A cylindrically symmetric universe in general relativity

A cylindrically symmetric universe with two degrees of freedom which is of Petrov Type I degenerate, has been derived. Various physical and geometrical properties of the model have also been discussed.     

Oscillation theorems for self-adjoint matrix Hamiltonian systems involving general means

By use of monotone functionals and positive linear functionals, a generalized Riccati transformation and the general means technique, some new oscillation criteria for the following self-adjoint Hamiltonian matrix system

(E)     

Canonical formulation of the embedded theory of gravity equivalent to Einstein’s general relativity

We study the approach in which independent variables describing gravity are functions of the space-time embedding into a flat space of higher dimension. We formulate a canonical formalism for such a theory in a form that requires imposing additional constraints, which are a part of Einstein’s equations. As a result, we obtain a theory with an eight-parameter gauge symmetry. This theory becomes equivalent to Einstein’s general relativity either after partial gauge fixing or after rewriting the metric in the form that is invariant under the additional gauge transformations. We write the action for such a theory. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 2, pp. 271–288, November, 2007.     

Characterization of the Newtonian Free Particle System in m\geqslant 2 Dependent Variables

We treat the problem of linearizability of a system of second order ordinary differential equations. The criterion we provide has applications to nonlinear Newtonian mechanics, especially in three-dimensional space. Let or , let , let , let and let

A partial Hamiltonian approach for current value Hamiltonian systems

We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.     

Persistence of lower dimensional tori of general types in Hamiltonian systems

This work is a generalization to a result of J. You (1999). We study the persistence of lower dimensional tori of general type in Hamiltonian systems of general normal forms. By introducing a modified linear KAM iterative scheme to deal with small divisors, we shall prove a persistence result, under a Melnikov type of non-resonance condition, which particularly allows multiple and degenerate normal frequencies of the unperturbed lower dimensional tori.

     

On a certain class of linear Hamiltonian maps

We discovered a certain class of linear Hamiltonian maps which are defined by explicit time dependent Hamiltonian functions. Our method is the analogy of Moser's construction in 1986, although it is not so difficult, but we think the results are new.

     

矩阵多元多项式的带余除法及其应用

给出矩阵多元多项式的带余除法,从而用微分代数的观点,得到把一类微分方程(组)化为无穷维Hamilton系统的充要条件及其具体无穷维Hamilton系统形式。再把此方法和吴方法相结合获得构造一类微分方程(组)的通解的新方法。几个例子表明这些方法都很有效的。     

On k-ordered Hamiltonian graphs

A Hamiltonian graph G of order n is k-ordered, 2 ≤ k ≤ n, if for every sequence v₁, v₂, …, v_k of k distinct vertices of G, there exists a Hamiltonian cycle that encounters v₁, v₂, …, v_k in this order. Define f(k, n) as the smallest integer m for which any graph on n vertices with minimum degree at least m is a k-ordered Hamiltonian graph. In this article, answering a question of Ng and Schultz, we determine f(k, n) if n is sufficiently large in terms of k. Let g(k, n) = − 1. More precisely, we show that f(k, n) = g(k, n) if n ≥ 11k − 3. Furthermore, we show that f(k, n) ≥ g(k, n) for any n ≥ 2k. Finally we show that f(k, n) > g(k, n) if 2k ≤ n ≤ 3k − 6. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 17–25, 1999     

一类Hamiltion系统的Abel积分的零点个数估计

In this paper, we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the system inside the class of all polynomial systems of degree n. The main result is that the upper bound for the number of zeros of the Abelian integral associated to this system is 3n-1.     

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.     

哈密尔顿多部竞赛图

本文证明了如下结果：设Ｔ为几乎正则ｎ－部竞赛图（ｎ　７）,则Ｔ必含哈密尔顿圈．     

Hamiltonian decompositions of strong products

It is shown that if both G₁ and G₂ are Hamiltonian decomposable, then so is their strong product. © 1998 John Wiley & Sons, Inc. J. Graph Theory 29: 45–55, 1998     

G2-manifolds and the ADM formalism

In this paper we study a Hamiltonian function on the cotangent bundle of the space of Riemannian metrics on a 3-manifold M and prove the orbits of the constrained Hamiltonian dynamical system correspond to $G_2$-manifolds foliated by hypersurfaces diffeomorphic to $M\times \mathrm{SO}(3)$.     

Antidirected Hamiltonian paths and directed cycles in tournaments

We prove that in a tournament of odd order $n\ge 5$, the number of antidirected Hamiltonian paths starting with a forward arc and the number of Hamiltonian circuits have the same parity.     

Hamiltonian systems as selfdual equations

Hamiltonian systems with various time boundary conditions are formulated as absolute minima of newly devised non-negative action functionals obtained by a generalization of Bogomolnyi’s trick of ‘dcompleting squares’. Reminiscent of the selfdual Yang-Mills equations, they are not derived from the fact that they are critical points (i.e., from the corresponding Euler-Lagrange equations) but from being zeroes of the corresponding non-negative Lagrangians. A general method for resolving such variational problems is also described and applied to the construction of periodic solutions for Hamiltonian systems, but also to study certain Lagrangian intersections.      

Resonances and O-curves in Hamiltonian systems

We investigate the problem of the existence of trajectories asymptotic to elliptic equilibria of Hamiltonian systems in the presence of resonances.