Dynamics of Coupled Cell Networks: Synchrony, Heteroclinic Cycles and Inflation

We consider the dynamics of small networks of coupled cells. We usually assume asymmetric inputs and no global or local symmetries in the network and consider equivalence of networks in this setting; that is, when two networks with different architectures give rise to the same set of possible dynamics. Focussing on transitive (strongly connected) networks that have only one type of cell (identical cell networks) we address three questions relating the network structure to dynamics. The first question is how the structure of the network may force the existence of invariant subspaces (synchrony subspaces). The second question is how these invariant subspaces can support robust heteroclinic attractors. Finally, we investigate how the dynamics of coupled cell networks with different structures and numbers of cells can be related; in particular we consider the sets of possible “inflations” of a coupled cell network that are obtained by replacing one cell by many of the same type, in such a way that the original network dynamics is still present within a synchrony subspace. We illustrate the results with a number of examples of networks of up to six cells.     

Computation of the Coupled Dynamics of Fibers in a Spray

The PUR-fiber-spray molding technology is a manufacturing process which produces polyurethane-based (PUR) composites by spraying the matrix together with reinforcing fibers in a tool form or on a substrate. Thereby chopped fibers are laterally (sidewise) injected in the polyurethane-air spray cone for wetting before the entire composite is spread on the substrate, where it starts curing. To investigate and compute the fiber orientation and density distribution in the final composites manufactured by this process, a new approach simplifying the multiply coupled interaction of the three phases is presented in this paper. Hereby it is presumed that the final position and orientation of a fiber on a substrate results from its dynamics and coupled interactions with air, PUR-droplets and other fibers within the spray cone. Thus, a model of the process is built, that computes the transient behavior of the air-liquid droplets mixture by the CFD code ANSYS Fluent and its influence on the dynamics of the fibers by an extra code called FIDYST. For this multiphase problem two approaches are presented for the droplet-fiber coupling using a concept called “homogenization” of the liquid phase (droplets in the continuous phase). (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

新的双曲函数有理展开法和符号计算构造差分mkdv的孤波解

本文通过利用一个广泛的题设提出一种推广的双曲函数展开法, 并利用此方法求解了 离散的 mKdV 方程, 获得了丰富的显式精确解. 此方法可以用于求其他非线性系统的精确解.     

格群的-Fuzzy子格群的等价刻画及应用

给出-Fuzzy子格群的的几种等价刻画,利用它们得到一些结果。     

A Characterization of Semirings Which Are Subdirect Products of a Distributive Lattice and a Ring

E -inversive semiring and a Clifford semiring and show that a semiring S is a subdirect product of a distributive lattice and a ring if and only if S is an E-inversive strong distributive lattice of halfrings. Further a Clifford semiring which is, in fact, an inversive subdirect product of a distributive lattice and a ring, is characterized as a strong distributive lattice of rings. Finally, as a consequence of these results we extend a result of Galbiati and Veronesi [2] in the case of Boolean semirings.     

用Eaves－Saigal不动点算法求解不可微优化

本文通过修改向量标号改造Ｅａｖｅｓ－Ｓａｉｇａｌ单纯同伦算法为上半连续集值映射零点的同伦算法，并给出了这一算法收敛的条件．最后，应用该方法到不可做优化问题的求解，得到一些收敛性结果．数值结果表明计算效果良好．     

The Cascade Algorithm for the Numerical Computation of Refinable Functions

The cascade algorithm is a method which can be used for the computation of refinable functions. We prove here that in general the cascade algorithm will not inherit the accuracy and refinability of the limit refinable function. We provide conditions for which the cascade iteration does indeed preserve accuracy.     

J-子空间格代数上中心化子和广义导子的刻画

设L是Banach空间X上的J-子空间格,AlgL是相应的(J-子空间格代数.设φ:AlgL→AlgL是可加映射,对每个K∈(J)(L),dimK≥2.该文证明了下列表述等价:(1)φ是中心化子;(2)φ满足AB=0■φ(A)B=Aφ(B)=0;(3)φ满足AB+BA=0■φ(A)B+φ(B)A=Aφ(B)+Bφ(A)=0;(4)φ满足ABC+CBA=0■φ(A)BC+φ(C)BA=ABφ(C)+CBφ(A)=0.作为应用,得到AlgL上在零点广义可导的可加映射的完全刻画.     

格矩阵的行列式与伴随矩阵

研究了格矩阵的行列式与伴随矩阵,给出了它们的一些代数性质,同时给出了由一个格矩阵构造一个传递矩阵的方法.     

Semidefinite Characterization and Computation of Zero-Dimensional Real Radical Ideals

For an ideal I??[x] given by a set of generators, a new semidefinite characterization of its real radical I(V _?(I)) is presented, provided it is zero-dimensional (even if I is not). Moreover, we propose an algorithm using numerical linear algebra and semidefinite optimization techniques, to compute all (finitely many) points of the real variety V _?(I) as well as a set of generators of the real radical ideal. The latter is obtained in the form of a border or Gröbner basis. The algorithm is based on moment relaxations and, in contrast to other existing methods, it exploits the real algebraic nature of the problem right from the beginning and avoids the computation of complex components.     

On Koetter's Algorithm and the Computation of Error Values

In this article, we show that Koetter's algorithm for decoding one-point codes can compute error evaluator polynomials as well. We also show that the error evaluators do not need to be computed. The updating functions used in Koetter's algorithm can be used to compute error values instead.     

The Norm of a Complex Banach Lattice

In this note we study the problem how the complexification of a real Banach space can be normed in such a way that it becomes a complex Banach space from the point of view of the theory of cross-norms on tensor products of Banach spaces. In particular we show that the norm of a complex Banach lattice can be interpretated in terms of the l-tensor product of real Banach lattices.     

The Reflexive Dimension of a Lattice Polytope

The reflexive dimension refldim(P) of a lattice polytope P is the minimal integer d so that P is the face of some d-dimensional reflexive polytope. We show that refldim(P) is finite for every P, and give bounds for refldim(kP) in terms of refldim(P) and k. Received July 2, 2004     

The Matrix of a Slim Semimodular Lattice

A finite lattice L is called slim if no three join-irreducible elements of L form an antichain. Slim semimodular lattices play the main role in G. Czédli and E. T. Schmidt (Algebra Univers, to appear), where lattice theory is applied to a purely group theoretical problem. Here we develop a unique matrix representation for these lattices.     

The Comparability Graph of a Modular Lattice

L of rank is d-connected if there exists a closed interval of rank 3 of L with , where is the M?bius function of L. Received: January 18, 1996