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This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows the basics. This book offers something new, which may satisfy the desire of such a reader. However, we state every definition and every essential fact concerning classical modular forms of one variable. One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically. Ultimately, we concentrate on the following two themes: (I) The correspondence between the forms of half-integral weight and those of integral weight. (II) The arithmeticity of various Dirichlet series associated with modular forms of integral or half-integral weight. Goro Shimura is currently a professor emeritus of mathematics at Princeton University.

Numerical analysis --- numerieke analyse

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This volume provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear variational problems. The author avoids giving the results in the most general, abstract form so that it is easier for the reader to understand more clearly the essential ideas involved. Many examples are included to show the usefulness of the derived error estimates. Audience This volume is suitable for researchers and graduate students in applied and computational mathematics, and in engineering.

Numerical analysis --- numerieke analyse

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This book sets out to state computationally verifiable initial conditions for predicting the immediate appearance of the guaranteed and fast convergence of iterative root finding methods. Attention is paid to iterative methods for simultaneous determination of polynomial zeros in the spirit of Smale's point estimation theory, introduced in 1986. Some basic concepts and Smale's theory for Newton's method, together with its modifications and higher-order methods, are presented in the first two chapters. The remaining chapters contain the recent author's results on initial conditions guaranteing convergence of a wide class of iterative methods for solving algebraic equations. These conditions are of practical interest since they depend only on available data, the information of a function whose zeros are sought and initial approximations. The convergence approach presented can be applied in designing a package for the simultaneous approximation of polynomial zeros.

Numerical analysis --- numerieke analyse

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Numerical analysis --- numerieke analyse

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The volume LNCS 12296 constitutes the papers of the 17th International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research which will be held online in September 2020. The 32 regular papers presented together with 4 abstracts of fast-track papers were carefully reviewed and selected from a total of 72 submissions. Additionally, this volume includes the 4 abstracts and 2 invited papers by plenary speakers. The conference program also included a Master Class on the topic “Recent Advances in Optimization Paradigms and Solving Technology".

Numerical analysis --- numerieke analyse