Sample-path conservation laws,with applications to scheduling queues and fluid systems

The achievable-region approach, based on strong conservation laws, has most often been applied to stochastic scheduling and other control problems in the context of performance measures that are steady-state expected quantities. For some problems, however, strong conservation laws hold for performance measures at every time point on every sample path. We exploit this property to study optimal control for certain scheduling problems on a sample-path basis. Examples include preemptive scheduling to minimize a weighted sum of work in the system in each class, nonpreemptive scheduling to minimize a weighted sum of the number of customers in each class (when all classes have the same service-time distribution), and scheduling the processing of fluid in a multiclass fluid system operating in a random environment. The last problem is solved by considering the related Skorohod problem and its minimal solution. This revised version was published online in June 2006 with corrections to the Cover Date.     

Oscillations of higher order differential equations of neutral type

In this paper, sufficient conditions have been obtained for oscillation of solutions of a class of nth order linear neutral delay-differential equations. Some of these results have been used to study oscillatory behaviour of solutions of a class of boundary value problems for neutral hyperbolic partial differential equations.     

Recurrence relations for the coefficients of the Fourier series expansions with respect to q-classical orthogonal polynomials

We propose an algorithm to construct recurrence relations for the coefficients of the Fourier series expansions with respect to the q-classical orthogonal polynomials p_k(x;q). Examples dealing with inversion problems, connection between any two sequences of q-classical polynomials, linearization of ϑ_m(x) p_n(x;q), where ϑ_m(x) is x^mor (x;q)_m, and the expansion of the Hahn-Exton q-Bessel function in the little q-Jacobi polynomials are discussed in detail. This revised version was published online in June 2006 with corrections to the Cover Date.     

Numerical analysis of a quadratic matrix equation

The quadratic matrix equation AX²+ BX + C = 0in n x nmatricesarises in applications and is of intrinsic interest as oneof the simplest nonlinear matrix equations. We give a completecharacterization of solutions in terms of the generalized Schurdecomposition and describe and compare various numerical solutiontechniques. In particular, we give a thorough treatment offunctional iteration methods based on Bernoulli’s method.Other methods considered include Newton’s method with exact line searches, symbolic solution and continued fractions.We show that functional iteration applied to the quadraticmatrix equation can provide an efficient way to solve the associated quadratic eigenvalue problem (²A + B + C)x = 0.     

UNILATERAL EIGENVALUE PROBLEMS FOR NONLINEARLY ELASTIC PLATES： AN APPROACH VIA PSEUDO-MONOTONE OPERATORS

gi.TheTOpologicalDegreeforGeneralizedMonotoneOperatorsMonotoneoperatortheoryisoftenanefficienttoolforprovingtheexistenceofsolutionstononlinearProblems.Inparticular,thepseudo-monotoneoperatorsintroducedbyBrezis[2]areveryusefulforstudyingnonlinearellipticproblems.Weconsiderherethefollowingclassesofmappingsofgeneralizedmonotonetype.(QM)=theclassofquasi-mollotoneoperators,(S )=theclassofoperatorsoftype(S ),(PM)=theclassofpseudthmonotoneoperators,(LS)=theclassofLeray-Schauderoperators(compac…     

求线性规划对偶问题最优解的一种方法

线性规划对偶问题的最优解有重要的经济意义,中给出了一种较为简捷的求对偶问题最优解的方法。     

Minimizing makespan on a single burn-in oven in semiconductor manufacturing

This paper considers a scheduling problem for a single burn-in oven in semiconductor manufacturing industry where the oven is a batch processing machine and each batch processing time is represented by the largest processing time among those of all the jobs contained in the batch. The objective measure of the problem is the maximum completion time (makespan) of all jobs. This paper investigates a static case in which all jobs are available to process at time zero, and also analyzes a dynamic case with different job-release times, for which a branch-and-bound algorithm and several heuristics are exploited. The worst case error performance ratios of the heuristics are also derived.     

Forelli-Rudin type theorem in pluriharmonic Bergman spaces with small index

It is proved that the Bergman type operatorT, is a bounded projection from the pluriharmonic Bergman spaceL ^p (B)∩h(B) onto Bergman spaceL ^p (B) ∩ H(B) for 0p 1 ands (p¹-1)(n+1). As an application it is shown that the Gleason’s problem can be solved in Bergman space L^P(B)∩H(B) for 0p 1. Project supported by the National Natural Science Foundation of China (Grant No. 19871081) and the Doctoral Program Foundation of the State Education Commission of China.     

Combining approximate solutions for linear discrete ill-posed problems

Linear discrete ill-posed problems of small to medium size are commonly solved by first computing the singular value decomposition of the matrix and then determining an approximate solution by one of several available numerical methods, such as the truncated singular value decomposition or Tikhonov regularization. The determination of an approximate solution is relatively inexpensive once the singular value decomposition is available. This paper proposes to compute several approximate solutions by standard methods and then extract a new candidate solution from the linear subspace spanned by the available approximate solutions. We also describe how the method may be used for large-scale problems.     

Two Points Blow-up in Solutions of the Nonlinear Schrödinger Equation with Quartic Potential on \mathbb{R}

We consider the blow-up problem for the nonlinear Schrödinger equation with quartic self-interacting potential on . We exhibit a class of initial data leading to the blow-up solutions which have at least two L ²-concentration points.