The Dynamics of Stretchable Rods in the Inertial Case

Nonlinear amplitude equations for the near-threshold behavior of twisted extensible elastic rods under tension with inertial and dissipative dynamics are derived. In the inertial case localized solutions to the amplitude equations are derived and a linear stability criterion for the pulse solutions is obtained using the Hamiltonian formulation of the problem.     

Bounded Sobolev norms for linear Schrödinger equations under resonant perturbations

We prove that the Sobolev norms for a 1-D periodic Schrödinger equation remain bounded under small resonant perturbations.     

Matrix-Based Analytical Model of Critical Coupling Length of Titanium In-Diffused Integrated-Optic Directional Coupler on Lithium Niobate Substrate

The critical coupling length Lc is the most important design parameter of an integrated-optic directional coupler, which is the basic building block of a variety of optical integrated circuits. The existing methods of estimating Lc of a Ti in-diffused waveguide directional coupler on LiNbO3 substrate are based on the beam propaga tion method (BPM), which requires huge computing time. A considerably simpler and computationally faster analytical method involving only multiplication of 2 x 2 matrices with no iterations is described in this article. A staircase type step-index profile is generated from the one-dimensional effective index profile in the lateral direction by partitioning the latter into a large number of thin sections of different refractive indices. The overall transfer matrix of the step-index layered structure so obtained may be computed by the progressive multiplication of individual transfer matrices (2 x 2) relating the field components in adjacent layers. Hence the wave amplitude in any layer may be computed as a function of the input wave amplitude for different angles of incidence. This method has been successfully employed to compute the propagation constants for symmetric and asymmetric guided modes in the coupled region of the directional coupler and hence compute the coupling length. The values of Lc computed for a variety of devices agree closely with the published experimental results reported by several research groups. The computer program implementing the model runs reasonably fast in an ordinary PC and is versatile enough to consider arbitrary waveguide dimensions. Ti film thickness, and diffusion parameters for any wavelength of input light and for both transverse electric and transverse magnetic polarizations.     

Greedily constructing Hamiltonian paths, Hamiltonian cycles and maximum linear forests

There are various greedy schemas to construct a maximal path in a given input graph. Associated with each such schema is the family of graphs where it always results a path of maximum length, or a Hamiltonian path/cycle, if there exists one. Considerable amount of work has been carried out, regarding the characterization and recognition problems of such graphs. We present here a systematic listing of previous results of this type and fill up most of the remaining empty entries.     

THE SYMMETRY CONSTRAINT AND LEVY EVOLUTION EQUATION HIERARCHY

1IntroductionThesymmetryconstraintgivestheinterrelationbetweenhigher-dimensionalintegrablesystemsandlower-dimensionalintegrablesystemsandprovidesadirectmethodtoconstructsolutionsofhigher-dimensionalintegrablesystemsbysolvinglower-dimensionalintegrablesyst…     

Finding a minimum path cover of a distance-hereditary graph in polynomial time

A path cover of a graph G=(V,E) is a set of pairwise vertex-disjoint paths such that the disjoint union of the vertices of these paths equals the vertex set V of G. The path cover problem is, given a graph, to find a path cover having the minimum number of paths. The path cover problem contains the Hamiltonian path problem as a special case since finding a path cover, consisting of a single path, corresponds directly to the Hamiltonian path problem. A graph is a distance-hereditary graph if each pair of vertices is equidistant in every connected induced subgraph containing them. The complexity of the path cover problem on distance-hereditary graphs has remained unknown. In this paper, we propose the first polynomial-time algorithm, which runs in O(|V|⁹) time, to solve the path cover problem on distance-hereditary graphs.     

A topological classification of integrable geodesic flows on the two-dimensional sphere with an additional integral quadratic in the momenta

Summary The analytic expression for a Riemannian metric on a 2-sphere, having integrable geodesic flow with an additional integral quadratic in momenta, is given in [Ko1]. We give the topological classification, up to topological equivalence of Liouville foliations, of all such metrics. The classification is computable, and the formula for calculating the complexity of the flow is straightforward. We prove Fomenko's conjecture that, from the point of view of complexity, the integrable geodesic flows with an additional integral linear or quadratic in momenta exhaust “almost all” integrable geodesic flows on the 2-dimensional sphere.     

Minimal orbits close to periodic frequencies

Let with h analytic of small norm. The problem of Arnold's diffusion consists in finding conditions on h which guarantee the existence of orbits Q of with connecting two arbitrary points of frequency space. Recently, J. N. Mather has found a sufficient condition for Arnold's diffusion; this condition is not read on h itself, but on the set of all action-minimizing orbits of . In this paper we try to characterize those action-minimizing orbits whose mean frequency is close to periodic. Received: November 26, 1996     

The number and distributions of limit cycles for a class of cubic near-Hamiltonian systems

This paper concerns with the number of limit cycles for a cubic Hamiltonian system under cubic perturbation. The fact that there exist 9-11 limit cycles is proved. The different distributions of limit cycles are given by using methods of bifurcation theory and qualitative analysis, among which two distributions of eleven limit cycles are new.     

含Hopf项和Maxwell-Chern-Simons项O(3)非线性σ模型的分数自旋和分数统计性质

研究了（2＋1）维时空中含Hopf项和Maxwell-Chern-Simons(MCS)项的非线性σ模型的分数自旋性质.根据约束Hamilton系统的Faddeev-Senjanovic(FS)路径积分量子化方案,对该系统进行量子化，由量子Noether定理给出了量子守恒角动量，说明了在量子水平上该系统仍具有分数自旋的性质. 关键词： 约束Hamilton系统 分数自旋 O(3)σ模型