Interior proximal methods for variational inequalities are, in fact, designed to handle problems on polyhedral convex sets or balls, only. Using a slightly modified concept of Bregman functions, we suggest an interior proximal method for solving variational inequalities (with maximal monotone operators) on convex, in general non-polyhedral sets, including in particular the case in which the set...

We study the simplicial quantum gravity in three dimensions. Motivated by Boulatov's model which generates a sum over simplicial complexes weighted with the Turaev·Viro invariant, we introduce boundary operators in the simplicial gravity associated to compact orientable surfaces. An amplitude of the boundary operator is given by a sum over triangulations in the interior of the boundary surface....

The investigation of the far field operator and the Factorization Method in inverse scattering theory leads naturally to the study of corresponding interior transmission eigenvalue problems. In contrast to the classical Dirichletor Neumann eigenvalue problem for −∆ in bounded domains these interior transmiision eigenvalue problem fail to be selfadjoint. In general, existence of eigenvalues is a...

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...

In this paper, we study a singular Sturm–Liouville problem with an eigenparameter-dependent boundary condition and transmission conditions at two interior points. Using operator-theoretical formulation, transfer the to operator in appropriate Hilbert space. It is proved that self-adjoint. We also give asymptotic formulas of eigenvalues problem. Moreover, Green’s function discussed.

In this paper, notions of L-topological derived internal relation space, interior operator enclosed space and closure are introduced. It is proved that all these spaces categorically isomorphic to space.

In this paper, we consider a complex network of strings. Suppose that the network is comprised of eight strings with a fixed vertex, and other exterior vertices that are imposed velocity feedback controller. The displacement is not continuous at one interior node, while at the other interior nodes continuity holds and the force is not balanced at all interior nodes. We design controllers for th...

Maxwell’s equations are considered with transparent boundary conditions, with initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The proposed computational scheme only involves the interior domain and its boundary. The transparent boundary conditions are imposed via a time-dependent boundary integ...