Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to...

ISBN: 978-6-1311-2098-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! 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. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." Данное издание не является оригинальным....

ISBN: 978-6-1312-5200-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! 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. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." Данное издание не является оригинальным....

ISBN: 978-6-1312-5207-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, Stirling numbers of the second kind, together with Stirling numbers of the first kind, are one of the two types of Stirling numbers. They commonly occur in the combinatorics, where they appear in the study of partitions. The Stirling numbers of the first and second kind can be understood to be inverses of one-another, when taken as triangular matrices. This article is devoted to specifics of Stirling numbers of the second kind; further identities linking the two kinds, and general information, is given in the article on Stirling numbers. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1303-3422-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, Stirling numbers of the second kind, together with Stirling numbers of the first kind, are one of the two types of Stirling numbers. They commonly occur in the combinatorics, where they appear in the study of partitions. The Stirling numbers of the first and second kind can be understood to be inverses of one-another, when taken as triangular matrices. This article is devoted to specifics of Stirling numbers of the second kind; further identities linking the two kinds, and general information, is given in the article on Stirling numbers. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1303-4773-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, Stirling numbers arise in a variety of combinatorics problems. They are named after James Stirling, who introduced them in the 18th century. Two different sets of numbers bear this name: the Stirling numbers of the first kind and the Stirling numbers of the second kind. Several different notations for the Stirling numbers are in use. Stirling numbers of the first kind are written with a small s, and those of the second kind with a large S. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-6214-0
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Can be obtained by rearranging Stirling's extended formula and observing a coincidence between the resultant power series and the Taylor series expansion of the hyperbolic sine function. This approximation is good to more than 8 decimal digits for z with a real part greater than 8. Robert H. Windschitl suggested it in 2002 for computing the Gamma function with fair accuracy on calculators with limited program or register memory (see link 'Toth'). Gergo Nemes proposed in 2007 an approximation which gives the same number of exact digits as the Windschitl approximation but is much simpler. Данное издание не является оригинальным. Книга печатается...

ISBN: 978-6-1312-5214-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, Stirling numbers arise in a variety of combinatorics problems. They are named after James Stirling, who introduced them in the 18th century. Two different sets of numbers bear this name: the Stirling numbers of the first kind and the Stirling numbers of the second kind. Stirling numbers of the first kind, together with the Stirling numbers of the second kind, are the two types of Stirling numbers. They commonly occur in combinatorics, where they appear in the study of permutations. The Stirling numbers of the first and second kind can be understood to be inverses of one-another, when taken as triangular matrices. This article is devoted to specifics of Stirling numbers of the...

ISBN: 978-6-1303-3296-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, Stirling numbers of the first kind, together with the Stirling numbers of the second kind, are the two types of Stirling numbers. They commonly occur in combinatorics, where they appear in the study of permutations. The Stirling numbers of the first and second kind can be understood to be inverses of one-another, when taken as triangular matrices. This article is devoted to specifics of Stirling numbers of the first kind; further identities linking the two kinds, and general information, is given in the article on Stirling numbers. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1303-4759-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, Stirling numbers arise in a variety of combinatorics problems. They are named after James Stirling, who introduced them in the 18th century. Two different sets of numbers bear this name: the Stirling numbers of the first kind and the Stirling numbers of the second kind. Stirling numbers of the first kind, together with the Stirling numbers of the second kind, are the two types of Stirling numbers. They commonly occur in combinatorics, where they appear in the study of permutations. The Stirling numbers of the first and second kind can be understood...

ISBN: 978-6-1303-3288-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The use of exponential generating functions or EGFs to study the properties of Stirling numbers is a classical exercise in combinatorics and possibly the canonical example of how symbolic combinatorics, the method that encapsulates the fundamental theorem of combinatorial enumeration, is used. It also illustrates the parallels in the construction of these two types of numbers, lending support to the binomial-style notation that is used for them. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-6234-8
Издательство: Книга по требованию
Дата выхода: июль 2011

Two stochastic volatility extensions of the Swap Market Model, one with jumps and the other without, are derived. In both stochastic volatility extensions of the Swap Market Model the instantaneous volatility of the forward swap rates evolves according to a square-root diffusion process. In the jump-diffusion stochastic volatility extension of the Swap Market Model, the proportional log-normal jumps are applied to the swap rates dynamics. The speed, the flexibility and the accuracy of the fast fractional Fourier transform made possible a fast calibration to European swaption market prices. A specific functional form of the instantaneous swap rate volatility structure was used to meet the observed evidence that volatility of the...

ISBN: 978-3-6391-4196-2
Издательство: Книга по требованию
Дата выхода: июль 2011

ISBN: 978-3-8383-0088-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, some boundary value problems can be solved using the methods of stochastic analysis. Perhaps the most celebrated example is Shizuo Kakutani's 1944 solution of the Dirichlet problem for the Laplace operator using Brownian motion. However, it turns out that for a large class of semi-elliptic second-order partial differential equations the associated Dirichlet boundary value problem can be solved using an It? process that solves an associated stochastic differential equation. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1312-5265-5
Издательство: Книга по требованию
Дата выхода: июль 2011

The relatively new subject of stochastic differential equations has increasing importance in both theory and applications. The subject draws upon two main sources, probability/stochastic processes and differential equations/dynamical systems. There exists a significant ``culture gap" between the corresponding research communities. The objective of the dissertation project is to present a concise yet mostly self-contained theory of stochastic differential equations from the differential equations/dynamical systems point of view, primarily incorporating semigroup theory and functional analysis techniques to study the solutions. Prerequisites from probability/stochastic processes are developed as needed. For continuous-time stochastic...

