In this paper, we construct a class of Mixed Generalized Multiscale Finite Element Methods for the approximation on coarse grid an elliptic problem in thin two-dimensional domains. We consider equation with homogeneous boundary conditions domain walls. For reference solution problem, use Method fine that resolves complex geometry level. To lower dimensional model, Method, which is based some mu...

A competitive economic equilibrium problem involving utility functions is considered. The equilibrium problem is reformulated by means of a quasi-variational inequality and an existence result of equilibrium under weaker assumption than strong monotonicity is obtained. In this more general setting, when the excess demand operator is not a single valued-map, we are led to study a generalized var...

The concept of generalized cases has been proven useful when searching for configurable and flexible products, for instance, reusable components in the area of electronic design automation. This paper addresses the similarity assessment and retrieval problem for case bases consisting of traditional and generalized cases. While approaches presented earlier were restricted to continuous domains, ...

A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results repres...

In this paper we provide first existence results for solutions of the generalized equilibrium problem with composed functions (GEPC) under generalized convexity assumptions. Then we construct by employing some tools specific to the theory of conjugate duality two gap functions for (GEPC). The importance of these gap functions is to be seen in the fact that they equivalently characterize the sol...

In this paper, we develop a mixed Fourier-generalized Jacobi rational spectral method for two-dimensional exterior problems. Some basic results on the mixed Fourier-generalized Jacobi rational orthogonal approximations are established. Two model problems are considered. The convergence for the linear problem is proved. Numerical results demonstrate its spectral accuracy and efficiency.