ShuMing Chang^{*}
Department of Mathematics
National Tsing Hua University
Hsinchu, Taiwan
m863254@am.nthu.edu.tw
ChangShou Lin
Department of Mathematics
National ChungCheng University
ChiaYi, Taiwan
cslin@math.ccu.edu.tw
TaiChia Lin
Department of Mathematics
National Taiwan University
Taipei, Taiwan
tclin@math.ntu.edu.tw
WenWei Lin and ShihFeng Shieh
National Tsing Hua University
Hsinchu, Taiwan
wwlin@am.nthu.edu.tw and sfshieh@am.nthu.edu.tw
Abstract : In this paper we propose two iterative methods, a Jacobitype iteration (JI) and a GaussSeideltype iteration (GSI), for the computation of energy states of the timeindependent vector GrossPitaevskii equation (VGPE) which describes a multicomponent BoseEinstein condensate (BEC). A discretization of the VGPE leads to a nonlinear algebraic eigenvalue problem (NAEP). We prove that the GSI method converges locally and linearly to a solution of the NAEP if and only if the associated minimized energy functional problem has a strictly local minimum. The GSI method can thus be used to compute ground states and positive bound states, as well as the corresponding energies of a multicomponent BEC. Numerical experience shows that the GSI converges much faster than JI and converges globally within 10 to 20 steps and discovers a new phenomenon called verticillate multiplying, i.e., the generation of multiple verticillate structures.
Rong Si Chen
Department of Statistics
Fuzhou University
Fuzhou, Fujian, 350002, P.R.China
chenrongsi@fzu.edu.cn
Abstract : A coronoid system is a benzenoid system with a hole, i.e., a nonhexagonal internal face. Several relations between the coefficients of the permanental and characteristic polynomials of benzenoid systems were recently established by Gutman et al.. In this note we investigate relations between the coefficients of the permanental and characteristic polynomials of coronoid systems.
LiZhi Cheng
Department of Mathematics and System Science
National University of Defense Technology
Changsha, Hunan, 410073 P.R. China
clzcheng@vip.sina.com
Abstract : This paper summarizes our recently works related to the construction of integer discrete transforms that includes integer DCTs, DSTs, DWTs, DHT and integer wavelets transforms with parameters, discuss the application of these integer transforms in image processing such as in digital watermarking, information hiding, information disgusising, image superresolution, and finally, we use the combination of wavelet and multigrid method to solve illconditioned systems.
MaoTing Chien
Department of Mathematics
Soochow University
Taipei, Taiwan 11102
mtchien@scu.edu.tw
Abstract : Let C and D be two ellipses on the plane with C inside D. A well known Poncelet's closure theorem asserts that if there is an npolygon inscribed in D and circumscribed about C, then for any point l on D there is a unique such inscribed npolygon having l as one of its vertices. The inside ellipse C is called a Poncelet curve.
The numerical range of a matrix A Î M_{n} is defined as the set W(A) = { x^{*} A x : x Î C^{n}, x = 1 }. Let A Î M_{n} be a completely nonunitary contraction. It is known that the boundary curve of W(A) is a Poncelet curve. We study the Poncelet property arising from the numerical range.
SzeBi Hsu
Department of Mathematics
National Tsing Hua University
Hsinchu, Taiwan
YingHen Hsieh^{*}
Department of Applied Mathematics
National Chung Hsing University
Taichung, Taiwan
hsieh@amath.nchu.edu.tw
Abstract : The Severe Acute Respiratory Syndrome (SARS) epidemic of November 2002 to July 2003 came with much fanfare and left swiftly, resulting in more than 8000 probable cases worldwide and 774 casualties. Many had believe that the simple ageold system of quarantine those individuals suspected of being infected had been instrumental in quick containment of the infections. In this work we propose a differential equations model which includes quarantine and other intenvention measures implemented by the health authority, include those to prevent nosocomial infections and decrease frequency of contacts among general public. We also consider the possible behavior change by the general populance to avoid infection in response to the severity of the outbreak in general, and to these measures in particular. Full analysis is given for the model without quarantine. For the general model with quarantine, basic reproduction number is derived and partial analysis is provided. We will show that introducing quarantine measures in the model could produce bistability in the system, thus changing the basic dynamics of the system. We also give examples where bistable steady states (one diseasefree and the another endemic) exist. The results indicate that the measures will be effective in reducing infections only if the quarantined/isolated SARS patients can successfully reduce their contact rate and/or transmission probabilities for each contact. Hence diligent adherence to the quarantine order by the quarantined individuals is essential to any intevention measures. Moreover, the effectiveness of quarantine for infectious diseases like SARS, for which no infection is being prevented during the quarantine period, can only be indirect and therefore must be combined with other intervention measures in order to fully contain the outbreaks.
