Seiberg-Witten theory as a complex version of Abelian Higgs model

The adiabatic limit procedure associates with every solution of Abelian Higgs model in (2 + 1) dimensions a geodesic in the moduli space of static solutions. We show that the same procedure for Seiberg-Witten equations on 4-dimensional symplectic manifolds introduced by Taubes may be considered as a complex (2+2)-dimensional version of the (2 + 1)-dimensional picture. More precisely, the adiabatic limit procedure in the 4-dimensional case associates with a solution of Seiberg-Witten equations a pseudoholomorphic divisor which may be treated as a complex version of a geodesic in (2+1)-dimensional case.     

On bounded maximum width sequential confidence ellipsoids based on generalized U-statistics

For a vector of (estimable) functionals of several independent distributions, sequential confidence ellipsoids (of bounded maximum width) based on a class of generalized U-statistics are studied. A stopping rule along with a procedure for choosing the component sample sizes at each stage is developed, so that the proposed confidence ellipsoid has a confidence coefficient asymptotically (as the prescribed maximum width shrinks to zero) equal to a preassigned 1 - α (0 < α < 1), and the expected total sample size is minimized for the procedure. Asymptotic efficiency of the procedure is also studied. The case of von Mises' functionals is treated briefly at the end.     

On random observation processes for stochastic approximation

Summary In [1] a new procedure is given to estimate the root of a regression equation. The purposes of this paper are to extend the Lemma 1 in [1] and to give a process involving a randomly determined sequence of observations for finding thermaximum of a regression function. The process is similar to that of [1]. Kiefer and Wolfowitz [2] gave a stochastic approximation procedure for the latter purpose. Their process needs the condition of the unimodality of the regression function which is not required for our case.     

Zero-one integer programs with few constraints —Efficient branch and bound algorithms

The 0–1 integer programming problem and its special case, the 0–1 knapsack problem are frequently encountered in modeling various design and decision making processes. This paper is a follow-up paper to [4] and deals with the development of an effective solution procedure for 0–1 integer programs with few constraints. Detailed computational experiments are carried out and different separation, branching and bounding rules are compared using an experimental branch and bound code. An efficient branch and bound procedure is developed, tested and compared with previously developed optimal algorithms. It is suggested that this procedure may also be used as a heuristic method for large problems by early termination of the tree search. This scheme is tested and found to be very effective.     

On constrained optimization problems with nonsmooth cost functionals

In this paper we present a computational procedure for minimizing a class ofL ₁-functionals subject to conventional as well as functional constraints. The computational procedure is based on the idea of enforced smoothing together with a method of converting the functional constraints into conventional equality constraints. For illustration, two examples are solved using the proposed procedure.     

Embedding learning capability in Lagrangean relaxation: An application to the travelling salesman problem

This paper presents an effective procedure that finds lower bounds for the travelling salesman problem based on the 1-tree using a learning-based Lagrangian relaxation technique. The procedure can dynamically alter its step-size depending upon its previous iterations. Along with having the capability of expansion–contraction, the procedure performs a learning process in which Lagrange multipliers are influenced by a weighted cost function of their neighbouring nodes. In analogy with simulated annealing paradigm, here a learning process is equivalent to escaping local optimality via exploiting the structure of the problem. Computational results conducted on Euclidean benchmarks from the TSPLIB library show that the procedure is very effective.     

关于Schwarz交替法的拟边界松弛方法

§1.松弛方法 我们讨论二阶自共轭椭圆型方程的Dirichlet问题.设Ω?R~2为一多边形区域. a(u,v)=(f,v),v∈H_0~1(Ω),f∈H~(-1)(Ω), u∈H_0~1(Ω)是定义在其上的边值问题的变分形式,这里取齐次边界条件仅为叙述问题方便.双线性型a(·,·)满足:     

Facets of the knapsack polytope

A necessary and sufficient condition is given for an inequality with coefficients 0 or 1 to define a facet of the knapsack polytope, i.e., of the convex hull of 0–1 points satisfying a given linear inequality. A sufficient condition is also established for a larger class of inequalities (with coefficients not restricted to 0 and 1) to define a facet for the same polytope, and a procedure is given for generating all facets in the above two classes. The procedure can be viewed as a way of generating cutting planes for 0–1 programs.     

Construction of a game''s value in certain fixed-time differential games

A procedure is given for the construction of a maximal μ-stable bridge /1/ in a fixed-time nonstationary game. A procedure is suggested for the construction of the game's value for two classes of fixed-time games. Examples are presented.     

Experiments with an interactive procedure for MOLP given weak orders on variables and objectives

In this paper we describe computational experiments with an interactive procedure for solving a multiobjective linear-programming model. The point of departure for this paper is the work described in Gass and Dror [4] and Dror and Gass [1] in which an interactive solution procedure is outlined. Here we describe improvements in the original procedure, as well as computational experiments, and demonstrate the procedure's ability to explore successfully the solution space of a multiobjective problem.     

Zur numerischen Lösung gewöhnlicher Differential-gleichungen mit Splines in einem Sonderfall

In an earlier paper [1] a general procedure has been presented to obtain polynomial spline approximations for the solution of the initial value problem for ordinary differential equations. In this paper the general procedure is described by an equivalent one step method. Furthermore two convergence theorems are proved for a special case which is not included in the general convergence or divergence theory given in [1].     

