High Quality Content by WIKIPEDIA articles! A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90 degree angle).The side opposite the right angle is called the hypotenuse (side c in the figure above). The sides adjacent to the right angle are called legs (or catheti, singular: cathetus). Side a may be identified as the side adjacent to angle B and opposed to (or opposite) angle A, while side b is the side adjacent to angle A and opposed to angle B.As with any triangle, the area is equal to one half the base multiplied by the corresponding height. In a right triangle, if one leg is taken as the base then the other is height, so the area of a right...

ISBN: 978-6-1312-5526-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, a rigid analytic space is an analogue of a complex analytic space over a nonarchimedean field. They were introduced by John Tate in 1962, as an outgrowth of his work on uniformizing p-adic elliptic curves with bad reduction using the multiplicative group. In contrast to the classical theory of p-adic analytic manifolds, rigid analytic spaces admit meaningful notions of analytic continuation and connectedness. However, this comes at the cost of some conceptual complexity. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1312-5434-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In category theory, a branch of mathematics, a rigid category is a monoidal category where every object is rigid, that is, has a dual X* (the internal Hom [X, 1]) and a morphism 1 ? X ? X* satisfying natural conditions. The category is called right rigid or left rigid according to whether it has right duals or left duals. They were first defined by Dold and Puppe in 1978.An inverse is an object X-1 such that both X ? X-1 and X-1 ? X are isomorphic to 1, the one object of the monoidal category. If an object X has a left (resp. right) inverse X-1 with respect to the tensor product then it is left (resp. right) rigid, and X* = X-1. This means every autonomous category is rigid. Данное...

ISBN: 978-6-1312-5506-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, a rigid analytic space is an analogue of a complex analytic space over a nonarchimedean field. They were introduced by John Tate in 1962, as an outgrowth of his work on uniformizing p-adic elliptic curves with bad reduction using the multiplicative group. In contrast to the classical theory of p-adic analytic manifolds, rigid analytic spaces admit meaningful notions of analytic continuation and connectedness. However, this comes at the cost of some conceptual complexity. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1329-6648-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The MixColumns operation performed by the Rijndael cipher, along with the shift-rows step, is the primary source of diffusion in Rijndael. Each column is treated as a polynomial over GF(28) and is then multiplied modulo x4 + 1 with a fixed polynomial c(x) = 3x3 + x2 + x + 2; the inverse of this polynomial is c ? 1(x) = 11x3 + 13x2 + 9x + 14.In cryptography, the Advanced Encryption Standard (AES) is an encryption standard adopted by the U.S. government. The standard comprises three block ciphers, AES-128, AES-192 and AES-256, adopted from a larger collection originally published as Rijndael. Each of these ciphers has a 128-bit block size, with key sizes of 128, 192 and 256 bits, respectively....

ISBN: 978-6-1312-5591-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! This article describes the S-box used by the Rijndael (aka AES) cryptographic algorithm.The S-box is generated by determining the multiplicative inverse for a given number in Rijndael's finite field (zero, which has no inverse, is set to zero).In cryptography, the Advanced Encryption Standard (AES) is an encryption standard adopted by the U.S. government. The standard comprises three block ciphers, AES-128, AES-192 and AES-256, adopted from a larger collection originally published as Rijndael. Each of these ciphers has a 128-bit block size, with key sizes of 128, 192 and 256 bits, respectively. The AES ciphers have been analyzed extensively and are now used worldwide, as was the case with its...

ISBN: 978-6-1312-5600-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the operations of addition and multiplication.A bijective ring homomorphism is called a ring isomorphism. A ring homomorphism whose domain is the same as its range is called a ring endomorphism. A ring automorphism is a bijective endomorphism.Injective ring homomorphisms are identical to monomorphisms in the category of rings: If f:R?S is a monomorphism which is not injective, then it sends some r1 and r2 to the same element of S. Consider the two maps g1 and g2 from Z[x] to R which map x to r1 and r2, respectively; f o g1 and f o g2 are identical, but since f is a monomorphism this is...

ISBN: 978-6-1312-5612-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings (group rings, division rings, universal enveloping algebras), as well as an array of properties that proved to be of interest both within the theory itself and for its applications, such as homological properties and polynomial identities.Commutative rings are much better understood than noncommutative ones. Due to its intimate connections with algebraic geometry and algebraic number...

