简单约束非线性方程组的射影尺度牛顿方法

基于射影尺度牛顿方法,本文使用新的势函数以取代原有的势函数,得到一类求解非线性方程组的数值算法.在合适的假设下,证明了算法的全局强收敛性和局部二次收敛速度.数值试验的结果说明了算法的有效性.     

The Field Descent Method

We obtain a broadly applicable decomposition of group ring elements into a “subfield part” and a “kernel part”. Applications include the verification of Lander’s conjecture for all difference sets whose order is a power of a prime >3 and for all McFarland, Spence and Chen/Davis/Jedwab difference sets. We obtain a new general exponent bound for difference sets. We show that there is no circulant Hadamard matrix of order v with 4<v<548, 964, 900 and no Barker sequence of length l with 13 < l ≤ 10²².     

Superlinear primal-dual affine scaling algorithms for LCP

We describe an interior-point algorithm for monotone linear complementarity problems in which primal-dual affine scaling is used to generate the search directions. The algorithm is shown to have global and superlinear convergence with Q-order up to (but not including) two. The technique is shown to be consistent with a potential-reduction algorithm, yielding the first potential-reduction algorithm that is both globally and superlinearly convergent.Corresponding author. The work of this author was based on research supported by the Office of Scientific Computing, U.S. Department of Energy, under Contract W-31-109-Eng-38.The work of this author was based on research supported by the National Science Foundation under grant DDM-9109404 and the Office of Naval Research under grant N00014-93-1-0234. This work was done while the author was a faculty member of the Systems and Industrial Engineering Department at the University of Arizona.     

Multiple positive solutions for a semilinear equation with prescribed singularity

Variational methods are used to prove the existence of multiple positive solutions for a semilinear equation with prescribed finitely many singular points. Some exact local behavior for positive solutions are also given.     

Kinetics of a Migration-Driven Aggregation-Fragmentation Process

We propose a reversible model of the migration-driven aggregation-fragmentation process with the sym-metric migration rate kernels K(k;j) = K‘(k;j) = λkjv and the constant aggregation rates I1, I2 and fragmentationrates J1, J2. Based on the mean-field theory, we investigate the evolution behavior of the aggregate size distributions inseveral cases with different values of index v. We find that the fragmentation reaction plays a more important role in the kinetic behaviors of the system than the aggregation and migration. When J1 = 0 and J2 = 0, the aggregate sizedistributions ak(t) and bk(t) obey the conventional scaling law, while when J1 ＞ 0 and J2 ＞ 0, they obey the modifiedscaling law with an exponential scaling function. The total mass of either species remains conserved.     

Effective-field theory of spin glasses and the coherent-anomaly method. II. Double-Cluster approximation

An improved version of a cluster-effective-field theory for spin glasses, namely the double-cluster approximation, is formulated. The present version is based not on theself-consistency condition, but on thedouble-cluster-consistency condition. The advantages of the approximation combined with the coherentanomaly method are discussed. The critical data of the spin-glass susceptibility are estimated for the two-, three-, and four-dimensional ±J models.     

Second order fluid models with general boundary behaviour

A crucial property of second order fluid models is the behaviour of the fluid level at the boundaries. Two cases have been considered: the reflecting and the absorbing boundary. This paper presents an approach for the stationary analysis of second order fluid models with any combination of boundary behaviours. The proposed approach is based on the solution of a linear system whose coefficients are obtained from a matrix exponent. A practical example demonstrates the suitability of the technique in performance modeling. This work is partially supported by the Italian-Hungarian bilateral R&D programme, by OTKA grant n. T-34972, by Italian Ministry for University and Research (MIUR) through PRIN project Famous and by EEC project Crutial.     

Shortest single axioms for commutative moufang loops of exponent 3

In this note, we attempt to find all shortest single product axioms for commutative Moufang loops of exponent 3. These investigations were aided by the automated theorem-prover Prover9 and the model-generator Mace4.     

Brownian models of multiclass queueing networks: Current status and open problems

This paper is concerned with Brownian system models that arise as heavy traffic approximations for open queueing networks. The focus is on model formulation, and more specifically, on the formulation of Brownian models for networks with complex routing. We survey the current state of knowledge in this dynamic area of research, including important open problems. Brownian approximations culminate in estimates of complete distributions; we present numerical examples for which complete sojourn time distributions are estimated, and those estimates are compared against simulation.