Siming Huang
Institute of Policy and Management
Chinese Academy of Sciences
Beijing 100080, China
simhua@mail.casipm.ac.cn
Abstract : We will summerize the results of inverse problems of optimization, both invserse problems of combinatorial optimization and inverse problems of mathematical programming problems. We will discuss its implications in computational complexity theory and more deep implications.
Sanjeev Kumar
Department of Mathematics
Institute of Basic Science, Khandari
Dr. B.R. Ambedkar University, Agra.(India) 282002
sanjeevibs@yahoo.co.in
Abstract : Hemodialysis is a very important phenomenon during the study of the blood, because it removes metabolic wastes uric acid etc. from the blood. The most of the wastes removed during the process are contained in plasma. So to analyze the hemodialysis, one must first understand the flow behavior of the blood in the tubes, therefore, we are considering a twolayered model of the blood flow through a circular tube hemodialyser. Since the viscosity of the plasma layer is less than that of a blood, hence this plasma layer near the wall acts as a natural lubricant for the blood flow. In dialysis, we have flows which have peripheral plasma layer with less red cells. Such flows are called twolayered. Since red blood cells contain an iron compound, so the blood may be considered as a magnetic fluid. It has been already studied that a magnetic field can push red cells away from the hemodialyser membrane. We solved numerically this problem using the finite difference techniques and obtained the result for blood velocity for the different values of pressure force.
ShuMing Chang
Department of Mathematics
National Tsing Hua University
Hsinchu, 300, Taiwan
m863254@am.nthu.edu.tw
YuenCheng Kuo^{*}
Department of Mathematics
National Center for Theoretical Sciences
Hsinchu, 300, Taiwan
m883207@am.nthu.edu.tw
WenWei Lin
Department of Mathematics
National Tsing Hua University
Hsinchu, 300, Taiwan
wwlin@am.nthu.edu.tw
Abstract : We develop a continuation BSORLanczosGalerkin method for the computation of positive bound states of timeindependent, coupled GrossPitaevskii equations (CGPEs) which describe a multicomponent BoseEinstein condensate (BEC). A discretization of the CGPEs leads to a nonlinear algebraic eigenvalue problem (NAEP). The solution curve with respect to some parameter of the NAEP is then followed by the proposed method. For a singlecomponent BEC, we prove that there exists a unique global minimizer (the ground state) which is represented by an ordinary differential equation with the initial value. For a multicomponent BEC, we prove that m identical ground/bound states will bifurcate into m different ground/bound states at a finite repulsive intercomponent scattering length. Numerical results show that various positive bound states of a two/threecomponent BEC are solved efficiently and reliably by the continuation BSORLanczosGalerkin method.
Chunhui Lai
Department of Mathematics
Zhangzhou Teachers College, Zhangzhou
Fujian 363000, P. R. of China
zjlaichu@public.zzptt.fj.cn
Abstract : A sequence S is potentially K_{p,1,1} graphical if it has a realization containing a K_{p,1,1} as a subgraph, where K_{p,1,1} is a complete 3partite graph. Let s(K_{p,1,1}, n) denote the smallest degree sum such that every nterm graphical sequence S with s(S) ³ s(K_{p,1,1}, n) is potentially K_{p,1,1} graphical. In this paper, we prove that s(K_{p,1,1}, n) ³ (p+1)(n1)+1 for p and n are all even; s(K_{p,1,1}, n) ³ (p+1)(n1)+2 for p is even but n is odd; s(K_{p,1,1}, n) ³ (p+1)(n1)+2 for p is odd. We conjectured that equality holds for n ³ 2p+4. We proved that this conjecture is true for p = 3, n ³ 7.
