空间中的角和距离

空间中的角和距离是数学竞赛的考点之一，一般以选择题和填空题的形式出现，主要考查基本概念和空间点、线、面之间的位置关系，解题以通性通法为主．     

Note on the Constraint on Modified Energy-Momentum Relation

Quantum gravity can modify the usual energy-momentum dispersion relation. We provide evidence for the argument that the modified dispersion relation is constrained by the black hole thermodynamics, for consistency of quantum gravity.     

New Spinor Field Realizations of the Non-Critical W3 String

We investigate the new spinor field realizations of the W3 algebra, making use of the fact that the W3 algebra can be linearized by the addition of a spin-1 current. We then use these new realizations to build the nilpotent Becchi-Rouet-Stora-Tyutin charges of the spinor non-critical W3 string.     

键座渗流与稀磁体系的相变

本文首先将键渗流和座渗流中的普适关系加以推广,建立了键座渗流的相界关系;接着研究了稀磁体系的相变问题,应用Potts模型,推出稀磁体系的铁磁-顺磁和反铁磁-顺磁相交的相界关系。与已往文献中处理这类问题所采用的级数法、有限集团近似、数值模拟和重整化群等方法相比,本文所给出的解析式具有使用方便、简单、物理概念清晰,且较为精确等优点.     

交流源作用下介观RLC电路系统量子态随时间的演化

根据量子不变量理论，同时考虑介观电容器极板间电子波函数的耦合作用和电路的耗散,研究介观RLC电路系统在交流电流源作用下动力学的演化过程，并且得到描述系统量子态随时间的演化算符.进一步的分析结果表明，介观RLC电路系统的波函数将由任意的初态演化到一般的压缩态. 关键词： 介观RLC电路 交变电源 不变量理论 时间演化算符     

沿直线的垂直方向匀速直线运动的带电直线的电场

本文利用相对论变换关系计算了沿直线的垂直方向匀速运动的带电直线的电场.     

Single-period Two-product Inventory Model with Reorder and Substitution

In market, excess demands for many products can be met by reorder even during one period, and retailers usually adopt substitution strategy for more benefit. Under the retailer's substitution strategy and permission of reorder, we develop the profits maximization model for the two-substitutable-product inventory problem with stochastic demands and proportional costs and revenues. We show that the objective function is concave and submodular, and therefore the optimal policy exists. We present the optimal conditions for order quantity and provide some properties of the optimal order quantities. Comparing our model with Netessine and Rudi's, we prove that reorder and adoption of the substitution strategy can raise the general profits and adjust down the general stock level.     

高能e+e－湮没强子多重数的质量关系

利用一个描述强子质量谱成功的夸克模型确定出得到的强子多重数普适质量关系〈n〉=aexp(–bm)中的参数b,发现对于介子、重子是一个普适的常数.利用这个质量公式给出计算各种粒子多重数的表达式,进而以高能e⁺e^－湮没为例计算出各种粒子多重数与实验以及其他模型做了比较,表明这个没有任何假定的质量关系同样能够解释实验.     

The Casimir effect of Reissner-NordstrSm black hole

The stress tensor of a massless scalar field satisfying a mixed boundary condition in a （1 ＋ 1）-dimensional Reissner- Nordstrom black hole background is calculated by using Wald＇s axiom. We find that Dirichlet stress tensor and Neumann stress tensor can be deduced by changing the coefficients of the stress tensor calculated under a mixed boundary condition. The stress tensors satisfying Dirichlet and Neumann boundary conditions are discussed. In addition, we also find that the stress tensor in conformal flat spacetime background differs from that in flat spacetime only by a constant.     

Fractional-Linear Transformations of Operator Balls; Applications to Dynamical Systems

The operator sets, which are the subject of this paper, have been studied in many papers where, under different restrictions on the generating operators, convexity, compactness in the weak operator topology, and nonemptiness were proved for sets of different classes under study. Then the results obtained were used in these papers to solve several applied problems. Namely, they played the key role in establishing the dichotomy of nonautonomous dynamical systems, with either continuous or discrete time. In the present paper, we generalize and sharpen the already known criteria and obtain several new criteria for convexity, compactness, and nonemptiness of several special operator sets. Then, using the assertions obtained, we construct examples of sets of the form under study which are nonconvex, noncompact in the weak operator topology, as well as empty, and are generated by ＂smooth＂ operators of a special class. The existence problem for such sets remained open until the authors of this paper announced some of its results.