Yung-Ling Lai and Ting-Jiyun Ke

Department of Computer Science and Information Engineering

National Chiayi University

Chiayi, Taiwan

yllai@mail.ncyu.edu.tw, s0930317@mail.ncyu.edu.tw

**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.

Jin-Rong Liang

Department of Mathematics

East China Normal University

Shanghai, 200062, P. R. of China

jrliang@math.ecnu.edu.cn

**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).

Yin-Heng Lin

Department of Applied Mathematics

National Chiao Tung University

Hsinchu 300, Taiwan

yhlin.am91g@nctu.edu.tw

J.-W. He

Institute of Mathematics

Fudan University

Shanghai 200433, China

jiweihe@163.com

Di-Ming Lu^{*}

Department of Mathematics

Zhejiang University

Hangzhou 310027, China

dmlu@zju.edu.cn

**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(A^{op}) is a reduced (2,p)-algebra and generated
by E^{1}(A^{op}). The (2,p)-algebra structure of the Koszul dual
E(A^{op}) 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.

Jun Luo

School of Mathematics and Computing Science

Zhongshan University

Guangzhou 510275, China

mcsluoj@zsu.edu.cn

**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 Ì **C** is
locally connected if and only if A(p,r,R)\M have at
most finite nay components touching the two circles C_{p}(r): = {z:|z-p| = r} and C_{p}(R) at the same time for every annulus
A(p,r,R): = {z: r < |z-p| < R} centered at p Î 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 {U_{i}} is
a infinite collection of disjoint simply connected regions in the
extended complex plane [^(**C**)]. Then the complement of
their union È_{i}U_{i} is locally connected if and only if
every boundary ¶U_{i} is locally connected and the
diameter sequence |U_{i}| 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 MÇN
is locally connected if and only if both M and N are. (Here,
every Euclidean space **R**^{n} is unicoherent, i.e. the
common part of two closed connected sets M,N with MÈN = **R**^{n} is also connected.)

**Principle of Adding Holes**. Suppose that
M Ì **C** is a locally connected continuum and that
{U_{k}} is the family of all the components of the complement
**C**\M. Then the union of M with an arbitrary
number of U_{k}'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
{f_{k}}_{k = 1}^{q} 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.

Che-Man Cheng and Xiao-Qing Jin

Department of Mathematics

University of Macau,

Macao SAR, China.

fstcmc@umac.mo and xqjin@umac.mo

Vai-Kuong Sin^{*}

Department of Electromechanical Engineering

University of Macau

Macao SAR, China.

vksin@umac.mo

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

Boting Yang^{*}

Department of Computer Science

University of Regina, Canada

boting@cs.uregina.ca

Danny Dyer

Department of Mathematics

Simon Fraser University, Canada

tddyer@sfu.ca

Brian Alspach

Department of Mathematics and Statistics

University of Regina, Canada

alspach@math.uregina.ca

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

File translated from T

On 09 Dec 2004, 09:47.