QUantale中的闭滤子

在Quantale中讨论了与Gabriel拓扑密切关联的闭滤子,给出了闭滤子与闭映射之间的相互确定关系．证明了凝聚左侧Quantale Q的闭滤子全体F(Q)在包含序下构成Frame,并且Q的紧闭滤子全体Fc(Q)是F(Q)的子Frame．最后,证明了凝聚双侧交换Quantale的紧闭滤子全体在包含序下构成Coherent Frame．     

阻抗式和简单调压室甩荷时水位波动的显式计算方法

目前对调压室水位波动的研究主要有图解法和数值计算。尚未看到考虑阻力项后调压室水位波动随时间变化的显函数计算方法。本文从调压室的基本微分方程出发，采用泰勒级数展开式推导了阻抗式和简单式调压室甩荷时水位波动的显式计算方法。运用这种方法不仅可以计算调压室水位波动的过程，而且可以方便的计算调压室的最高涌浪和第二振幅。     

Mechanics of rubber shear springs

FEA calculations have been carried out for a model rubber shear spring, consisting of a block of a highly elastic material, bonded between two rigid parallel plates and sheared by displacing one of the plates parallel to the other in its own plane. The block was prevented from deforming in the perpendicular direction, and thus was deformed in plane strain. Stress distributions along the bond-line and the center-line are reported and compared with those expected from the theory of large elastic deformations. Unexpected tensile stresses were found to develop in the interior of the sheared block. They are attributed to the absence on the end surfaces of the stresses needed to maintain a simple shear, causing a pronounced change in the reference pressure—a consequence that is usually overlooked. Because the internal stresses are governed by the boundary conditions, they were strongly affected by the shape of the end surfaces. In addition, they were reduced markedly by assigning values to Poisson's ratio slightly lower than 0.5, thus allowing some volume expansion of the rubber. Strain energy release rates were also evaluated for growth of a crack along the bond-line, starting at the edges, and compared with those reported previously by Lindley and Teo [Energy for crack growth at the bonds of rubber springs, Plast. Rubber Mat. Appl. 4 (1979) 29-37], Muhr et al. [A fracture mechanics study of natural rubber-to-metal bond failure, J. Adhes. Sci. Technol. 10 (1996) 593-616], Gregory and Muhr [Stiffness and fracture analysis of bonded rubber blocks in simple shear, in: D. Boast, V.A. Coveny (Eds.), Finite Element Analysis of Elastomers, Professional Engineering Publications, Bury St. Edmunds, UK, 1999, pp. 265-274] and Gough and Muhr [Initiation of failure of rubber close to bondlines, in: Proceedings of the International Rubber Conference, Maastricht, Netherlands, June 2005, IOM Communications Ltd., London, 2005, pp. 165-174]. They confirm that a long crack at the compression edge will grow faster than one at the tension edge, but the results for short cracks were inconclusive.     

On Litoff’s theorem

We give a short proof of Litoff’s theorem from the viewpoint of completely reducible modules.     

Bifurcation and chaos of a simple walking model driven by a rhythmic signal

The walk of animals is achieved by the interaction between the dynamics of their mechanical system and the central pattern generator (CPG). In this paper, we analyze dynamic properties of a simple walking model of a biped robot driven by a rhythmic signal from an oscillator. In particular, we examine the long-term global behavior and the bifurcation of the motion that leads to chaotic motion, depending on the model parameter values. The simple model consists of a hip and two legs connected at the hip through a rotational joint. The joint is driven by a rhythmic signal from an oscillator, which is an open loop. In order to analyze the bifurcation, we first obtained approximate solutions of the walking motion and then constructed discrete dynamics using the Poincaré map. As a result, we found that consecutive period-doubling bifurcations occur as the model parameter values change, and that the walking motion leads to chaotic motion over the critical value of the model parameters. Moreover, we approximately obtained the period-doubling solutions and the critical value by employing a Newton-Raphson method. Our analytical results were verified by the numerical simulations.     

On Quillen?s Theorem A for posets

A theorem of McCord of 1966 and Quillen?s Theorem A of 1973 provide sufficient conditions for a map between two posets to be a homotopy equivalence at the level of complexes. We give an alternative elementary proof of this result and we deduce also a stronger statement: under the hypotheses of the theorem, the map is not only a homotopy equivalence but a simple homotopy equivalence. This leads then to stronger formulations of the simplicial version of Quillen?s Theorem A, the Nerve Lemma and other known results. In particular we establish a conjecture of Kozlov on the simple homotopy type of the crosscut complex and we improve a well-known result of Cohen on contractible mappings.     

A relation-algebraic approach to simple games

Simple games are a powerful tool to analyze decision-making and coalition formation in social and political life. In this paper, we present relation-algebraic models of simple games and develop relational specifications for solving some basic problems of them. In particular, we test certain fundamental properties of simple games and compute specific players and coalitions. We also apply relation algebra to determine power indices. This leads to relation-algebraic specifications, which can be evaluated with the help of the BDD-based tool Rel View after a simple translation into the tool’s programming language. In order to demonstrate the visualization facilities of Rel View we consider an example of the Catalonian Parliament after the 2003 election.     

Ricci Positive Metrics on the Moment-Angle Manifolds

In this paper, the authors consider the problem of which (generalized) moment-angle manifolds admit Ricci positive metrics. For a simple polytope $P$, the authors can cut off one vertex $v$ of $P$ to get another simple polytope $P_{v}$, and prove that if the generalized moment-angle manifold corresponding to $P$ admits a Ricci positive metric, the generalized moment-angle manifold corresponding to $P_{v}$ also admits a Ricci positive metric. For a special class of polytope called Fano polytopes, the authors prove that the moment-angle manifolds corresponding to Fano polytopes admit Ricci positive metrics. Finally some conjectures on this problem are given.     

求解一类二阶段有补偿问题的对偶梯度法

利用对偶理论，本文给出了求解一类具有简单补偿的非线性二阶段问题的新对偶梯度法．在假设目标函数为可分连续可微凸函数的条件下，在每一选代步可将原二阶段有补偿问题转化为几个一维凸规划问题，大大简化了问题的求解．所给算法简单易行，文中还证明了该算法的全局收敛性．