Some exponentially decreasing error bounds for a numerical inversion of the Laplace transform

Convergence properties of a class of least-squares methods for finding approximate inverses of the Laplace transform are obtained by using reproducing kernel Hilbert space techniques (or, alternatively, related minimization techniques) and some classical interpolation results.     

Exit times for a class of piecewise exponential Markov processes with two-sided jumps

We consider first passage times for piecewise exponential Markov processes that may be viewed as Ornstein–Uhlenbeck processes driven by compound Poisson processes. We allow for two-sided jumps and as a main result we derive the joint Laplace transform of the first passage time of a lower level and the resulting undershoot when passage happens as a consequence of a downward (negative) jump. The Laplace transform is determined using complex contour integrals and we illustrate how the choice of contours depends in a crucial manner on the particular form of the negative jump part, which is allowed to belong to a dense class of probabilities. We give extensions of the main result to two-sided exit problems where the negative jumps are as before but now it is also required that the positive jumps have a distribution of the same type. Further, extensions are given for the case where the driving Lévy process is the sum of a compound Poisson process and an independent Brownian motion. Examples are used to illustrate the theoretical results and include the numerical evaluation of some concrete exit probabilities. Also, some of the examples show that for specific values of the model parameters it is possible to obtain closed form expressions for the Laplace transform, as is the case when residue calculus may be used for evaluating the relevant contour integrals.     

关于具有泛分解的态射的广义逆

本文给出了预加范畴中具有泛分解的态射的（１,…,ｉ）－逆存在的条件及其表达式．特别地,得到了这类态射的Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ边和群逆存在的一些新的充要条件和新的表达式．     

On Semiprime Goldie Modules

In this article, we investigate some properties of right core inverses. Particularly, new characterizations and expressions for right core inverses are given, using projections and {1, 3}-inverses. Also, we introduced and investigated a new generalized right core inverse which is called right pseudo core inverse. Then, we provide the relation schema of (one-sided) core inverses, (one-sided) pseudo core inverses, and EP elements.     

On Hermitian generalized inverses and positive semidefinite generalized inverses

The main aim of this paper is to investigate the Hermitian and positive semidefinite generalized inverses of a square matrix. First, we present some conditions for the existence of Hermitian and positive semidefinite generalized inverses. Further, expressions of these generalized inverses are given. Finally, we give two numerical examples to demonstrate our results.     

Three-dimensional thermal shock problem of generalized thermoelastic half-space

A three-dimensional model of the generalized thermoelasticity with one relaxation time is established. The resulting non-dimensional coupled equations together with the Laplace and double Fourier transforms techniques are applied to a specific problem of a half space subjected to thermal shock and traction free surface. The inverses of Fourier transforms and Laplace transforms are obtained numerically by using the complex inversion formula of the transform together with Fourier expansion techniques. Numerical results for the temperature, thermal stress, strain and displacement distributions are represented graphically.     

具有核的态射广义Moore-Penrose逆

本文研究了具有核的态射广义Moore-Penrose逆.利用加边态射的可逆性,获得了态射广义Moore-Penrose逆存在的一些新的充要条件及相关表达式,推广了态射Moore-Penrose逆的相应结论.     

Estimating quadrature errors for an efficient method for quasi-singular boundary integral

The numerical resolution of the boundary integral equations applied to the differential equations of Laplace, Helmholtz and Maxwell requires the handling of quasi-singular integrals with different order of singularity. The numerical approximation of the integral equations of different kinds is made by boundary finite elements. In this paper, we present a complete survey for estimating quadrature errors for the numerical techniques proposed by Huang and Cruse [Q. Huang, T.A. Cruse, Some notes on singular integral techniques in boundary element analysis, Int. J. Numer. Methods Eng. 36 (15) (1993) 2643-2659], to calculate the quasi-singular integrals. To validate the accuracy and efficiency of these techniques and approve our study some numerical examples are presented and discussed.     

Time-dependent analysis of an <Emphasis Type="Italic">M</Emphasis> / <Emphasis Type="Italic">M</Emphasis> / <Emphasis Type="Italic">c</Emphasis> preemptive priority system with two priority classes

We analyze the time-dependent behavior of an M / M / c priority queue having two customer classes, class-dependent service rates, and preemptive priority between classes. More particularly, we develop a method that determines the Laplace transforms of the transition functions when the system is initially empty. The Laplace transforms corresponding to states with at least c high-priority customers are expressed explicitly in terms of the Laplace transforms corresponding to states with at most \(c - 1\) high-priority customers. We then show how to compute the remaining Laplace transforms recursively, by making use of a variant of Ramaswami’s formula from the theory of M / G / 1-type Markov processes. While the primary focus of our work is on deriving Laplace transforms of transition functions, analogous results can be derived for the stationary distribution; these results seem to yield the most explicit expressions known to date.     

右$c$-群逆及其应用

研究了由右$c$-正则元确定的一类新的群逆,将之称为右$c$-群逆.证明了每个右$c$-群可逆元都是群可逆的,并通过反例说明了群可逆元未必是右$c$-群可逆的.给出了右$c$-群可逆元是群可逆元的条件,并对右$c$-群可逆元的强clean分解进行了研究.作为应用,从右$c$-群逆的角度对abelian环和直接有限环给出了一些新刻画.     

Some unit square integrals

In this article, we prove some identities which allow us to evaluate some multiple unit square integrals. In our examples, we will give the value of some double and triple integrals. We then prove several classical integral formulas with the help of these identities and present others that seem to be new. Finally, we get double integrals for classical constants and different expressions for two Ramanujan’s integral formulas.     

