Fermi, Majorana and the Statistical Model of Atoms

We give an account of the appearance and first developments of the statistical model of atoms proposed by Thomas and Fermi, focusing on the main results achieved by Fermi and his group in Rome. Particular attention is addressed to the unknown contribution to this subject by Majorana, anticipating some important results reached later by leading physicists.     

Symmetries of Itô and Stratonovich Dynamical Systems and Their Conserved Quantities

A new definition for the symmetries of Itô and Stratonovich dynamicalsystem is given. Determining systems of symmetries for Itô andStratonovich systems have been obtained, and their relation has beendiscussed. It has been shown that some of the Lie point symmetries ofthe Fokker–Planck equation can be constructed using the symmetries ofItô dynamical systems. Conserved quantities can be found from thesymmetries of stochastic dynamical systems which do not arise from aHamiltonian. The results have been applied to an example.     

Approximate symmetries and conservation laws for Itô and Stratonovich dynamical systems

A new definition for the approximate symmetries of Itô dynamical system is given. Determining systems of approximate symmetries for Itô and Stratonovich dynamical systems have been obtained. It has been shown that approximate conservation laws can be found from the approximate symmetries of stochastic dynamical systems which do not arise from a Hamiltonian. The results have been applied to an example.     

Dirac Fields in 3D de Sitter Spacetime

We show that the Dirac equation is separable in the circularly symmetric metric in three dimensions and when the background spacetime is de Sitter we find exact solutions to the radial equations. Using these results we show that the de Sitter horizon has a cross section equal to zero for the massless Dirac field, as in the case of the scalar field. Also, using the improved brick wall model we calculate the fermionic entropy associated with the de Sitter horizon and we compare it with some results previously published.     

地源热泵的运行特性模拟研究

依据圆柱源理论,建立起了耦合地面热泵机组和地下埋管换热器特性的模拟模型,该模型可用于长期运行的地源热泵系统的短时间步长运行特性模拟。探讨了模拟过程中有关参数的确定方法,并运用所建模型对地源热泵的冬季和夏季运行特性进行了模拟。运行特性模拟与实验数据的验证结果表明,所建模型可以对地源热泵的运行特性做出符合实际的预测。     

A Note on Cactus Trees: Variational vs. Recursive Approach

In this article we deal with the variational approach to cactus trees (Husimi trees) and the more common recursive approach, that are in principle equivalent for finite systems. We discuss in detail the conditions under which the two methods are equivalent also in the analysis of infinite (self-similar) cactus trees, usually investigated to the purpose of approximating ordinary lattice systems. Such issue is hardly ever considered in the literature. We show (on significant test models) that the phase diagram and the thermodynamic quantities computed by the variational method, when they deviates from the exact bulk properties of the cactus system, generally provide a better approximation to the behavior of a corresponding ordinary system. Generalizing a property proved by Kikuchi, we also show that the numerical algorithm usually employed to perform the free energy minimization in the variational approach is always convergent.     

Directed Motion of a Molecular Motor Based on the Four-State Model with Unequal Substeps

A periodic one-dimensional four-state hopping model is proposed. In the model, the substeps betweenarbitrary adjacent states are unequal, and an explicit solution of the master equation is first obtained for the probabilitydistribution as a function of the time and position for any initial distribution with all the transients included. Next, thetransient behaviors in the initial period of time and the characteristic time to reach the steady state for the molecularmotor are discussed. Finally, we compare the steady state results to experiments and illustrate qualitatively the kineticbehaviors of a molecular motor under external load F.     

一般线性模型下方差最小范数二次无偏估计的稳健性

本文给出了一般线性模型下,由最小二乘得到的方差估计与最小范数二次无偏估计相等的充分必要条件,并且当Gauss-Markov估计与最小二乘估计相等时,可以得到一个简单的等价条件。     

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.     

Bilevel programming approach applied to the flow shop scheduling problem under fuzziness

This paper presents a fuzzy bilevel programming approach to solve the flow shop scheduling problem. The problem considered here differs from the standard form in that operators are assigned to the machines and imposing a hierarchy of two decision makers with fuzzy processing times. The shop owner considered higher level and assigns the jobs to the machines in order to minimize the flow time while the customer is the lower level and decides on a job schedule in order to minimize the makespan. In this paper, we use the concepts of tolerance membership function at each level to define a fuzzy decision model for generating optimal (satisfactory) solution for bilevel flow shop scheduling problem. A solution algorithm for solving this problem is given. Mathematics Subject Classification: 90C70, 90B36, 90C99