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July 15,2009 Volume 2,Issue 13 Pages 1315-1416 Subject Area:Differential Algebra,Applied Mathematics,Fuzzy Mathematics,Dynamical System |
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Title: Fixed point theorems for a class of mixed monotone operators | ||||
Authors: SUN Qinfu, LUAN Shixia PP: 1412~1416 Abstract: By using the cone theory and monotone iterative method, the existence and uniqueness of solutions of non-monotone operator equations without continuity and compactness conditions are studied, some new fixed point theorems of mixed monotone operators, increasing operators and decreasing operators are obtained, and the iteration sequences which converge to solution of operator equations and the error estimates are also given.The results improve and generalize some known results, and facilitate application. Keywords: applied mathematics; cone theory; mixed monotone operators; normal cone; fixed point |
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Title: The new way about shipborne gun firing against the shore targets | ||||
Authors: WANG Jinyun, ZHOU Huijie PP: 1407~1411 Abstract: This paper introduces a new way which is different from traditional firing way on shipborne gun firing against the shore target based on GPS inertial navigation system and real-time ballistic computation. It establishes one mathematic model to confirm target parameter based on GPS inertial navigation system. Moreover, it gives a means of obtaining firing data against the shore target based on real-time ballistic computation. At last it gives some data simulation. The result proves that this way is fast, precise and credible and plays an active role in actual combat about opposite-shore firing without relying on radar, photoelectric system and firing table. Keywords: applied mathematics; GPS inertial navigation system; real-time ballistic computation; shipborne gun firing against the shore target; simulation |
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Title: Filtering regularization method for solving the Cauchy problem of the Helmholtz equation | ||||
Authors: CHENG Hao, FENG Xiaoli, FU Chuli PP: 1402~1406 Abstract: The Cauchy problem of the Helmholtz equation is severely ill-posed, i.e.〖KG-*3〗, the solution (if it exists) does not continuously depend on the data. This paper adopts the filtering regularization method to recover the solution’s continuous dependence on the data and obtains the H錸lder-type error estimation between the exact solution and the regularized approximate solution. Keywords: applied mathematics; the Cauchy problem of the Helmholtz equation; ill-posed problem; filtering regularization |
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Title: Comprehensive evaluation of water resource use efficiency based on projection pursuit model | ||||
Authors: ZHANG Kun, ZHENG Bao, ZHANG Wei, CUI Li PP: 1396~1401 Abstract: This paper establishes an evaluation index system based on some indexes of the water resources, including water consumption per unit gross domestic product (GDP) of agriculture, water consumption per unit GDP of industry, emissions of chemical oxygen demand (COD) per capita, and water consumption of life per capita. Projection pursuit model is used to study the comprehensive evaluation of water resource use efficiency. Projection pursuit can be used to project high dimensional data to low dimensional space and find the optimum projection vector of data in one-dimensional space, which is helpful to comprehensively evaluate the value and direction of every index in comprehensive evaluation. Keywords: applied mathematics; water resource use efficiency; comprehensive evaluation; projection pursuit model |
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Title: The transformation between regression analysis and variance analysis about double factors experiments | ||||
Authors: LI Xiaoyan, HU Xijian PP: 1392~1395 Abstract: This paper introduced the fundamental rules of regression analysis and variance analysis and discussed the two methods by giving a practical example of double factors experiment without repetition in the real world. For regression analysis, the experiment data should be observed carefully and the relativity between independent variables and resultant variables and the changing rules should be studied. The proposal model was presented and the values of the parameters and corresponding credible intervals were assessed. For variance analysis, although the number of data was great, when the factor levels were not too much, the experiment design mode could be changed into orthogonality by adjusting the data structure, and thus the judgement on the effects arose by some factor could be carried out independently (variance analysis). And it came to a conclusion that under some appropriate conditions one method can be replaced by another to explain the phenomena. Keywords: statistics; regression analysis; variance analysis; the least squares principle; the sum of the warp square; double factors |
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Title: Analysis of financial investment risk based on historical data | ||||
Authors: SUN Hao,LIU Yang, DING Genhong PP: 1384~1391 Abstract: This paper develops two models to analyze financial investment risk based on historical data, which are respectively mathematical statistics probability model and VaR (value at risk) model. Firstly, it analyzes the historical data by Pearsonion 〖JX-*4〗χ〖JX*4〗2 goodness of fit test and probability test to determine a common statistic hypothesis testing model, utilizing the properties of normal distribution. Secondly, it builds a VaR model via devising the expression of VaR and computer simulation, with the comparison of the results solved by above mentioned models. Afterwards, for study of the expression of measure of risk, relationship among the parameters M, L, 1-α and T is built based on above two mentioned models. In addition, models testing and evaluation are given. To sum up the above arguments, model stability and reliability are guaranteed via multi-assumption and testing. Keywords: mathematical statistics; VaR model; confidence probability; financial investment; earnings |
