Large Deviations for the Markov Binomial Distribution

Considering the Markov binomial distribution, we study large deviations for the Poisson approximation. Apart from the standard choice of parameters, we use the approach where the parameter of approximation depends on the argument of the approximated distribution function.     

On the Number of Lost Customers in Stationary Loss Systems in the Light Traffic Case

For the stationary loss systems M/M/m/K and GI/M/m/K, we study two quantities: the number of lost customers during the time interval (0,t] (the first system only), and the number of lost customers among the first n customers to arrive (both systems). We derive explicit bounds for the total variation distances between the distributions of these quantities and compound Poisson–geometric distributions. The bounds are small in the light traffic case, i.e., when the loss of a customer is a rare event. To prove our results, we show that the studied quantities can be interpreted as accumulated rewards of stationary renewal reward processes, embedded into the queue length process or the process of queue lengths immediately before arrivals of new customers, and apply general results by Erhardsson on compound Poisson approximation for renewal reward processes.     

A bracket power characterization of analytic spread one ideals

The main theorem characterizes, in terms of bracket powers, analytic spread one ideals in local rings. Specifically, let be regular nonunits in a local (Noetherian) ring and assume that , the integral closure of , where . Then the main result shows that for all but finitely many units in that are non-congruent modulo and for all large integers and it holds that for and not divisible by , where is the -th bracket power of . And, conversely, if there exist positive integers , , and such that has a basis such that , then has analytic spread one.

     

基于AVR单片机的万能材料试验机控制系统

采用AVR单片机AT90S8515作为控制核心,通过步进电机带动丝杠运动,利用光栅编码器、高精度力传感器、2个引伸计分别测量了位移、力及试件横、纵变形,在老式电子万能材料实验机上建立了新型计算机控制系统,可方便测定弹性模量和泊松比.     

Planar Line Processes for Void and Density Statistics in Thin Stochastic Fibre Networks

Using results for the distribution of perimeters of random polygons arising from random lines in a plane, we obtain new analytic approximations to the distributions of areas and local line densities for random polygons and compute various limiting properties of random polygons. Using simulation, we show that the lengths of adjacent sides of polygons generated by random line processes in the plane are correlated with ρ=0.616±0.001.     

On intensities of perturbed random measures on Hausdorff spaces

Abstract

This article studies classes of random measures on topological spaces perturbed by stochastic processes (a.k.a. modulated random measures). We render a rigorous construction of the stochastic integral of functions of two variables and showed that such an integral is a random measure. We establish a new Campbell-type formula that, along with a rigorous construction of modulation, leads to the intensity of a modulated random measure. Mathematical formalism of integral-driven random measures and their stochastic intensities find numerous applications in stochastic models, physics, astrophysics, and finance that we discuss throughout the article.     

Flexible software reliability growth model with testing effort dependent learning process

A lot of importance has been attached to the testing phase of the Software Development Life Cycle (SDLC). It is during this phase it is checked whether the software product meets user requirements or not. Any discrepancies that are identified are removed. But testing needs to be monitored to increase its effectiveness. Software Reliability Growth Models (SRGMs) that specify mathematical relationships between the failure phenomenon and time have proved useful. SRGMs that include factors that affect failure process are more realistic and useful. Software fault detection and removal during the testing phase of SDLC depend on how testing resources (test cases, manpower and time) are used and also on previously identified faults. With this motivation a Non-Homogeneous Poisson Process (NHPP) based SRGM is proposed in this paper which is flexible enough to describe various software failure/reliability curves. Both testing efforts and time dependent fault detection rate (FDR) are considered for software reliability modeling. The time lag between fault identification and removal has also been depicted. The applicability of our model is shown by validating it on software failure data sets obtained from different real software development projects. The comparisons with established models in terms of goodness of fit, the Akaike Information Criterion (AIC), Mean of Squared Errors (MSE), etc. have been presented.     

Flow prolongation of some tangent valued forms

We study the prolongation of semibasic projectable tangent valued k-forms on fibered manifolds with respect to a bundle functor F on local isomorphisms that is based on the flow prolongation of vector fields and uses an auxiliary linear r-th order connection on the base manifold, where r is the base order of F. We find a general condition under which the Frölicher-Nijenhuis bracket is preserved. Special attention is paid to the curvature of connections. The first order jet functor and the tangent functor are discussed in detail. Next we clarify how this prolongation procedure can be extended to arbitrary projectable tangent valued k-forms in the case F is a fiber product preserving bundle functor on the category of fibered manifolds with m-dimensional bases and local diffeomorphisms as base maps.     

Long‐range analysis of density fitting in extended systems

Density fitting scheme is analyzed for the Coulomb problem in extended systems from the correctness of long‐range behavior point of view. We show that for the correct cancellation of divergent long‐range Coulomb terms it is crucial for the density fitting scheme to reproduce the overlap matrix exactly. It is demonstrated that from all possible fitting metric choices the Coulomb metric is the only one which inherently preserves the overlap matrix for infinite systems with translational periodicity. Moreover, we show that by a small additional effort any non‐Coulomb metric fit can be made overlap‐preserving as well. The problem is analyzed for both ordinary and Poisson basis set choices. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008