ISBN: 978-6-1312-5638-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In algebra and in particular in algebraic combinatorics, the ring of symmetric functions, is a specific limit of the rings of symmetric polynomials in n indeterminates, as n goes to infinity. This ring serves as universal structure in which relations between symmetric polynomials can be expressed in a way independent of the number n of indeterminates (but its elements are neither polynomials nor functions). Among other things, this ring plays an important role in the representation theory of the symmetric groups. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1303-3775-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the ring of integers is the set of integers making an algebraic structure Z with the operations of integer addition, negation, and multiplication. It is a commutative ring, and is the prototypical such by virtue of satisfying only those equations holding of all commutative rings with identity; indeed it is the initial commutative ring, as well as being the initial ring.More generally the ring of integers of an algebraic number field K, often denoted by OK (or mathcal O_K), is the ring of algebraic integers contained in K.Using this notation, we can write Z = OQ since Z as above is the ring of integers of the field Q of rational numbers. And indeed, in algebraic number theory the...

ISBN: 978-6-1312-5632-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, a ringed space is, intuitively speaking, a space together with a collection of commutative rings, the elements of which are "functions" on each open set of the space. Ringed spaces appear throughout analysis and are also used to define the schemes of algebraic geometry.An arbitrary topological space X can be considered a locally ringed space by taking OX to be the sheaf of real-valued (or complex-valued) continuous functions on open subsets of X (there may exist continuous functions over open subsets of X which are not the restriction of any continuous function over X). The stalk at a point x can be thought of as the set of all germs of continuous functions at x; this is a local...

ISBN: 978-6-1312-5645-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Rippling refers to a group of meta-level heuristics, developed primarily in the Mathematical Reasoning Group in the School of Informatics at the University of Edinburgh, and most commonly used to guide inductive proofs in automated theorem proving systems. Rippling may be viewed as a restricted form of rewrite system, where special object level annotations are used to ensure fertilization upon the completion of rewriting, with a measure decreasing requirement ensuring termination for any set of rewrite rules and expression.Raymond Aubin was the first person to use the term "rippling out" whilst working on his 1976 PhD thesis at the University of Edinburgh. He recognised a common pattern of...

ISBN: 978-6-1312-5648-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Risch algorithm, named after Robert H. Risch, is an algorithm for the calculus operation of indefinite integration (i.e., finding antiderivatives). The algorithm transforms the problem of integration into a problem in algebra. It is based on the form of the function being integrated and on methods for integrating rational functions, radicals, logarithms, and exponential functions. Risch, who developed the algorithm in 1968, called it a decision procedure, because it is a method for deciding if a function has an elementary function as an indefinite integral; and also, if it does, determining it. The Risch algorithm is described (in more than 100 pages) in "Algorithms for Computer Algebra" by...

ISBN: 978-6-1312-5690-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Risch algorithm, named after Robert H. Risch, is an algorithm for the calculus operation of indefinite integration (i.e., finding antiderivatives). The algorithm transforms the problem of integration into a problem in algebra. It is based on the form of the function being integrated and on methods for integrating rational functions, radicals, logarithms, and exponential functions. Risch, who developed the algorithm in 1968, called it a decision procedure, because it is a method for deciding if a function has an elementary function as an indefinite integral; and also, if it does, determining it. The Risch algorithm is described (in more than 100 pages) in "Algorithms for Computer Algebra" by...

ISBN: 978-6-1329-6663-6
Издательство: Книга по требованию
Дата выхода: июль 2011

Till a few years ago, malnutrition in children with cancer was persistently ignored.Recently it is recognized that malnutrition is closely related to late stage of malignancy and is a poor prognostic sign.Compared with adults, children are at a greater risk for nutritional depletion since they have a more rapid metabolic rate and greater caloric needs for growth and development.In this book, our aim is to pursue an active investigation of effect malnutrition on children with malignancy using meta analysis.The studies we have included here were conducted in the Department of Pediatric Haemato-Oncology, Bangabandhu Sheikh Mujib Medical University (BSMMU).Meta analysis is a statistical method to combine evidences or results obtained from...

ISBN: 978-3-6392-0303-5
Издательство: Книга по требованию
Дата выхода: июль 2011

Risk assessment is a step in a risk management process. Risk assessment is the determination of quantitative or qualitative value of risk related to a concrete situation and a recognized threat (also called hazard). Quantitative risk assessment requires calculations of two components of risk: R, the magnitude of the potential loss L, and the probability p, that the loss will occur. Methods may differ whether it is about general financial decisions or environmental or public health risk assessment. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-0295-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematical finance, a risk-neutral measure, which is an equivalent martingale measure, or Q-measure is a probability measure that results when one assumes that the current value of all financial assets is equal to the expected value of the future payoff of the asset discounted at the risk-free rate. The concept is used in the pricing of derivatives. In an actual economy, prices of assets depend crucially on their risk. Investors typically demand payment for bearing uncertainty. Therefore, today's price of a claim on a risky amount realised tomorrow will generally differ from its expected value. Most commonly, investors are risk-averse and today's price is below the expectation,...