^{f} Project Supported by NNSF of China(10271105), NSF of Fujian, Science and Technology Project of Fujian, Fujian Provincial Training Foundation for ``BaiQuanWan Talents Engineering" , Project of Fujian Education Department and Project of Zhangzhou Teachers College.
Yicheng Liu and Zhixiang Li^{*}
Department of Mathematics and System Science,
Science School, National University of Defence Technology
Changsha, 410073, P.R. China
liuyc2001@hotmail.com
Abstract : Motivated by generalizing the principle of contraction mapping in complete metric space, Boyd and Wong[2] and Burton[5] introduced a class of contraction mapping respectively, and showed two useful fixed point theorems. In this paper, we introduce the concept of property L and obtain several fixed point results which were generalization of Boyd and Wong's [2] and Burton's [5]. As an application, some existence results of positive almost periodic solution are obtained, which extend the corresponding results in [6], [8].
Key words: Fixed point theorem, Almost periodic solution, Delay integral equation.
2000 Mathematics Subject Classification: 34K14, 47H10
Feng Ling
Department of Computer Science
Zhaoqing University
Zhaoqing, Guangdong, 526061, P. R. China
lingf@zqu.edu.cn
Abstract : This study discusses the solution of the following equations:

where
 (1) 
 (2) 
 (3) 
 (4) 
 (5) 
 (6) 
 (7) 
 (8) 
 (9) 
 (10) 
The temperature, T(x,t), as a function of depth and time, is found from a knowledge of the periodically varying surface temperature and the thermal parameters of a stratified medium. The applications of this approximate method to some problems in the geoscience also are discussed.
Qun Luo
Department of Mathematics
Zhaoqing University
Zhaoqing, Guangdong 526061, P.R.China
luoqun@zqu.edu.cn
Abstract : In this paper, in topological ordered spaces, we obtain Ky Fan's section Theorem and discuss its applications.
Ky Fan's section Theorem Let X be a nonempty L convex subset of a topological semilattice with pathconnected intervals M, and C Ì X ×X:
LiQuan Mei
School of Science
Xi'an Jiaotong University
Xi'an, 710049, P.R.China
lqmei@mail.xjtu.edu.cn
Abstract : Small changes in parameters, load
cases or model specifications for crash simulation may result in
huge changes in the results, characterizing the crash behavior of
an automotive design. For a BMW model differences between the
position of a node in two simulation runs of up to 10 cm were
observed, just as a result of roundoff differences in the case of
parallel computing. The paper shows that numerical properties of
the simulation codes as well as bifurcations in the crash behavior
in the certain parts of the design are reasons for scatter of
simulation results. The tool DIFFCRASH compares simulation
results and uses data mining technology to cluster those nodes of
the car model, which show similar scatter among the simulation
runs and then trace back to a certain part to remove the uncertain
behavior. DIFFCRASH is the only activity using data mining
technology for crash simulation stability analysis.
Keywords: Uncertainty analysis, Crash Simulation, Data
Mining, Clustering.
^{f} This project was funded by the German Ministry for Education and Research(BMB+F)
Mikhail Kovalyov
Department of
Mathematics
University of Alberta
Edmonton, AB,
T6G 2G1, Canada
mkovalyo@ualberta.ca
Abstract : The Heisenbeg uncertainty principle was obtained by Heisenberg and Bohr alomst a century ago in the context of quantum mechanics, its mathematical formulation based on Fourier transform followed a few years later. We show that a rather large class of nonlineaar waves obtained as solutions of KdV satisfies a remarkably simmilar uncertainty principle
XiaoYuan Qian
Department of Applied Mathematics
Dalian University of Technology
Dalian, China 116024
xyqian@vip.sina.com
Abstract : In this paper we propose an algorithm which is applied to reconstruct surfaces from scattered point data. Given a set of unorganized points sampled from a surface with boundary, even possibly nonorientable, the algorithm is applied to automatically reconstruct a topologically correct surface in the form of a piecewiselinear model.
