Cost benefit analysis of series systems with warm standby components

This paper deals with the cost benefit analysis of series systems with warm standby components. The time-to-repair and the time-to-failure for each of the primary and warm standby components is assumed to have the negative exponential distribution. We develop the explicit expressions for the mean time-to-failure, MTTF, and the steady-state availability, A _T () for three configurations and perform a comparative analysis. Under the cost/benefit (C/B) criterion, comparisons are made based on assumed numerical values given to the distribution parameters, and to the cost of the components. The configurations are ranked based on: MTTF, A _T (), and C/B where B is either MTTF or A _T ().     

The negative gradient flow for the <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-integral of Ricci curvature

 In this paper, the negative gradient flow for the L ²-integral of Ricci curvature on a 3-manifold is considered. It is not known whether the solution to this fourth order geometric evolution equation exists, and whether it will develop singularities in finite time. Based on the trick of De Turck and the idea of Hamilton on the flow of Ricci curvature, the local existence on any compact Riemannian manifold is obtained. In addition, the conditions for the occurences of singularities in finite time during the evolution and the asymptotic behavior of the flow on a 3-manifold are discussed. Received: 22 April 2002 / Revised version: 5 January 2003 Published online: 24 April 2003 This work is partially supported by the Foundations of NNSF of China, the Foundation for University Key Teacher by MEC and Shanghai Priority Academic Discipline.     

Pointwise gradient estimates of solutions to onedimensional nonlinear parabolic equations

We present here an improved version of the method introduced by the first author to derive pointwise gradient estimates for the solutions of one-dimensional parabolic problems. After considering a general qualinear equation in divergence form we apply the method to the case of a nonlinear diffusion-convection equation. The conclusions are stated first for classical solutions and then for generalized and mild solutions. In the case of unbounded initial datum we obtain several regularizing effects for t > 0. Some unilateral pointwise gradient estimates are also obtained. The case of the Dirichlet problem is also considered. Finally, we collect, in the last section, several comments showing the connections among these estimates and the study of the free boundaries associated to the solutions of the diffusion-convection equation.     

<Emphasis FontCategory="NonProportional">L</Emphasis>-Matrices and solvability of linear complementarity problems by a linear program-Matrices and solvability of linear complementarity problems by a linear program

The classes ofL ₁-matrices,L ₂-matrices,L ₃-matrices andW-matrices are introduced to study solvability of a linear complementarity problem via solving a linear program. Three sufficient conditions are presented to guarantee that a linear complementarity problem is solvable via a linear program. The new sufficient conditions are weaker than the ones introduced by Mangasarian. This fact is also illustrated by an example. Partially supported by NSFC. This author is also with College of Business Administration of Human University as a Lotus chair professor.     

Mann-Whitney test for associated sequences

Let {X ₁, ...,X _m } and {Y ₁, ...,Y _n } be two samples independent of each other, but the random variables within each sample are stationary associated with one dimensional marginal distribution functionsF andG, respectively. We study the properties of the classical Wilcoxon-Mann-Whitney statistic for testing for stochastic dominance in the above set up.     

Variations on the Theorem of Birkhoff – von Neumann and Extensions

 The theorem of Birkhoff – von Neumann concerns bistochastic matrices (i.e., matrices with nonnegative real entries such that all row sums and all column sums are equal to one). We consider here real matrices with entries unrestricted in sign and we extend the notion of permutation matrices (integral bistochastic matrices); some generalizations of the theorem are derived by using elementary properties of graph theory. Received: October 10, 2000 Final version received: April 11, 2002     

On Positive and Weakly Positive Implicative BCI-Algebras

Prove that the notion of positive implicative BCI-algebras coincides with that of weakly positive implicative BCI-algebras, thus the whole results in the latter are still true in the former, in particular, one of these results answers definitely the first half of J. Meng and X.L. Xin’s open problem: Does the class of positive implicative BCI-algebras form a variety? The second half of the same problem is: What properties will the ideals of such an algebra have? Here, some further properties are obtained.     

An Algorithm to Construct <Emphasis Type="BoldItalic">k</Emphasis>-Regular <Emphasis Type="BoldItalic">k</Emphasis>-Connected Graphs with the Maximum <Emphasis Type="BoldItalic">k</Emphasis>-Diameter

 Let f(2m,k) be the Maximum k-diameter of k-regular k-connected graphs on 2m vertices. In this paper we give an algorithm and prove that we can construct k-regular k-connected graphs on 2m vertices with the maximum k-diameter using it. We also prove some known results about f(2m,k) and verify that we can get some unknown values of f(2m,k) by our algorithm. Received: December 1, 2000 Final version received: March 12, 2002 Acknowledgments. We thank the referee for many useful suggestions.     

A large-scale application of the partial coverage uncapacitated facility location problem

The traditional, uncapacitated facility location problem (UFLP) seeks to determine a set of warehouses to open such that all retail stores are serviced by a warehouse and the sum of the fixed costs of opening and operating the warehouses and the variable costs of supplying the retail stores from the opened warehouses is minimized. In this paper, we discuss the partial coverage uncapacitated facility location problem (PCUFLP) as a generalization of the uncapacitated facility location problem in which not all the retail stores must be satisfied by a warehouse. Erlenkotter's dual-ascent algorithm, DUALOC, will be used to solve optimally large (1600 stores and 13?000 candidate warehouses) real-world implemented PCUFLP applications in less than two minutes on a 500?MHz PC. Furthermore, a simple analysis of the problem input data will indicate why and when efficient solutions to large PCUFLPs can be expected.     

An optimal replenishment policy for items with inventory-level-dependent demand and fixed lifetime under the LIFO policy

In a recent paper, Hwang and Hahn considered inventory replenishment problems for an item with an inventory-level-dependent demand rate and a fixed lifetime. They developed an EQQ model under the situation of considering the first-in–first-out (FIFO) issuing policy. First, this paper reconsiders Hwang and Hann's problem by employing the last-in–first-out (LIFO) issuing policy, which is more practical in the retail industry. An inventory model is developed. Secondly, the concavity of the objective function is proved. Thirdly, this paper presents conditions where the present model has a unique optimal solution and a method for finding the global optimal solution. A simple solution procedure and sensitivity analyses of parameters are also provided.