Isolating blocks for Morse flows

We present a constructive general procedure to build Morse flows on n-dimensional isolating blocks respecting given dynamical and homological boundary data recorded in abstract Lyapunov semi-graphs. Moreover, we prove a decomposition theorem for handles which, together with a special class of gluings, insures that this construction not only preserves the given ranks of the homology Conley indices, but it is also optimal in the sense that no other Morse flow can preserve this index with fewer singularities.      

Exact smooth classification of hamiltonian vector fields on two-dimensional manifolds

A complete exact classification of Hamiltonian systems with Morse Hamiltonians on two-dimensional manifolds is given, i.e., the systems are classified up to diffeomorphisms mapping vector fields into vector fields. The classification imposes no restrictions on Morse functions. Translated fromMatematicheskie Zametki, Vol. 61, No. 2, pp. 179–200, February, 1997. Translated by O. V. Sipacheva     

Hyperplane Singularities of Analytic Functions of Several Complex Variables

A new class of non-isolated singularities called hyperplane singularities is introduced. Special deformations with simplest critical points are constructed and an algebraic expression for the number of Morse points is given. The topology of the Milnor fibre is completely studied.     

THE GAUSS MAP OF SUBMANIFOLDSIN SPACES OF CONSTANT CURVATURE

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Pseudospin and spin symmetry in Dirac-Morse problem with a tensor potential

Under the conditions of the pseudospin and spin symmetry, approximate analytical solutions of the Dirac-Morse problem with Coulomb-like tensor potential are presented. The energy eigenvalue equations are found and corresponding radial wave functions are obtained in terms of confluent hypergeometric functions. The energy eigenvalues are calculated numerically in the absence and presence of the tensor potential. We also investigate the contribution of the potential parameters to the energy splitting of the pseudospin and spin doublets.     

An approximate scheme to determine the vibratory density of states in a quasi-harmonic solid

In a new and realistic conception of solids, an analytical approach is presented to find the phonon density of states in a quasi-harmonic one-dimensional solid by starting from the fact that a solid with strong interatomic forces can be regarded as an atomic array of quantum anharmonic oscillators under a Morse potential. In fact, our quasi-harmonic approximation is derived by assuming a large enough solid with an involved anharmonic parameter as a sufficiently small quantity. In this context, a mathematical relationship between the above parameter and the matrix element relative to oscillator’s strength is obtained.     

MULTIPLICITY OF SOLUTIONS TO ASYMPTOTICALLY LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL SYSTEM

In this paper,we consider an asymptotically linear second-order ordinary differential system with Dirchlet boundary value conditions. Under some conditions,we show the multiplicity of solutions to the system by the Morse theory and an index theory.     

Some Abstract Critical Point Theorems for Self-adjoint Operator Equations and Applications

By using the index theory for linear bounded self-adjoint operators in a Hilbert space related to a fixed self-adjoint operator A with compact resolvent,the authors discuss the existence and multiplicity of solutions for(nonlinear) operator equations,and give some applications to some boundary value problems of first order Hamiltonian systems and second order Hamiltonian systems.     

一维均匀Morse晶格体系的热流棘齿效应

本文系统研究了系统两端无平均温差时一维均匀Morse晶格中的热流棘齿效应. Morse晶格的两端分别与两个热浴相接触, 其中一端热浴温度周期调制,另一端热浴温度保持不变, 两端热浴温度长时平均相等. 数值结果表明, 当对一端热浴温度进行周期调制时, 系统中便会有稳定的定向热流产生. 通过改变调制频率和强度, 可以控制热流的大小及方向. 在合适的频率范围内, 可观察到一种非常有趣的现象——非定态负热导现象, 即系统中产生的定向热流逆着系统温度梯度方向由低温端流向高温端. 通过热波动力学分析(分析热流及温度分