飞机空中加油问题的研究

讨论了飞机的空中加油问题,通过比较不同方案下主机的最大作战半径,找到了辅机给主机空中加油的最佳方案,分析了存在多个基地时各基地的位置及辅机在各基地的数量,研究了二维坐标下主机的最佳飞行路径,给出了解决问题的办法.整个思路由浅入深,通过考虑辅机数目n分别为1,2,3,4的特殊情况进而探讨一般的规律,包括辅机在基地无加油时间和有加油时间以及主机在空中盘旋等不同假设条件下的复杂情况,并将统计出的数据列表对比,获得了更直观的认识.在最后进行了展望,希望结合实际中的飞机空中加油问题综合考虑风力、风向等随机因素的影响,拓展到3维空间的更复杂模型中,使飞机的空间加油问题变得更有实际意义.     

强相依高斯序列的最大值与和的联合渐近分布

{X_n,n≥1)是标准高斯序列,T_(ij)=cov(X_i,X_j)。本文在强相依条件rijlog(j-i)→r∈(0,∞)(j-i→ ∞)下,得到了高斯序列的最大值M_n与标准化部分和S_n=sum from i=1 to n(X_i/(E(sum from i=1 to n X_i)~2)/(1/2))     

热质的运动和传递-最低热质能耗散原理和热质运动方程

过增元基于质能方程提出了热质的概念.在非平衡热力学中,存在最低能量耗散原理,根据该原理可以导出热传导,扩散及粘性流动等不可逆输运过程的方程式.当采用热质模型对传热现象进行描述时,发现热质的运动也满足最小作用量原理:最低热质能耗散原理,根据该原理可以推导得出热质运动的动量守恒方程。     

On the existence of a variational principle for an operator equation with second derivative with respect to “ time”

Using methods of nonlinear functional analysis, we define the structure of an evolution operator equation of second order that can be formulated in direct variational terms.     

广义混合隐拟h变分不等式的解的存在性与算法

本文在Hilbert空间中,引入了一类广义混合隐拟h变分不等式.运用变分原理,给出了广义混合隐拟h变分不等式逼近解的迭代算法,证明了这类变分不等式解的存在性定理,同时,得到迭代序列的收敛性.并改进和推广了[6~8]一些已知结果.     

ON THE BOTTLENECK CAPACITY EXPANSION PROBLEMS ON NETWORKS

This article considers a class of bottleneck capacity expansion problems. Such problems aim to enhance bottleneck capacity to a certain level with minimum cost. Given a network G(V, A, C) consisting of a set of nodes V= {v1,v2,…,vn},a set of arcs A ■ {(vi, vj) | i=1,2,…, n;j=1,2,…,n} and a capacity vector C. The component cij of C is the capacity of arc (vi ,vj). Define the capacity of a subset A' of A as the minimum capacity of the arcs in A, the capacity of a family F of subsets of A is the maximum capacity of its members. There are two types of expanding models. In the arc-expanding model, the unit cost to increase the capacity of arc (vi, vj) is wij. In the node-expanding model, it is assumed that the capacities of all arcs (vi,vj) which start at the same node vi should be increased by the same amount and that the unit cost to make such expansion is wi. This article considers three kinds of bottleneck capacity expansion problems (path, spanning arborescence and maximum flow) in both expanding models. For each kind of expansion problems, this article discusses the characteristics of the problems and presents several results on the complexity of the problems.     

Nonobtuse Tetrahedral Partitions that Refine Locally Towards Fichera-Like Corners

Linear tetrahedral finite elements whose dihedral angles are all nonobtuse guarantee the validity of the discrete maximum principle for a wide class of second order elliptic and parabolic problems. In this paper we present an algorithm which generates nonobtuse face-to-face tetrahedral partitions that refine locally towards a given Fichera-like corner of a particular polyhedral domain. The first author was supported by the Swedish Foundation for Strategic Research, the second author was supported by Grant No. 49051 of the Academy of Finland, the third author was supported by Grant No. A 1019201 of the Academy of Sciences of the Czech Republic and by Institutional Research Plan AV0Z 10190503.     

非自治动力系统的原像熵

本文对紧致度量空间上的连续自映射序列应用生成集和分离集引入了点原像熵、原像分枝熵以及原像关系熵等几类原像熵的定义并进行了研究.主要结果是:(1) 证明了这些熵都是等度拓扑共轭不变量.(2)讨论了这些原像熵之间及它们与拓扑熵之间的关系,得到了联系这些熵的不等式.(3)证明了对正向可扩的连续自映射序列而言, 两类点原像熵相等,原像分枝熵与原像关系熵也相等.(4)证明了对(a).由闭Riemann 流形上的一个扩张映射经充分小的C1-扰动生成的自映射序列,以及(b).有限图上等度连续的自映射序列,有零原像分枝熵.     

The incompatibility between local hidden variable theories and the fundamental conservation laws

I discuss in detail the result that the Bell’s inequalities derived in the context of local hidden variable theories for discrete quantized observables can be satisfied only if a fundamental conservation law is violated on the average. This result shows that such theories are physically nonviable, and makes the demarcating criteria of the Bell’s inequalities redundant. I show that a unique correlation function can be derived from the validity of the conservation law alone and this coincides with the quantum mechanical correlation function. Thus, any theory with a different correlation function, like any local hidden variable theory, is incompatible with the fundamental conservation laws and space-time symmetries. The results are discussed in the context of two-particle singlet and triplet states, GHZ states, and two-particle double slit interferometry. Some observations on quantum entropy, entanglement, and nonlocality are also discussed.     

高地应力下大型地下洞室拱形优化研究

高地应力区的大型洞室开挖会引起洞室拱周附近围岩应力集中和塑性区加大以及塑性应变的增加，但过高的应力集中会增加岩爆发生的几率，塑性区的加深会促使围岩失稳；洞室拱形形状会影响围岩应力集中和塑性区大小的分布，因此，以某高地应力下的大型发电洞岩体地质资料为依托，用弹塑性有限元分析高地应力地下大型发电洞室常采用的3种洞室拱形（即单心圆拱、三心圆拱和椭圆拱）对拱部围岩应力的影响，计算结果表明这种影响是非常明显的，有的应力集中系数达到3．33，无论采用哪种拱形，均避不开拱座附近应力集中现象。根据开挖后拱部围岩的塑性耗散能可以判断，无论初始地应力侧压系数是多少，椭圆拱是最优的，其次是三心圆拱。