The well-posedness of the Korteweg-de Vries-Benjamin-Ono equation

The well-posedness of the Cauchy problem to the generalized Korteweg-de Vries-Benjamin-Ono equation is considered. Local results for data in (s?−1/8) and the global well-posedness for data in are obtained if l=2. Moreover, for l=3, the problem is locally well-posed for data in H^s (s?1/4). The main idea is to use the Fourier restriction norm method.     

Modeling,Mathematical and Numerical Analysis of Electrorheological Fluids

Many electrorheological fluids are suspensions consisting of solid particles and a carrier oil. If such a suspension is exposed to a strong electric field the effective viscosity increases dramatically. In this paper we first derive a model which captures this behaviour. For the resulting system of equations we then prove local in time existence of strong solutions for large data. For these solutions we finally derive error estimates for a fully implicit time-discretization.     

四阶非线性特征值问题的正解

本文考虑了四阶非线性特征值问题d4u/dt4=λg(t)f(u,u″),0＜t＜1,u(0)=u(1)=0,au″(0)-bu″′(0)=0,cu″(1)+du″′(1)=0.其中g(t)∈C((0,1),[0,∞)),f(u,v)∈C([0,∞)×(-∞,0],[0,∞)),a≥0,b≥0,c ≥0,d ≥ 0,且△=ac+ad+bc＞0.利用锥压缩与拉伸不动点定理,获得了上述问题正解的存在性结果.     

Explicit Solution of a Non-Linear Filtering Problem for Lévy Processes with Application to Finance

In this paper we explicitly solve a non-linear filtering problem with mixed observations, modelled by a Brownian motion and a generalized Cox process, whose jump intensity is given in terms of a Lévy measure. Motivated by empirical observations of R. Cont and P. Tankov we propose a model for financial assets, which captures the phenomenon of time inhomogeneity of the jump size density. We apply the explicit formula to obtain the optimal filter for the corresponding filtering problem.     

An Implementation for the Algorithm of Janet bases of Linear Differential Ideals in the Maple System

In this paper, an algorithm for computing the Janet bases of linear differential equations is described, which is the differential analogue of the algorithm JanetBasis improved by Gerdt. An implementation of the algorithm in Maple is given. The implemented algorithm includes some subalgorithms: Janet division,Pommaret division, the judgement of involutive divisor and reducible, the judgement of conventional divisor and reducible, involutive normal form and conventional normal form, involutive autoreduction and conventional autoreduction, PJ-autoreduction and so on. As an application, the Janet Bases of the determining system of classical Lie symmetries of some partial differential equations are obtained using our package.     

On the Continuity of Pathwise Solutions to Langevin Equations in Infinite Dimensions

We fix a rich probability space (,F,P). Let (H,) be a separable Hilbert space and let be the canonical cylindrical Gaussian measure on H. Given any abstract Wiener space (H,B,) over H, and for every Hilbert–Schmidt operator T: HBH which is (|{}|,)-continuous, where |{}| stands for the (Gross-measurable) norm on B, we construct an Ornstein–Uhlenbeck process : (,F,P)×[0,1](B,|{}|) as a pathwise solution of the following infinite-dimensional Langevin equation d _t =db _t +T( _t )dt with the initial data ₀=0, where b is a B-valued Brownian motion based on the abstract Wiener space (H,B,). The richness of the probability space (,F,P) then implies the following consequences: the probability space is independent of the abstract Wiener space (H,B,) (in the sense that (,F,P) does not depend on the choice of the Gross-measurable norm |{}|) and the space C _B consisting of all continuous B-valued functions on [0,1] is identical with the set of all paths of . Finally, we present a way to obtain pathwise continuous solutions :d _t =

Three solutions of constant sign for a system of discrete equations

We consider the following system of discrete equations

Finding All Maximal Cliques in Dynamic Graphs

Clustering applications dealing with perception based or biased data lead to models with non-disjunct clusters. There, objects to be clustered are allowed to belong to several clusters at the same time which results in a fuzzy clustering. It can be shown that this is equivalent to searching all maximal cliques in dynamic graphs like G _t = (V,E _t), where E _{t – 1} E _t, t = 1,...,T; E ₀ = . In this article algorithms are provided to track all maximal cliques in a fully dynamic graph.     

Acceleration waves analyzed by a new continuum model of solids incorporating microscopic thermal vibrations

Acceleration waves propagating in isotropic solids at finite temperatures are studied by applying the method of singular surfaces to a new continuum model derived statistical-mechanically from a three-dimensional lattice model. The continuum model explicitly takes into account the microscopic thermal vibrations of the constituent atoms as one of the field variables. The propagation speeds and the ratios of mechanical and thermal amplitudes for both longitudinal and transverse waves are consistently determined. The differential equations that govern the time variation of the amplitudes of the waves are also derived. The analytical results, which are valid over a wide temperature range that includes the melting point, are evaluated numerically for several materials, and their physical implications are discussed. One of the findings to be emphasized is that of the singularities of the characteristic quantities at the melting point.Received: 13 March 2003, Accepted: 20 June 2003PACS: 62.30. + d, 65.40.-bM. Sugiyama: Correspondence to Dedicated to Prof. Ingo Müller on the occasion of his 65th birthday.     

Dynamic Behavior of Rigid–Plastic Sector Plates

The paper studies the dynamic behavior of perfect rigid-plastic plates in the form of a sector with hinged or clamped sides under short-term intensive loads. Two dynamic deformation mechanisms are demonstrated. The dynamic equation is derived for each of the mechanisms. The realization conditions for the mechanisms are analyzed. Analytical expressions are derived for the ultimate (high) loads and the maximum residual deflection. Numerical examples are given