High Quality Content by WIKIPEDIA articles! In linguistics, number names (or numerals) are specific words in a natural language that represent numbers. In writing, numerals are symbols also representing numbers. In linguistics, the terms representing numbers can be classified according to their use: * Cardinal numerals: describe quantity - one, two, three, etc. * Ordinal numerals: describe position in a sequential order - first, second, third, etc.; the terms next and last may also be considered a kind of ordinals. * Partitive numerals: describe division into fractions - half, third, quarter, etc. * Multiplicative numerals: describe repetition - once, twice, thrice, etc. Данное издание не является...

ISBN: 978-6-1303-3363-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles!In mathematics education, a number sentence is typically an equation or inequality expressed using numbers and common symbols. The term is used in primary level mathematics teaching in the US, UK, Australia, New Zealand and South Africa.The term is used as means of asking students to write down equations using simple mathematical symbols (numerals, the four basic mathematical operators, equality symbol). Sometimes boxes or shapes are used to indicate unknown values. As such number sentences are used to introduce students to notions of structure and algebra prior to a more formal treatment of these concepts. Данное издание не является оригинальным. Книга...

ISBN: 978-6-1311-4076-1
Издательство: Книга по требованию
Дата выхода: июль 2011

Number, Natural Number, Negative and Non – negative numbers, Rational Number, real Number, Complex Number, Computable Number, Polygonal number, Roman Numerals, 0 (number), Triangular number, Tetrahedral Number Irrational Number, Prime number, Algebraic number, Prime number Theorem, Mythical Number, Numeral System, Hyper complex Number, Imaginary number, Integer, Infinity, Indian Numerals, Hindu – Arabic numeral System, Hebrew numerals, Greek numerals, Transcendental number, Serreal, Telephone number, Serial Number and International Standard Book Number Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1300-0037-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. Number theory may be subdivided into several fields, according to the methods used and the type of questions investigated. The terms "arithmetic" or "the higher arithmetic" as nouns are also used to refer to number theory. These are somewhat older terms, which are no longer as popular as they once were. However the word "arithmetic" is popularly used as an adjective rather than the more cumbersome phrase "number-theoretic", and also "arithmetic of" rather than "number theory of". e.g. (arithmetic...

ISBN: 978-6-1303-3370-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Number Forms are Unicode characters which have specific meaning as numbers, but are constructed from other characters. They consist primarily of vulgar fractions and roman numerals. They are placed in the Unicode codepoint range 0x2150 through 0x218F (hexadecimal). Unicode is a computing industry standard for the consistent representation and manipulation of text expressed in most of the world's writing systems. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1311-6149-0
Издательство: Книга по требованию
Дата выхода: июль 2011

Nonpolynomial Spline Methods (NPSMs) are presented for solving single and system of boundary value problems (BVPs) of orders two, four, six and an 2mth order BVPs respectively. Also, the numerical solution of singular second order BVPs is considered. Optimal order approximations to the solutions of these boundary value problems are obtained. The matrix properties of these BVPs, arising from the discretization of systems of BVPs by NPSMs, are discussed. Sufficient conditions for the optimal convergence for NPSMs are obtained. Also, NPSMs generalize other recent finite difference methods and polynomial spline methods through arbitrary choices of some defined parameters in these methods. Numerical results demonstrated by the NPSMs are shown...

ISBN: 978-3-8433-8664-7
Издательство: Книга по требованию
Дата выхода: июль 2011

This work pertains to modern, interdisciplinary research trends in nanomaterials. The author presents a novel method with major potential for various applications such as ferromagnetic brakes and valves; nanosized shock absorbers, and in the medical field, heart valves and medical nanorobots. A mathematical model is constructed with numerical solutions proposed for the system of equations describing the model. The underlying assumption is that a ferromagnetic suspension can be regarded as a continuous medium. Such an assumption was originally suggested in Peskin’s Immersed Boundary (IB) method. The IB method is coupled with Chorin’s Projection method to construct a finite differences scheme for solving a boundary value case. The...

