Nondifferentiable reverse convex programs and facetial convexity cuts via a disjunctive characterization

Disjunctive Programs can often be transcribed as reverse convex constrained problems with nondifferentiable constraints and unbounded feasible regions. We consider this general class of nonconvex programs, called Reverse Convex Programs (RCP), and show that under quite general conditions, the closure of the convex hull of the feasible region is polyhedral. This development is then pursued from a more constructive standpoint, in that, for certain special reverse convex sets, we specify a finite linear disjunction whose closed convex hull coincides with that of the special reverse convex set. When interpreted in the context of convexity/intersection cuts, this provides the capability of generating any (negative edge extension) facet cut. Although this characterization is more clarifying than computationally oriented, our development shows that if certain bounds are available, then convexity/intersection cuts can be strengthened relatively inexpensively.     

Facet inequalities from simple disjunctions in cutting plane theory

The duality between facets of the convex hull of disjunctive sets and the extreme points of reverse polars of these sets is utilized to establish simple rules for the derivation of all facet cuts for simple disjunctions, namely, elementary disjunctions in nonnegative variables. These rules generalize the cut generation procedure underlying polyhedral convexity cuts with negative edge extensions. The latter are also shown to possess some interesting properties with respect to a biextremal problem that maximizes the distance, from the origin, of the nearest point feasible to the cut. A computationally inexpensive procedure is given to generate facet cuts for simple disjunctions which are dominant with respect to any specified preemptive ordering of variables.     

系列脉冲偏磁场作用下硬磁泡的形成

实验研究了系列脉冲偏场作用下外延石榴石薄膜的硬磁泡(包括哑铃畴)的形成规律。发现系列脉冲对畴段的作用不是单次脉冲作用(软畴段硬化的物理过程)的简单迭加,而有其特有的规律性,存在着硬畴段进一步硬化及硬畴段软化的另两个物理过程。运用上述三个物理过程对实验结果作了解释。 关键词：     

Digital computation of transient characteristics of an induction motor on switched supply

A novel method of computing the nonlinear differential equations relating to the transient behaviour of an induction motor using a polynomial series, is presented. The stator and rotor currents and the angle of rotation are expressed as polynomial series dependent on time. These are then substituted into the differential equations of the induction motor to compute the polynomial coefficients and, consequently, the transient quantities. Since the equations are nonlinear, the computations are carried out using the step-by-step method. The stator and rotor currents, speed and torque are calculated for acceleration and braking conditions. The results are compared both analytically and experimentally.     

Studies on the dependence of optical Rotatory Power on Chemical Constitution

Proceedings - Mathematical Sciences -     

旋转流体实验设备改造

论述了旋转流体实验装置改造所存在的问题及改进的措施。     

Polarizing interferometer with constant radial and azimuthal shears

An interferometer is described in which a rotatable Wollaston prism is used to achieve constant radial and azimuthal shears in a converging beam. These displacements may have applications in speckle shearing interferometry for the deformation measurement of objects with axial symmetry.     

FeCl_3·6H_2O Catalyzed Reaction of Aromatic Aldehydes with 5, 5-Dimethyl-1, 3-cyclohexandione in Ionic Liquids

Room temperature ionic liquids with low melting point (<100℃) salts represent a new class of non-molecular, ionic solvents. Especially those based on the 1-N-alkyl-3- methylimidazolium cations, have shown great promise as an attractive alternative to conventional solvents for catalytic reactions1. On the other hand, FeCl3·6H2O was considered to be an environmentally benign Lewis acid and has been used successfully in several kinds of organic reactions2. Recently we have focused our interes…     

On the Stability of Davey-Stewartson System - A Dressing Operator Approach

The problem of stability associated with perturbations around solitonic excitations of Davey-Stewartson equation in three dimension is discussed within the framework of dressing operator approach of Zakharov. The system is stable so far as long time behaviour is concerned and unstable for large transverse directions depending upon the sign of the eigenvalue of the linearized problem.