Partially Strictly Monotone and Nonlinear Penalty Functions for Constrained Mathematical Programs

We introduce the concept of partially strictly monotone functions and apply it to construct a class of nonlinear penalty functions for a constrained optimization problem. This class of nonlinear penalty functions includes some (nonlinear) penalty functions currently used in the literature as special cases. Assuming that the perturbation function is lower semi-continuous, we prove that the sequence of optimal values of nonlinear penalty problems converges to that of the original constrained optimization problem. First-order and second-order necessary optimality conditions of nonlinear penalty problems are derived by converting the optimality of penalty problems into that of a smooth constrained vector optimization problem. This approach allows for a concise derivation of optimality conditions of nonlinear penalty problems. Finally, we prove that each limit point of the second-order stationary points of the nonlinear penalty problems is a second-order stationary point of the original constrained optimization problem.     

Low-threshold interband cascade lasers operating above room temperature

Mid-IR type-II interband cascade lasers were demonstrated in pulsed mode at temperatures up to 325 K and in continuous mode up to 200 K. At 80 K, the threshold current density was 8.9 A/cm² and a continuous wave output power of 140 mW/facet was obtained.     

Non-elliptic deformation field near the tip of a mixed-mode crack in a compressible hyperelastic material

This paper gives an asymptotic analysis of the deformation field near the tip of an arbitrary mixed-mode crack in a compressible hyperelastic harmonic material which loses ellipticity at sufficiently large deformations. It is found that the near-tip deformation field is characterized by a localized non-elliptic deformation band issuing from the crack-tip and bounded by two curves of discontinuous deformation gradient. Explicit expression for the near-tip deformation field is obtained both inside and outside the localized deformation band. In particular, a simple relation is derived that determines the orientation of the deformation band in terms of two complex governing parameters of the near-tip fields inside and outside the deformation band, respectively.     

Noncollinear optical parametric amplification in lithium triborate seeded by a cw Ti:sapphire laser

Experimental investigations of a type-I noncollinear phase-matched optical parametric amplification based on lithium triborate, which was pumped by a 5-ns second-harmonic pulses from a Q-switched Nd:YAG, seeded by a cw Ti:sapphire laser at 800 nm, was presented. The experiments generated 2-ns signal output pulses at 800 nm, the maximum signal output pulse energy reached 19 μJ, the corresponding parametric gain was 44 dB. Furthermore, the experiments demonstrate that the 65 nm-FWHM parametric fluorescence gain spectrum could also be observed. A quantitative account of the ultrabroadband parametric fluorescence gain spectrum was given with our theory. The experimental measurements are in agreement with theoretical calculations.     

Optical investigation of cavitation erosion by laser-induced bubble collapse

By means of a new force sensor based on optical beam deflection (OBD), the mechanical effects of laser-matter interaction underwater at different incident laser energy are investigated in detail. The experimental results show that a target underwater is impacted in turn by laser-plasma ablation force and high-speed liquid-jet impulse induced by bubbles collapse in the vicinity of a solid boundary. Furthermore, the amplitudes of the two forces increase monotonously with laser energy. According to the ablation force detected by the experiment and the theoretical relationship between laser intensity and ablation pressure, the value of liquid-jet impact against a solid boundary can be easily obtained. In addition, based on the model of a collapsing bubble, some characteristic parameters, such as the liquid-jet impact velocity, the maximum bubble radius, the bubble energy can also be obtained at different laser energy, which are valuable in the corresponding research fields.     

求解非对称线性方程组的QMRGCGS方法

1 引言 求解非对称线性方程组Ax=b的双共轭梯度方法(BCG)[3]和它的变形共轭梯度平方方法(CGS)[6]都有典型的不规则收敛行为,后来Freund和Nachtigal提出一种BCG类方法,即拟极小剩余方法(QMR)[7],用来补救BCG方法的收敛性并且产生了光滑的收敛曲线。然而,象BCG方法一样,QMR方法要用到系数矩阵A及其转置A~T与向量的乘积,为了解决这一问题,Freund提出TFQMR方法,此方法具有拟极小剩余性,同时不需用到A~T与向量的乘积。     

Optimal control of the obstacle in a quasilinear elliptic variational inequality

In this paper we consider an obstacle control problem where the state satisfies a quasilinear elliptic variational inequality and the control function is the obstacle. The state is chosen to be close to the desire profile while the H² norms of the obstacle is not too large. Existence and necessary conditions for the optimal control are established.     

Regular Approximations of Singular Sturm-Liouville Problems with Limit-Circle Endpoints

For any self-adjoint realization S of a singular Sturm-Liouville equation on an interval (a,b) with limit-circle endpoints, we construct a family of self-adjoint realizations S _r ,r ∈ (0,∞), of this equation on subintervals (a _r ,b _r ) of (a,b) such that every eigenvalue of S is the limit of a continuous eigenvalue branch of this family. Of particular interest are the cases when at least one endpoint is oscillatory or the leading coefficient function changes sign. In these cases, we show that the index determining each continuous eigenvalue branch has an infinite number of jump discontinuities and give an explicit characterization of these discontinuities.     

Synthesis,and Antimycobacterial and Cytotoxic Evaluation of Certain Fluoroquinolone Derivatives

Certain 1‐ethyl‐ and 1‐aryl‐6‐fluoro‐1,4‐dihydroquinol‐4‐one derivatives were synthesized and evaluated for antimycobacterial and cytotoxic activities. Preliminary results indicated that, for 1‐aryl‐6‐fluoroquinolones, both 7‐(piperazin‐1‐yl)‐ and 7‐(4‐methylpiperazin‐1‐yl) derivatives, 9b and 11a , are able to completely inhibit the growth of M. tuberculosis at a concentration of 6.25 μg/ml, while the 7‐[4‐(2‐oxo‐2‐phenylethyl)piperazin‐1‐yl] derivative 13 exhibits only 31% growth inhibition at the same concentration. For 1‐ethyl‐6‐fluoroquinolones, both 7‐[4‐(2‐oxopropyl)piperazin‐1‐yl]‐ and 7‐[4‐(2‐oxo‐2‐phenylethyl)piperazin‐1‐yl]‐derivatives, 2a and 2b , respectively, show complete inhibition, while their 2‐iminoethyl and substituted phenyl counterparts 3a and 2c are less active. In addition, the 6,8‐difluoro derivative was a more‐favorable inhibitor than its 6‐fluoro counterpart ( 2b vs. 2d ). These results deserve full attention especially because 2a, 2b, 9b , and 11a are non‐cytotoxic at a concentration of 100 μM . Furthermore, compound 9b proved to be a potent anti‐TB agent with selective index (SI)>40 and an EC₉₀ value of 5.75 μg/ml.     

Isolating the most recent entry in a random recursive tree by random cuts

A recursive tree is constructed by starting with a root node and repeatedly adjoining new nodes to one node of the tree already constructed. Such a tree can represent, for example, the heirarchy of a workforce of a company that grows via recruiting. At times of economic depression, the company may decide to lay off participants, and in some cases it is a fair policy to relieve the last senior worker (most recent entry in the tree). If we remove an edge from such a tree then it falls into two subtrees one of which contains the most recent entry. If we continue to remove edges from the successively smaller subtrees that contain the most recent entry, we eventually isolate the most recent entry. We consider how many randomly selected edges must be removed in average before isolating the most recent entry by this procedure.