Poster Presentation An Application of Graph Coloring on Traffic Management

Yung-Ling Lai and Ting-Jiyun Ke
Department of Computer Science and Information Engineering
National Chiayi University
Chiayi, Taiwan,

Abstract : When drive in town, every driver like to be able to go through the crossroad as smooth as possible. How to control the traffic signal in order to let all vehicle pass through the intersection safely and smoothly is an important issue. This paper provide a solution for traffic lights control problem by using graph coloring. We propose a graph structure to represent the traffic map. By apply graph vertex-coloring algorithm to our graph structure, it will reduce the traffic lights one can hit in the whole route and be able to shorten the time that the vehicle needs to wait on the traffic light.

Synchronous Behavior of Fixational Eye Movements

Jin-Rong Liang
Department of Mathematics
East China Normal University
Shanghai, 200062, P. R. of China

Abstract : Phase synchronization and cross correlation among four components of fixational eye movements of both eyes are studied. Comparison between synchronization technique and cross correlation is given. (Four components denote horizontal and vertical movement components of both eyes).

Patterns Generation and Transition Matrices in Higher Dimensional Lattice Models

Yin-Heng Lin
Department of Applied Mathematics
National Chiao Tung University
Hsinchu 300, Taiwan

Abstract : The aim of this paper is to study the pattern generation problems for more symbols on larger lattice with edge 2l in d-dimensional models, d 3. Defining orderings for pattern U on S2l×2l××2l on Z2l×2l××2l Zd+1 enable us to derive simple recursion formulas for generating ordering matrices and the corresponding transition matrices. Furthermore, the spatial entropy can be computed through the maximum eigenvalue of transition matrices.

Higher Koszul Algebras and A-infinity Algebras

J.-W. He
Institute of Mathematics
Fudan University
Shanghai 200433, China

Di-Ming Lu*
Department of Mathematics
Zhejiang University
Hangzhou 310027, China

Abstract : We study a class of A-algebras, named (2,p)-algebras, which is related to the class of p-homogeneous algebras, especially to the class of p-Koszul algebras. A general method to construct (2,p)-algebras is given. Koszul dual of an elementary algebra is defined in terms of A-algebra. It is proved that a p-homogeneous algebra A is p-Koszul if and only if the Koszul dual E(Aop) is a reduced (2,p)-algebra and generated by E1(Aop). The (2,p)-algebra structure of the Koszul dual E(Aop) of a p-Koszul algebra A is described explicitly. A necessary and sufficient condition for a p-homogeneous algebra to be a p-Koszul algebra is also given when the higher multiplications on the Koszul dual are ignored.

A revisit to local connectivity problems in the plane

Jun Luo
School of Mathematics and Computing Science
Zhongshan University
Guangzhou 510275, China

Abstract : This note considers basic facts on local connectivity of continua in the plane, and tries to find possible applications to particular fractals in C of interest, like tiles and their boundaries. Our first aim is to obtain a criterion for conitnua (compact connected sets) in C to be locally connected. As a metric continuum is locally connected if and only if it is a curve[Whyburn], i.e. the image of the interval [0,1] under some continuous mapping, what we are discussing in this paper is to decide when a particular continuum/fractal is a curve.

Main Theorem .     A continuum M C is locally connected if and only if A(p,r,R)\M have at most finite nay components touching the two circles Cp(r): = {z:|z-p| = r} and Cp(R) at the same time for every annulus A(p,r,R): = {z: r < |z-p| < R} centered at p M.

Our second aim is to show some interesting fundamental facts, which can in some sense be related to structure of tiles and quadratic Julia sets.

Principle of Digging Holes.     Suppose that {Ui} is a infinite collection of disjoint simply connected regions in the extended complex plane [^(C)]. Then the complement of their union iUi is locally connected if and only if every boundary Ui is locally connected and the diameter sequence |Ui| converges to zero. (Here, the necessary part consisting of Torhorst Theorem [Whyburn] and a Schönflies condition [Kuratowski].)

Local Connectivity and Unicoherence.    If two connected closed sets M,N cover C, the common part MN is locally connected if and only if both M and N are. (Here, every Euclidean space Rn is unicoherent, i.e. the common part of two closed connected sets M,N with MN = Rn is also connected.)

Principle of Adding Holes.    Suppose that M C is a locally connected continuum and that {Uk} is the family of all the components of the complement C\M. Then the union of M with an arbitrary number of Uk's is still a locally connected continuum.

Our third aim is to answer a question from recent studies on topological property of tiles, or attractors of general IFS's.

Boundary Structure of a Plane Tile.    Suppose that {fk}k = 1q is an IFS consisting of injective contractions on the plane which satisfies the open set condition. If the attractor T is connected, then its boundary T is a locally connected continuum.

Stability of T. Chan's Preconditioner from Numerical Range

Che-Man Cheng and Xiao-Qing Jin
Department of Mathematics
University of Macau,
Macao SAR, China. and

Vai-Kuong Sin*
Department of Electromechanical Engineering
University of Macau
Macao SAR, China.

Abstract : A matrix is said to be stable if the real parts of all the eigenvalues are negative. In this paper, for any matrix An, we discuss the stability properties of T. Chan's preconditioner cU(An) from the viewpoint of the numerical range. An application in numerical ODEs is also given.

Sweeping Graphs with Recontamination

Boting Yang*
Department of Computer Science
University of Regina, Canada

Danny Dyer
Department of Mathematics
Simon Fraser University, Canada

Brian Alspach
Department of Mathematics and Statistics
University of Regina, Canada

Abstract : In this poster, we show that recontamination may reduce the sweep numbers for some sweep models.

File translated from TEX by TTH, version 2.00.
On 09 Dec 2004, 09:47.