The purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of Sturm-Liouville problem with equation of the form w??=(?2f(x)?R(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in C2(a,b which has a single zero (so called turning point) at point 0x=x and R(x) is a continuously differentiable function. ...

Charles-Augustin de Coulomb introduced his equations over two centuries ago. These equations quantified the force and the energy of interacting electrical charges. The electrical permittivity of free space was factored into Coulomb’s equations. A century later James Clear Maxwell showed that the velocity of light emerged as a consequence this permittivity. These constructs were a crowning achie...

We consider the problem of microstructural evolution in binary alloys in two dimensions. The microstructure consists of arbitrarily shaped precipitates embedded in a matrix. Both the precipitates and the matrix are taken to be elastically anisotropic, with different elastic constants. The interfacial energy at the precipitate– matrix interfaces is also taken to be anisotropic. This is an extens...

We consider the problem of determining an inclusion D made of di erent elastic material in an elastic isotropic body from boundary measurements of traction and displacement. We prove that the volume of D can be estimated, from above and below, by an easily expressed quantity related to work, only depending on the boundary traction and displacement.

Cracks cause to change dynamic response of beams and make discontinuity in slope of the deflection of the beams. The dynamic analysis of the Euler-Bernoulli cracked beam on the elastic foundation subjected to the concentrated load is presented in this paper. The stiffness of the elastic foundation and elastic supports influence on vibrational characteristics of the cracked beam. The Dynamic Gre...