Generalized Local Time of the Indefinite Wiener Integral:White Noise Approach

In this paper,the generalized local time of the indefinite Wiener integral Xt is discussed through white noise approach,which means to regard the local time as a Hida distribution.Moreover,similar resu...     

The discrete logarithm problem from a local duality perspective

The discrete logarithm problem is analyzed from the perspective of Tate local duality. Local duality in the multiplicative case and the case of Jacobians of curves over p-adic local fields are considered. When the local field contains the necessary roots of unity, the case of curves over local fields is polynomial time reducible to the multiplicative case, and the multiplicative case is polynomial time equivalent to computing discrete logarithm in finite fields. When the local field does not contains the necessary roots of unity, similar results can be obtained at the cost of going to an extension that contains these roots of unity. There was evidence in the analysis that suggests that the minimal extension where the local duality can be rationally and algorithmically defined must contain the roots of unity. Therefore, the discrete logarithm problem appears to be well protected against an attack using local duality. These results are also of independent interest for algorithmic study of arithmetic duality as they explicitly relate local duality in the case of curves over local fields to the multiplicative case and Tate-Lichtenbaum pairing (over finite fields).     

Krigings over space and time based on latent low-dimensional structures

We propose a new nonparametric approach to represent the linear dependence structure of a spatiotemporal process in terms of latent common factors.Though it is formally similar to the existing reduced rank approximation methods,the fundamental difference is that the low-dimensional structure is completely unknown in our setting,which is learned from the data collected irregularly over space but regularly in time.Furthermore,a graph Laplacian is incorporated in the learning in order to take the advantage of the continuity over space,and a new aggregation method via randomly partitioning space is introduced to improve the efficiency.We do not impose any stationarity conditions over space either,as the learning is facilitated by the stationarity in time.Krigings over space and time are carried out based on the learned low-dimensional structure,which is scalable to the cases when the data are taken over a large number of locations and/or over a long time period.Asymptotic properties of the proposed methods are established.An illustration with both simulated and real data sets is also reported.     

Partial regularity for the Navier-Stokes-Fourier system

This paper addresses a nonstationary flow of heat-conductive incompressible Newtonian fluid with temperature-dependent viscosity coupled with linear heat transfer with advection and a viscous heat source term, under Navier/Dirichlet boundary conditions. The partial regularity for the velocity of the fluid is proved for each proper weak solution, that is, for such weak solutions which satisfy some local energy estimates in a similar way to the suitable weak solutions of the Navier-Stokes system. Finally, we study the nature of the set of points in space and time upon which proper weak solutions could be singular.     

Sparse Approximations of the Schur Complement for Parallel Algebraic Hybrid Solvers in 3D

<正>In this paper we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems.In earlier works,the local Schur complements were computed exactly using a sparse direct solver.The robustness of the preconditioner comes at the price of this memory and time intensive computation that is the main bottleneck of the approach for tackling huge problems.In this work we investigate the use of sparse approximation of the dense local Schur complements.These approximations are computed using a partial incomplete LU factorization.Such a numerical calculation is the core of the multi-level incomplete factorization such as the one implemented in pARMS. The numerical and computing performance of the new numerical scheme is illustrated on a set of large 3D convection-diffusion problems;preliminary experiments on linear systems arising from structural mechanics are also reported.     

On the Collision Local Time of Fractional Brownian Motions

In this paper, the existence and smoothness of the collision local time are proved for two independent fractional Brownian motions, through L2 convergence and Chaos expansion. Furthermore, the regularity of the collision local time process is studied.     

Existence of Positive Solutions for Higher Order Boundary Value Problem on Time Scales

In this paper,we investigate the existence of positive solutions of a class higher order boundary value problems on time scales.The class of boundary value problems educes a four-point(or three-point or two-point) boundary value problems,for which some similar results are established.Our approach relies on the Krasnosel’skii fixed point theorem.The result of this paper is new and extends previously known results.     

一类具有交叉扩散效应的三种群诱饵-捕食系统整体解的存在性（英文）

The prey-predator system of three species with cross-diffusion pressure is known to possess a local solution with the maximal existence time T ≤ ∞.By obtaining the bounds of W21-norms of the local solution independent of T,it is established the global existence of the solution.     

The pointwise estimates of solutions for a nonlinear convection diffusion reaction equation

This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the optimal L~p,1≤ p ≤ +∞,convergence rate of solutions for small initial data.Then we establish the local existence of solutions,the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data.Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates.     

