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January 15,2010
Volume 3,Issue 1
Pages 1-108
Subject Area:Foundation of Mathematics,Combinatorial Mathematics,Applied Mathematics

Title: Network model based on the balanced supply chains

Authors: ZHU Jiarong
PP: 102～108
Abstract: From the angle of the given structures of cost and consumption in the supply chains, this paper illustrates an efficient algo rithm about the network model based on the balanced supply chains of the same category, which is under the balance of the sale and market. Firstly, it allows for the factors of the manufacturers, vendors and customers and so on. Secondly, it analyses and designs the network model and its nature by means of convex quadratic function. Lastly, the maximum profit of the manufacturer and distributor will be found out correctly in the way of adopting of Matlab package programming, which shows the output of each manufacturer, the amount of trade between the manufacturer and the seller, the amount of trade between the seller and the market and even the price of each product.
Keywords: operational research; management of supply chain; balanced network model; convex quadratic function; maximum profit; Matlab package programming

Title: A new type of optimization method based on conjugate directions

Authors: PAN Xin
PP: 96～101
Abstract: In this paper, a new type of optimization method based on conjugate directions is proposed.Each search direction is generated in the subspace spanned by two conjugate directions, and can be guaranteed descent. It can be proved that this type of method has quadratic termination property without exact line search. The new method is designed to be required only the storage of 4 vectors such that it is suitable for large scale optimization problems. Numerical experiences show that the new method is effective.
Keywords: operational research; quadratic termination property; conjugate directions; iterated-subspace; large scale optimization problems

Title: Nowhere-zero 3-flows in lexicographic products of graphs

Authors: SHU Chi, XU Yong
PP: 92～95
Abstract: This paper looked at the lexicographic product of two nontrivial graphs admits a nowhere-zero 3-flow. First of all, it decomposed the graph, the graph which was decomposed is some paths and cycles, and the lexicographic products of path and path, path and cycle, cycle and cycle are Z3-connected. Then it is still Z3-connected when stick these graphs up. The main result can be observed. In graph theory, there are a wide range of research in the 3-flow problem, so this study is very significant. It resolves another 3-flow problem of products in graphs, in addition to the Cartesian product and the tensor product of two graphs.
Keywords: graph theory; nowhere-zero flow; lexicographic product; Z3-connected

Title: Methods for constructing Archimedean Copula functions

Authors: LIU Weiwei, GUO Tiexin
PP: 87～91
Abstract: Based on the advantages of Archimedean Copula such as simple form, symmetry, combinableness, this paper presents three approaches to construct Archimedean Copula functions. Firstly, a kind of product generators is constructed. Secondly, a hybrid form of multi-Archimedean Copula functions is given by coefficient of weighting to describe the complex correlating structure of financial markets or the correlation between variables. Finally, an introduction is shown about the method using Markov operator to construct Copula functions in this paper. This provides a method to construct high-dimensional Copula functions by low-dimensional Copula functions.
Keywords: stochastic analysis; Copula; Archimedean Copula; generator

Title: Design of a unified algorithm to rapid calculation on multiplication

Authors: CAI Guowu, SUI Xianglin, LIU Fenglei
PP: 79～86
Abstract: The paper presents a simple and common fast multiply calculate algorithm, which is named P-C algorithm. The algorithm can not only be fit to fast calculate the multiplication of two or more long numbers, but also fit to any others. The algorithm is simpler and more efficient than the normal vertical methods of two numbers’ multiplication, and is analyzed in detail through a lot of examples
Keywords: foundations of mathematics; fast multiple calculation; P-C algorithm; mental arithmetic

Title: Analysis of an estimate in multiple hypothesis testing

Authors: WU Xiaoxia, ZHAO Hualing, LIU Fuxiang
PP: 74～78
Abstract: This paper gives analysis on the estimate of the parameter-the proportion of the true null hypothesis in the application of false discovery rate standard control test error rate in multiple hypothesis testing. There are several methods described and the mixture model is introduced to obtain a new maximum likelihood estimate of the parameter by EM algorithms. A simulation study demonstrates the superiority of the new estimation methods by comparing the simulation results.
Keywords: hypothesis testing; multiple testing; false discovery rate; mixture model; EM algorithms

Title: Algorithm for minimum connected k-tuple totally dominating set problem in disk graph

