifies each sample in terms of the sampling period (T), while the Z transform only refers to each sample by integer index value. The star transform is so named because it is frequently represented by an asterisk or "star" in the notation. The inverse star transform represents a signal that has been sampled at interval T. The inverse star transform is not the original signal, x(t), but is instead a sampled version of the...

ISBN: 978-6-1312-5022-4
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A star number is a centered figurate number that represents a centered hexagram, such as the one that Chinese checkers is played on. The nth star number is given by the formula 6n(n - 1) + 1. The first 43 star numbers are 1, 13, 37, 73, 121, 181, 253, 337, 433, 541, 661, 793, 937, 1093, 1261, 1441, 1633, 1837, 2053, 2281, 2521, 2773, 3037, 3313, 3601, 3901, 4213, 4537, 4873, 5221, 5581, 5953, 6337, 6733, 7141, 7561, 7993, 8437, 8893, 9361, 9841, 10333, 10837 (sequence A003154 in OEIS). Geometrically, the nth star number is made up of a central point and 12 copies of the (n-1)th triangular number — making it numerically equal to the nth centered dodecagonal number, but differently arranged....

ISBN: 978-6-1312-4995-2
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In graph theory, a star Sk is the complete bipartite graph K1,k, a tree with one internal node and k leaves. A star with 3 edges is called a claw. The star Sk is edge-graceful when k is even and not when k is odd. It is edge-transitive, unit distance and has diameter 2, girth ?, chromatic index k and chromatic number 2. Claws are notable in the definition of claw-free graphs, graphs that do not have any claw as an induced subgraph. A star is a special kind of tree. As with any tree, stars may be encoded by a Prufer sequence; the Prufer sequence for a star K1,k consists of k ? 1 copies of the center vertex. Several graph invariants are defined in terms of stars. Star arboricity is the minimum...

ISBN: 978-6-1312-4966-2
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High Quality Content by WIKIPEDIA articles! A star-shaped polygon (not to be confused with star polygon) is a polygonal region in the plane which is a star domain, i.e., a polygon P is star-shaped, if there exists a point z such that for each point p of P the segment zp lies entirely within P. The set of all points z with the described property is called the kernel of P. Star-shaped polygons are of interest in computational geometry and its applications such as motion planning because of its relation to the notion of visibility: the star-shaped polygon may be informally defined as the one whose whole interior is visible from a single point, assuming that the polygon boundary is not transparent. Convex polygons are star shaped, and a...

ISBN: 978-6-1312-5037-8
Издательство: Книга по требованию
Дата выхода: июль 2011