We are interested in the Euler--Maruyama discretization of a stochastic differential equation dimension $d$ with constant diffusion coefficient and bounded measurable drift coefficient. In scheme, randomization time variable is used to get rid any regularity assumption this variable. prove weak convergence order 1/2 total variation distance. When has spatial divergence sense distributions $\rho...

Real images usually have sparse approximations under some tight frame systems derived from either framelets, over sampled discrete (window) cosine or Fourier transform. In this paper, we propose a method for image deblurring in tight frame domains. It is reduced to finding a sparse solution of a system of linear equations whose coefficients matrix is rectangular. Then, a modified version of the...

In this paper, we report our experiments in the TREC 2008 Relevance Feedback Track. Our main goal is to study a novel problem in feedback, i.e., optimization of the balance of the query and feedback information. Intuitively, if we over-trust the feedback information, we may be biased to favor a particular subset of relevant documents, but undertrusting it would not take advantage of feedback. I...

We compute holographic complexity for the nonsupersymmetric Janus deformation of ${\mathrm{AdS}}_{5}$ according to volume conjecture. The result is characterized by a power-law ultraviolet divergence. When ball-shaped region located around interface considered, subleading logarithmic divergent term and finite part appear in corresponding subregion complexity. Using two different prescriptions r...

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.

In this paper we continue towards the goal of resolving the Dirichlet and Neumann problems for general divergence form higher order elliptic operators with L data. The investigation of the second-order case has spanned the past three decades in the subject, drawing from the field of harmonic analysis and giving back to it many tools, and by now the real coefficient case is relatively well under...

Simulations are performed to investigate the nonlinear dynamics of a (2+1)-dimensional chemotaxis model of Keller-Segel (KS) type with a logistic growth term. Because of its ability to display auto-aggregation, the KS model has been widely used to simulate self-organization in many biological systems. We show that the corresponding dynamics may lead to a steady-state, divergence in a finite tim...

We compare the radiative transfer equation for media with constant refractive index with the radiative transfer equation for media with spatially varying refractive indices [J. Opt. A Pure App. Opt. 1, L1 (1999)] and obtain approximate conditions under which the former equation is accurate for modeling light propagation in scattering media with spatially varying refractive indices. These condit...