Abstract-The complete solution for an embedded elliptical crack in an infinite solid and subjected to arbitrary tractions on the crack surface is rederived from Vijayakumar and Atluri’s general solution procedure. The general procedure for evaluating the necessary elliptic integrals in the generalized solution for elliptical crack is also derived in this paper. The generalized solution is emplo...

In this article, we introduce a new iterative algorithm by the shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of common solutions of general system of finite variational inequalities, the set of solutions of fixed points for nonexpansive semigroups and the set of common fixed points for an infinite family of st...

This paper describes the author’s RIM3 Fortran code. RIM3 delivers a computational solution to the acoustic field produced by a vibrating plate placed on an infinite baffle. The mathematical model is based on the Rayleigh integral. The method is implemented in three-dimensions in a manner that is similar to the boundary element method and is applied to test cases and results are given. The soft...

Let G be a group hyperbolic relative to a collection of subgroups {Hλ, λ ∈ Λ}. We say that a subgroup Q ≤ G is hyperbolically embedded into G, if G is hyperbolic relative to {Hλ, λ ∈ Λ} ∪ {Q}. In this paper we obtain a characterization of hyperbolically embedded subgroups. In particular, we show that if an element g ∈ G has infinite order and is not conjugate to an element of some Hλ, λ ∈ Λ, th...

This paper studies connections between the preprojective representations of a valued quiver, the (+)-admissible sequences of vertices, and the Weyl group by associating to each preprojective representation a canonical (+)-admissible sequence. A (+)-admissible sequence is the canonical sequence of some preprojective representation if and only if the product of simple reflections associated to th...

A general class of nonlinear infinite dimensional optimization problems is considered that covers semi-linear elliptic control problems with distributed control as well as boundary control. Moreover, pointwise inequality constraints on the control and the state are incorporated. The general optimization problem is perturbed by a certain class of perturbations, and we establish convergence of lo...

Let G be an infinite abelian group with |2G| = |G|. We show that if G is not the direct sum of a group of exponent 3 and the group of order 2, then G possesses a perfect additive basis; that is, there is a subset S ⊆ G such that every element of G is uniquely representable as a sum of two elements of S. Moreover, if G is the direct sum of a group of exponent 3 and the group of order 2, then it ...

For a train moving along curved path, centrifugal forces are induced in addition to gravitational loads. In this paper, the 2.5D approach for loads straight path is extended treating both vertical and horizontal path. Firstly, closed-form solutions problem derived cases of Then, with finite/infinite elements Cartesian coordinates summarized. By approximating by number small chordwise segments u...