In this paper, we study the problem concerning stability and asymptotic behaviours of solutions for a degenerate Landau-Lifshitz equation in micromagnetics involving only the nonlocal magnetostatic energy. Due to the lack of derivative estimates, we do not have the compactness needed for strong convergence and the natural convergence is weak* convergence. By formulating the problem in a new fra...

We present a generalization of V. Temlyakov’s weak greedy algorithm, and give a sufficient condition for norm convergence of the algorithm for an arbitrary dictionary in a Hilbert space. We provide two counter-examples to show that the condition cannot be relaxed for general dictionaries. For a class of dictionaries with more structure, we give a more relaxed necessary and sufficient condition ...

We study a projection and upwind finite difference scheme for a combustion model problem. Convergence to weak solutions is proved under the Courant-Friedrichs-Lewy condition. More assumptions are given on the ignition temperature; then convergence to strong detonation wave solutions or to weak detonation wave solutions is proved.

This paper has examined the phenomenon of convergence of per capita out put levels across the IC countries for the 1960-1998 periods. Three concepts of convergence, i.e., sigma beta and relative beta, have been used. The estimated beta values reveals only a very weak convergence (?=.0014) across IC for 1960-1998 period. But when a more homogeneous group of countries were selected, the results s...

This paper focuses on the relationships between stratified $L$-conver-gence spaces, stratified strong $L$-convergence spaces and stratifiedlevelwise  $L$-convergence spaces. It has been known that: (1) astratified $L$-convergence space is precisely a left-continuousstratified levelwise $L$-convergence space; and (2) a  stratifiedstrong $L$-convergence space is naturally a stratified $L$-converg...