YungLing Lai and DingTai Ron^{*}
Department of Computer Science and Information Engineering
National Chiayi University
Chaiyi, Taiwan
yllai@mail.ncyu.edu.tw, jacky@mail.csie.ncyu.edu.tw
Abstract : In some festival or big party, when there were a huge amount of users using mobile phone, it happens very often that either it is too busy in the GSM Network so one can not dial out or easy to get disconnection while talking to another mobile user. Setting some base stations to enhance the mobile communication in the busy communication region is a reasonable solution. In the GSM Network the communication between two nonadjacent stations will transited through a shortest path. When the stations on the path is busy, the signal may consider go through another path which is longer than the original path. Then there is dilation in the network of the transition. A GSM network can be represented by a graph G = (V,E) where the vertices indicate the base stations and the edges denote the adjacency between base stations. Then, the bandwidth of G represents the dilation of the network and adding an additional vertex v¢ on edge (u,v) , which is known as an elementary refinement operation to graph G, is the same as adding a base station between two adjacent base stations. In this paper, we present some results by applying the elementary refinement operation to the edges on the caterpillar graphs.
YuenCheng Kuo
Department of Mathematics,
National Tsing Hua University
Hsinchu, 300, Taiwan
d883207@oz.nthu.edu.tw
WenWei Lin
Department of Mathematics
National Tsing Hua University
Hsinchu, 300, Taiwan
wwlin@am.nthu.edu.tw
ShihFeng Shieh^{*}
Department of Mathematics
National Tsing Hua University
Hsinchu, 300, Taiwan.
sfshieh@am.nthu.edu.tw
Abstract : In this paper, we prove that the solution curve of the ground/positive bound states of a twocomponent BoseEinstein condensate has a supercritical pitchfork bifurcation at some finite values of the intercomponent scattering length. The ground state solutions will bifurcate into two symmetric solutions with respect to some suitable axis on the symmetric domain, when two components of BEC has equal intracomponent scattering lengths. Furthermore, we show that the ground/positive bound states repel each other and form segregated nodal domain when the repulsive scattering length goes to infinity.
Jun Wang, Fangyu Sun^{*}, Bangti Jin
Department of Mathematics
Zhejiang University
Hangzhou
310027, P.R. China
fysun@sun.zju.edu.cn
Abstract : In this paper, we consider the application of the method of fundamental solutions for the numerical solution of a threedimensional inverse problem in linear elasticity, i.e., Cauchy problems associated with Navier equations. Regularization methods are the most efficient and powerful methods for illposed problems, and two regularization methods, i.e., Tikhonov regularization method and truncated singular value decomposition, are employed to solve the system of Linear equations arising from the method of fundamental solutions, with the regularization parameter determined by the Lcurve method. Numerical experiments indicate that the method proposed can yield stable, accurate solutions for the inverse problem, and both the two regularization methods have high accuracy.
Key words: Method of fundamental solutions, Cauchy problem, Regularization, Linear elasticity, Inverse problem.
QuanFang Wang
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
Beijing 100080, P. R. China
wang@amss.ac.cn
Abstract : Recent development of control theory cause the rapidly research of numerical approximation for controlled systems. This work is to address numerical approximation of optimal control for nonlinear damped kleinGordon equations. We implement three processes to achieve prospective purpose.
(a). Present theoretical results on optimal control based upon variational method thanks to J. L. Lions.
(b). Construct a semidiscrete algorithm to solve nonlinear control state system and adjoint system based on finite element approach.
(c). Implement numerical approximation to get optimal control and optimal state by minimizing the quadratic cost functions.