分组测试与迫进控制标准

1引言 在第二次世界大战期间,珍珠港事件发生后,美国为了反击德国法西斯挑起的侵略战争,多次进行大规模的征兵活动．在征兵活动中,需要对大量报名入伍者进行健康检查,看其身体是否符合入伍的条件．其中一项健康检查的内容是血液抗体检测,通过血液抗体检测,查出梅毒的携带者．当时,由于被检测者数量巨大,部队又急需补充兵员,检测时间紧、任务重,这就需要找到一种科学的检测方法,用尽可能少的测试次数检测出所有病毒携带者,这一问题后来称为搜索坏硬币的最优化问题．在这个问题中,被检测者抽象为硬币,血液不带病毒者抽象为标准硬币,血液带病毒者抽象为伪硬币,检测的设备称为装置．如何用特定性能的若干台装置,以尽可能少的测试次数从由硬币组成的集合中检测出全部伪硬币,是一个有很强实际背景的最优化问题,正因为如此,近一段时间组合搜索中的伪硬币问题一直受到人们的广泛关注．     

A RECURSIVE ALGORITHM AND ITS CONVERGENCE FOR PARAMETER ESTIMATION OF CONVOLUTION MODEL

In this article, the problem on the estimation of the convolution model parameters is considered. The recursive algorithm for estimating model parameters is introduced from the orthogonal procedure of the data, the convergence of this algorithm is theoretically discussed, and a sufficient condition for the convergence criterion of the orthogonal procedure is given. According to this condition, the recursive algorithm is convergent to model wavelet A- = （1, α1,..., αq）.     

Simulation of Stationary Gaussian Processes in [0, 1] d

Abstract

A method for simulating a stationary Gaussian process on a fine rectangular grid in [0, 1]^d ??^d is described. It is assumed that the process is stationary with respect to translations of ?^d, but the method does not require the process to be isotropic. As with some other approaches to this simulation problem, our procedure uses discrete Fourier methods and exploits the efficiency of the fast Fourier transform. However, the introduction of a novel feature leads to a procedure that is exact in principle when it can be applied. It is established that sufficient conditions for it to be possible to apply the procedure are (1) the covariance function is summable on ?^d, and (2) a certain spectral density on the d-dimensional torus, which is determined by the covariance function on ?^d, is strictly positive. The procedure can cope with more than 50,000 grid points in many cases, even on a relatively modest computer. An approximate procedure is also proposed to cover cases where it is not feasible to apply the procedure in its exact form.     

On the connection between discontinuous step-like and smooth kink-type classical solutions in quantum field theory

A nonperturbative procedure for subtracting singularities caused by finite discontinuities of the field configurations is suggested. This procedure is applied to the Lorentz-covariant quantization of(1+1)-dimensional topological kinks. In the course of this procedure, quantum copies of a classical kink naturally appear. These copies have the same topological charge but have negligibly small sizes and masses because the subtraction procedure eliminates divergences caused by the field differentiations at the discontinuity points. These effects are investigated in detail for those(1+1)-dimensional scalar field models where classical kinks exist.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 108, No. 2, pp. 212–248, August, 1996.     

Suboptimal policy determination for large-scale Markov decision processes,part 2: Implementation and numerical evaluation

We present an implementation of the procedure for determining a suboptimal policy for a large-scale Markov decision process (MDP) presented in Part 1. An operation count analysis illuminates the significant computational benefits of this procedure for determining an optimal policy relative to a procedure for determining a suboptimal policy based on state and action space aggregation. Results of a preliminary numerical study indicate that the quality of the suboptimal policy produced by the 3MDP approach shows promise.This research has been supported by NSF Grants Nos. ECS-80-18266 and ECS-83-19355.     

一类差分方程组的矩阵追赶法及稳定性

[1]中曾给出一种解用隐式格式逼近杆弹性振动方程时所得的差分方程组的矩阵追赶法,并对常系数情形,讨论了追过程的合理性,但是,对有些常见的情形,必须经过适当处理才能使用此方法,本文提出了一种能适用于最一般情形的方法,并对变系数的情形,讨论了追过程和赶过程的稳定性。     

Local cuts revisited

We present a variant of the local cut generation procedure by Applegate, Bixby, Chvátal and Cook. Unlike the original procedure, our method immediately yields a facet of the projected polytope as the solution of a single LP, without the need for the time-consuming tilting step. Moreover, our facets have big volume in general.     

Effect of impulsive change of wall velocity and wall temperature in viscous heat-conducting gas

A study of compression waves produced in a viscous heat-conducting gas by the impulsive start of a one-dimensional piston and by the inpulsive change of piston wall temperature is made using Laplace Transform Technique for Prandt1 number unity. Expressions for velocity, temperature and density have also been obtained using small-time expansion procedure in this case. For arbitrary Prandt1 number solutions have been developed using large-time expansion procedure. A number of graphs exhibiting the distribution of the fluid velocity, temperature and density have been drawn.     

Passive optimal control of an antisymmetric angle-ply laminate

Using the maximum principle of Ref. 1, a procedure to find numerical solutions of certain optimal control problems is given. As an application of this procedure, the optimal control of an antisymmetric angle-ply laminate is worked out in detail. Numerical solutions are given in the form of graphs.