79 resultados para Trigonometric polynomials
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A group-theoretic method of obtaining more general class of generating functions from a given class of partial quasi-bilateral generating functions involving Hermite, Laguerre and Gegenbaur polynomials are discussed.
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* Part of this work was done while the second author was on a visit at Tel Aviv University in March 2001
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* This work has been supported by the Office of Naval Research Contract Nr. N0014-91-J1343, the Army Research Office Contract Nr. DAAD 19-02-1-0028, the National Science Foundation grants DMS-0221642 and DMS-0200665, the Deutsche Forschungsgemeinschaft grant SFB 401, the IHP Network “Breaking Complexity” funded by the European Commission and the Alexan- der von Humboldt Foundation.
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* Dedicated to the memory of Prof. N. Obreshkoff
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The maximal cardinality of a code W on the unit sphere in n dimensions with (x, y) ≤ s whenever x, y ∈ W, x 6= y, is denoted by A(n, s). We use two methods for obtaining new upper bounds on A(n, s) for some values of n and s. We find new linear programming bounds by suitable polynomials of degrees which are higher than the degrees of the previously known good polynomials due to Levenshtein [11, 12]. Also we investigate the possibilities for attaining the Levenshtein bounds [11, 12]. In such cases we find the distance distributions of the corresponding feasible maximal spherical codes. Usually this leads to a contradiction showing that such codes do not exist.
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Estimates Calculating Algorithms have a long story of application to recognition problems. Furthermore they have formed a basis for algebraic recognition theory. Yet use of ECA polynomials was limited to theoretical reasoning because of complexity of their construction and optimization. The new recognition method “AVO- polynom” based upon ECA polynomial of simple structure is described.
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Mathematics Subject Classification: 26A33, 33E12, 33C20.
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Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90
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AMS Subj. Classification: 65D07, 65D30.
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Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09
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2000 Mathematics Subject Classification: 12D10.
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2000 Mathematics Subject Classification: 13P05, 14M15, 14M17, 14L30.
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2000 Mathematics Subject Classification: 16R50, 16R10.
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2000 Mathematics Subject Classification: 12D10.
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2000 Mathematics Subject Classification: Primary 20F55, 13F20; Secondary 14L30.