Furthermore, error estimation and necessary optimality condition are verified the effectiveness of our scheme. As our future work, the proposed approximation can be applied to a wide class nonlinear control systems arising in real world.
WeiZhi Wu
Information College
Zhejiang Ocean University
Zhoushan, Zhejiang, 316004, P. R. China
wuwz@zjou.net.cn
Abstract : The theory of rough sets, proposed by Pawlak in 1982, is an extension of set theory for the study of intelligent systems characterized by insufficient and incomplete information. Using the concepts of lower and upper approximations in rough set theory, knowledge hidden in information systems may be unravelled and expressed in the form of decision rules. The basic operators in rough set theory are approximations. There are at least two approaches for the development of the rough approximation operators, the constructive and axiomatic approaches. This paper discusses a general framework for the study of rough approximation operators within which both constructive and axiomatic approaches are used. In the constructive approach, various pairs of lower and upper rough approximation operators are defined. Basic properties of rough approximation operators are investigated. The connections between binary relations and rough approximation operators are further established. In the axiomatic approach, operatororiented characterizations of rough approximation operators are proposed, that is, approximation operators are defined by axioms. Different axiom sets of upper and lower settheoretic operators guarantee the existence of different types of binary crisp or fuzzy relations which produce the same operators.
Keywords: Approximation operators; Binary relations; Fuzzy sets; Fuzzy rough sets; Rough fuzzy sets; Rough sets.
Xiaowei Yang^{*}
Department of Applied Mathematics
South China University of Technology
Guangzhou 510640, P. R. China
xwyang@scut.edu.cn
Zhifeng Hao
Department of Applied Mathematics
South China University of Technology
Guangzhou 510640, P. R. China
mazfhao@scut.edu.cn
Shu Yu
College of Computer Science and Engineering
South China University of Technology
Guangzhou 510640, P. R. China
Yu_{}shu@126.com
Abstract : Support vector machine (SVM) is a powerful new tool for data classification and function estimation. The training problem in SVM is equivalent to solve a linearly constrained convex quadratic programming (QP) problem with a number of variables equal to the one of data points. This optimization problem is known to be challenging when the number of data points exceeds a few thousands. In order to speed up learning and apply SVM into the practice, the algorithms for online learning based on SVM have been researched. In this paper, these algorithms are reviewed in detail and the future work is also given.
XiaoMing Zeng
Department of Mathematics
Xiamen University
Xiamen, 361005,
China
xmzeng@jingxian.xmu.edu.cn
Abstract : Loop subdivision surfaces is a very popular subdivision scheme for triangular meshes. It is known that Loop subdivision scheme is an approximating subdivision scheme. Using Loop subdivision rules any triangular mesh can be refined. In the limit of an infinite number of subdivisions a smooth surface is obtained. Then, how well is the rate of convergence of control meshes? The aim of this paper is to give the theoretical analysis to this problem. we estimate the rate of convergence of control meshes of Loop surfaces by means of the first order difference of control points. We prove that the control meshes converge to the limit surface at an exponential rate. Our estimate is the optimum. In addition, as an application of our estimate we give a computational formula of subdivision depth for Loop subdivision surfaces by means of the bound of KobbeltDaubertSeidel.
Kewen Zhao
Department of Mathematics
Qiongzhou University
Wuzhishan,572200
Hainan, P.R.China
Kewen@bxemail.com
Abstract : Let G be a simple graph of order n ³ 3. We denote by d(x), N(x), respectively, the degree number and the neighborhood of x in G. And we denote by a, d, respectively, the independent number and the minimum degree of G.
In 1952 Dirac [1] obtained the classical result of Hamiltonian:
Theorem A^{[1]}: Let G be a graph of order n ³ 3, if d ³ /2, then G is Hamiltonian.
In 1960 Ore [2] generalized the above result of Dirac as follow:
Theorem B^{[2]}: Let G be a graph of order n ³ 3, if d(x)+d(y) ³ n for each pair of nonadjacent vertices x,y, then G is a Hamiltonian.