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Title: A kind of two-dimensional fuzzy group | ||||
Authors: SUN Xudong, NIE Shengchuan, GUO Sizong PP: 1380~1383 Abstract: Unlike the traditional research of two-dimensional fuzzy set, this paper discusses the fuzzy set based on the definition of the fuzzy point in the two-dimensional plane. At the same time, according to the method of circular fuzzy structured element, a special type of two-dimensional fuzzy number is discussed in detail (be comprised of elliptical fuzzy number and circular fuzzy number). In order to study the algebraic properties of the two-dimensional fuzzy number, this paper first defines a kind of algebraic operation, and studies a class of two-dimensional fuzzy number’s algebraic system that is formed by the circular fuzzy structured element. The paper proves that algebraic system is a group and gives its properties. Keywords: fuzzy mathematics; circular fuzzy structured element; two-dimensional fuzzy number; group |
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Title: Matrix equations problem for row symmetricmatrices and its optimal approximation | ||||
Authors: GAO Cuijin, ZHAO Lijun, HU Xiyan PP: 1373~1379 Abstract: This paper uses the symmetric property of row symmetric matrices fully and by partitioning of matrix and reduction of order, which result in considerable simplification of solving the matrix equations problem for row symmetric matrices and its optimal approximation. The expression of basic structure of row symmetric matrices according to the properties of row symmetric matrices is obtained first. Based on this, convert the matrix equations problem for row symmetric matrices into ordinary matrix equations problem, the scale of converted matrix equations problem is half of that for the original problem. By the singular value decomposition of matrix, the necessary and sufficient condition for the existence of the solutions to matrix equations problem for row symmetric matrices is obtained, and the expression of general solutions is provided. Finally, based on the orthogonal invariance of Frobenius norm, the expression of the optimal approximate solution to matrix equations problem for row symmetric matrices is got. Keywords: computational mathematics; row symmetric matrices; singular value decomposition; optimal approximation |
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Title: The research of the optimal gym lineup problem | ||||
Authors: LIU Ping, WANG Xiaofeng PP: 1366~1372 Abstract: This paper takes women’s gym team competition as a model to discuss and analyze the optimal lineup problem. After analyzing different problems in this model, it gives objective functions and restrict conditions, and establishes the corresponding 0~1 programming model. Lingo mathematics software is used to compute and obtain the optimal lineup of this team for several different cases. In this mathematical model, two objective functions are established: the first-class objective function is “the greatest probability of the team winning”, while the second-class objective function is “the team winning the highest scores”. In order to facilitate the solution and computation, two objective functions are summed up in a weighted manner to turn a multi-objective programming model into a single-objective programming compromise model. Finally, both of the factors are considered in analysis, and the solution of optimal lineup problem is obtained. Keywords: computational mathematics; optimal lineup problem; 0~1 programming; optimal solution |
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Title: Study of synchronization in new chaotic system | ||||
Authors: GUO Lifeng, ZHANG Ting, JIANG Hao, LIU Kaiming PP: 1362~1365 Abstract: This paper studies the chaotic synchronization in a new chaotic system. A kind of nonlinear controller was designed by use of linear negative feedback method to realize the synchronization. By means of Lyapunov stability theorem, it was proved that the dynamics of the synchronization error was globally and asymptotically stable. Numerical simulations by Matlab were provided to demonstrate the validity of the proposed nonlinear controller for achieving the chaotic synchronization. Keywords: differential dynamic system; new chaotic system; chaotic synchronization; Lyapunov stability |
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Title: Analysis on the asymptotic of the solution for a stochastic Gompertz competition model | ||||
Authors: WANG Fangfang, ZHANG Jianxun PP: 1356~1361 Abstract: This paper considers a stochastic Gompertz competition model with the influence of environment. It is difficult to get an explicit solution, so based on the existence and uniqueness of the solution for this model and in order to gain a deeper understanding of the population growth, this paper continues to analyze its asymptotic behavior and gives the asymptotic moment estimation and upper rate estimation of the solution by Lyapunov method, and receives the boundedness for asymptotic moment and upper rate. Keywords: differential dynamic system; stochastic differential equation; asymptotic; Lyapunov function method; Gompertz model |
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Title: Detection on the complexity characteristic analysis methods of temperature time series | ||||
