The Constrained MKP Hierarchy and the Generalized Kupershmidt–Wilson Theorem

The constrained Modified KP hierarchy is considered from the viewpoint of modification. It is shown that its second Poisson bracket, which has a rather complicated form, is associated to a vastly simpler bracket via a Miura-type map. Similar results are established for a natural reduction of the MKP.     

Construction of Hamiltonian Cycles in Layered Cubic Planar Graphs

 In this paper, a class of cubic planar graphs is given that have Hamiltonian cycles that can be constructed in linear time. A member of this class is called a layered cubic planar graph, and consists of a sequence of cycles C ₀ ,C ₁ ,…,C _n such that each pair of successive cycles, C _i , C _i+1 , is joined by a matching. The cycles can be pictured as concentric circles, and the edges of the matchings as radial line segments between successive circles. The subgraph bounded by two successive cycles forms a layer; each face in layer i is incident to a fixed number k _i+1 of edges in the matching in layer i+1. The problem that initially motivated this work is that of identifying classes of convex cubic polyhedra that can be easily edge three-colored. Received: September 21, 1998 Final version received: July 21, 1999     

Realization of Dirac Bracket Algebras Through First-Class Functions and Quantization of Constrained Systems

It is shown that a Dirac bracket algebra is isomorphic to the original Poisson bracket algebra of first-class functions subject to first-class constraints. The isomorphic image of the Dirac bracket algebra in the star-product commutator algebra is found.     

二阶渐近周期奇异哈密顿系统同宿轨道

运用集中紧性方法和Ekeland变分原理研究R^2中二阶渐近周期奇异Hamilton系统ue (1 g(t))V‘u(t,u)=0的极小问题，并证明该系统具有两条非平凡同宿轨道。     

Electronic structure and optical spectra of transition metal complexes by the effective Hamiltonian method

Summary A semiempirical effective Hamiltonian treatment is proposed for transition metal complexes, taking into accountd-electron correlations, weak covalency of the metal-ligand bonds and the electronic structure of the ligand sphere. The technique uses the variation wave function which differs from the usual Hartree-Fock antisymmetrized product of molecular orbitals extended over the whole complex. The scheme is implemented and parameters describing the metal-ligand interactions are adjusted to reproduced-d-excitation spectra of a number of octahedral MF ₆ ^4– (M=Mn, Fe, Co, Ni) anions, Mn(FH) ₆ ²⁺ cation, CoCl ₆ ^4– anion, and a tetrahedral CoCl ₄ ^2– anion. The values of the parameters are reasonable, thus confirming the validity of the proposed scheme.     

THE POINCAR BIFURCATION OF CUBIC HAMILTONIAN SYSTEMS WITH DOUBLE CENTERS

In this paper, we discuss the Poincare bifurcation of cubic Hamiltonian systems with double centers and prove that the systems may at least generate two limit cycles and at most generate three limit cycles outside the lemniscate after a small cubic perturbation.     

Polynomial algorithms that prove an NP-Hard hypothesis implies an NP-hard conclusion

A number of results in hamiltonian graph theory are of the form “ implies ”, where is a property of graphs that is NP-hard and is a cycle structure property of graphs that is also NP-hard. An example of such a theorem is the well-known Chvátal–Erd s Theorem, which states that every graph G with κ is hamiltonian. Here κ is the vertex connectivity of G and is the cardinality of a largest set of independent vertices of G. In another paper Chvátal points out that the proof of this result is in fact a polynomial time construction that either produces a Hamilton cycle or a set of more than κ independent vertices. In this note we point out that other theorems in hamiltonian graph theory have a similar character. In particular, we present a constructive proof of a well-known theorem of Jung (Ann. Discrete Math. 3 (1978) 129) for graphs on 16 or more vertices.     

The visibility graph of congruent discs is Hamiltonian

We show that the visibility graph of a set of disjoint congruent discs in is Hamiltonian, as long as the discs are not all supported by the same line. The proof is constructive, and leads to efficient algorithms for obtaining a Hamilton circuit.     

Treatment of Dirac Fields in Light—Front Coordinates by Dirac‘s Method for Constrained Hamiltonian Systems

Dirac‘s method which itself is for constrained Boson fields and particle systems is followed and developed to treat Dirac fields in light-front coordinates.