The Limit of Finite Sample Breakdown Point of Tukey’s Halfspace Median for General Data

Under special conditions on data set and underlying distribution, the limit of finite sample breakdown point of Tukey＇s halfspace median （1） has been obtained in the literature. In this paper, we establish the result under weaker assumptions imposed on underlying distribution （weak smoothness） and on data set （not necessary in general position）. The refined representation of Tukey＇s sample depth regions for data set not necessary in general position is also obtained, as a by-product of our derivation.

Acousto-Diffusive Waves in a Piezoelectric-Semiconductor-Piezoelectric Sandwich Structure

The propagation of acoustic waves in a homogeneous isotropic semiconducting layer sandwiched between two homogeneous transversely isotropic piezoelectric halfspaces has been investigated. The mathematical model of the problem is depicted by a set of partial differential equations of motion, Gauss equation in piezoelectric material and electron diffusion equation in semiconductor along with the boundary conditions to be satisfied at the piezoelectric-semiconductor interfaces. The secular equations describing the symmetric and asymmetric modes of wave propagation have been derived in compact form after obtaining the analytical expressions for various field quantities that govern the wave motion. The complex secular equation has been solved numerically using functional interaction method along with irreducible cardano method. The computer simulated results are obtained with the help of MATLAB software for 6 mm cadmium selenide (CdSe) piezoelectric material and n-type silicon (Si) semiconductor in respect of dispersion curve, attenuation and specific loss factor of energy dissipation for symmetric (sym) and asymmetric (asym) modes of wave propagation. The study may find applications in non-destructive testing, resonators, waveguides etc.

MODAL ACOUSTIC IMPEDANCE FORCE ON A SPHERICAL SOURCE NEAR A RIGID INTERFACE

The modal acoustic radiation load on a spherical surface undergoing angularly periodic axisymmetric harmonic vibrations while immersed in an acoustic halfspace with a rigid (infinite impedance) planar boundary is analyzed in an exact fashion using the classical technique of separation of variables. The formulation utilizes the appropriate wave field expansions, the classical method of images and the appropriate translational addition theorem to simulate the relevant boundary conditions for the given configuration. The associated acoustic field quantities such as the modal impedance matrix and the modal acoustic radiation force acting on the spherical surface are determined. The analytical results are illustrated with a numerical example in which the spherical surface, excited in vibrational modes of various orders, is immersed near an impervious rigid wall. The presented solution could eventually be used to validate those obtained by numerical approximation techniques.

Hypersingular integral-partial differential equations for a planar interface crack in bimaterial

With the rapidly increasing use of composite materials, a great deal of interest in the interface crack has been generated among the technicians, metal physicists and materials scientists. To the authors’ knowledge, many researches on this subject have been taken. However, they are usually applied to two-dimensional cases. For the three-dimensional ones, very few analyses have been done because of the great complexity on mathematics and mechanics. In this study, based on the point-force solutions for two perfectly

THE GENERALIZED JACOBIAN OF THE PROJECTION ONTO THE INTERSECTION OF A HALF-SPACE AND A VARIABLE BOX

This paper is devoted to studying the generalized Jacobian for the projection onto the intersection of a closed half-space and a variable box. This paper derives the explicit formulas of an element in the set of the generalized HS Jacobian for the projection. In particular, we reveal that the generalized HS Jacobian can be formulated as the combination of a diagonal matrix and few rank-one symmetric matrices, which are crucial for future design of efficient second order nonsmooth methods for solving the related optimization problems.