ISBN: 978-3-6391-7390-1
Издательство: Книга по требованию
Дата выхода: июль 2011

The book has three chapters and an Appendix on different methods to calculate approximate areas of plain regions enclosed by curves. Tutorials, Tests and Examination Papers of different Universities where the author taught the course at the faculties of Engineering and Business Studies are provided. A short bibliography of books on the subject and alphabetical index of the topics covered are given in the end.The first chapter accounts the different methods for numerical solutions of ordinary differential equations. Picard's, Taylor's, Euler's, Runge-Kutta, Milne's and Adams-Bashforth's methods are given. The problems of curve fittings and spline fittings are explained in the second chapter. The ‘Gaussian method of least squares' for...

ISBN: 978-3-8433-8489-6
Издательство: Книга по требованию
Дата выхода: июль 2011

Der Indeterminismus vieler Probleme der Natur- und Wirtschaftswissenschaften wird in vielen Fallen Mittels stochastischen Differentialgleichungen (SDE) modelliert und analysiert worden. Weil man solche Gleichungen nicht immer exakt losen konnte, ist die Notwendigkeit der Durchfuhrung numerischer Verfahren. Im Gegensatz zum klassischen und Ordnung eins Euler Verfahren, hat das stochastische Verfahren Ordnung 0,5. In dieser Arbeit handel es sich um eine Effiziente Implementierung von Milstein Verfahren (Ordnung eins) zur Simulation von Systemen stochastischer Differentialgleichungen, die die Approximation des doppelfachen Ito Integrales verlangt. Данное издание не является оригинальным. Книга...

ISBN: 978-3-6392-0879-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Numerical ordinary differential equations is the part of numerical analysis which studies the numerical solution of ordinary differential equations. This field is also known under the name numerical integration, but some people reserve this term for the computation of integrals. Many differential equations cannot be solved analytically, in which case we have to satisfy ourselves with an approximation to the solution. The algorithms studied here can be used to compute such an approximation. An alternative method is to use techniques from calculus to obtain a series expansion of the solution. Данное издание не является оригинальным. Книга...

ISBN: 978-6-1303-1902-1
Издательство: Книга по требованию
Дата выхода: июль 2011

The numerical approximation of solutions of ordinary differential equations played an important role in Numerical Analysis and still continues to be an active field of research. In this book we are mainly concerned with the numerical solution of the first-order system of nonlinear two-point boundary value problems. We will focus on the problem of solving singular perturbation problems since this has for many years been a source of difficulty to applied mathematicians, engineers and numerical analysts alike. Firstly, we consider deferred correction schemes based on Mono-Implicit Runge-Kutta (MIRK) and Lobatto formulae. As is to be expected, the scheme based on Lobatto formulae, which are implicit, is more stable than the scheme based on...

ISBN: 978-3-6391-3787-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! This page is about the history of mathematical constant ?. There is a summarizing table at chronology of computation of ?. See also history of ? for other aspects of the evolution of our knowledge about mathematical properties of ?. The earliest evidenced conscious use of an accurate approximation for the length of a circumference with respect to its radius is of 3+1/7th in the designs of the Old Kingdom pyramids in Egypt. The Great Pyramid at Giza, built c.2550-2500 B.C, was precisely 1760 cubits around with a height of 280 cubits (1760/280=2xPi). Egyptologists such as Professors Flinders Petrie and I.E.S Edwards have shown that these circular...

ISBN: 978-6-1303-3394-2
Издательство: Книга по требованию
Дата выхода: июль 2011

The monograph at hand deals with the numerical solution of multiscale problems arising in the modeling of processes in fluid and thermo dynamics. Many of these processes, governed by partial differential equations, are relevant in engineering, geoscience, and environmental studies. More precisely, this monograph discusses the efficient numerical computation of effective macroscopic thermal conductivity tensors of high-contrast composite materials. The term "high-contrast" refers to large variations in the conductivities of the constituents of the composite. Additionally, this monograph deals with the numerical solution of Brinkman's equations. This system of equations adequately models viscous flows in (highly) permeable media. It was...

