On HNBUE class after specific age

In this article we introduce new classes of life distributions namely harmonic new better (worse) than used in expectation after specific age t₀ HNBUE¹t₀ (HNWUE¹t₀). The closure properties under various reliability operations such as convolution, mixture, mixing and the homogeneous Poisson shock model of these classes are studied. Furthermore, nonparametric test is proposed to test exponentiality vs. the HNBUE¹t₀ class. The critical values and the powers of this test are calculated to assess the performance of the test. It is shown that the proposed test have high efficiencies for LFR and Weibull distributions. Sets of real data are used as examples to elucidate the use of the proposed test for practical problems.     

Network flows with age dependent decay rates

This paper considers the problem of maximizing the output flow in a multicommodity network in which flow entering an arc experiences a decay rate which is a function of three factors: the arc, the commodity, and the age of the commodity as it enters the arc. An arc-chain linear programming formulation of the problem is given. The algorithm for solving the problem involves a novel column generation scheme for basis entry embedded in the revised simplex algorithm. An efficient algorithm for generating, at each iteration, such a column is provided and illustrated with a numerical example.     

Opportunity-based age replacement with different intensity rates

This article considers an opportunity-based age replacement model with different intensity rates. Most of the articles suppose that opportunities are generated according to a homogeneous Poisson process, where the intensity rate does not change with time. However, social, economical, and physical environments can change the intensity rate. We suppose the intensity rate changes at specific age. The occurrence of opportunities is independent to the failure of a component. Pre ventive replacement is carried out at the first opportunity after ageT. If the component breaks down then it is replaced immediately. We derive the expected cost per unit time for an infinite time horizon. An optimal policy to minimize the expected cost per unit time is derived. Finally, numerical examples are given.     

A comparison of the Lee-Carter model and AR-ARCH model for forecasting mortality rates

With the decline in the mortality level of populations, national social security systems and insurance companies of most developed countries are reconsidering their mortality tables taking into account the longevity risk. The Lee and Carter model is the first discrete-time stochastic model to consider the increased life expectancy trends in mortality rates and is still broadly used today. In this paper, we propose an alternative to the Lee-Carter model: an AR(1)-ARCH(1) model. More specifically, we compare the performance of these two models with respect to forecasting age-specific mortality in Italy. We fit the two models, with Gaussian and t-student innovations, for the matrix of Italian death rates from 1960 to 2003. We compare the forecast ability of the two approaches in out-of-sample analysis for the period 2004-2006 and find that the AR(1)-ARCH(1) model with t-student innovations provides the best fit among the models studied in this paper.     

Propagation dynamics of a nonlocal periodic organism model with non-monotone birth rates

This work is concerned with a nonlocal reaction–diffusion system modeling the propagation dynamics of organisms owning mobile and stationary states in periodic environments. We establish the existence of the asymptotic speed of spreading for the model system with monotone birth function via asymptotic propagation theory of monotone semiflow, and then discuss the case for non-monotone birth function by using the squeezing technique. In terms of the truncated problem on a finite interval, we apply the method of super- and sub-solutions and the fixed point theorem combined with regularity estimation and limit arguments to obtain the existence of time periodic traveling waves for the model system without quasi-monotonicity. The non-existence proof is to use the results of the spreading speed. Finally, as an application, we study the spatial dynamics of the model with the birth rate function of Ricker type and numerically demonstrate analytic results.     

Dynamics of SIS model with saturation incidence,infection age and impulsive birth

In this paper, an impulsive birth and infection age SIS epidemic model is studied. Since infection age is an important factor of epidemic progression, we incorporate the infection age into the model. In this model, we analyze the dynamical behaviors of this model and point out that there exists an infection‐free periodic solution that is globally asymptotically stable if R₀<1. When R₁>1, R₂<1, then the disease is permanent. Our results indicate that a large period T of pulse, or a small pulse birth rate p is the sufficient condition for the eradication of the disease. Copyright © 2009 John Wiley & Sons, Ltd.     

Asynchronous exponential growth for an age dependent population equation with delayed birth process

We show that the solutions of a population equation with age structure and delayed birth process have asynchronous exponential growth (AEG). We use operator matrices and Hille-Yosida operators as well as Perron-Frobenius techniques.     