ISBN: 978-6-1329-6677-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematical finance, a risk-neutral measure, equivalent martingale measure, or Q-measure is a probability measure that results when one assumes that the current value of all financial assets is equal to the expected value of the future payoff of the asset discounted at the risk-free rate. The concept is used in the pricing of derivatives.In an actual economy, prices of assets depend crucially on their risk. Investors typically demand payment for bearing uncertainty. Therefore, today's price of a claim on a risky amount realised tomorrow will generally differ from its expected value. Most commonly, investors are risk-averse and today's price is below the expectation, remunerating those who...

ISBN: 978-6-1312-5721-6
Издательство: Книга по требованию
Дата выхода: июль 2011

Работа посвящена изучению и развитию разрывного метода Галеркина (RKDG-метода), который является обобщением метода конечных объемов на случай кусочно-полиномиальной пространственной аппроксимации решения. Актуальность применения RKDG-метода обусловлена сложностью современных прикладных задач и необходимостью использования численных методов, позволяющих получать высокий порядок аппроксимации на...

ISBN: 978-3-8433-1757-3
Издательство: Книга по требованию
Дата выхода: январь 2011

High Quality Content by WIKIPEDIA articles! In computational complexity theory, RL (Randomized Logarithmic-space), sometimes called RLP (Randomized Logarithmic-space Polynomial-time), is the complexity class of problems solvable in logarithmic space and polynomial time with probabilistic Turing machines with one-sided error. It is named in analogy with RP, which is similar but has no logarithmic space restriction. The probabilistic Turing machines in the definition of RL never accept incorrectly but are allowed to reject incorrectly less than 1/3 of the time; this is called one-sided error. The constant 1/3 is arbitrary; any x with 0 Данное издание не является оригинальным. Книга...

ISBN: 978-6-1312-5768-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In abstract algebra, a rng (also called a pseudo-ring or non-unital ring) is an algebraic structure satisfying the same properties as a ring, except that multiplication need not have an identity element. The term "rng" (pronounced rung) is meant to suggest that it is a "ring" without an "identity element", i. Many authors do not require rings to have a multiplicative identity, so the concept discussed here is just what these authors call a ring. Of course all rings are rngs. A simple example of a rng that is not a ring is given by the even integers with the ordinary addition and multiplication of integers. Another example is given by the set of all 3-by-3 real matrices whose bottom row is zero....

ISBN: 978-6-1320-0444-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In graph theory the road coloring theorem, known until recently as the road coloring conjecture, deals with synchronized instructions. The issue involves whether by using such instructions, one can reach or locate an object or destination from any other point within a network (which might be a representation of city streets or a maze). In the real world, this phenomenon would be as if you called a friend to ask for directions to his house, and he gave you a set of directions that worked no matter where you started from. This theorem also has implications in symbolic dynamics. The theorem was first conjectured in 1970 by Benjamin Weiss and Roy Adler. It was proved by Avraham Trahtman in...

ISBN: 978-6-1305-2965-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Robert Eastaway is an author who is active in the popularisation of mathematics. He is a former pupil of The King's School, Chester, England and has a degree in Engineering and Management Science from the University of Cambridge. He was made President of the UK Mathematical Association for 2007/2008. Eastaway is a keen cricket player and was one of the originators of the International Rankings of Cricketers. He is also a former puzzle-writer for the New Scientist Magazine and he has been involved in live mathematics shows on Virgin Radio (now Absolute Radio). He is the Director of Maths Inspiration, a national programme of maths lectures for teenagers which involves some of the UK's leading...

ISBN: 978-6-1308-9276-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In probability theory, Robbins' problem of optimal stopping, named after Herbert Robbins, is sometimes referred to as the fourth secretary problem or the problem of minimizing the expected rank with full information. Its statement is as follows. Let X1, ... , Xn be independent, identically distributed random variables, uniform on [0, 1]. We observe the Xk's sequentially and must stop on exactly one of them. No recall of preceding observations is permitted. What stopping rule minimizes the expected rank of the selected observation, and what is its corresponding value? Данное издание не является оригинальным. Книга печатается по...

ISBN: 978-6-1312-5794-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In abstract algebra, a Robbins algebra is an algebra containing a single binary operation, usually denoted by lor, and a single unary operation usually denoted by neg. From these axioms, Huntington derived the usual axioms of Boolean algebra. Specifically, what Huntington proved was that if we take lor to interpret Boolean join, neg to interpret Boolean complement and use lor and neg to define Boolean meet and the constants 0 and 1, then the axioms for a Boolean algebra are satisfied.Very soon thereafter, Herbert Robbins posed the Robbins conjecture, namely that the Huntington axiom could be replaced with Robbins's axiom, and the result would still be a Boolean algebra in the sense explained in...

ISBN: 978-6-1312-5780-3
Издательство: Книга по требованию
Дата выхода: июль 2011