An inequality connecting entropy distance,Fisher Information and large deviations

In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large deviation rate functional. In addition to possessing various favourable properties, we show that this generalised Fisher Information converges to the classical Fisher Information in an appropriate limit. We then use this generalised Fisher Information and the aforementioned inequality to qualitatively study coarse-graining problems for jump processes on discrete spaces.     

Propagation of mesons in asymmetric nuclear matter in a density-dependent coupling model

We study the propagation of the light mesons σ,ω,ρ, and a₀(980) in dense hadronic matter in an extended derivative scalar coupling model. Within the scheme proposed it is possible to unambiguously define effective density-dependent couplings at the Lagrangian level. We first apply the model to study asymmetric nuclear matter with fixed isospin asymmetry, and then we pay particular attention to hypermatter in β-equilibrium. The equation of state and the potential contribution to the symmetry coefficient arising from the mean-field approximation are investigated. Received: 16 October 2001 / Accepted: 10 January 2002     

Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices

Let U_m be an m×m Haar unitary matrix and U_[m,n] be its n×n truncation. In this paper the large deviation is proven for the empirical eigenvalue density of U_[m,n] as m/n→λ and n→∞. The rate function and the limit distribution are given explicitly. U_[m,n] is the random matrix model of quq, where u is a Haar unitary in a finite von Neumann algebra, q is a certain projection and they are free. The limit distribution coincides with the Brown measure of the operator quq.     

大焦深成像系统仿真实验研究

如何增大非相干光学成像系统的焦深是应用光学研究领域的热点问题.本文对采用高次非球面光学掩模板与图像处理相结合增大成像光学系统焦深的新方法进行了深入分析,建立了大焦深成像系统仿真实验模型,并进行了大焦深成像系统仿真实验.实验结果证明了该方法在维持原相对孔径的同时使光学系统在较大的离焦范围内有好的成像质量.实际应用中还要综合考虑模板参量、信噪比等关键因素.     

Decentralized iterative learning control for a class of large scale interconnected dynamical systems

The problem of decentralized iterative learning control for a class of large scale interconnected dynamical systems is considered. In this paper, it is assumed that the considered large scale dynamical systems are linear time-varying, and the interconnections between each subsystem are unknown. For such a class of uncertain large scale interconnected dynamical systems, a method is presented whereby a class of decentralized local iterative learning control schemes is constructed. It is also shown that under some given conditions, the constructed decentralized local iterative learning controllers can guarantee the asymptotic convergence of the local output error between the given desired local output and the actual local output of each subsystem through the iterative learning process. Finally, as a numerical example, the system coupled by two inverted pendulums is given to illustrate the application of the proposed decentralized iterative learning control schemes.     

Internal Rotation of the Methyl Group in Cations of Toluene Derivatives

The potential of the internal rotation of the methyl group was determined for o-, m-, and p-fluorotoluene cations by pulsed field ionization spectroscopy. The potential of the internal rotational motion was also surveyed for other toluene derivative cations. It was found that the barrier height generally increases by ionization. The increase in the barrier height has been discussed in connection with the reduction of the internal rotational constant B by ionization. The geometrical distortion of the methyl group during the internal rotation has been suggested.     

On the blow-up rate of large solutions for a porous media logistic equation on radial domain

In this paper we establish the exact blow-up rate of the large solutions of a porous media logistic equation. We consider the carrying capacity function with a general decay rate at the boundary instead of the usual cases when it can be approximated by a distant function. Obtaining the accurate blow-up rate allows us to establish the uniqueness result. Our result covers all previous results on the ball domain and can be further adapted in a more general domain.     

子系统为S≥3的非线性大系统在近平衡区内的稳定性

本文采用文[1,2]中提出的平衡结构法研究子系统s≥3的非线性大系统在近平衡区内的稳定性;得到了判别这类大系统稳定性的两个一般性准则.     

Stress and heat flux stabilization for viscous compressible medium equations with a nonmonotone state function

We study a system of quasilinear equations describing one-dimensional flow of a viscous compressible heat-conducting medium with a nonmonotone state function and mass force. The large-time behavior of solutions is considered for arbitrarily large initial data. In spite of possible nonuniqueness and discontinuity of the stationary solution, we prove L²-stabilization for the stress and heat flux as t → ∞ along with corresponding global energy estimates for them. The new method of proof utilizes a combination of energy type equalities for the stress and heat flux. Consequently, H¹-stabilization of the velocity and temperature along with global estimates for their derivatives are valid as well.     

A theory of coupled diffusion and large deformation in polymeric gels

A large quantity of small molecules may migrate into a network of long polymers, causing the network to swell, forming an aggregate known as a polymeric gel. This paper formulates a theory of the coupled mass transport and large deformation. The free energy of the gel results from two molecular processes: stretching the network and mixing the network with the small molecules. Both the small molecules and the long polymers are taken to be incompressible, a constraint that we enforce by using a Lagrange multiplier, which coincides with the osmosis pressure or the swelling stress. The gel can undergo large deformation of two modes. The first mode results from the fast process of local rearrangement of molecules, allowing the gel to change shape but not volume. The second mode results from the slow process of long-range migration of the small molecules, allowing the gel to change both shape and volume. We assume that the local rearrangement is instantaneous, and model the long-range migration by assuming that the small molecules diffuse inside the gel. The theory is illustrated with a layer of a gel constrained in its plane and subject to a weight in the normal direction. We also predict the scaling behavior of a gel under a conical indenter.