ISBN: 978-3-8381-1069-1
Издательство: Книга по требованию
Дата выхода: июль 2011

Fluid-structure interaction problems arise in many application fields such as flows around elastic structures or blood flow problems in arteries. One method for solving such a problem is based on a reduction to an equation at the interface, involving the so-called Steklov-Poincare operators. This interface equation is solved by a Newton iteration for which directional derivatives with respect to the interface perturbation have to be evaluated appropriately. One step of the Newton iteration requires the solution of several decoupled linear sub-problems in the structure and the fluid domains. These sub-problems are spatially discretized by a finite element method on hybrid meshes containing different types of elements. For the time...

ISBN: 978-3-8383-7366-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! La numeration arabe comporte plusieurs systemes d'ecriture. On peut en effet utiliser les lettres de l'alphabet arabe, il s'agit de la numeration abjad, ou des signes issus de l'ecriture indienne nagari, ces chiffres indo-arabes sont parfois appeles « chiffres arabo-indiens ». La numeration abjad, surtout dans sa variante orientale, est tres proche de la Gematria hebraique. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1317-8698-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Numeracy is the ability to reason with numbers and other mathematical concepts. To be numerically literate, a person has to be comfortable with logic and reasoning. Some of the areas that are involved in numeracy include: basic numbers, orders of magnitude, geometry, algebra, probability and statistics. The portmanteau of "numerical literacy" was coined in 1959 by the UK Committee on Education, presided over by Sir Geoffrey Crowther. Innumeracy is a lack of numeracy. In the United States, numeracy is also known as Quantitative Literacy, and is familiar to math educators and intellectuals. There is also substantial overlap between conceptions of numeracy and conceptions of statistical literacy....

ISBN: 978-6-1303-3376-8
Издательство: Книга по требованию
Дата выхода: июль 2011

Numeral system. Number names, Number system, Arabic numerals, Grapheme, Positional notation, Eye of Horus, Quinary, Octal, Decimal, Duodecimal, Vigesimal Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1300-5936-1
Издательство: Книга по требованию
Дата выхода: июль 2011

Optimierung ist in der Strukturmechanik seit vielen Jahren ein wichtiges und gut ausgebautes Themengebiet, welches sich auch im industriellen Einsatz bewahrt hat. Die Stromungsoptimierung konnte sich bisher jedoch im industriellen Einsatz nicht erfolgreich durchsetzen. Ursachen hierfur sind zum Einen der hohe Rechenaufwand fur die Losung komplexer partieller Differentialgleichungen und zum Anderen die schwierige Formulierung der Zielfunktion sowie der Nebenbedingungen. Dennoch ist die Integration dieser Thematik in der Industrie von hoher Bedeutung. In der vorliegenden Arbeit werden die Grundlagen der numerischen Stromungsmechanik sowie der optimalen Steuerung dargelegt und ein Steuerungsbeispiel hergeleitet. Es wird gezeigt, in wie weit...

ISBN: 978-3-6393-2892-9
Издательство: Книга по требованию
Дата выхода: июль 2011

For the success of geological sequestration, an accurate estimation of migration patterns of green-house gases is essential. Numerical and mathematical modeling of processes in a domain requires grid generation in the domain, discretization of the continuum equations on the generated grid, solution of the formed linear or nonlinear system of discrete equations and finally visualization of the results. In this work, we present CO2 flow in porous media. We present the mathematical models and their discretization for capturing major physical processes associated with carbon dioxide deposition in geological formations. Some important simulations of practical applications in 2D and 3D are presented. The author has done the verification of the...

ISBN: 978-3-6391-5995-0
Издательство: Книга по требованию
Дата выхода: июль 2011

The logistic Lotka-Volterra predator-prey equations with diffusion based on Luckinbill's experiment with Didinium nasutum as predator and Paramecium aurelia as prey, have been solved numerically along with a third equation to include prey-taxis in the system. The effect of prey-taxis on the dynamics of the population has been examined using three initial conditions, four response functions and three data sets. The stability of the points of equilibria have been established for each model using Routh-Hurwitz conditions and the variational matrix criteria. This has further been verified through numerical simulations. The effect of bifurcation value of the prey-taxis coefficient on the numerical solution has been examined in each case. It...