In 1984 Fan [3] generalized the above results:
Theorem C^{[3]}: Let G be a 2connected graph of order n ³ 3, if max {d(x),d(y)} ³ n/2 for each pair vertices x,y of d(x,y) = 2, then G is Hamiltonian.
In 1991 Faudree et al [4] considered neighborhood unions condition and obtained:
Theorem D^{[4]}: G is 2connected graph of order n ³ 3 and, if N(x) ÈN(y) ³ n  d for each pair nonadjacent vertices x,y Î V(G), then G is Hamiltonian.
Theorem E^{[4]}: Let G be a 2connected graph of order n ³ 19 , if N(x) ÈN(y) ³ (2n+5)/3 for each pair nonadjacent vertices x,y, then G is pancyclic.
In 1994 we [5] improved the Theorem E of Faudree et alas follow:
Theorem F^{[5]}: Let G be a 2connected graph of order n ³ 18, if N(x) ÈN(y) ³ (2n+4)/3 for each pair nonadjacent vertices x,y, then G is pancyclic.(MR 96B:05093 by Faudree RJ).
Now, In this Abstract we show the follow progress on Theorem EF:
Theorem 1: Let G be a 2connected graph of order n ³ 10, if N(x) ÈN(y) ³ (2n3)/3 for each pair nonadjacent vertices x,y, then G is pancyclic.
In 1993 Prof. Guantao Chen (Georgia State University)[6] generalized the Fan type condition of Theorem C as follow:
Theorem G^{[6]}: Let G be a 2connected graph of order n ³ 3, if max{d(x),d(y)} ³ n/2 for each pair vertices x,y with satisfying 1 £ N(x)ÇN(y) £ a1, then G is Hamiltonian.
In 1996 Prof. Guantao Chen, Egawa,Liu X and Saitoet al [7] generalized above results of Theorem AC:
Theorem H^{[7]}: If G is a kconnected (k ³ 2) graph of order n, and max{ d(v),v Î S } ³ n/2 for every independent set S of order k with exist two distinct vertices x,y in S satisfies d(x,y) = 2, then G is Hamiltonian.
Now, in this Abstract we generalize the above results of Theorem AC and Theorem GH as follow:
Theorem 2: If G is a kconnected (k ³ 2) graph of order n, and max{ d(v),v Î S } ³ n/2 for every independent set S of order k which two distinct vertices x,y in S satisfies 1 £ N(x) ÇN(y) £ a1, then G is Hamiltonian.
And we generalize Theorem AD and Theorem G as follow:
Theorem 3: G is 2connected graph and, for each pair vertices x,y Î V(G) with 1 £ N(x) ÇN(y) £ a1, max{d(x),d(y)} ³ n/2 or N(x) ÈN(y) ³ nd, then G is Hamiltonian.
Reference
[1] Dirac GA, Some theorems on abstract graphs. Proc. London Math.Soc.2 (1952) 6981.
[2] Ore.O, Note on Hamiltonian circuits. Amer.Math.Monthly 67(1960) 55.
[3] Fan GH, New sufficient conditions for cycles in graphs. J.Combin.Theory Ser.B 37(1984) 221227
[4] Faudree RJ, Gould RJ, Jacobson MS and Lesniak L, Neighborhood unions and highly Hamilton graphs. Ars Combinatoria 31( 1991) 139148.
[5] Kewen Zhao, Neighborhood condition for pancyclic graphs.Proceedings of the Third ChinaUSA international conference on Graph Theory,Combinatorics, Algorisms and Applications. World Scientific Publishing.Co Pte Ltd 1994,233240.
[6] Chen GT, Hamiltonian graphs involving neighborhood intersections. Discrete Math.112 (1993) 253258.
[7] Chen GT, Egawa Y,Liu X and Saito A, Essential independent set and Hamiltonian cycles. J.Graph Theory 21(1996) 243250
[8] Gould RJ, Advances on the Hamiltonian problemA survey. Graph and Combin. 19(2003) 752.