in this paper, we prove the generalized hyers-ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-archimedean $mathcal{l}$-fuzzy normed spaces.

The generalized local maximum principle for a difference operator L» asserts that if Lam(jc) > 0 then Vu cannot attain its positive maximum at the net-point x. Here r is a local net-operator such that Tu = u + 0(/i) for any smooth function u. This principle, with simple forms of V, is proved for some quite general classes of second-order elliptic operators Lh, whose associated global matrices a...

This paper presents the concepts of $(L,M)$-fuzzy Q-convergence spaces and stratified $(L,M)$-fuzzy Q-convergence spaces. It is shown that the category of stratified $(L,M)$-fuzzy Q-convergence spaces is a bireflective subcategory of the category of $(L,M)$-fuzzy Q-convergence spaces, and the former is a Cartesian-closed topological category. Also, it is proved that the category of stratified $...

Numerical methods for parabolic homogenization problems combining finite element methods (FEMs) in space with Runge-Kutta methods in time are proposed. The space discretization is based on the coupling of macro and micro finite element methods following the framework of the Heterogeneous Multiscale Method (HMM). We present a fully-discrete analysis in both space and time. Our analysis relies on...

In the 1970’s Paul Erdős and Dominic Welsh independently posed the problem of whether all finite partial linear spaces L are embeddable in finite projective planes. Except for the case when L has a unique embedding in a projective plane with few additional points, very little has been done which is directly applicable to this problem. In this paper it is proved that every finite partial linear ...

Generalized block Lanczos methods for large unsymmetric eigenproblems are presented, which contain the block Arnoldi method, and the block Arnoldi algorithms are developed. The convergence of this class of methods is analyzed when the matrix A is diagonalizable. Upper bounds for the distances between normalized eigenvectors and a block Krylov subspace are derived, and a priori theoretical error...

The activation dynamics of nets are considered from a rigorous mathematical point of view. A net is identified with the dynamical system defined by a continuously differentiable vector field on the space of activation vectors, with fixed weights, biases, and inputs. Chaotic and oscillatory nets are briefly discussed, but the main goal is to find conditions guaranteeing that the trajectory of ev...

Some fixed point convergence properties are proved for compact and demicompact maps acting over closed, bounded and convex subsets of a real Hilbert space. We also show that for a generalized nonexpansive mapping in a uniformly convex Banach space the Ishikawa iterates converge to a fixed point. Finally, a convergence type result is established for multivalued contractive mappings acting on clo...

This paper analyzes some schemes for reducing the computational burden of digital scrambling. Some such schemes have been shown not to affect the mean squared L 2 discrepancy. This paper shows that some discrepancy-preserving alternative scrambles can change the variance in scrambled net quadrature. Even the rate of convergence can be adversely affected by alternative scramblings. Finally, some...