ISBN: 978-3-6390-9835-8
Издательство: Книга по требованию
Дата выхода: июль 2011

In this book, a time continuous version of the discrete time Couzin-Vicsek algorithm (CVA), which describes the iterations of individual among animals societies such as schools of fish and flocks of birds, is used to simulate the velocities and positions of self-driven particles (SDPs). This algorithm is based on the discrete CVA, which assumes that at each time step, the velocities and positions of the SDPs are updated, and the velocity director of each particle is change to the director of the average velocity of the neighboring particles with addition of noise. We study the behavior of the SDPs subjected to different model parameters such as the interaction radius both in noise and noise free environments, analyzing the stability of...

ISBN: 978-3-8383-8468-9
Издательство: Книга по требованию
Дата выхода: июль 2011

From the first time the author encountered General Linear Methods in general and Almost-Runge-Kutta methods in particular, and realized the enormous potentials and possibilities they provide, there has been a deep desire in the author, to draw the attention of researchers and mathematicians to these methods. As such, in this book the author has engaged in a detailed and comprehensive analysis of Almost Runge-Kutta (ARK) methods, derived new and effective methods especially for non-stiff differential equations. The book provides a comprehensive introduction to numerical methods for solving Ordinary Differential equations, it includes a detailed coverage of Runge-Kutta, linear multistep, and general linear methods,and thoroughly breaks...

ISBN: 978-3-8443-0012-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Numerical Continuation is a method of computing approximate solutions of a system of parameterized nonlinear equations, F(u,lambda) = 0 The parameter ? is usually a real scalar, and the solution an n-vector. For a fixed parameter value ?,, F(ast,lambda) maps Euclidean n-space into itself. Often the original mapping F is from a Banach space into itself, and the Euclidean n-space is a finite dimensional approximation to the Banach space. A steady state, or fixed point, of a parameterized family of flows or maps are of this form, and by discretizing trajectories of a flow or iterating a map, periodic orbits and heteroclinic orbits can also be posed as a solution of F = 0. Данное...

ISBN: 978-6-1303-3404-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! L'Inde a developpe un grand nombre de systemes de numeration, dont chacun peut, a juste titre, etre appele systeme numerique indien. Les systemes presentes ici sont decimaux. Les graphies ci-contre sont une liste de chiffres en ecriture devanagari, suivis de leur prononciation en hindi, et enfin de leur correspondance en chiffres dits « arabes ». Les chiffres arabes sont une evolution du systeme indien. La graphie correspondant au chiffres arabes au Moyen-Orient est d'ailleurs dite « indienne » dans ces pays. Le systeme de numeration traditionnel indien, utilise de nos jours en Inde, Pakistan, Bangladesh, et Myanmar (Birmanie), s'appuie sur un regroupement des decimales (au dela de trois)...

ISBN: 978-6-1318-0953-8
Издательство: Книга по требованию
Дата выхода: июль 2011

Magnetische Flussigkeiten(Ferrofluide) sind Suspensionen magnetischer Nanopartikel in geeigneten, nichtmagnetischen Tragerflussigkeiten. Die haufigste Anwendung der Ferrofluide ist zur Zeit die als Dichtung. In dieser Arbeit konzentrieren wir uns auf ein mathematisches Modell fur Abdichtungen mit Ferrofluiden von Drehfuhrungen und auf die Entwicklung von Algorithmen zur numerischen Behandlung des Modells. Die Stromungsverhaltnisse in Magnetfluiddichtungen werden mit Hilfe eines mathematischen zweidimensionalen gekoppelten Modells beschrieben. Es ist gezeigt, dass die Reduktion des dreidimenionalen Modells auf eine zweidimenionale Betrachtungsweise zulassig ist. Das Modell besteht aus den Navier-Stokes-Gleichungen fur die Sekundarstromung...

ISBN: 978-3-8364-8604-0
Издательство: Книга по требованию
Дата выхода: июль 2011