Design of Finite Element Tools for Coupled Surface and Volume Meshes

Many problems with underlying variational structure involve a coupling of volume with surface effects.A straight-forward approach in a finite element discretiza- tion is to make use of the surface triangulation that is naturally induced by the volume triangulation.In an adaptive method one wants to facilitate"matching"local mesh modifications,i.e.,local refinement and/or coarsening,of volume and surface mesh with standard tools such that the surface grid is always induced by the volume grid. We describe the concepts behind this approach for bisectional refinement and describe new tools incorporated in the finite element toolbox ALBERTA.We also present several important applications of the mesh coupling.     

Chaos Decomposition of Local Time for d-Dimensional Fractional Brownian Motion with N-Parameter

In this paper, the existence and chaos decomposition of local time of fractional Brownian motion are studied within the canonical framework of white noise analysis. We prove that the local time of -dimensional fractional Brownian motion with 1-parameter is a Hida distribution through white noise approach. Under some conditions, it exists in . Moreover, the Wiener-Ito chaos decomposition of it is also given in terms of Hermite polynomials. Finally, similar results of -dimensional fractional Brownian motion with -parameter are also obtained. We popularize some results in Bakun (2000) for the case of Brownian motion.     

An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate

In this paper, the unsteady boundary-layer flows caused by an impulsively stretching flat plate is solved by means of an analytic approach. Unlike perturbation techniques, this approach gives accurate analytic approximations uniformly valid for all dimensionless time. Besides, a simple but accurate analytic formula for the local skin friction is given, which agrees well with numerical results and thus is useful in the related industries. To the best of our knowledge, this type of analytic solutions has been never reported. Furthermore, the proposed analytic approach has general meaning and therefore may be applied in the similar way to other unsteady boundary-layer flows to get accurate analytic solutions valid for all time.     

Self-intersection Local Time of Planar Brownian Motion Based on a Strong Approximation by Random Walks

The main purpose of this work is to define planar self-intersection local time by an alternative approach which is based on an almost sure pathwise approximation of planar Brownian motion by simple, symmetric random walks. As a result, Brownian self-intersection local time is obtained as an almost sure limit of local averages of simple random walk self-intersection local times. An important tool is a discrete version of the Tanaka?CRosen?CYor formula; the continuous version of the formula is obtained as an almost sure limit of the discrete version. The author hopes that this approach to self-intersection local time is more transparent and elementary than other existing ones.     

分式Brown运动的局部时:白噪声分析法

本文利用白噪声分析的方法,讨论了分式布朗运动的局部时,即将其看作一个Hida分布.进一步,给出分式布朗运动的局部时的混沌分解以及局部时平方可积性.     

布朗运动和次分数布朗运动混合的局部时

本文研究了布朗运动和次分数布朗运动混合的局部时问题.利用白噪声分析方法和次分数布朗运动的另一种表示形式,证明了该局部时是一个Hida广义泛函.进一步,借助于S-变换给出了该局部时的混沌表示.最后获得了该局部时的正则性条件.推广了布朗运动局部时的一些结果.     

分式Brownian运动的多重相交局部时

本文研究了分式布朗运动的多重相交局部时的问题.利用白噪声分析的方法,获得了分式布朗运动的多重相交局部时的展开式.进行适当的截取,展开式在白噪声广义泛函意义下存在,并给出它们的核函数.推广了布朗运动的多重相交局部时.     

Higher-order time integration with a local Lax–Wendroff procedure for a central scheme on an overlapping grid

We have implemented a high-order Lax–Wendroff type time integration for a central scheme on an overlapping grid for conservation law problems. Using a local iterative approach presented by Dumbser et al. (JCP, 2008) [12], we extend a local high-order spatial reconstruction on each cell to a local higher-order space–time polynomial on the cell. We rewrite the central scheme in a fully discrete form to avoid volume integration in the space–time domain. The fluxes at cell interfaces are calculated directly via integrating a higher-order space–time reconstruction of the flux. We compare this approach with the corresponding multi-stage Runge–Kutta time integration (RK). Numerical results show that the new time integration is more cost-effective.     

A local least-squares method for solving nonlinear partial differential equations of second order

In this paper a mesh-free method for the treatment of time-independent and time-dependent nonlinear PDEs of second order is presented. The basic idea of the discretization is a local least-squares approximation, similar to the moving least-squares approach in data approximation. However, in our approach the PDE is incorporated as an additional minimization constraint. The discretization leads to a fixed-point problem, which is solved by iteration. Because of the local nature of the method only small dimensional matrix inversions have to be done. The approximation error of the discretization—even on unstructured meshes—is comparable to respective versions of finite elements. As a by-product the method provides an a posteriori measure for the local approximation error. We discuss implementational aspects and present numerical simulations.