Projections on Convex Sets in the Relaxed Limit

The paper establishes the continuity of the best approximation, or the projection, of a function in L _p for p[1,), on a closed convex set in the space, when the set varies and converges to a limit set in the Young-measure relaxation of the space. To this end a strong-type convergence and a convexity structure are identified on the space of Young measures. The appropriate convergence of sets with respect to which the continuity holds is the Mosco convergence of sets associated with the strong-type convergence of functions.     

Sharper uncertainty principles associated with Lp-norm

Motivated by the well-established phase derivative embedded technique, this study devotes to sharper uncertainty principles related to the L^p-norm type of uncertainty product, giving rise to two kinds of uncertainty inequalities that improve the classical result through providing tighter lower bounds. The conditions that truly reach these better estimates are obtained. Examples and simulations are carried out to verify the correctness of the derived results, and finally, possible applications in time-frequency analysis are also given.     

Mountain Pass Solutions for a Double-Well Energy

We establish the existence of a mountain pass solution for a variational integral involving a quasiconvex function with a double-well structure in the geometrically linear elasticity setting. We show that under small dead-load perturbations, the Neumann boundary value problem has at least three solutions, a global minimizer, a local minimizer and a mountain pass solution. We show that our variational integral satisfies a Weak Palais-Smale condition (WPS) hence the mountain pass lemma applies.     

On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius

We generalize the Jensen-Shannon divergence and the Jensen-Shannon diversity index by considering a variational definition with respect to a generic mean, thereby extending the notion of Sibson’s information radius. The variational definition applies to any arbitrary distance and yields a new way to define a Jensen-Shannon symmetrization of distances. When the variational optimization is further constrained to belong to prescribed families of probability measures, we get relative Jensen-Shannon divergences and their equivalent Jensen-Shannon symmetrizations of distances that generalize the concept of information projections. Finally, we touch upon applications of these variational Jensen-Shannon divergences and diversity indices to clustering and quantization tasks of probability measures, including statistical mixtures.     

测定圆柱体杨氏模量的原理分析

分析了测量圆柱体弯曲形变杨氏模量的实验原理,得出了理论公式,将测量拉压形变、弯曲形变的杨氏模量以及扭转形变的剪切模量3个实验中样品形状统一成圆柱体.     

杨氏模量测定的不确定度计算

对于杨氏模量实验中,各量的不确定度进行了分析和计算。     

用动力学法测杨氏模量实验及其实验装置的研制

介绍了新研制的用动力学法杨氏模量的实验装置,它具有功耗低,灵敏度高的特点;教学中测量悬线不同位置时的共振频率,用作图法拟合出其精确值,以减少由于悬线不在节点引起的系统性误差,测量精密度比传统的静态拉伸法高一个量级以上。     

用迈克耳孙干涉仪测量杨氏模量

提出用迈克耳孙干涉仪测金属杨氏模量的新方法,并从实验上测定了碳钢丝的杨氏模量。     

掺杂石英系单模光纤对BSBS频移的影响

报道了对几种掺杂SiO₂石英系单模光纤的背向受激布里渊散射(BSBS)谱的实验结果,结果表明其布里渊散射斯托克斯频移主要取决于纤芯的掺杂材料和浓度,进一步分析证明了光纤掺杂后将主要通过调制杨氏模量的变化,从而导致BSBS频移量减小.