Current Issue

Previous Issue | Next Issue

July 15,2010
Volume 3,Issue 13
Pages 1299-1417
Subject Area:Fractal Geometry,Elliptic Partial Differential Equations,Fuzzy Mathematics,Applied Mathematics,Graph Theory,Dynamical System,Decision Theory,Harmonic Analysis

Title: Threshold autoregressive model about year catches of ermine

Authors: HUANG Wenxian
PP: 1411～1417
Abstract: This paper analyses the nonlinear data of year catches of ermine and sets up a threshold autoregressive model SETAR(2;3;10.778 8) with R language and Eviews 3.1. To estimate the parameter of the model SETAR(l; d; r1, r2, …, rl-1), it uses the dot value map, range of local search, Akaike information criterion (AIC) to estimate the l, d, r1, r2,…, rl-1 respectively. These estimate methods greatly reduce the complexity of the algorithm, and model s results can explain very well the law of survival of lynx in a stable state, such as survival cycle, sexual maturity. Model's results show that such a threshold autoregressive parameter estimation method is effective and practical.
Keywords: time series analysis; threshold autoregression; non linear; dot value; range of local search; Akaike information criterion

Title: The relationship of graphics dimension between fractal interpolation function and its fractional calculus

Authors: LIANG Yunyun
PP: 1405～1410
Abstract: This paper gives the iterated function systems (IFS) of Riemann Liouville (R L) fractional calculus of fractal interpolation function (FIF) using the FIF s iterated function systems, and discusses the relationship of graphics dimension between FIF and its fractional calculus. The conclusion is as follows: dimB(ΓD-νf)=dimB(Γf)-ν, dimB(ΓDμf)=dimB(Γf)+μ, namely fractional integration can reduce the dimension and fractional differential can increase the dimension.
Keywords: fractal interpolation; iterated function systems; fractional calculus; graphics dimension

Title: The existence of solution for p Laplacian quasilinear elliptic equation with nonlinear boundary conditions and Dirichlet boundary condition

Authors: ZHANG Hongyan, ZHAO Peihao
PP: 1395～1404
Abstract: Firstly, the paper considers the existence of solution for p Laplacian equation with a Dirichlet boundary conditions, and shows that this problem has two positive solutions. Secondly, it considers the existence of solution for p Laplacian equation with nonlinear boundary conditions, and shows that this problem has at least one nontrivial weak solution.
Keywords: functional analysis； quasilinear elliptic equation; critical exponent; the multiple solutions; nonlinear boundary condition; nontrivial weak solution

Title: Positive solutions of elliptic equations with nonlinear boundary conditions

Authors: SONG Xiuchao, ZHENG Mingfa, LIANG Guohong, LIU Guangrong, XU Yayi
PP: 1390～1394
Abstract: This paper deals with the existence of positive solution of elliptic equation with nonlinear boundary condition in a smooth bounded domain in 瘙} n.Assuming the existence of a positive supersolution, and 0 is a subsolution, then a nondecreasing sequence is obtained. The existence result is obtained by the maximum principle, unique solvability of the linear Robin problem and Newton’s method of iteration.
Keywords: elliptic equation; positive solution; nonlinear boundary condition; super, sub solution; Newton’s method of iteration

Title: The classification and improvement of similarities based on Vague mathematics

Authors: CUI Yinge, DENG Sien, GUO Zhuanna
PP: 1384～1389
Abstract: The paper studied on the system of axioms of similarities according to two levels. Firstly, it makes a classification and improvement of the traditional system of axioms. Secondly, it discusses on the Vague set, and adds some new criterions into the axiom system. In addition, it makes an analysis and comparison on each factor. Furthermore, it sets some examples to show the disadvantages.
Keywords: fuzzy mathematics; similarity; method summary; true or false membership grade

Title: A class of H1N1 dynamic model and its stability analysis

Authors: LIU Lele, ZHANG Juan, YANG Xiaozhong
PP: 1377～1383
Abstract: In this paper, the dynamic model of the spread of H1N1 influence is proposed and analyzed. The basic reproduction number R0 is obtained, which determines whether the disease dies out or remains endemic. If R0 is less than 1, there only exists one disease free equilibrium point, which glueally is asymptotically stable, the H1N1 influence will die out; and if R0 is greater than 1, there exists one stable endemic equilibrium point except for the disease free equilibrium point, the disease will not become die out but remain endemic. The results show that quarantine measures are effective for the control of the H1N1 spread.
Keywords: biomathematics; H1N1 epidemic model; equilibrium; stability

