A parametric solution for simple stress—strength model of failure with an application

Estimation of P(R ⩽ S) is considered for the simple stress—strength model of failure. Using the Pareto and Power distributions together with their combined form a useful parametric solution is obtained and is illustrated numerically. It is shown that these models are also applicable when only the tails of distributions for R and S are considered. An application to the failure study concerning the fractures is also included     

Analysis of ϕ-divergence for loglinear models with constraints under product-multinomial sampling

The loglinear model under product-multinomial sampling with constraints is considered. The asymptotic expansion and normality of the restricted minimum φ-divergence estimator (RMφDE) which is a generalization of the maximum likelihood estimator is presented. Then various statistics based on φ-divergence and RMφDE are used to test various hypothesis test problems under the model considered. These statistics contain the classical loglikelihood ratio test statistics and Pearson chi-squared test statistics. In the last section, a simulation study is implemented.     

A model for embedding finite coverings defined by principal bundles into bundles of manifolds

For any finite group G we construct a canonical model for embedding a principal G-bundle fibrewise into a given locally trivial fibration with a connected manifold M of dimension n⩾2 as fibre. The construction uses configuration spaces. We apply the construction to obtain a canonical model for the class of principal G-bundles which are polynomial when considered as covering maps. Finally, we give an algebraic characterization of the polynomial principal G-bundles in terms of homomorphisms into braid groups.     

Soliton solutions of a BBM(m, n) equation with generalized evolution

We consider a BBM(m, n) equation which is a generalization of the celebrated Benjamin-Bona-Mahony equation with generalized evolution term. By using two solitary wave ansatze in terms of sech^p(x) and tanh^p(x) functions, we find exact analytical bright and dark soliton solutions for the considered model. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. The conditions of existence of solitons are presented. Note that, it is always useful and desirable to construct exact analytical solutions especially soliton-type envelope for the understanding of most nonlinear physical phenomena.     

Nonnegative quadratic estimation and quadratic sufficiency in general linear models

Notions of linear sufficiency and quadratic sufficiency are of interest to some authors. In this paper, the problem of nonnegative quadratic estimation for β^′Hβ+hσ² is discussed in a general linear model and its transformed model. The notion of quadratic sufficiency is considered in the sense of generality, and the corresponding necessary and sufficient conditions for the transformation to be quadratically sufficient are investigated. As a direct consequence, the result on (ordinary) quadratic sufficiency is obtained. In addition, we pose a practical problem and extend a special situation to the multivariate case. Moreover, a simulated example is conducted, and applications to a model with compound symmetric covariance matrix are given. Finally, we derive a remark which indicates that our main results could be extended further to the quasi-normal case.     

Asymptotic efficiency of ridge estimator in linear and semiparametric linear models

The linear model with a growing number of predictors arises in many contemporary scientific endeavor. In this article, we consider the commonly used ridge estimator in linear models. We propose analyzing the ridge estimator for a finite sample size n and a growing dimension p. The existence and asymptotic normality of the ridge estimator are established under some regularity conditions when p→∞. It also occurs that a strictly linear model is inadequate when some of the relations are believed to be of certain linear form while others are not easily parameterized, and thus a semiparametric partial linear model is considered. For these semiparametric partial linear models with p>n, we develop a procedure to estimate the linear coefficients as if the nonparametric part is not present. The asymptotic efficiency of the proposed estimator for the linear component is studied for p→∞. It is shown that the proposed estimator of the linear component asymptotically performs very well.     

New families of estimators and test statistics in log-linear models

In this paper we consider categorical data that are distributed according to a multinomial, product-multinomial or Poisson distribution whose expected values follow a log-linear model and we study the inference problem of hypothesis testing in a log-linear model setting. The family of test statistics considered is based on the family of ?-divergence measures. The unknown parameters in the log-linear model under consideration are also estimated using ?-divergence measures: Minimum ?-divergence estimators. A simulation study is included to find test statistics that offer an attractive alternative to the Pearson chi-square and likelihood-ratio test statistics.     

