On W-solvability for special vectorial Hamilton-Jacobi systems

We study the solvability of special vectorial Hamilton-Jacobi systems of the form F(Du(x))=0 in a Sobolev space. In this paper we establish the general existence theorems for certain Dirichlet problems using suitable approximation schemes called W^1,p-reduction principles that generalize the similar reduction principle for Lipschitz solutions. Our approach, to a large extent, unifies the existing methods for the existence results of the special Hamilton-Jacobi systems under study. The method relies on a new Baire's category argument concerning the residual continuity of a Baire-one function. Some sufficient conditions for W^1,p-reduction are also given along with certain generalization of some known results and a specific application to the boundary value problem for special weakly quasiregular mappings.     

A note on the critical points of equilibrium paths in imperfect structures

In a recent work (Int. J. Solids Struct. 37 (2000) 1561) by one of the authors, an extended system for calculating critical points of equilibrium paths in imperfect structures was presented. However, the extremum nature of these points was not analyzed explicitly in that paper. In this note, we will fill in the gap and establish a sufficient condition for determining the buckling strength of imperfect structures.     

On the equilibrium set of magnetostatic energy by differential inclusion

This paper concerns the set of equilibriums of the nonlocal magnetostatic energy for saturated magnetizations. We study the stability of the equilibrium set under the weak-star convergence using methods of differential inclusion and quasiconvex analysis. The equilibrium set is shown to be unstable under the weak-star convergence and an estimate on its weak-star closure is obtained. This estimate is also shown to be accurate when the physical domain is an ellipsoid.     

圆形阵列光电探测系统双目标识别方法

针对双弹丸同时着靶情况下的立靶坐标测量问题,提出一种圆形阵列光电探测系统的双目标识别方法.采用光电探测器件组成1个圆形的探测阵列,并将3个发光角度均为60°的扇形一字线激光器均匀设置于圆形探测阵列上组成探测光幕.当2发弹丸同时穿过探测光幕时,会在圆形探测阵列上产生6个弹丸投影,通过信号处理电路识别6个弹丸投影的中心位置...     

Two new approaches to computing Hopf bifurcation problems

We consider the computation of Hopf bifurcation for ordinary differential equations. Two new extended systems are given for the calculation of Hopf bifurcation problems: the first is composed of differential-algebraic equations with index 1, the other consists of differential equations by using a symmetry inherited from the autonomous system of ordinary differential equations. Both methods are especially suitable for calculating bifurcating periodic solutions since they transform the Hopf bifurcation problem into regular nonlinear boundary value problems which are very easy to implement. The bifurcation solutions become isolated solutions of the extended system so that our methods work both in the subcritical and supercritical case. The extended systems are based on an additional parameter ε; practical experience shows that one gets convergence for ε sufficiently large so that a substantial part of the bifurcating branch can be computed. The two methods are illustrated by numerical examples and compared with other procedures.     

Characterization of energy minimizers in micromagnetics

We present a new characterization of minimizing sequences and possible minimizers (all called the minimizing magnetizations) for a nonlocal micromagnetic-like energy (without the exchange energy). Our method is to replace the nonlocal energy functional and its relaxation with certain local integral functionals on divergence-free fields obtained by a two-step minimization of some auxiliary augmented functionals. Through this procedure, the minimization problem becomes equivalent to the minimization of a new local variational functional, called the dual variational functional, which has a unique minimizer. We then precisely characterize the minimizing magnetizations of original nonlocal functionals in terms of the unique minimizer of the dual variational functional. Finally, we give some remarks and ideas on solving the dual minimization problem.     

一种新型固体Q开关Cr4＋∶YAG的实验研究

对一种适用于Ｎｄ３＋∶ＹＡＧ激光系统的新型被动Ｑ开关掺铬钇铝石镏石（Ｃｒ４＋∶ＹＡＧ）进行了实验研究，得到单脉冲能量为１４５ｍＪ、脉宽为３０～４０ｎｓ、效率接近１％、动静比达４０％以上的结果。     

改进型1-3压电复合材料结构参数对其谐振性能的影响

研究了水声换能器用的1-3改进型(称1-3-2型)压电复合材料的结构参数(陶瓷体积分数)对其谐振性能的影响.1-3-2型压电复合材料是由1-3型复合材料和陶瓷基底两部分组成,利用Newnham串并联理论、均匀场理论和混合定律,得到1-3-2型复合材料的压电方程,从而推导出1-3-2型复合材料的各项等效性能参数,并通过实验对频率常数、机电耦合系数和声阻抗等参数的理论推导进行了验证,实验结果与理论计算符合较好。