Authors: LI Yefang, AI Wenbao, SHUAI Tianping
PP: 70～73
Abstract: To alleviate the broadcasting storm in wireless sensor network (WSN), fault tolerant connected dominating set (CDS) whose nodes have different transmission ranges was studied as the virtual backbone in this paper. A general fault tolerant CDS problem, called k-MTCDS (minimum connected k-tuple totally dominating set), was proposed in bidirectional disk graph and a centralized approximation algorithm which has a better approximation ratio was given.
Keywords: combinatorial optimization; minimum connected k-tuple totally dominating set; maximum independent set; bidirectional disk graph; wireless senor network

Title: A kind of counterexample function in the analysis

Authors: GU Xianming, HOU Haishan, ZHU Shouqiang, SONG Zecheng
PP: 61～69
Abstract: In order to strengthen the teaching effect of higher learning analytics courses and help students understand and grasp the profound substance of the concepts and theorems, the paper featured a host of examples to do a more in-depth study of the common counter-examples issue in the analytics, and gave modification suggestions for the relevant reference and a widely used form of counter-examples. The paper studied how to structure a kind of counterexample function in the analysis and widespread application emphatically, further pointed out the misunderstandings easily appeared in the concept and theorem of continuity, derivable, integrable, and other analytic properties of the function and gave the corresponding counter-example finally.
Keywords: mathematical analysis; counterexample structure; continuity; generalized derivatives; integrable

Title: Another way to prove the Euler formula

Authors: GONG Yicheng, LIU Guangming, LI Deyi
PP: 58～60
Abstract: The research object of this article is the proof methods of the Euler formula, which connects the exponential function and trigonemetric function via the mystrous imaginary number. By constructing a suitable fuction and then basing on the Lagrange mean-value theorem, a new proof method of the Euler formula is put up with, where the derivatives of the three involving complex functions are analogic to the real fuctions. It can be seen from the proof process that the new proof method is simpler and easier to be undestood than the known proof methods, such as the Taylor Seriers method and the intgral method etc.
Keywords: applied mathematics; Euler formula; complex function; derivative; analogy; Lagrange mean-value theorem

Title: The KMV model when the asset prices follow a jump-diffusion process

Authors: CAI Yansi, GAO Zhimin
PP: 53～57
Abstract: This paper researched on credit risk measurement models, introduced the KMV model; made use of the Black-Scholes formula to apply the option pricing model in the measurement of credit risk, defined the default point, and gained the dis tan ce to default and expected default frequency. On this basis, the paper imported the jump-diffusion process to the value of the assets, using arbitrage-free principle, generalized the KMV model, and gained the corresponding dis tan ce to default and expected default frequency. At last, it summarized the adaptability of the KMV model in China based on the specific conditions in which, and developed one credit risk model, which is adapt to China.
Keywords: applied mathematics; KMV model; Black-Scholes formula; jump-diffusion process

Title: Blind proxy multi-signature scheme based on elliptic curve

Authors: DU Chunfen, ZHOU Meng
PP: 47～52
Abstract: On base of elliptic curve discrete logarithm, this paper firstly designed a blind proxy signature scheme, and then proposed a first class of blind proxy multi-signature scheme and a second class of blind proxy multi-signature scheme. They have the properties of two proxy signature schemes, and their security was demonstrated.
Keywords: cryptography; blind proxy multi-signature; euiptic curve cryptopraphy system; discrete logarithon problem

Title: Estimation of VaR based on conditional Copula-GARCH model

Authors: DUAN Fulin, LI Yuan
PP: 41～46
Abstract: By combining Copula techniques with GARCH model, conditional Copula-GARCH model is provided to avoid defects of classical risk analysis models. Not only the non-linear dependence between financial markets is able to be caught, but also the more flexible multivariate distribution which can be use to analyze portfolio VaR is able to be obtained from this model. The estimation of conditional Copula-GARCH model is fully discussed in this paper. The empirical results getting from Shanghai and Shenzhen stock markets indicate that employing Frank Copula and Gumbel Copula can estimate VaR more accurately than Clayton Copula.
Keywords: applied mathematics; GARCH model; conditional Copula; value at risk; multi-distribution function; inference functions for margins

