溃坝问题的间断有限元方法

本文研究90年代初提出的Runge-Kutta间断Galerkin有限元方法，给出该方法的精度分析，通过经典算例验证该方法处理间断问题、捕捉锐利波形的能力，并将其推广到求解浅水问题．针对坝底无摩擦，无坡度的理想情形进行讨论，给出方溃坝和圆溃坝问题的数值模拟结果．     

面积比较与上调和函数及其应用

本文研究了无穷远处具非负截曲率的完备非紧流形的几何和解析性质,并将 它应用于调和映照.     

Benson真有效意义下集值优化的广义最优性条件

本文引入了关于集值映射的α-阶Clarke切导数、α-阶邻接切导数及α-阶 伴随切导数的概念,借此建立了约束向量集值优化Benson真有效解导数型的Kuhn- Tucker条件.     

Remarks on a Noble''''s Theorem

Noble proved the following Theorem: If A (?) X with a nonisolated point and B (?) Y, then A × B is bounded in X×Y if and only if the projection map π : X × Y → X is a z-map with respect to A × B and A, A is bounded in X and B is bounded in Y. In this note, we give two examples showing the necessary and sufficient conditions of Noble's theorem are not right.     

Connecting orbits among Denjoy minimal sets for monotone twist map

In a Birkhoff region of instability for an exact area-preserving twist map, we construct some orbits connecting distinct Denjoy minimal sets. These sets correspond to the local, instead of global minimum of the Lagrangian action. In the earlier work, Mather constructed connecting orbits among Aubry-Mather sets and the global minimizer of the Lagrangian action.     

Diffraction of a Plane Discontinuos Wave in Layered Anisotropic Elastic Media

The problem of transformation of the front of a plane longitudinal shock wave by curvilinear interfaces of layered anisotropic elastic media with different mechanical properties is considered. To solve the nonlinear Snell equations, the approach based on a synthesis of the Newton method and the algorithm of parametric continuation of a solution is used. The cases of focusing and scattering of rays by convex and concave interfaces of layered composite media and by convex lenses are investigated. Numerical examples are given for various ratios between the parameters of the elastic media.     

On the Solution of Discontinuous IVPs by Adaptive Runge–Kutta Codes

In this paper an automatic technique for handling discontinuous IVPs when they are solved by means of adaptive Runge–Kutta codes is proposed. This technique detects, accurately locates and passes the discontinuities in the solution of IVPs by using the information generated by the code along the numerical integration together with a continuous interpolant of the discrete solution. A remarkable feature is that it does not require additional information on the location of the discontinuities. Some numerical experiments are presented to illustrate the reliability and efficiency of the proposed algorithms.     

Compact Kähler Surfaces with Trivial Canonical Bundle

The classical conjectures of Weil on K3 surfaces – that the set of suchsurfaces is connected; that a version of the Torelli theorem holds; thateach such surface is Kähler; and that the period map issurjective – are reconsidered in the light of a generalisation of theNakai–Moishezon criterion, and short proofs of all the conjectures aregiven. Most of the proofs apply equally or with minor variation tocomplex 2-tori, the only other compact Kähler surfaces with trivialcanonical bundle.     

On Fučik Spectra and Periodic Solutions

In this paper, we continue extending the theory of boundary-value problems to ordinary differential equations and inclusions with discontinuous right-hand side. To this end, we construct a new version of the method of shifts along trajectories. We compare the results obtained by the new approach and those obtained by the method of Fuik spectra.