A Relation of the Noncommutative Parameters in Generalized Noncommutative Phase Space

We introduce the deformed boson operators which satisfy a deformed boson algebra in some special types of generalized noncommutative phase space. Based on the deformed boson algebra, we construct coherent state representations. We calculate the variances of the coordinate operators on the coherent states and investigate the corresponding Heisenberg uncertainty relations. It is found that there are some restriction relations of the noncommutative parameters in these special types of noncommutative phase space.

THE GENERALIZED EINSTEIN RELATION ON A COMPACT ORIENTABLE RIMANNIAN MANIFOLD

A generalized Einstein relation is established for a drifted Brownian motion on a compact orientable Remannian manifole. The original form of such relation comes from an explicit formula of diffusion coeffcient by using the autocorrelation function of the velocity of the Einstein fluctuation theory of the diffusion process

Generalized δ-entropy condition to Riemann solution for Chaplygin gas in traffic flow

The Riemann problem for the Aw-Rascle model in the traffic flow with the Delta initial data for the Chaplygin gas is studied. The solutions are constructed globally under the generalized Rankine-Hugoniot relations, the δ-entropy conditions, and the generalized δ-entropy conditions. A new Delta wave, which is called a primary Delta wave, is defined in some solutions. The primary Delta wave satisfies the generalized Rankine- Hugoniot relations and the generalized δ-entropy conditions. It generates initially from the Delta initial data, which either evaluates a Delta wave, whose weight becomes stronger and stronger, or disappears at a finite time.

Two-dimensional non-selfsimilar initial value problem for adhesion particle dynamics

A two-dimensional non-selfsimilar initial value problem for adhesion particle dynamics with two pieces of constant states separated by a circular ring is considered. By using the generalized characteristic method and the generalized Rankine-Hugoniot relation, which is a system of ordinary equations, the global solution which includes delta-shock waves and vacuum is constructed.

Lyapunov function as potential function: A dynamical equivalence

For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively proved that any dynamics with a Lyapunov function has a corresponding physical realization： a friction force, a Lorentz force, and a potential function. Such construction establishes a set of equations with physical meaning for Lyapunov function and suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems. In addition, a connection is found that the Lyapunov equation is a reduced form of a generalized Einstein relation for linear systems, revealing further insights of the construction.

Information entropy for static spherically symmetric black holes

By using the new equation of state density derived from the generalized uncertainty relation, the number of the quantum states near event horizon is obtained, with which then the information entropy of static spherically symmetric black holes has been discussed. It is found that the divergent integral of quantum states near the event horizon can be naturally avoided if using the new equation of state density without introducing the ultraviolet cut-off. The information entropy of black holes can be obtained precisely by the residue theorem, which is shown to be proportional to the horizon area. The information entropy of black holes obtained agrees with the Bechenstein-Hawking entropy when the suitable cutoff factor is adopted.

Exact Solutions to Maccari's System

Based on the generalized Riccati relation,an algebraic method to construct a series of exact solutionsto nonlinear evolution equations is proposed.Being concise and straightforward,the method is applied to Maccari'ssystem,and some exact solutions of the system are obtained.The method is of important significance in exploring exactsolutions for other nonlinear evolution equations.

THE INEFFICIENCY OF THE LEAST SQUARES ESTIMATOR AND ITS BOUND

It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.

Generating Relations for Grothendieck Groups of Trivial Extension Algebras

In this paper we describe explicitly the generating relations for the Grothendieck groups of trivial extension algebras of tame hereditary algebras.

SOME LIMIT PROPERTIES AND THE GENERALIZED AEP THEOREM FOR NONHOMOGENEOUS MARKOV CHAINS

Let(ξ_n)_(n=0)~∞ be a Markov chain with the state space X = {1, 2, · · ·, b},(g_n(x, y))_(n=1)~∞ be functions defined on X × X, and F_(m_n,b_n)(ω) =1 /b_n sum from k=m_n+1 to m_n+b_n g_k(ξ_(k-1), ξ_k).In this paper the limit properties of F_(m_n,b_n)(ω) and the generalized relative entropy density f_(m_n,b_n)(ω) =-(1/b_n) log p(ξ_(m_n,m_n+b_n)) are discussed, and some theorems on a.s. convergence for(ξ_n)_n=0~∞ and the generalized Shannon-McMillan(AEP) theorem on finite nonhomogeneous Markov chains are obtained.

Presenting Little q-Schur Algebras uk（2, r）

Little q-Schur algebras were introduced as homomorphic images of the infinitesimal quantum groups by Du, Fu and Wang. In this paper, we obtain a presentation by generators and relations for little q-Schur algebras uk（2, r）.

An Algorithm to Identify Positive Cycles in GPRs

The purpose of this paper is to identify cycles, and in particular positive cycle(s), in an activity network under generalized precedence relations (GPRs). An algorithm is provided to search for such cycle(s). An improved depth-first search is adopted. An efficient arc-oriented representation is used in the algorithm to save on computer storage requirement.