Spectral Galerkin method and its application to a Cauchy problem of Helmholtz equation

Based on a mathematical model of laser beams, we present a spectral Galerkin method for solving a Cauchy problem of the Helmholtz equation in a rectangle, where the Cauchy data pairs are given at y?=?0 and boundary data are for x?=?0 and x?=?π. The solution is sought in the interval 0?<?y?<?1. The spectral Galerkin method is considered as a regularization method. We then perform an analysis on the error bound for this method. For illustration, several numerical experiments are constructed to demonstrate the feasibility and efficiency of the proposed method.     

On tests of independence in a trivariate exponential distribution

In this paper we consider the problem of testing a null hypothesis H₀ against an alternative hypothesis H_a, related to a trivariate model. H₀ is transformed into a hypothesis concerning the equality of scale parameters of three exponential distributions, following Bhattacharyya and Johnson. Two conditional tests for the transformed hypothesis are considered, and simple expressions for the power functions of our tests are obtained.     

The limiting problem of the drift-diffusion-Poisson model with discontinuous p-n-junctions

In this paper, the authors consider the limiting problem of the drift-diffusion-Poisson model for semiconductors. Different from previous papers, the model considered involve some special doping profiles D which have the property that the function is allowed to have a jump-discontinuity and sign changing property but D² is required to be Lipschitz continuous. The existence, uniqueness and large-time asymptotic behavior of the global (in time) solutions are given.     

Global existence of solutions of a strongly coupled quasilinear parabolic system with applications to electrochemistry

This paper consists of two parts. In the first part, we proved the global existence of weak solutions of a strongly coupled quasilinear parabolic system in Rⁿ using weak compactness method. In the second part, we considered the electrochemistry model studied in Choi and Lui (J. Differential Equations 116 (1995) 306) where the Poisson equation governing the electric potential is replaced by a local electro-neutrality condition. In one space dimension, the equations for the model is of the form considered in the first part of this paper except that the coefficient matrix is discontinuous at places where all the charged ions vanish. We approximate the equations by nicer operators and pass to the limit to obtain global existence of weak solutions. The non-negativity of weak solutions and L²-stability of the steady-state solutions are also shown under additional hypotheses.     

Construction of sports schedules with multiple venues

A graph theoretical model is presented for constructing calendars for sports leagues where balancing requirement have to be considered with respect to the different venues where competitions are to be located. An inductive construction is given for leagues having a number of teams 2n which is of the form 2^p in particular.     

The evolution to a steady state for a porous medium model

An initial boundary value problem is considered for a nonlinear diffusion equation, the diffusivity being a function of the dependent variable. Dirichlet boundary conditions, independent of time, are considered and positive solutions are assumed. This paper is mainly concerned with the rate of convergence, in time, of the unsteady to the steady state. This is done by obtaining an upper estimate for a positive-definite, integral measure of the perturbation (i.e., unsteady-steady state) using differential inequality techniques.A previous result is recalled where the diffusivity k(τ)=τn (n being a positive constant) appropriate to mass transport, or filtration, in a porous medium. The present paper treats an alternative model, sharing some of the characteristics of the previous one: k(τ)=eτ−1, τ being non-negative.The paper concludes by considering a “backwards in time” initial boundary value problem for the perturbation (amenable to the same techniques) and establishes that the solution ceases to exist beyond a critical, computable time.     

Aging for interacting diffusion processes

We study the aging phenomenon for a class of interacting diffusion processes {Xt(i),i∈Zd}. In this framework we see the effect of the lattice dimension d on aging, as well as that of the class of test functions f(Xt) considered. We further note the sensitivity of aging to specific details, when degenerate diffusions (such as super random walk, or parabolic Anderson model), are considered. We complement our study of systems on the infinite lattice, with that of their restriction to finite boxes. In the latter setting we consider different regimes in terms of box size scaling with time, as well as the effect that the choice of boundary conditions has on aging. The key tool for our analysis is the random walk representation for such diffusions.     

