The Experts below are selected from a list of 19842 Experts worldwide ranked by ideXlab platform
Shaoshi Chen - One of the best experts on this subject based on the ideXlab platform.
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ISSAC - Existence Problem of Telescopers for Rational Functions in Three Variables: the Mixed Cases
Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation, 2019Co-Authors: Shaoshi Chen, Chaochao ZhuAbstract:We present criteria on the existence of telescopers for trivariate rational functions in four mixed Cases, in which discrete and continuous variables appear simultaneously. We reduce the existence problem in the trivariate Case to the exactness testing problem, the separation problem and the existence problem in the Bivariate Case. The existence criteria help us to determine the termination of Zeilberger's algorithm for the input functions studied in this paper.
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existence problem of telescopers beyond the Bivariate Case
International Symposium on Symbolic and Algebraic Computation, 2016Co-Authors: Shaoshi Chen, Qing-hu Hou, George Labahn, Rong-hua WangAbstract:In this paper, we solve the existence problem of telescopers for rational functions in three discrete variables. We reduce the problem to that of deciding the summability of Bivariate rational functions, a problem which has recently been solved. This existence criteria is used, for example, for detecting the termination of Zeilberger's algorithm to the function classes studied in this paper.
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Existence Problem of Telescopers: Beyond the Bivariate Case
arXiv: Symbolic Computation, 2016Co-Authors: Shaoshi Chen, Qing-hu Hou, George Labahn, Rong-hua WangAbstract:In this paper, we solve the existence problem of telescopers for rational functions in three discrete variables. We reduce the problem to that of deciding the summability of Bivariate rational functions, which has been solved recently. The existence criteria we present is needed for detecting the termination of Zeilberger's algorithm to the function classes studied in this paper.
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ISSAC - Existence Problem of Telescopers: Beyond the Bivariate Case
Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '16, 2016Co-Authors: Shaoshi Chen, Qing-hu Hou, George Labahn, Rong-hua WangAbstract:In this paper, we solve the existence problem of telescopers for rational functions in three discrete variables. We reduce the problem to that of deciding the summability of Bivariate rational functions, a problem which has recently been solved. This existence criteria is used, for example, for detecting the termination of Zeilberger's algorithm to the function classes studied in this paper.
Rong-hua Wang - One of the best experts on this subject based on the ideXlab platform.
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existence problem of telescopers beyond the Bivariate Case
International Symposium on Symbolic and Algebraic Computation, 2016Co-Authors: Shaoshi Chen, Qing-hu Hou, George Labahn, Rong-hua WangAbstract:In this paper, we solve the existence problem of telescopers for rational functions in three discrete variables. We reduce the problem to that of deciding the summability of Bivariate rational functions, a problem which has recently been solved. This existence criteria is used, for example, for detecting the termination of Zeilberger's algorithm to the function classes studied in this paper.
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Existence Problem of Telescopers: Beyond the Bivariate Case
arXiv: Symbolic Computation, 2016Co-Authors: Shaoshi Chen, Qing-hu Hou, George Labahn, Rong-hua WangAbstract:In this paper, we solve the existence problem of telescopers for rational functions in three discrete variables. We reduce the problem to that of deciding the summability of Bivariate rational functions, which has been solved recently. The existence criteria we present is needed for detecting the termination of Zeilberger's algorithm to the function classes studied in this paper.
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ISSAC - Existence Problem of Telescopers: Beyond the Bivariate Case
Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '16, 2016Co-Authors: Shaoshi Chen, Qing-hu Hou, George Labahn, Rong-hua WangAbstract:In this paper, we solve the existence problem of telescopers for rational functions in three discrete variables. We reduce the problem to that of deciding the summability of Bivariate rational functions, a problem which has recently been solved. This existence criteria is used, for example, for detecting the termination of Zeilberger's algorithm to the function classes studied in this paper.
Xavier Dahan - One of the best experts on this subject based on the ideXlab platform.
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size of coefficients of lexicographical groobner bases the zero dimensional radical and Bivariate Case
International Symposium on Symbolic and Algebraic Computation, 2009Co-Authors: Xavier DahanAbstract:This work is limited to the zero-dimensional, radical, and Bivariate Case. A lexicographical Grobner basis can be simply viewed as Lagrange interpolation polynomials. In the same way the Chinese remaindering theorem generalizes Lagrange interpolation, we show how a triangular decomposition is linked to a specific Grobner basis (not the reduced one). A bound on the size of the coefficients of this specific Grobner basis is proved using height theory, then a bound is deduced for the reduced Grobner basis. Besides, the link revealed between the Grobner basis and the triangular decomposition gives straightforwardly a numerical estimate to help finding a lucky prime in the context of modular methods.
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ISSAC - Size of coefficients of lexicographical Groöbner bases: the zero-dimensional, radical and Bivariate Case
Proceedings of the 2009 international symposium on Symbolic and algebraic computation - ISSAC '09, 2009Co-Authors: Xavier DahanAbstract:This work is limited to the zero-dimensional, radical, and Bivariate Case. A lexicographical Grobner basis can be simply viewed as Lagrange interpolation polynomials. In the same way the Chinese remaindering theorem generalizes Lagrange interpolation, we show how a triangular decomposition is linked to a specific Grobner basis (not the reduced one). A bound on the size of the coefficients of this specific Grobner basis is proved using height theory, then a bound is deduced for the reduced Grobner basis. Besides, the link revealed between the Grobner basis and the triangular decomposition gives straightforwardly a numerical estimate to help finding a lucky prime in the context of modular methods.
Manuel Úbeda-flores - One of the best experts on this subject based on the ideXlab platform.
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Some new characterizations and properties of quasi-copulas
Fuzzy Sets and Systems, 2009Co-Authors: José Antonio Rodríguez-lallena, Manuel Úbeda-floresAbstract:In this paper we characterize the concept of quasi-copula in three different ways: as a special subclass of aggregation operators, in terms of its associated volume and-for the Bivariate Case-in terms of non-increasing tracks on [0,1]^2. We also provide sufficient conditions and new properties for quasi-copulas.
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Extremes of the mass distribution associated with a trivariate quasi-copula
Comptes Rendus Mathematique, 2007Co-Authors: Bernard De Baets, Hans De Meyer, Manuel Úbeda-floresAbstract:Abstract We identify the extremes of the mass distribution associated with a trivariate quasi-copula and compare our findings with the Bivariate Case. To cite this article: B. De Baets et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).
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On Measures of Multivariate Concordance
2006Co-Authors: Ali Dolati, Manuel Úbeda-floresAbstract:In this paper we formulate a definition for measures of multivariate concordance comparable to the set of axioms proposed by Scarsini (9) for the Bivariate Case. In particular, we study measures of multivariate concordance based on orthant dependence, and provide their sample version. Several examples illustrate our results.
A. Stepanov - One of the best experts on this subject based on the ideXlab platform.
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Numbers of near-maxima for the Bivariate Case
Statistics & Probability Letters, 2009Co-Authors: Ismihan Bairamov, A. StepanovAbstract:Let be independent and identically distributed random vectors with continuous distribution. Let Kn(a,b1,b2) be the number of sample elements that belong to the open rectangle -- numbers of near-maxima in the Bivariate Case. In the present paper, we discuss asymptotic properties of Kn(a,b1,b2) and Kn([infinity],0,[infinity]).