Theorem

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  • Logic for Computer Science" provides an introduction to mathematical logic, with emphasis on proof theory and procedures for constructing formal proofs of formulae algorithmically. It is designed primarily for students, computer scientists, and, more generally, for mathematically inclined readers interested in the formalization of proofs and the foundations of automatic theorem proving. Since the main emphasis of the text is on the study of proof systems and algorithmic methods for constructing proofs, it contains features rarely found in other texts on logic.

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  • In this chapter we investigate a general optimization problem in a real normed space. For such a problem we present assumptions under which at least one minimal point exists. Moreover, we formulate simple statements on the set of minimal points. Finally the existence theorems obtained are applied to approximation and optimal control problems.

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  • Let X be a smooth quasiprojective subscheme of Pn of dimension m ≥ 0 over Fq . Then there exist homogeneous polynomials f over Fq for which the intersection of X and the hypersurface f = 0 is smooth. In fact, the set of such f has a positive density, equal to ζX (m + 1)−1 , where ζX (s) = ZX (q −s ) is the zeta function of X. An analogue for regular quasiprojective schemes over Z is proved, assuming the abc conjecture and another conjecture. 1. Introduction The classical Bertini theorems say that if a subscheme...

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  • The induction hypotheses Application to endoscopic and stable expansions Cancellation of p-adic singularities Separation by infinitesimal character Elimination of restrictions on f Local trace formulas Local Theorem 1 Weak approximation Global Theorems 1 and 2 10. Concluding remarks Introduction This paper is the last of three articles designed to stabilize the trace formula. Our goal is to stabilize the global trace formula for a general connected group, subject to a condition on the fundamental lemma that has been established in some special cases.

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  • The usual index theorems for holomorphic self-maps, like for instance the classical holomorphic Lefschetz theorem (see, e.g., [GH]), assume that the fixed-points set contains only isolated points. The aim of this paper, on the contrary, is to prove index theorems for holomorphic self-maps having a positive dimensional fixed-points set. The origin of our interest in this problem lies in holomorphic dynamics.

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  • We produce a canonical filtration for locally free sheaves on an open p-adic annulus equipped with a Frobenius structure. Using this filtration, we deduce a conjecture of Crew on p-adic differential equations, analogous to Grothendieck’s local monodromy theorem (also a consequence of results of Andr´ and of Mebkhout). Namely, given a finite locally free sheaf on an open e p-adic annulus with a connection and a compatible Frobenius structure, the module admits a basis over a finite cover of the annulus on which the connection acts via a nilpotent matrix. ...

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  • In this paper, we solve the following extension problem. Problem 1. Suppose we are given a function f : E → R, where E is a given subset of Rn. How can we decide whether f extends to a Cm−1,1 function F on Rn ? Here, m ≥ 1 is given. As usual, Cm−1,1 denotes the space of functions whose (m − 1)rst derivatives are Lipschitz 1. We make no assumption on the set E or the function f. This problem, with Cm in place of Cm−1,1, goes back to Whitney [15], [16], [17]. To answer it, we prove the following sharp form of the Whitney extension theorem....

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  • The purpose of this paper is to give a generalization of Mason’s theorem by the Wronskian technique over fields of characteristic 0. Keywords: The Wronskian technicque, Marson’s theorem. 1. Introduction Let F be a fixed algebraically closed field of characteristic 0. Let f (z) be a polynomial non - constants which coefficients in F and let n(1/f ) be the number of distinct zeros of f . Then we have the following. Marson’s theorem. ([2]). Let a(z), b(z), c(z) be relatively prime polynomials in F and not all constants such that a + b = c. Then max {deg(a), deg(b),...

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  • Tham khảo sách 'real functions of several variables - examples of applications of gauβ’s and stokes’s theorems and related topics calculus 2c-9', khoa học tự nhiên, toán học phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả

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  • We discuss algorithms for generation within the Lambek Theorem Proving Framework. Efficient algorithms for generation in this framework take a semantics-driven strategy. This strategy can be modeled by means of rules in the calculus that are geared to generation, or by means of an algorithm for the Theorem Prover. The latter possibility enables processing of a bidirectional calculus. Therefore Lambek Theorem Proving is a natural candidate for a 'uniform' architecture for natural language parsing and generation.

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  • it follows as a theorem from a set of axioms and inference rules. Especially by the work of Van Benthem (1986) and Moortgat (1988) this view, which we will name with Moortgat (1987a) Lambek Theorem Proving (LTP; Lambek, 1958), has become popular among a number of linguists. The descriptive power of LTP can be extended if unification (Shieber, 1986) is added. Several theories have been developed that combine categorial formalisms and unification based formalisms. Within Unification Categorial Grammar (UCG, Calder et al., 1988, Zeevat et al.

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  • Chapter 8 provides knowledge of sampling methods and central limit theorem. When you have completed this chapter, you will be able to: Explain under what conditions sampling is the proper way to learn something about a population, describe methods for selecting a sample, define and construct a sampling distribution of the sample mean,...

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  • Lecture Electric circuit theory: Circuit theorems presents the following content: Source transformation, linearity and superposition, Thévenin Equivalent Subcircuits, Norton Equivalent Subcircuits, maximum power transfer.

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  • There are many books on linear algebra, in which many people are really great ones (see for example the list of recommended literature). One might think that one does no books on this subject. Choose a person's words more carefully, it can deduce that this book contains everything needed and the best possible, and so any new book, just repeat the old ones. This idea is evident wrong, but almost everywhere. New results in linear algebra and are constantly appearing so refreshing, simple and neater proof of the famous theorem.

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  • This book is devoted to the theory of probabilistic information measures and their application to coding theorems for information sources and noisy chan- nels. The eventual goal is a general development of Shannon's mathematical theory of communication, but much of the space is devoted to the tools and methods required to prove the Shannon coding theorems. These tools form an area common to ergodic theory and information theory and comprise several quantitative notions of the information in random variables, random processes, and dynamical systems....

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  • This book contains the basics of linear algebra with an emphasis on nonstandard and neat proofs of known theorems. Many of the theorems of linear algebra obtained mainly during the past 30 years are usually ignored in text-books but are quite accessible for students majoring or minoring in mathematics. These theorems are given with complete proofs. There are about 230 problems with solutions.

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasij-nonexpansive mappings Jong Kyu Kim

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  • Written by two foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and for experts in related fields.

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Fixed Point Theorems for Generalized Weakly Contractive Condition in Ordered Metric Spaces

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Common Fixed Point Theorems for Four Mappings on Cone Metric Type Space

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