Laplace Transform and Moments of Waiting Times in Poisson Driven (max,+) Linear Systems

(Max,+) linear systems can be used to represent stochastic Petri nets belonging to the class of event graphs. This class contains various instances of queueing networks like acyclic or cyclic fork-and-join queueing networks, finite or infinite capacity tandem queueing networks with various types of blocking, synchronized queueing networks and so on. It also contains some basic manufacturing models such as kanban networks, assembly systems and so forth.In their 1997 paper, Baccelli, Hasenfuss and Schmidt provide explicit expressions for the expected value of the waiting time of the nth customer in a given subarea of a (max,+) linear system. Using similar analysis, we present explicit expressions for the moments and the Laplace transform of transient waiting times in Poisson driven (max,+) linear systems. Furthermore, starting with these closed form expressions, we also derive explicit expressions for the moments and the Laplace transform of stationary waiting times in a class of (max,+) linear systems with deterministic service times. Examples pertaining to queueing theory are given to illustrate the results.     

A new way to evaluate the Probability and Fresnel integrals

In this article, we show how Laplace Transform may be used to evaluate variety of nontrivial improper integrals, including Probability and Fresnel integrals. The algorithm we have developed here to evaluate Probability, Fresnel and other similar integrals seems to be new. This method transforms the evaluation of certain improper integrals into evaluation of improper integrals of the corresponding Laplace transform, which in many cases are much easier.     

Evaluation of Certain Integrals Involving the Product of Classical Hermite's Polynomials Using Laplace Transform Technique and Hypergeometric Approach

In this paper some novel integrals associated with the product of classical Hermite's polynomials ∫_(-∞)~(+∞)(x~2)~mexp(-x~2){Hr (x)}2dx, ∫_0~∞exp(-x~2)H_(2k)(x)H_(2s+1)(x)dx,∫_0~∞exp(-x~2)H_(2k)(x)H_(2s)(x)dx and ∫_0~∞exp(-x~2)H_(2k+1)(x)H_(2s+1)(x)dx,are evaluated using hypergeometric approach and Laplace transform method, which is a different approach from the approaches given by the other authors in the field of special functions. Also the results may be of significant nature, and may yield numerous other interesting integrals involving the product of classical Hermite's polynomials by suitable simplifications of arbitrary parameters.     

On Some Applications of Geometry of Banach Spaces and Some New Results Related to the Fixed Point Theory in Orlicz Sequence Spaces

We present some applications of the geometry of Banach spaces in the approximation theory and in the theory of generalized inverses. We also give some new results, on Orlicz sequence spaces, related to the fixed point theory. After a short introduction, in Section 2 we consider the best approximation projection from a Banach space $X$ onto its non-empty subset and proximinality of the subspaces of order continuous elements in various classes of Köthe spaces. We present formulas for the distance to these subspaces of the elements from the outside of them. In Section 3 we recall some results and definitions concerning generalized inverses of operators (metric generalized inverses and Moore-Penrose generalized inverses). We also recall some results on the perturbation analysis of generalized inverses in Banach spaces. The last part of this section concerns generalized inverses of multivalued linear operators (their definitions and representations). The last section starts with a formula for modulus of nearly uniform smoothness of Orlicz sequence spaces $\ell^\Phi$equipped with the Amemiya-Orlicz norm. From this result a criterion for nearly uniform smoothness of these spaces is deduced. A formula for the Domínguez-Benavides coefficient $R(a,l_\Phi)$ is also presented, whence a sufficient condition for the weak fixed point property of the space $\ell^\Phi$is obtained.     

Identities for the Hankel transform and their applications

In the present paper the authors show that iterations of the Hankel transform with Kν-transform is a constant multiple of the Widder transform. Using these iteration identities, several Parseval-Goldstein type theorems for these transforms are given. By making use of these results a number of new Goldstein type exchange identities are obtained for these and the Laplace transform. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given as illustration of the results presented here.     

Solving Symmetric Arrowhead and Special Tridiagonal Linear Systems by Fast Approximate Inverse Preconditioning

A new class of approximate inverses for arrowhead and special tridiagonal linear systems, based on the concept of sparse approximate Choleski-type factorization procedures, are introduced for computing fast explicit approximate inverses. Explicit preconditioned iterative schemes in conjunction with approximate inverse matrix techniques are presented for the efficient solution of symmetric linear systems. A theorem on the rate of convergence of the explicit preconditioned conjugate gradient scheme is given and estimates of the computational complexity are presented. Applications of the proposed method on linear and nonlinear systems are discussed and numerical results are given.     

On the Existence of Weak Solutions of Nonlinear Integral Equations in Banach Spaces

In this paper, we use the techniques of measure of weak noncompactness and Henstock–Kurzweil–Pettis integrals to discuss the existence theorem of weak solutions for a class of the nonlinear integral equations and obtain a new result, which improves and extends some relevant results for differential and integral equations in Banach spaces.     

Error Bounds for Uniform Asymptotic Expansions—Modified Bessel Function of Purely Imaginary Order

The authors modify a method of Olde Daalhuis and Temme for representing the remainder and coefficients in Airy-type expansions of integrals. By using a class of rational functions, they express these quantities in terms of Cauchy-type integrals; these expressions are natural generalizations of integral representations of the coefficients and the remainders in the Taylor expansions of analytic functions. By using the new representation, a computable error bound for the remainder in the uniform asymptotic expansion of the modified Bessel function of purely imaginary order is derived.     

关于环上矩阵的群逆与Drazin逆

本文给出了环上一类方阵有群逆，｛１，５｝－道的充要条件及其它们的表式，推广了体（域）上关于群逆的Ｃｌｉｎｅ定理．此外还首次得到了矩阵有Ｄｒａｚｉｎ逆的判别准则及其它的表式．