Two-Commodity Inventory System with Individual and Joint Ordering Policies and Renewal Demands

Abstract

This article analyzes a two-commodity continuous review inventory system with renewal demands. The ordering policy is a combination of policies namely ordering individual commodities and ordering jointly both commodities. The steady state probability distribution for the joint inventory levels is computed. Various system performance measures in the steady state are derived. The results are illustrated numerically.     

Local Linear Estimation of Jump-Diffusion Models by Using Asymmetric Kernels

This article addresses the problem of nonparametric estimation of the first and second infinitesimal moments by using the local linear method of the underlying jump-diffusion models. The motivation behind the study is to use the asymmetric kernels instead of standard kernel smoothing. The basic idea relies on replacing the symmetric kernel by asymmetric kernel and provides a new way of obtaining the nonparametric estimation for jump-diffusion models. We prove that the estimators based on the local linear method for jump-diffusion models are consistent and asymptotically follow normal distribution under the condition of recurrence and stationarity.     

L~1空间中带弱奇异核的第二类Fredholm积分方程的数值解法

在L¹空间中,研究带弱奇异核的第二类Fredholm积分方程.将弱奇异核转换成连续核,给出了一种数值求解的算法,并举出具体算例.     

Weighted Norm Inequalities with General Weights for the Commutator of Calderón

In this paper, by a sharp function estimate and an idea of Lerner, the authors establish someweighted estimates for the m-multilinear integral operator which is bounded from L1(Rn)×···×L1 (Rn)to L1/m,∞ (Rn),, and the associated kernel K(x; y1, . . . , ym)) enjoys a regularity on the variable x. As anapplication, weighted estimates with general weights are given for the commutator of Calderón.     

Superconvergence of the iterated degenerate kernel method

First, in this paper, a generally theory for the iterated operator approximation is developed. Some of the known results of the superconvergence of the various iterated schemes can be formulated as special cases of this theory. The method is then subsequently used to prove the superconvergence of the iterated degenerate kernel method for the Fredholm equations of the second kind. A similar result of the superconvergence of the degenerate kernel method for the Hammerstein equations is also given.     

Existence of Solutions of Some Degenerate Nonlinear Elliptic Fourth-order Equations with L 1 -data

This article deals with a class of degenerate nonlinear elliptic fourth-order equations with L 1 -right-hand sides. Equations of the given class have divergence form and their coefficients satisfy a strengthened ellipticity condition with two different weights associated, respectively, to the first- and the second-order derivatives of unknown function. Under suitable hypotheses on the weighted functions involved we establish solvability in a Sobolev space of Dirichlet problem for equations under consideration.     

Hölder Estimates of Solutions on the Equation u t = Δ G ( u )

In this paper we are concerned with the Hölder estimates of solutions of the Cauchy problem for the degenerate parabolic Eq. (1) with the initial data (2), where the diffusion function G ( u ) can be a constant on a non-zero measure set, such as the equations of two-phase Stefan's type. Under the condition | GG "/ G ' 2 | h g , g 2 h 1/2 N , the global estimates | o ( G f ( u ))| h M , on R N ‐ R + , is obtained by using the maximum principle, where f is a constant given in (9).     

Error estimation for non-uniform sampling in shift invariant space

To reconstruct a function from its sampling value is not always exact, error may arise due to a lot of reasons, therefore error estimation is useful in reconstruction. For non-uniform sampling in shift invariant space, three kinds of errors of the reconstruction formula are discussed in this article. For every kind of error, we give an estimation. We find the accuracy of the reconstruction formula mainly depends on the decay property of the generator and the sampling function.     

Families of completely positive maps associated with monotone metrics

An operator convex function on (0,∞)$(0,\infty )$ which satisfies the symmetry condition k(x⁻¹)=xk(x)$k(x^{-1})=xk(x)$ can be used to define a type of non-commutative multiplication by a positive definite matrix (or its inverse) using the primitive concepts of left and right multiplication and the functional calculus. The operators for the inverse can be used to define quadratic forms associated with Riemannian metrics which contract under the action of completely positive trace-preserving maps.