ISBN: 978-3-6391-2648-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Stochastic resonance (SR) is observed when noise added to a system changes the system's behaviour in some fashion. More technically, SR occurs if the signal-to-noise ratio of a nonlinear system or device increases for moderate values of noise intensity. It often occurs in bistable systems or in systems with a sensory threshold and when the input signal to the system is "sub-threshold". For lower noise intensities, the signal does not cause the device to cross threshold, so little signal is passed through it. For large noise intensities, the output is dominated by the noise, also leading to a low signal-to-noise ratio. For moderate intensities, the noise allows the signal to reach threshold, but...

ISBN: 978-6-1312-5276-1
Издательство: Книга по требованию
Дата выхода: июль 2011

In probability theory, a stochastic process, or sometimes random process, is the counterpart to a deterministic process. Instead of dealing with only one possible "reality" of how the process might evolve under time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths are more probable and others less. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1303-0223-8
Издательство: Книга по требованию
Дата выхода: июль 2011

Stochastic replicator dynamics pertains to a population of players (individuals, businesses, animals, bacteria, etc.), each programmed to use a single strategy (or type of behavior). The dynamics aspect is related to the change in proportions of players who are applying the given strategies. This work examines the stochastic replicator dynamics driven by white Gaussian noise (WGN) in the Stratonovich form. This approach provides more natural results concerning stochastic stability, instability and extinction of pure strategies of stochastic replicator dynamics models. It is demonstrated that the asymptotic behavior of the system with two pure strategies depends only on the pay-off matrix and does not depend on the intensity of the random...

ISBN: 978-3-6390-1250-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Stochastic volatility models are used in the field of Mathematical finance to evaluate derivative securities, such as options. The name derives from the models' treatment of the underlying security's volatility as a random process, governed by state variables such as the price level of the underlying security, the tendency of volatility to revert to some long-run mean value, and the variance of the volatility process itself, among others. Stochastic volatility models are one approach to resolve a shortcoming of the Black-Scholes model. In particular, these models assume that the underlying volatility is constant over the life of the derivative, and...

ISBN: 978-6-1311-6688-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Monte Carlo method-based optimization techniques sample the objective function by randomly "hopping" from the current solution vector to another with a difference in the function value of ?E. The acceptance probability of such a trial jump is in most cases chosen to be minleft(1;expleft(-betacdotDelta Eright)right) (Metropolis criterion) with an appropriate parameter ?. The general idea of STUN is to circumvent the slow dynamics of ill-shaped energy functions that one encounters for example in spin glasses by tunneling through such barriers. This goal is achieved by Monte Carlo sampling of a transformed function that lacks this slow dynamics. In the "standard-form" the transformation reads....

ISBN: 978-6-1312-5277-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Stochastic diffusion search (SDS), was first described in 1989 as a population-based, pattern-matching algorithm [Bishop, 1989]. It belongs to a family of swarm intelligence and naturally inspired search and optimisation algorithms which includes ant colony optimization, particle swarm optimization and genetic algorithms. Unlike stigmergetic communication employed in ant colony optimization, which is based on modification of the physical properties of a simulated environment, SDS uses a form of direct (one-to-one) communication between the agents similar to the tandem calling mechanism employed by one species of ants, Leptothorax acervorum. Данное издание не является...

ISBN: 978-6-1312-5261-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A stochastic differential equation is a differential equation in which one or more of the terms is a stochastic process, thus resulting in a solution which is itself a stochastic process. Typically, SDEs incorporate white noise which can be thought of as the derivative of Brownian motion; however, it should be mentioned that other types of random fluctuations are possible, such as jump processes. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-6263-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! An extensive theoretical literature has grown up around these algorithms, concerning conditions for convergence, rates of convergence, multivariate and other generalizations, proper choice of step size, possible noise models, and so on. These methods are also applied in control theory, in which case the unknown function which we wish to optimize or find the zero of may vary in time. In this case, the step size an should not converge to zero but should be chosen so as to track the function. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1312-5220-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In game theory, a stochastically stable equilibrium is a refinement of the evolutionarily stable state in evolutionary game theory, proposed by Dean Foster and Peyton Young. An evolutionary stable state S is also stochastically stable if under vanishing noise the probability that the population is in the vicinity of state S does not go to zero. The concept is extensively used in models of learning in populations, where "noise" is used to model experimentation or replacement of unsuccessful players with new players (random mutation). Over time, as the need for experimentation dies down or the population becomes stable, the population will converge towards a subset of evolutionarily stable...

ISBN: 978-6-1312-5279-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Stochastic simulation algorithms and methods were initially developed to analyse chemical reactions involving large numbers of species with complex reaction kinetics. The first algorithm, the Gillespie algorithm was proposed by Dan Gillespie in 1977. It is an exact procedure for numerically simulating the time evolution of a well-stirred chemically reacting system. The algorithm is a Monte Carlo type method. In order to determine the next event in a stochastic simulation, the rates of all possible changes to the state of the model are computed, and then ordered in an array. Next, the cumulative sum of the array is taken, and the final cell contains the number R, where R is the total event rate....

ISBN: 978-6-1304-9693-7
Издательство: Книга по требованию
Дата выхода: июль 2011