Title: Global attractivity of a class of nonlinear delay equations on time scales

Authors: LI Hongjuan, ZHOU Zhan
PP: 1365～1376
Abstract: This paper studied the global attractivity of the zero solution for a class of nonlinear delay dynamic equations with the 3/2 stability method. Basic theory on time scales and a series of important inequalities are used. Through calculation and reasoning, modifying the conditions of the original theorem and related lemmas, some new sufficient conditions are obtained, which improve the corresponding conclusions in the original literature. Also, some errors in the proofs of the main results of the related literature are corrected. The results unify the discrete and continuous cases according to the characteristics of time scales.
Keywords: applied mathematics; global attractivity; nonlinear dynamic equations; delay; time scales

Title: Absolute ruin in the compound Poisson risk model with threshold dividend strategy

Authors: LI Wenting, NIU Mingfei
PP: 1355～1364
Abstract: The paper investigated the absolute ruin problem in the compound Poisson risk model with threshold dividend strategy. The integro differential equations for the expected discounted value of all dividends until absolute ruin and expected discounted penalty function are first derived. In the case of exponential claim amounts, the explicit expressions for expected discounted penalty function m(u; b) and absolute ruin probability ψ(u; b) are obtained.
Keywords: insurance mathematics; absolute ruin; Gerber Shiu discounted penalty function; threshold dividend strategy; integro differential equation; the expected discounted dividend payments

Title: A sufficient conditions for a planar graph of maximum degree six to be class 1

Authors: ZHOU Zhengtong, MIAO Lianying
PP: 1348～1354
Abstract: Let G be a planar graph of maximum degreeΔ， G is said to be class 1 if χ′(G)=Δ and class 2 if χ′(G)=Δ+1， where χ′(G)denotes the chromatic index of G. In 1965, Vizing proved that every planar graph of maximum degree at least eight is of class 1, and presented examples of planar graphs of class 2 for Δ∈{2,3,4,5}， and conjectured that the conclusion holds for the 6≤Δ≤7 case.By applying a discharg method， we proved that every simple planar graph G with Δ=6 is of class 1， if G contains no any 7 cycle
Keywords: graph theroy； planar graph; edge coloring; maximum degree; cycle

Title: A routing solution of ECn

Authors: SUN Kaiguang, WANG Yan
PP: 1342～1347
Abstract: The routing problem is a very important part in interconnection networks. This paper gives out all the node disjoint shortest paths (NDSP) between any two nodes in ECn showing that it is optimal in sense of its maximum possibility of NDSP which means one could get all the node disjoint shortest paths between any two nodes in ECn for its vertex transitivity.
Keywords: graph theroy; routing; node disjoint shortest path; Cayley graph

Title: Periodic and subharmonic solutions for discrete nonlinear equations with Jacobi operators

Authors: SHI Haiping1, LIU Zhongzhi1, ZHANG Hongqiang
PP: 1336～1341
Abstract: In this paper, by using the notable mountain pass lemma of critical point theory, some sufficient conditions for the existence and multiplicity of periodic and subharmonic solutions to a class of second order nonlinear functional difference equations with Jacobi operators are obtained. The proof is based on the mountain pass lemma in combination with variational technique. The problem gives a practicable method to solve the existence and multiplicity of periodic and subharmonic solutions of second order forward and backward functional difference equations.
Keywords: dynamic system; periodic and subharmonic solutions; mountain pass lemma; Jacobi operators; discrete variational theory

Title: Methods of uncertain linguistic multiple decision making based on quadratic programming

Authors: YANG Yang, WU Guangmou, DING Dechen
PP: 1330～1335
Abstract: The paper studies multiple attribute decision making, in which the information about attribute weight is unknown completely and the attribute values take the form of uncertain linguistic variables. Operational laws of uncertain linguistic variables and a formula of possibility degree for the comparison between uncertain linguistic variables were introduced. The concept of deviation degree between uncertain linguistic variables was defined. A quadratic programming model was developed, which could be used to determine the attribute weights. The uncertain linguistic weighting average (ULWA) operator was utilized to aggregate the uncertain linguistic variables corresponding to each alternative. A possibility degree matrix (complementary judgment matrix) was constructed by the formula of possibility degree. The alternatives were ranked by using the priority formula of complementary judgment matrixes and the most desirable one(s) was selected. Finally, an illustrative example was given to high light the procedure of the proposed algorithm.
Keywords: decision making theory; multiple attribute decision making; uncertain linguistic variables; quadratic programming; possibility

