992 resultados para special functions
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The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.
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In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R = Pr(X2 < X1 ) when X1 and X2 are independent random variables belonging to the same univariate family of distributions. The algebraic form for R = Pr(X2 < X1 ) has been worked out for the majority of the well-known distributions including Normal, uniform, exponential, gamma, weibull and pareto. However, there are still many other distributions for which the form of R is not known. We have identified at least some 30 distributions with no known form for R. In this paper we consider some of these distributions and derive the corresponding forms for the reliability R. The calculations involve the use of various special functions.
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Partially supported by Grant MM-428/94 of MESC.
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2000 MSC: 26A33, 33E12, 33E20, 44A10, 44A35, 60G50, 60J05, 60K05.
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Mathematics Subject Classification: 33E12, 33FXX PACS (Physics Abstracts Classification Scheme): 02.30.Gp, 02.60.Gf
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2000 Mathematics Subject Classification: 33D15, 33D90, 39A13
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This survey is devoted to some fractional extensions of the incomplete lumped formulation, the lumped formulation and the formulation of Lauwerier of the temperature field problem in oil strata. The method of integral transforms is used to solve the corresponding boundary value problems for the fractional heat equation. By using Caputos differintegration operator and the Laplace transform, new integral forms of the solutions are obtained. In each of the different cases the integrands are expressed in terms of a convolution of two special functions of Wrights type.
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2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15
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2000 Mathematics Subject Classification: 26A33, 33C60, 44A20
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Mathematics Subject Classification: 26A33, 33C60, 44A15
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, - u(x, y, t), D = [0, a] [0, b] [0, ). , 2x 2y. u v C(D). . , , (C(D), ).
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. , . , - . . . , . . , , . , - , . , .
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. , . - . . xx yy . . . . .
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MSC 2010: 33-00, 33C45, 33C52, 30C15, 30D20, 32A17, 32H02, 44A05