Inverse problems for Jacobi operators IV: interior mass-spring perturbations of semi-infinite systems

Motions of Infinite Mass-Spring Systems

In the study of physical, mechanical, and electrical systems one often encounters differentialdifference equations and recurrence relations. The sources from which these equations arise may be quite different but their mathematical forms are very similar. For example, there is an analogy between mass-spring systems and electrical systems whereby point masses correspond to inductances and spring...

Solving Semi-Infinite Optimization Problems with Interior Point Techniques

We introduce a new numerical solution method for semi-infinite optimization problems with convex lower level problems. The method is based on a reformulation of the semi-infinite problem as a Stackelberg game and the use of regularized nonlinear complementarity problem functions. This approach leads to central path conditions for the lower level problems, where for a given path parameter a smoo...

Inverse spectral problems for Sturm-Liouville operators with transmission conditions

Abstract: This paper deals with the boundary value problem involving the differential equation                      -y''+q(x)y=lambda y                                 subject to the standard boundary conditions along with the following discontinuity conditions at a point              y(a+0)=a1y(a-0),    y'(a+0)=a2y'(a-0)+a3y(a-0).  We develop the Hochestadt-Lieberman’s result for Sturm-Lio...

Interior-point algorithms for semi-infinite programming

Inverse Eigenvalue Problem for a Class of Spring-Mass Systems

This paper discusses the constructional problem for a class of spring-mass systems whose part particles are connected to the ground. The problem is converted to an inverse eigenvalue problem for Jacobi matrix. An inverse eigenvalue problem of determining the system from its some physical parameters and incomplete eigenpairs is solved. The necessary and sufficient condition for constructing the ...