Decomposition of transformations

The decomposition theorem for transformations without any additivity assumptions is proved. This result is new even for image transformations. We also introduce a new class of transformations with some additivity assumpt ions which includes image transformations. Using the transformation from this class we generalize the Aarnes factorization theorem to representable deficient topological measures. We also establish the relationship between the decomposition of a representable deficient topological measure and the decomposition of the transformation mentioned above.     

Global stability of a delayed SIR epidemic model with density dependent birth and death rates

An SIR   epidemic model with density dependent birth and death rates is formulated. In our model it is assumed that the total number of the population is governed by logistic equation. The transmission of infection is assumed to be of the standard form, namely proportional to I(t-h)/N(t-h)$I(t-h)/N(t-h)$ where N(t)$N(t)$ is the total (variable) population size, I(t)$I(t)$ is the size of the infective population and a time delay h   is a fixed time during which the infectious agents develop in the vector. We consider transmission dynamics for the model. Stability of an endemic equilibrium is investigated. The stability result is stated in terms of a threshold parameter, that is, a basic reproduction number _R0$R_0$.     

矩阵代数上的局部合同变换和局部相似变换

令F表示任意域,Mn（F）表示由F上所有n×n矩阵形成的结合代数.本文的目的是研究Mn（F）上具有如下性质的两类线性映射,其中一类线性映射在Mn（F）上每一点的取值与Mn（F）的某个合同变换在该点的取值相同,另一类线性映射在Mn（F）上每一点的取值与Mn（F）的某个相似变换在该点的取值相同,随着Mn（F）上的点不同,这些合同变换和相似变换可能也不同.利用矩阵的秩、幂等阵以及幂零阵的性质,通过矩阵计算的方法证明了第一类线性映射或者是合同变换或者是合同变换与转置变换的复合,第二类线性映射或者是相似变换或者是相似变换与转置变换的复合.由这个结果可知存在真正意义上的局部合同变换和局部相似变换,从而丰富了局部映射理论的研究。     

Diagonal transformations in quadrangulations of surfaces

In this paper, it will be shown that any two bipartite quadrangulations of any closed surface are transformed into each other by two kinds of transformations, called the diagonal slide and the diagonal rotation, up to homeomorphism, if they have the same and sufficiently large number of vertices. © 1996 John Wiley & Sons, Inc.     

Reduction of matrices by means of equivalent transformations and similarity transformations

The structure of polynomial matrices in connection with their reducibility by semiscalar-equivalent transformations and similarity transformations to simpler forms is considered. In particular, the canonical form of polynomial matrices without multiple characteristic roots with respect to the above transformations is indicated. This allows one to establish a canonical form with respect to similarity for a certain type of finite collections of numerical matrices. Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 769–782, November, 1998.     

Higher derivatives in gauge transformations

A mechanism of occurrence of higher derivatives of the coordinates in the symmetry transformation law in Noether's second theorem is elucidated. It is shown that the corresponding transformations in the Hamiltonian formalism are canonical in an extended phase space.Joint Institute for Nuclear Research; State University, Tbilisi. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 102, No. 1, pp. 56–65, January, 1995.     

Fusion transformations in Liouville theory

We study the fusion kernel for nondegenerate conformal blocks in the Liouville theory as a solution of difference equations originating from the pentagon identity. We propose an approach for solving these equations based on a “nonperturbative” series expansion that allows calculating the fusion kernel iteratively. We also find exact solutions for the special central charge values c = 1+6(b ? b^?1)², b ∈ ?. For c = 1, the obtained result reproduces the formula previously obtained from analytic properties of a solution of a Painlev´e equation, but our solution has a significantly simplified form.     

Variable transformations in numerical integration

We discuss some recent developments in the use of class S_m variable transformations for improving the accuracy of the trapezoidal rule approximations in numerical integration via the trapezoidal rule. These concern optimal choices of m. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gauge transformations in constrained theories

A method is proposed for constructing infinitesimal gauge transformations for an arbitrary degenerate Lagrangian without restrictions on the constraint algebra. It is thereby shown that in the general case degeneracy of a theory is due to its gauge invariance.Joint Institute for Nuclear Research; State University, Tbilisi. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 102, No. 1, pp. 66–73, January, 1995.