Wick型随机广义Burgers方程的确切解

借助白噪声分析、Hermite变换和扩展的双曲函数法,研究了Wick型随机广义Burgers'方程,求出了一些精确的Wick型孤立波解和周期波解.由于Wick型函数难以赋值,为此,我们得到一些特殊情形下的Wick型随机广义Burgers'方程的非Wick型解.     

Burgers and Kadomtsev-Petviashvili hierarchies: A functional representation approach

Functional representations of (matrix) Burgers and potential Kadomtsev-Petviashvili (pKP) hierarchies (and others), as well as some corresponding Bäcklund transformations, can be obtained surprisingly simply from a “discrete” functional zero-curvature equation. We use these representations to show that any solution of a Burgers hierarchy is also a solution of the pKP hierarchy. Moreover, the pKP hierarchy can be expressed in the form of an inhomogeneous Burgers hierarchy. In particular, this leads to an extension of the Cole-Hopf transformation to the pKP hierarchy. Furthermore, these hierarchies are solved by the solutions of certain functional Riccati equations.     

On the long‐time stability of a backward Euler scheme for Burgers' equation with polynomial force

In this work we examine the stability of a finite difference approximation for Burgers' equation. More precisely, we consider a Backward Euler discretization scheme in time and approximated the nonlinear term by a linear expression using techniques from 15 . The boundedness of the solution sequence with respect to Δt for t ε [0,∞) is proved with the help of the discrete Gronwall lemmas. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008     

Negation of binomial coefficients

We extend the concept of a binomial coefficient to all integer values of its parameters. Our approach is purely algebraic, but we show that it is equivalent to the evaluation of binomial coefficients by means of the Γ-function. In particular, we prove that the traditional rule of “negation” is wrong and should be substituted by a slightly more complex rule. We also show that the “cross product” rule remains valid for the extended definition.     

Compact operators without extended eigenvalues

A complex number λ is called an extended eigenvalue of a bounded linear operator T on a Banach space B if there exists a non-zero bounded linear operator X acting on B such that XT=λTX. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set {1}.     

Extended <Emphasis Type="Italic">B</Emphasis>-Well-Posedness and Property (H) for Set-Valued Vector Optimization with Convexity

The purpose of this paper is to study the extended well-posedness in the sense of Bednarczuk for set-valued vector optimization. This notion of well-posedness can be interpreted as some sort of well-posedness under perturbation in terms of Hausdorff set-convergence. To investigate the extended B-well-posedness, we generalize property (H) due to Miglierina and Molho to the set-valued and perturbed case. Under a convexity assumption, we show that the extended B-well-posedness is closely related to property (H). This work was supported by the Scientific Research Foundation of CUIT (CRF200704), the National Natural Science Foundation of China (10671135) and Specialized Research Fund for the Doctoral Program of Higher Education (20060610005).     

广义生-灭最小Q过程及其性质

本文给出具有突变率的广义生－灭最小Q过程及其性质。     

Metric regularity of the feasible set mapping in semi-infinite optimization

For parametric systems of (finitely many) equations and (infinitely many) inequalities the well-known concept of metric regularity is shown to be equivalent to the so-called extended Mangasarian-Fromovitz constraint qualification. By this, a corresponding result obtained by Robinson for finite optimization problems my be transferred to semi-infinite optimization. For the proof a local epigraph representation of the constraint set is mainly used.     

Calculation of transition metal compounds using an extension of the CNDO-formalism

A recently developed extension of the CNDO-method is used to study the electronic structure of a number of binuclear transition metal carbonyls and carboxylates with fourfold or quasi-fourfold symmetry. The results are compared to those available from nonempirical calculations. Special attention is paid to the nature of the metal-metal bond. Connections with qualitative MO-considerations allow a fairly general discussion of metal-metal bonding in binuclear transition metal complexes with basic fourfold symmetry. A few, up to now unknown, but possibly existing, complexes are considered.     

Numerical computations of two-dimensional solitary waves generated by moving disturbances

Two-dimensional solitary waves generated by disturbances moving near the critical speed in shallow water are computed by a time-stepping procedure combined with a desingularized boundary integral method for irrotational flow. The fully non-linear kinematic and dynamic free-surface boundary conditions and the exact rigid body surface condition are employed. Three types of moving disturbances are considered: a pressure on the free surface, a change in bottom topography and a submerged cylinder. The results for the free surface pressure are compared to the results computed using a lower-dimensional model, i.e. the forced Korteweg–de Vries (fKdV) equation. The fully non-linear model predicts the upstream runaway solitons for all three types of disturbances moving near the critical speed. The predictions agree with those by the fKdV equation for a weak pressure disturbance. For a strong disturbance, the fully non-linear model predicts larger solitons than the fKdV equation. The fully non-linear calculations show that a free surface pressure generates significantly larger waves than that for a bottom bump with an identical non-dimensional forcing function in the fKdV equation. These waves can be very steep and break either upstream or downstream of the disturbance.