‎Given a frame of a separable Hilbert space $H$‎, ‎we present some‎ ‎iterative methods for solving an operator equation $Lu=f$‎, ‎where $L$ is a bounded‎, ‎invertible and symmetric‎ ‎operator on $H$‎. ‎We present some algorithms‎ ‎based on the knowledge of frame bounds‎, ‎Chebyshev method and conjugate gradient method‎, ‎in order to give some‎ ‎approximated solutions to the problem‎. ‎Then we i...

tizzy k nearest neighbor rule (k-NNR) has been applied in a variety of substantive areas. Yang and Chen [l] described a fuzzy generalized k-NN algorithm which is a unified approach to a variety of fuzzy k-NNR’s. They created the strong consistency of posterior risk of the fuzzy generalized NNR. In this paper, we give their convergence rate. That is, the convergence rate of posterior risk of the...

It is shown that the Vitali convergence theorem remains valid for the -upper integral. Using this result we prove completeness of the space L( ) with respect to the k kp-upper norm for 1 p < 1 , describe convergence of its elements in terms of the space L( ) for 1 p < 1 , give a necessary and sufficient condition for a sequence from L( ) to converge in the k kp-upper norm to a function from L( ...

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...

Finite-difference schemes for the computation of value functions of nonlinear differential games with non-terminal payoff functional and state constraints are proposed. The solution method is based on the fact that the value function is a generalized viscosity solution of the corresponding Hamilton-Jacobi-Bellman-Isaacs equation. Such a viscosity solution is defined as a function satisfying dif...

In this paper, a new definition of locally convex L-topological vector spaces is given. The relationship between this new definition and the previous definition of locally convex L-topological vector spaces given by Yan and Fang in 1999 is investigated. Moreover, the concept of generalized L-fuzzy semi-norm is introduced. By using a family of generalized L-fuzzy semi-norms, a characterization o...

in this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted dirichlet spaces or bloch type spaces to $q_k$ type spaces.

Abstract The dependence of the chaotic phase Bose–Hubbard Hamiltonian on particle number N , system size L and density is investigated in terms spectral eigenstate features. We analyse development as limit infinite Hilbert space dimension approached along different directions, show that fastest route to chaos path at fixed n ≲ 1. → ∞ constant leads a slower convergence towards random matrix the...

In this paper, we define and study fuzzy generalized α-closed sets and r-open sets of a given L-fuzzy topological space and prime element r ∈ P (L) and coprime element α ∈ M(L). The concept of L-fuzzy ropen sets was introduced in [10], and it was proved that all r-open sets for L-fuzzy topological space form a new L-fuzzy topology, which is called stratiform L-fuzzy topology. Making use of the ...

Abstract Based on the new approach to modular forms presented in [6] that uses rational functions, we prove a dominated convergence theorem for certain Eisenstein space. It states rearrangements of Fourier series will converge very fast near cusp $$\tau = 0$$ τ = 0 ...