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  • Mathematics  (14)
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  • Mathematics  (14)
  • 1
    Online Resource
    Online Resource
    Analysis of a Patch Model for the Dynamical Transmission of Echinococcosis
    Hindawi Limited ; 2014
    In:  Abstract and Applied Analysis Vol. 2014 ( 2014), p. 1-13
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-13
    Abstract: A patch model for echinococcosis due to dogs migration is proposed to explore the effect of dogs migration among patches on the spread of echinococcosis. We firstly define the basic reproduction number R 0 . The mathematical results show that the dynamics of the model can be completely determined by R 0 . If R 0 〈 1 , the disease-free equilibrium is globally asymptotically stable. When R 0 〉 1 , the model is permanence and endemic equilibrium is globally asymptotically stable. According to the simulations, it is shown that the larger diffusion of dogs from the lower epidemic areas to the higher prevalence areas can intensify the spread of echinococcosis. However, the larger diffusion of dogs from the higher prevalence areas to the lower epidemic areas can reduce the spread and is beneficial for disease control.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2014/576365
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 2
    Online Resource
    Online Resource
    Optimal Control of Polymer Flooding Based on Maximum Principle
    Hindawi Limited ; 2012
    In:  Journal of Applied Mathematics Vol. 2012 ( 2012), p. 1-20
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2012 ( 2012), p. 1-20
    Abstract: Polymer flooding is one of the most important technologies for enhanced oil recovery (EOR). In this paper, an optimal control model of distributed parameter systems (DPSs) for polymer injection strategies is established, which involves the performance index as maximum of the profit, the governing equations as the fluid flow equations of polymer flooding, and the inequality constraint as the polymer concentration limitation. To cope with the optimal control problem (OCP) of this DPS, the necessary conditions for optimality are obtained through application of the calculus of variations and Pontryagin’s weak maximum principle. A gradient method is proposed for the computation of optimal injection strategies. The numerical results of an example illustrate the effectiveness of the proposed method.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2012/987975
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2012
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
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  • 3
    Online Resource
    Online Resource
    A Local Fractional Integral Inequality on Fractal Space Analogous to Anderson’s Inequality
    Hindawi Limited ; 2014
    In:  Abstract and Applied Analysis Vol. 2014 ( 2014), p. 1-7
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-7
    Abstract: Anderson's inequality (Anderson, 1958) as well as its improved version given by Fink (2003) is known to provide interesting examples of integral inequalities. In this paper, we establish local fractional integral analogue of Anderson's inequality on fractal space under some suitable conditions. Moreover, we also show that the local fractional integral inequality on fractal space, which we have proved in this paper, is a new generalization of the classical Anderson's inequality.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2014/797561
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 4
    Online Resource
    Online Resource
    Optimal Control for Multistage Nonlinear Dynamic System of Microbial Bioconversion in Batch Culture
    Hindawi Limited ; 2011
    In:  Journal of Applied Mathematics Vol. 2011 ( 2011), p. 1-11
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2011 ( 2011), p. 1-11
    Abstract: In batch culture of glycerol biodissimilation to 1,3-propanediol (1,3-PD), the aim of adding glycerol is to obtain as much 1,3-PD as possible. Taking the yield intensity of 1,3-PD as the performance index and the initial concentration of biomass, glycerol, and terminal time as the control vector, we propose an optimal control model subject to a multistage nonlinear dynamical system and constraints of continuous state. A computational approach is constructed to seek the solution of the above model. Firstly, we transform the optimal control problem into the one with fixed terminal time. Secondly, we transcribe the optimal control model into an unconstrained one based on the penalty functions and an extension of the state space. Finally, by approximating the control function with simple functions, we transform the unconstrained optimal control problem into a sequence of nonlinear programming problems, which can be solved using gradient-based optimization techniques. The convergence analysis and optimality function of the algorithm are also investigated. Numerical results show that, by employing the optimal control, the concentration of 1,3-PD at the terminal time can be increased, compared with the previous results.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2011/624516
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2011
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
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  • 5
    Online Resource
    Online Resource
    Variable Structure Disturbance Rejection Control for Nonlinear Uncertain Systems with State and Control Delays via Optimal Sliding Mode Surface Approach
    Hindawi Limited ; 2013
    In:  Abstract and Applied Analysis Vol. 2013 ( 2013), p. 1-16
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2013 ( 2013), p. 1-16
    Abstract: The paper considers the problem of variable structure control for nonlinear systems with uncertainty and time delays under persistent disturbance by using the optimal sliding mode surface approach. Through functional transformation, the original time-delay system is transformed into a delay-free one. The approximating sequence method is applied to solve the nonlinear optimal sliding mode surface problem which is reduced to a linear two-point boundary value problem of approximating sequences. The optimal sliding mode surface is obtained from the convergent solutions by solving a Riccati equation, a Sylvester equation, and the state and adjoint vector differential equations of approximating sequences. Then, the variable structure disturbance rejection control is presented by adopting an exponential trending law, where the state and control memory terms are designed to compensate the state and control delays, a feedforward control term is designed to reject the disturbance, and an adjoint compensator is designed to compensate the effects generated by the nonlinearity and the uncertainty. Furthermore, an observer is constructed to make the feedforward term physically realizable, and thus the dynamical observer-based dynamical variable structure disturbance rejection control law is produced. Finally, simulations are demonstrated to verify the effectiveness of the presented controller and the simplicity of the proposed approach.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2013/141058
