Differential Conditions for Constrained Nonlinear Programming via Pareto Optimization

We deal with the differential conditions for local optimality. The conditions that we derive for inequality constrained problems do not require constraint qualifications and are the broadest conditions based on only first-order and second-order derivatives. A similar result is proved for equality constrained problems, although the necessary conditions require the regularity of the equality constraints.     

Estimates from Below for the Spectral Function and for the Remainder in Local Weyl’s Law

We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl’s law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the Dirichlet box principle. Our results develop and extend the unpublished thesis of A. Karnaukh [Ka]. The first author was supported by NSERC, FQRNT, Alfred P. Sloan Foundation Fellowship and Dawson Fellowship. The second author was supported by NSERC and FQRNT. Received: April 2006 Revision: October 2006 Accepted: October 2006     

有效点、弱有效点和真有效点的锥刻画

利用集合在某点的相依切锥、法向锥和可行方向锥等研究向量优化问题的有效点、 弱有效点和真有效点的特征,对局部有效点、局部弱有效点和局部真有效点与集合的各 锥之间的关系作了刻画.     

Asymptotics in the Baum—Katz formula for random fields

In 1996, D. Deng established an analog of the Baum—Katz theorem on the convergence rate in the law of large numbers for multi-indexed random variables. The series describing the convergence rate depends, in a natural way, on the parameter characterizing the excess of the normalized sums over some level. In this paper, we find the precise asymptotics of the sum of this series with respect to the above-mentioned parameter. Thus, a generalization of a recent result due to A. Gut and A. Spataru is obtained.     

Stationary remaining service time conditional on queue length

In Mandelbaum and Yechiali [The conditional residual service time in the M/G/1 queue, http://www.math.tau.ac.il/∼uriy/publications (No. 30a), 1979] and in Fakinos [The expected remaining service time in a single-server queue, Oper. Res. 30 (1982) 1014-1018] a simple formula is derived for the (stationary) expected remaining service time in a M/G/1 queue, conditional on the number of customers in the system. We give a short new proof of the formula using Rate Conservation Law, and generalize to handle higher moments.     

Parallelization of population-based multi-objective meta-heuristics: An empirical study

In single-objective optimization it is possible to find a global optimum, while in the multi-objective case no optimal solution is clearly defined, but several that simultaneously optimize all the objectives. However, the majority of this kind of problems cannot be solved exactly as they have very large and highly complex search spaces. Recently, meta-heuristic approaches have become important tools for solving multi-objective problems encountered in industry as well as in the theoretical field. Most of these meta-heuristics use a population of solutions, and hence the runtime increases when the population size grows. An interesting way to overcome this problem is to apply parallel processing. This paper analyzes the performance of several parallel paradigms in the context of population-based multi-objective meta-heuristics. In particular, we evaluate four alternative parallelizations of the Pareto simulated annealing algorithm, in terms of quality of the solutions, and speedup.     

ISLAND, revisited

This paper is in answer to the comment on the GRG paper: Lockerbie N.A. Gen. Rel. Grav. 36, 593 (2004), made by A.V. Sanders, G.T. Gillies (ibid.). N. A. Lockerbie is a member of the STEP (Satellite Test of the Equivalence Principle) Science Study Team, and an Associate of the Institute for Gravitational Research at the University of Glasgow, Scotland, UK.     

Study of the structural and optical properties of GaN/AlN quantum dot superlattices

We study GaN/AlN Quantum Dot (QD) superlattices utilizing the STREL environment which allows the building of atomistic models, relaxation of the structures, the calculation of the electronic states and optical transitions and the visualization of the results. The forces are calculated using an appropriate Keating or Stillinger–Weber interatomic potential model and the electronic states and optical transitions using a tight-binding formulation which is economical and produces realistic electronic properties. The relaxed structure has strains mainly in the GaN region which are compressive and small tensile strains in the AlN region, mainly below the QD. In the calculation of the electronic states and of the optical transitions the strains are included realistically at the atomistic level. The study of the wavefunctions close to the fundamental gap show how these strains influence the form and spatial extent of the wavefunction. Very close to the fundamental gap the valence and some conduction states are confined in the QD and have considerable oscillator strength.     

有Edgeworth展式的分布的随机加权逼近的重对数律

本文研究了未知分布的逼近问题，利用随机加权法，给出了有Edgeworth展式的一类（未知）分布的模拟分布，证明了在一定条件下，模拟分布与未知分布的逼近精度达到O(n^-1√lnlnn），称之为随机加权逼近的重对数律。     

三维守恒律有限元方法逼近光滑解的误差估计

我们对一个三维守恒律的显式有限元方法证明了H^1范数的二阶误差估计。