Authors: XU Na, SHANG Pengjian, YUAN Guangcai PP: 1350~1355 Abstract: This paper introduces the multifractal detrended fluctuation analysis (MF-DFA) methods of discrete time series and uses them to study the temperature time series. It is demonstrated that the temperature time series has a complexity of multifractal behavior. Finally, the MF-DFA method is used in Beijing’s temperature time series with four-types of trends: sinusoidal, power-law, exponential and logarithm trends. Additional trends of multifractal from strong to weak are: the power-law, sinusoidal, logarithm and exponential trends. Keywords: dynamical system; multifractal detrended fluctuation analysis; multifractal spectrum; temperature time series; superposition trends |
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Title: Optimal harvesting from a kind of n dimensional mutualism model | ||||
Authors: LI Zhen, ZHANG Jianxun PP: 1345~1349 Abstract: Considering a kind of modificatory n dimensions Gilpin-Ayala mutualism models, whose sizes are given by stochastic differential equations driven by m dimensional Brownian motion, this paper studies the problem on optimal harvesting from the n populations that maximizes the expected total income from the harvest with cost, which are different with the sizes. By formulating a stochastic control problem, it obtains the optimal harvesting strategy and the corresponding optimal harvesting profit function explicitly. At last, it proves the theories. Keywords: biomathematics; optimal harvesting problem; stochastic differential equation; mutualism model; harvesting cost |
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Title: One method for getting the characteristic angle sequence function of square wave Koch-like curve | ||||
Authors: HAO Wuling, HAO Junjun PP: 1341~1344 Abstract: This paper deals with the formation conditions of the characteristic angle sequence function H of square wave Koch-like curve obtained at the first time iteration. And it achieves a simpler characteristic angle sequence function H′ by analyzing the formation conditions of H based on the method of undetermined coefficient. Moreover, the paper obtains the simplified characteristic angle sequence function H′ at the nth time iteration on the basis of inductive method. Thus, the analytic expressions of the square wave Koch-like curve can be calculated more easily and a more effective method for studying the rigorously self-similar and regular fractal curves which generators have 2n pieces (n is an integer) is presented. Keywords: geometry; fractal; characteristic angle sequence function; method of undetermined coefficient; square wave Koch-like curve |
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Title: Drazin inverse for a class of 2 block matrices | ||||
Authors: LIU Xifu, YANG Hu PP: 1337~1340 Abstract: This paper discusses the Drazin inverse of a special 2 block matrices: the Drazin inverse of the triangular matrix M when A is idempotent. Two main methods of matrix factorization are used to obtain the representation of the Drazin inverse of M: one is using the methods of block factorization and row and column transposition on M, then transforms M to a block matrix so that its representation for the Drazin inverse can be easily obtained; and another is decomposing M into the product of two matrices, then applies the formula of the Drazin inverse of the product of two matrices to compute the Drazin inverse of M. Under some new conditions, the results extend some known results on Drazin inverse. Keywords: algebra; Drazin inverse; block matrices; index; rank |
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Title: Initial boundary value problems for a class of second-order singular parabolic equations | ||||
Authors: WANG Shuxia, ZHANG Zhijun PP: 1329~1336 Abstract: Based on appropriate assumptions of nonlinear terms, by use of parabolic regularization method and method of upper and lower solutions, some existence results of solutions to a class of singular nonlinear parabolic equations with initial boundary values on a smooth domain Ω 瘙} N and some estimates of solutions on the space L2(0, T; W1,20(Ω))∩L∞(0, T; L2(Ω)) are obtained. Moreover, the uniqueness of solutions for two kinds of special problems is also obtained. Keywords: parabolic equations; regularization method; method of upper and lower solutions; existence; uniqueness |
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Title: A new method for solving high-order linear delay Fredholm-Volterra integro-differential equations with variable cofficients | ||||
Authors: WU Shurong, ZHANG Guofeng, DING Hengfei PP: 1322~1328 Abstract: In this paper, by means of the matrix relation between the Taylor and Chebyshev polynomials, the mentioned methods above are modified and developed in order to solve the systems of higher-order delay differential equations. This method transforms the integro-differential equations (IDE) system and the given conditions into the matrix equations by using the Chebyshev collocation method. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. In addition, examples are presented to illustrate the pertinent features of the method and the results are discussed. Keywords: ordinary differential equations; Chebyshev polynomials; Taylor polynomials; Chebyshev collocation method; delay differential system |
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Title: Superconvergence of time-space fully discrete discontinuous finite element for first order hyperbolic equation | ||||
Authors: CHEN Chuanmiao, LI Canhua PP: 1315~1321 Abstract: The bi-n defree time-space fully discrete discontinuous finite element on rectangular mesh for first order hyperbolic initial-boundary value problem is considered. Based on the element orthogonality analysis(EOA), new techniques for constructing comparison function and duality argument by use of element or thogonal expansion are applied, and superconvergence of the discontinuous finite element at Radau’s points is proved. Numerical experiments show that they have higher superconvergence. Keywords: first order hyperbolic equation; discontinuous finite element; full discretization Radau’s point; superconvergence |
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