Title: The prediction model of people-feeling temperature of Wuhan

Authors: ZHANG Guowen, CAI Liqin, XU Changshou, ZHAO Dongfang
PP: 34～40
Abstract: Firstly, the data that the research team got from the typical area of Wuhan and Wuhan observatory in 61 days between July and September of 2008 were dealt with in this paper, by changing them into the data without units. Secondly, a comparatively good linear prediction model for body feeling temperature: y=0.829 79x2-0.205 41x4 with the method of stepwise regression was got, and this model can be used in the field of daily estimation. Thirdly, a preferable nonlinear model: y=0.855 65x2-0.479 43x3+0.284 72x23-0.220 81x24-0.201 68x2x5 was got using SAS software. This model can be used in accurate body temperature measurement. Through this, it is concluded that in the professional service of weather reports, the highest temperature of weather report, humidity and wind speed can be taken into consideration to forecast the body feeling temperature.
Keywords: applied mathematics; maths model; data fitting; people-feeling temperature; statistic analysis

Title: A new computational method for a class of nonlinear bilevel programming by use of GRG

Authors: HUANG Yinzhu, ZHANG Shenggui
PP: 28～33
Abstract: This paper discusses a class of nonlinear bilevel programming in which the second level is convex. The bilevel programming is transformed into a single nonlinear programming by replacing the second level with its KKT condition, and with the help of general reduced gradient (GRG), a simple descent algorithm is given for it. The computational results of the examples show the feasibility and efficiency of the algorithm.
Keywords: applied mathematics; bilevel programming; Karush-Kuhn-Tucker condition; general reduced gradient; descent direction

Title: The infinitely differentiable solution of Lewy equation

Authors: WU Xiaoqing
PP: 19～27
Abstract: This paper uses the operator series method to solve the Lewy equation, and has obtained the analytical expression of local solution and global solution. It has analyzed the demonstration of Lewy theorem and thinks that the problem whether Lewy equation has continuously differentiable solution when the free term F′(t) is non-analytical can be resolved as whether the boundary value problem of the complex Cauchy-Riemann equation has continuously differentiable solution. This paper has proved that: 1) If complex Cauchy-Riemann equation has infinitely differentiable solution, then Lewy equation has infinitely differentiable solution; 2) If F(t) is an infinitely differentiable solution F(t)∈C∞(R) and lim|t|→∞t2F(n)(t)=0, n∈N, then the boundary value problem of the complex Cauchy-Riemann equation also has infinitely differentiable solution; 3) There exists the real infinitely differentiable function F(t) which is non-analytical in the interval ［-1,1］, but there exists the infinitely differentiable solution in the solid field of the origin of Lewy equation. Then the conclusion of Lewy theorem is untenable. And this paper has given the accurate solution of the integral form of Lewy equation.
Keywords: partial differential equation; Lewy equation; real analytical; infinitely differential solution; compactly supported set

Title: Analysis of a Godunov-mixed method for contaminant transport equations: non-equilibrium adsorption processes

Authors: SONG Huailing, LIU Gongjie
PP: 9～18
Abstract: The Godunov-mixed method is analyzed for approximating contaminant transport equation. The equation with nonlinear, non-equilibrium adsorption reactions is considered. This phenomenon gives rise to non-Lipschitz but monotone nonlinearities which complicate the analysis. Error estimate for a fully discrete formulation is derived. A numerical experiment is presented.
Keywords: numerical solution of partial differential equation; non-equilibrium adsorption; non-Lipschitz; Godunov-mixed; error estimate; numerical example

Title: A modified Tikhonov regularization method for a backward heat equation with Robin boundary conditions

Authors: ZHANG Weihua, FENG Xiaoli, FU Chuli
PP: 1～8
Abstract: In this paper, a backward heat equation with Robin boundary conditions is considered. u(x, 0) is recovered from the measured data u(x,T). This is a severely ill-posed problem, a small error on h(x) can cause a large error on the solution, so the numerical implementation of this problem is very difficult. So, some effective regularization methods are needed for this problem. Here, a modified Tikhonov regularization method is used to deal with this problem. The error estimation between the exact solution and its approximation is given. Numerical experiment shows that this method is effective.
Keywords: numerical solution of partial differential equation; ill-posed problem; Tikhonov regularization; backward heat conduction; Robin boundary

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