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Exponential Attractor for Lattice System of Nonlinear Boussinesq Equation (2013)

Min Zhao and Shengfan Zhou

Hindawi

In: Discrete Dynamics in Nature and Society

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Publication Date: 2013-09-13

Description: We study the lattice dynamical system of a nonlinear Boussinesq equation. We first verify the Lipschitz continuity of the continuous semigroup associated with the system. Then, we provide an estimation of the tail of the difference between two solutions of the system. Finally, we obtain the existence of an exponential attractor of the system.

Print ISSN: 1026-0226

Electronic ISSN: 1607-887X

Topics: Mathematics

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Adaptive Fault-Tolerant Control for Flight Systems with Input Saturation and Model Mismatch (2013)

Man Wang, Jianying Yang, and Nan Li

Hindawi

In: Discrete Dynamics in Nature and Society

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Publication Date: 2013-09-13

Description: A novel scheme for fault-tolerant control is proposed in this paper, in which model reference adaptive control method is incorporated with control allocation to cope with simultaneous actuator failures, input saturation, and model mismatch in the flight system. In order to reduce performance degradation caused by actuator failures, the proposed scheme redistributes the control signal to healthy actuators and updates the weighting matrix based on actuator effectiveness. Because of saturation errors resulting from actuator constraints and model mismatch caused by abnormal changes in the system, the original reference model may not be appropriate. Under this circumstance, an adaptive reference model which can also provide satisfactory performance is designed. Simulations of a flight control example are given to illustrate the effectiveness of the proposed scheme.

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Topics: Mathematics

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Opinion Impact Models and Opinion Consensus Methods in Ad Hoc Tactical Social Networks (2013)

Demin Li, Jie Zhou, Jingjuan Zhu, and Jiacun Wang

Hindawi

In: Discrete Dynamics in Nature and Society

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Publication Date: 2013-09-20

Description: Ad hoc social networks are special social networks, such as ad hoc tactical social networks, ad hoc firefighter social networks, and ad hoc vehicular social networks. The social networks possess both the properties of ad hoc network and social network. One of the challenge problems in ad hoc social networks is opinion impact and consensus, and the opinion impact plays a key role for information fusion and decision support in ad hoc social networks. In this paper, consider the impact of physical and logical distance on the opinions of individuals or nodes in heterogeneous social networks; we present a general opinion impact model, discuss the local and global opinion impact models in detail, and point out the relationship between the local opinion impact model and the global opinion impact model. For understanding the opinion impact models easily, we use the general opinion impact model to ad hoc tactical social networks and discuss the opinion impact and opinion consensus for ad hoc tactical social networks in the end.

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Topics: Mathematics

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A Review Study on Traction Energy Saving of Rail Transport (2013)

Xuesong Feng, Hanxiao Zhang, Yong Ding, Zhili Liu, Hongqin Peng, and Bin Xu

Hindawi

In: Discrete Dynamics in Nature and Society

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Publication Date: 2013-09-24

Description: The energy cost of a rail transport system is very big especially for the tractions of trains in its daily operation. Continual effort on decreasing the traction energy cost intensities of various rail transport modes has been made by many researchers and practitioners on different aspects for a long time. From the rail transport operation perspective, this study reviews such energy-saving research mainly focusing on the optimizations of train coasting schemes, the rational designs and utilizations of track alignments, the ameliorations of train attributes, and the improvements of system operations. According to the review work, it is confirmed that in sound responses to distinct track alignments, dynamically optimizing control programs of trains with their reasonably improved attributes ought to be further studied in view of the systematic transport operation of a rail line or network in an integrated manner as much as possible in the future research on traction energy saving of rail transport.

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Topics: Mathematics

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The Solutions of Second-Order Linear Matrix Equations on Time Scales (2013)

Kefeng Li and Chao Zhang

Hindawi

In: Discrete Dynamics in Nature and Society

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Publication Date: 2013-09-27

Description: This paper studies the solutions of second-order linear matrix equations on time scales. Firstly, the necessary and sufficient conditions for the existence of a solution of characteristic equation are introduced; then two diverse solutions of characteristic equation are applied to express general solution of the matrix equations on time scales.

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Heuristic for Stochastic Online Flowshop Problem with Preemption Penalties (2013)

Mohammad Bayat, Mehdi Heydari, and Mohammad Mahdavi Mazdeh

Hindawi

In: Discrete Dynamics in Nature and Society

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Publication Date: 2013-10-01

Description: The deterministic flowshop model is one of the most widely studied problems; whereas its stochastic equivalent has remained a challenge. Furthermore, the preemptive online stochastic flowshop problem has received much less attention, and most of the previous researches have considered a nonpreemptive version. Moreover, little attention has been devoted to the problems where a certain time penalty is incurred when preemption is allowed. This paper examines the preemptive stochastic online flowshop with the objective of minimizing the expected makespan. All the jobs arrive overtime, which means that the existence and the parameters of each job are unknown until its release date. The processing time of the jobs is stochastic and actual processing time is unknown until completion of the job. A heuristic procedure for this problem is presented, which is applicable whenever the job processing times are characterized by their means and standard deviation. The performance of the proposed heuristic method is explored using some numerical examples.

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Simulation Research of Space-Time Evolution of Emergency Logistics Network Reliability Based on Complex Network Theory (2013)

Li Huang, Wei Wang, and Minggong Wang

Hindawi

In: Discrete Dynamics in Nature and Society

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Publication Date: 2013-09-09

Description: We propose the conception and evaluation indexes of emergency logistics network connecting reliability to construct evaluation index system of complex network reliability, and describe these indexes quantitatively to evaluate the network connecting reliability. Moreover, the network topological model and the simulation methods of reliability measurement when the network is under attack are present. Finally, we take three classical emergency logistics networks as examples, and through emulation analysis we obtain the connecting reliability changing situation of these three networks under random attack, the changing curve of the ratio of effective demand nodes and emergence supply mileage of emergency logistics network with same network density but different forms, and then evaluate the emergency logistics network connecting reliability. This can provide references for the designing of emergency logistics network with high reliability and analysis means for research in other fields.

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Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions (2013)

Thanin Sitthiwirattham, Jessada Tariboon, and Sotiris K. Ntouyas

Hindawi

In: Discrete Dynamics in Nature and Society

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Publication Date: 2013-09-12

Description: We consider a discrete fractional boundary value problem of the form where , , , and is a continuous function. The existence of at least one solution is proved by using Krasnoselskii's fixed point theorem and Leray-Schauder's nonlinear alternative. Some illustrative examples are also presented.

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Boundedness of Solutions to Differential Equations of Fourth Order with Oscillatory Restoring and Forcing Terms (2013)

Cemil Tunç and Muzaffer Ateş

Hindawi

In: Discrete Dynamics in Nature and Society

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Publication Date: 2013-09-18

Description: This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth order. Using the Cauchy formula for the particular solution of nonhomogeneous differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded.

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Invariant Solutions for Nonhomogeneous Discrete Diffusion Equation (2013)

M. N. Qureshi, A. Q. Khan, M. Ayub, and Q. Din

Hindawi

In: Discrete Dynamics in Nature and Society

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Publication Date: 2013-09-20

Description: One-dimensional optimal systems for nonhomogeneous discrete heat equation with different source terms are calculated. By utilizing these optimal systems invariant solutions are found. Also generating solutions are calculated, using the elements of the symmetry algebra.

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