The cumulant representation of the Fourier path integral method is examined to determine the asymptotic convergence characteristics of the imaginary-time density matrix with respect to the number of path variables N included. It is proved that when the cumulant expansion is truncated at order p, the asymptotic convergence rate of the density matrix behaves like N(-(2p+1)). The complex algebra a...

Influenced by Higham, Mao and Stuart [10], several numerical methods have been developed to study the strong convergence of the numerical solutions to stochastic differential equations (SDEs) under the local Lipschitz condition. These numerical methods include the tamed Euler–Maruyama (EM) method, the tamed Milstein method, the stopped EM, the backward EM, the backward forward EM, etc. In this ...

In this paper we show that the family P d of probability distributions on R d with logconcave densities satisfies a strong continuity condition. In particular, it turns out that weak convergence within this family entails (i) convergence in total variation distance, (ii) convergence of arbitrary moments, and (iii) pointwise convergence of Laplace transforms. In this and several other respects t...

A singularly perturbed reaction-diiusion equation in two dimensions is considered. We assume analyticity of the input data, i.e., the boundary of the domain is an analytic curve and the right hand side is analytic. We show that the hp version of the nite element method leads to robust exponential convergence provided that one layer of needle elements of width O(p") is inserted near the domain b...

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...

Purpose. To measure the changes in fusional vergence in Chinese children with intermittent exotropia (IXT) and the association with the control of IXT. Methods. Ninety-two patients with IXT (8-15 years old) were compared with 86 controls. Exodeviation control was evaluated using the Revised Newcastle Control Score. Angle of deviation was measured using prism and alternate cover testing at dista...

We introduce the the classes of strongly V F λ (A, p)-summable sequences of fuzzy numbers and give some relations between these classes. We also give a natural relationship between strongly V F λ (A, p)convergence of sequences of fuzzy numbers and strongly S λ (A)-statistical convergence of sequences of fuzzy numbers.

In this paper, we discuss the equivalent conditions of pretopological and topological $L$-fuzzy Q-convergence structures and define $T_{0},~T_{1},~T_{2}$-separation axioms in $L$-fuzzy Q-convergence space. {Furthermore, $L$-ordered Q-convergence structure is introduced and its relation with $L$-fuzzy Q-convergence structure is studied in a categorical sense}.

We address the question of the rates of convergence of the p-version interior penalty discontinuous Galerkin method (p-IPDG) for second order elliptic problems with non-homogeneous Dirichlet boundary conditions. It is known that the p-IPDG method admits slightly suboptimal a-priori bounds with respect to the polynomial degree (in the Hilbertian Sobolev space setting). An example for which the s...