A slacks-based measure of efficiency in data envelopment analysis

In this paper, we will propose a slacks-based measure (SBM) of efficiency in Data Envelopment Analysis (DEA). This scalar measure deals directly with the input excesses and the output shortfalls of the decision making unit (DMU) concerned. It is units invariant and monotone decreasing with respect to input excess and output shortfall. Furthermore, this measure is determined only by consulting the reference-set of the DMU and is not affected by statistics over the whole data set. The new measure has a close connection with other measures proposed so far, e.g., Charnes–Cooper–Rhodes (CCR), Banker–Charnes–Cooper (BCC) and the Russell measure of efficiency. The dual side of this model can be interpreted as profit maximization, in contrast to the ratio maximization of the CCR model. Numerical experiments show its validity as an efficiency measurement tool and its compatibility with other measures of efficiency.     

On the invariant translation approximation property for discrete groups

Recently J.Roe considered the question of whether for a discrete group the reduced group -algebra is the fixed point algebra of Ad acting on the uniform Roe algebra . is said to have the invariant translation approximation property in this case. We consider a slight generalization of this property which, for exact , is equivalent to the operator space approximation property of . We also give a new characterization of exactness and a short proof of the equivalence of exactness of and exactness of for discrete groups.

     

逆极限的不变测度和一致正熵性质

In this paper, the interconnection of some ergodic properties between a continuous selfmap and its inverse limit is studied. It has been proved that (1) their invariant Borel probability measures are identical up to homeomorphism and (2) they preserve uniform positive entropy property simuitaneously. As applications, it is also proved that the upper semi-continu-ous properties of their entropy maps are restricted each other, and the entropy map of the asymptotically h-expansive continuous map is upper semi-contlnuous, at the same time a continuous map having u, p.e. is topological weakmixing.     

Nodal Solutions of a p-Laplacian Equation

We prove that the p-Laplacian problem –_p u = f(x, u),with u on a bounded domain R^N, with p > 1 arbitrary, has a nodal solution providedthat f : x R R is subcritical, and f(x, t) / |t|^p –² is superlinear. Infinitely many nodal solutions are obtainedif, in addition, f(x, –t) = –f(x, t). 2000 MathematicsSubject Classification 35J20, 35J65, 58E05.     

A Note on Calculation of Phase Space Path Integral by Means of Invariants

In this note we use the method of invariant to calculate the phase space path integral appearing in our previous article.     

动边界量子含时谐振子系统的Lewis-Riesenfeld相位与Berry相位

根据Lewis-Riesenfeld的量子不变量理论,计算了一维动壁无限深势阱内频率随时间变化的谐振子的Lewis-Riesenfeld相位,发现刘登云文中“非绝热Berry相位”与Lewis-Riesenfeld相位中的几何部分完全一致.也许更为重要的是,证明了至少对于做正弦振动的边界,在绝热近似下,该系统不存在非零的Berry相位. 关键词： Berry相位 Lewis-Riesenfeld相位 量子不变量 动边界     

图胞映射的一种改进方法

通过引入新的概念,提出了图胞映射动力系统中瞬态胞的新的分类方法,基于新的分类方法研究了动力系统中不变流形的胞映射逼近问题;并结合计算机的计算速度与内存特点,建立了完成上述压缩分类的有效算法.通过对典型算例Henon映射的应用分析,证实了该方法的有效性. 关键词： 图胞映射方法 不变流形 Henon映射     

自旋为1/2的XY模型亚铁磁棱型链的物性和有序-无序竞争

利用不变本征算符法, 计算低温下自旋为1/2的XY模型一维亚铁磁棱型链系统的元激发谱, 讨论在此系统中不同的特殊情形下的元激发能量, 从而给出体系的三个临界磁场强度的解析解H_C1, H_C2, H_peak. 分析不同外磁场下 体系的磁化强度随温度的变化规律, 发现三个临界磁场强度的解析解H_C1, H_C2, H_peak是正确的, 并从三个元激发对磁化强度的贡献进行了说明. 低温下磁化强度随外磁场的变化呈现1/3磁化平台. 体系的磁化率随温度或者外磁场的变化都出现了双峰现象. 这说明双峰源于二聚体分子内电子自旋平行排列的铁磁交换作 用能和二聚体与单基体分子间电子自旋反平行排列的反铁磁交换作用能, 热无序能, 外磁场强度相关的自旋磁矩势能之间的竞争.     

Derivation of baroclinic Ertel–Rossby invariant-based thermally-coupled vorticity equation in moist flow

For the potential vorticity （PV） invariant, there is a PV-based complete-form vorticity equation, which we use heuris- tically in the present paper to answer the following question： for the Ertel-Rossby invariant （ERI）, is there a corresponding vorticity tendency equation？ Such an ERI-based thermally-coupled vorticity equation is derived and discussed in detail in this study. From the obtained new vorticity equation, the vertical vorticity change is constrained by the vertical velocity term, the term associated with the slope of the generalized momentum surface, the term related to the horizontal vorticity change, and the baroclinic or solenoid term. It explicitly includes both the dynamical and thermodynamic factors＇ influence on the vorticity change. For the ERI itself, besides the traditional PV term, the ERI also includes the moisture factor, which is excluded in dry ERI, and the term related to the gradients of pressure, kinetic energy, and potential energy that reflects the fast-manifold property. Therefore, it is more complete to describe the fast motions off the slow manifold for severe weather than the PV term. These advantages are naturally handed on and inherited by the ERI-based thermally-coupled vorticity equation. Then the ERI-based thermally-coupled vorticity equation is further transformed and compared with the traditional vorticity equation. The main difference between the two equations is the term which describes the contribution of the solenoid term to the vertical vorticity development. In a barotropic flow, the solenoid term disappears, then the ERI-based thermally-coupled vorticity equation can regress to the traditional vorticity equation.     

在同位旋SU(2)不变耦合模型中研究 p pbar -> n nbar 核子反应的重整化无穷阶链图效应

本文采用描述中性及荷电 pion 介子（pion0,pion+,pion-）与核子-反核子强相互作用的同位旋SU(2)不变耦合模型,计算出在pion0 及 pion+, pion- 重整化链图传播下 p pbar -> n nbar 核子反应微分截面的“精确”解析结果;并且将此结果与在 pion0 及 pion+, pion- 树图传播下的微分截面作了对比分析,得到相应的辐射修正重要信息。本文完成的工作对进一步深入研究三种荷电状态 pion 介子与核子-反核子强相互作用的同位旋SU(2)不变耦合模型以及深入理论探讨质子-反质子对撞实验,都将提供某些理论研究的参考价值。