Title: Adaptive NN control for a class of large scale stochastic systems with time delays

Authors: LI Jing， LI Junmin
PP: 1322～1329
Abstract: A design scheme to the decentralized adaptive neural network (NN) output feedback control is proposed for a class of large scale stochastic nonlinear systems with time delays by virtue of nonlinear observer, neural network and backstepping techniques. The requirement for nonlinear time delay interconnections of the systems is relaxed. The whole closed loop system can be proved to be asymptotically stable in probability by constructing an overall state quartic and parameter quadratic Lyapunov Krasovskii functional. The simulation results demonstrate the effectiveness of the proposed control scheme.
Keywords: control theory; adaptive control; neural network; output feedback decentralized stabilization; large scale stochastic nonlinear time delay systems; nonlinear observer

Title: Ruin probability of perturbed inhomogeneous Poisson risk model

Authors: LIU Junfeng, ZHANG Nan
PP: 1317～1321
Abstract: This paper developed and investigated an inhomogeneous Poisson risk model perturbed by a Brownian motion based on classic risk model, where the arriving number of the premium income is assumed to be a inhomogeneous Poisson process and there exist two kinds of claims in this model. From the discussion for this new risk model, a general formula of upper bound for the ruin probability is obtained by martingale approach.
Keywords: probability theory; ruin probability; risk model; stochastic premium; martingale

Title: Asymptotic growth of bisexual Galton Watson branching processwith population size dependent mating in varying environments

Authors: CUI Qiaofen
PP: 1312～1316
Abstract: The model of bisexual Galton Watson branching processes with population size dependent mating in varying environments is introduced. In this model, offspring distribution is no longer independent and identically distributed but conditioned by varying environments. The asymptotic growth problems of mating unit{Zn}∞n=0, female{Fn}∞n=0 and male{Mn}∞n=0 sequences with the branching process, as well as the equivalent relationship between the three convergences are discussed.
Keywords: probability theory; bisexual branching process; mating function; varying environment; asymptotic growth

Title: A class of quartic algebraic curves homoclinic cycles of quadratic system

Authors: NI Chunxia, HUANG Meihua, LI Xuepeng
PP: 1304～1311
Abstract: Calculating by Mathematica software, the paper was devoted to the quartic invariant algebraic curves in quadratic system and the stability of equilibrium was discussed. The nonexistence of the limited orbit was proved by using the method of Dulac function. The paper obtained sufficient and necessary condition such that the homoclinic cycle of the system was defined by the isolation of closed branch, and the corresponding global phase was drawn.
Keywords: fundamental mathematics; uadratic system; algebra invariant; homoclinic

Title: Boundedness of operators in generalized Morrey spaces on homogeneous spaces

Authors: ZHU Jianbao, LIU Mingju
PP: 1299～1303
Abstract: Homogeneous space is a natural underlying space when singular integral operators are studied, which is very important to study the local behavior of solutions to second order elliptic partial differential equations. The main result of this paper is to give a sufficient condition which sublinear operators and commutators generated by BMO functions and linear operators are bounded from generalized Morrey spaces Lp(X) to Lq(X). Some results have been obtained and the results in this paper improve and extend the known results.
Keywords: fundamental mathematics; harmonic analysis; homogeneous spaces; generalized Morrey spaces; sublinear operator; commutator

Alert Name:
Alerting to:
Authentication email will be sent to your email address in 24 hours
Frequency:
Email Message Format:	Plain text Graphical(HTML)

Complete the form below and we will recommend the selected titles to your friends on your behalf. * Indicates a required field.
Your name*:
Your email address*:
Recipient's name*:
Recipient's email address*:
(multiple recipient's names and email addresses should be separated with semicolons)
Your comments:	I thought you would find the page(s) useful.

Your name:
Your email address:
Recipient's name:
Recipient's email address:
(multiple recipient's names and email addresses should be separated with semicolons)
Your comments:	I thought you would find this page useful.

Disclaimer: This message was sent to your friend using the "Send it to a friend" facility on the Sciencepaper Online’ WWW site, http://www.paper.edu.cn/en. The Sciencepaper Online is not responsible for the content of this email, and anything said in this email does not necessarily reflect the Sciencepaper Online's views.

	Check out RSS, or use RSS reader to subscribe this item