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2013
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 6
    Online Resource
    Online Resource
    Convergence of Relaxed Matrix Parallel Multisplitting Chaotic Methods for H -Matrices
    Hindawi Limited ; 2014
    In:  Journal of Applied Mathematics Vol. 2014 ( 2014), p. 1-9
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2014 ( 2014), p. 1-9
    Abstract: Based on the methods presented by Song and Yuan (1994), we construct relaxed matrix parallel multisplitting chaotic generalized USAOR-style methods by introducing more relaxed parameters and analyze the convergence of our methods when coefficient matrices are H -matrices or irreducible diagonally dominant matrices. The parameters can be adjusted suitably so that the convergence property of methods can be substantially improved. Furthermore, we further study some applied convergence results of methods to be convenient for carrying out numerical experiments. Finally, we give some numerical examples, which show that our convergence results are applied and easily carried out.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2014/594185
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
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  • 7
    Online Resource
    Online Resource
    Global Behaviors of a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate
    Hindawi Limited ; 2014
    In:  Abstract and Applied Analysis Vol. 2014 ( 2014), p. 1-18
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-18
    Abstract: We study a class of discrete SIRS epidemic models with nonlinear incidence rate F ( S ) G ( I ) and disease-induced mortality. By using analytic techniques and constructing discrete Lyapunov functions, the global stability of disease-free equilibrium and endemic equilibrium is obtained. That is, if basic reproduction number ℛ 0 〈 1 , then the disease-free equilibrium is globally asymptotically stable, and if ℛ 0 〉 1 , then the model has a unique endemic equilibrium and when some additional conditions hold the endemic equilibrium also is globally asymptotically stable. By using the theory of persistence in dynamical systems, we further obtain that only when ℛ 0 〉 1 , the disease in the model is permanent. Some special cases of F ( S ) G ( I ) are discussed. Particularly, when F ( S ) G ( I ) = β S I / ( 1 + λ I ) , it is obtained that the endemic equilibrium is globally asymptotically stable if and only if ℛ 0 〉 1 . Furthermore, the numerical simulations show that for general incidence rate F ( S ) G ( I ) the endemic equilibrium may be globally asymptotically stable only as ℛ 0 〉 1 .
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2014/249623
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
    Location Call Number Limitation Availability
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    Online Resource
  • 8
    Online Resource
    Online Resource
    Spatiotemporal Patterns in a Ratio-Dependent Food Chain Model with Reaction-Diffusion
    Hindawi Limited ; 2014
    In:  Abstract and Applied Analysis Vol. 2014 ( 2014), p. 1-9
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-9
    Abstract: Predator-prey models describe biological phenomena of pursuit-evasion interaction. And this interaction exists widely in the world for the necessary energy supplement of species. In this paper, we have investigated a ratio-dependent spatially extended food chain model. Based on the bifurcation analysis (Hopf and Turing), we give the spatial pattern formation via numerical simulation, that is, the evolution process of the system near the coexistence equilibrium point ( u 2 * , v 2 * , w 2 * ) , and find that the model dynamics exhibits complex pattern replication. For fixed parameters, on increasing the control parameter c 1 , the sequence “holes → holes-stripe mixtures → stripes → spots-stripe mixtures → spots” pattern is observed. And in the case of pure Hopf instability, the model exhibits chaotic wave pattern replication. Furthermore, we consider the pattern formation in the case of which the top predator is extinct, that is, the evolution process of the system near the equilibrium point ( u 1 * , v 1 * , 0 ) , and find that the model dynamics exhibits stripes-spots pattern replication. Our results show that reaction-diffusion model is an appropriate tool for investigating fundamental mechanism of complex spatiotemporal dynamics. It will be useful for studying the dynamic complexity of ecosystems.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2014/130851
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
    Location Call Number Limitation Availability
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    Online Resource
  • 9
    Online Resource
    Online Resource
    Exact Finite Difference Scheme and Nonstandard Finite Difference Scheme for Burgers and Burgers-Fisher Equations
    Hindawi Limited ; 2014
    In:  Journal of Applied Mathematics Vol. 2014 ( 2014), p. 1-12
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2014 ( 2014), p. 1-12
    Abstract: We present finite difference schemes for Burgers equation and Burgers-Fisher equation. A new version of exact finite difference scheme for Burgers equation and Burgers-Fisher equation is proposed using the solitary wave solution. Then nonstandard finite difference schemes are constructed to solve two equations. Numerical experiments are presented to verify the accuracy and efficiency of such NSFD schemes.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2014/597926
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
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    Online Resource
  • 10
    Online Resource
    Online Resource
    Left and Right Inverse Eigenpairs Problem for κ -Hermitian Matrices
    Hindawi Limited ; 2013
    In:  Journal of Applied Mathematics Vol. 2013 ( 2013), p. 1-6
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2013 ( 2013), p. 1-6
    Abstract: Left and right inverse eigenpairs problem for κ -hermitian matrices and its optimal approximate problem are considered. Based on the special properties of κ -hermitian matrices, the equivalent problem is obtained. Combining a new inner product of matrices, the necessary and sufficient conditions for the solvability of the problem and its general solutions are derived. Furthermore, the optimal approximate solution and a calculation procedure to obtain the optimal approximate solution are provided.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2013/230408
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2013
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
    Location Call Number Limitation Availability
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