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Regular coordinates and reduction of deformation equations for Fuchsian systems

Yoshishige Haraoka (2012)

Banach Center Publications

For a Fuchsian system d Y / d x = ( j = p ( A j ) / ( x - t j ) ) Y , (F) t , t , . . . , t p being distinct points in ℂ and A , A , . . . , A p M ( n × n ; ) , the number α of accessory parameters is determined by the spectral types s ( A ) , s ( A ) , . . . , s ( A p ) , where A = - j = 1 p A j . We call the set z = ( z , z , . . . , z α ) of α parameters a regular coordinate if all entries of the A j are rational functions in z. It is not yet known that, for any irreducibly realizable set of spectral types, a regular coordinate does exist. In this paper we study a process of obtaining a new regular coordinate from a given one by a coalescence of eigenvalues of the matrices...

Reliability for Beta Models

Nadarajah, Saralees (2002)

Serdica Mathematical Journal

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...

Renewal Processes of Mittag-Leffler and Wright Type

Mainardi, Francesco, Gorenflo, Rudolf, Vivoli, Alessandro (2005)

Fractional Calculus and Applied Analysis

2000 MSC: 26A33, 33E12, 33E20, 44A10, 44A35, 60G50, 60J05, 60K05.After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and the renewal process of Wright type, so named by us because special functions of Mittag-Leffler and of Wright type appear in the definition of the relevant waiting times. We compare these three processes with each other, furthermore consider corresponding...

Representations of Jordan algebras and special functions

Giancarlo Travaglini (1991)

Colloquium Mathematicae

This paper is concerned with the action of a special formally real Jordan algebra U on an Euclidean space E, with the decomposition of E under this action and with an application of this decomposition to the study of Bessel functions on the self-adjoint homogeneous cone associated to U.

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