Asymptotic behavior of an unstirred chemostat model with internal inhibitor

This paper deals with a chemostat model with an internal inhibitor. First, the elementary stability and asymptotic behavior of solutions of the system are determined. Second, the effects of the inhibitor are considered. It turns out that the parameter μ, which measures the effect of the inhibitor, plays a very important role in deciding the stability and longtime behavior of solutions of the system. The results show that if μ is sufficiently large, this model has no coexistence solution and one of the semitrivial equilibria is a global attractor when the maximal growth rate a of the species u lies in certain range; but when a belongs to another range, all positive solutions of this model are governed by a limit problem, and two semitrivial equilibria are bistable. The main tools used here include monotone system theory, degree theory, bifurcation theory and perturbation technique.     

On the optimal switching level for an M/G/1 queueing system

A cost function is studied for an M/G/1 queueing model for which the service rate of the virtual waiting time process U_t for U_t<K differs from that for U_t > K. The costs considered are costs for maintaining the service rate, costs for switching the service rate and costs proportional to the inventory U_t. The relevant cost factors for the system operating below level K differ from those when U_t > K. The cost function which is considered only for the stationary situation of the U_t-process expresses the average cost per unit time. The problem is to find that K for which the cost function reaches a minimum. Criteria for the possibly optimal cases are found; they have an interesting intuitive interpretation, and require the knowledge of only the first moment of the service time distribution.     

Algorithm for a general discrete k-out-of-n: G system subject to several types of failure with an indefinite number of repairpersons

A discrete k-out-of-n: G system with multi-state components is modelled by means of block-structured Markov chains. An indefinite number of repairpersons are assumed and PH distributions for the lifetime of the units and for the repair time are considered. The units can undergo two types of failures, repairable or non-repairable. The repairability of the failure can depend on the time elapsed up to failure. The system is modelled and the stationary distribution is built by using matrix analytic methods. Several performance measures of interest, such as the conditional probability of failure for the units and for the system, are built into the transient and stationary regimes. Rewards are included in the model. All results are shown in a matrix algorithmic form and are implemented computationally with Matlab. A numerical example of an optimization problem shows the versatility of the model.     

Space-time discontinuous galerkin method for maxwell equations in dispersive media

In this paper, a unified model for time-dependent Maxwell equations in dispersive media is considered. The space-time DG method developed in [29] is applied to solve the underlying problem. Unconditional L²-stability and error estimate of order O(τ^r+1+h^k+1/2) are obtained when polynomials of degree at most r and k are used for the temporal discretization and spatial discretization respectively. 2-D and 3-D numerical examples are given to validate the theoretical results. Moreover, numerical results show an ultra-convergence of order 2r+1 in temporal variable t.     

Stable oscillations in a predator-prey model with time lag

The Lotka-Volterra model with carrying capacity at the prey and time delay in the equation concerning the predator is considered. The time delay is taken into consideration by an integral with the weight function a exp(?at). It is shown that under certain conditions imposed upon the parameters of the system a supercritical Hopf bifurcation takes place at a certain value a₀, of a and the bifurcating closed paths are orbitally asymptotically stable for values of a below a₀.     

Averaging of acoustic equation for partially perforated viscoelastic material with channels filled by a liquid

Acoustic equations for combined media consisting of partially perforated viscoelastic material and viscous incompressible liquid filling pores are considered. An averaged model is constructed for the model under consideration, and boundary conditions connecting equations of the obtained averaged model on the boundary between solid viscoelastic material and porous viscoelastic material filled by a viscous incompressible liquid are found. The convergence of limit problems to the solution of corresponding averaged problem with respect to the norm of the space L ² is proved.