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Existence of Solutions for the Evolution p(x)-Laplacian Equation Not in Divergence Form (2012)

Changchun Liu, Junchao Gao, and Songzhe Lian

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-17

Description: The existence of weak solutions is studied to the initial Dirichlet problem of the equation ut=udiv(|∇u|p(x)−2∇u), with inf p(x)>2. We adopt the method of parabolic regularization. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions.

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Electronic ISSN: 1687-0042

Topics: Mathematics

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Derivatives of Multivariate Bernstein Operators and Smoothness with Jacobi Weights (2012)

Jianjun Wang, Zuoxiang Peng, Shukai Duan, and Jia Jing

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-21

Description: Using the modulus of smoothness, directional derivatives of multivariate Bernstein operators with weights are characterized. The obtained results partly generalize the corresponding ones for multivariate Bernstein operators without weights.

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Topics: Mathematics

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Note on the Choquet Integral as an Interval-Valued Aggregation Operators and Their Applications (2012)

Lee-Chae Jang

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-21

Description: The concept of an interval-valued capacity is motivated by the goal to generalize a capacity, and it can be used for representing an uncertain capacity. In this paper, we define the discrete interval-valued capacities, a measure of the entropy of a discrete interval-valued capacity, and, Choquet integral with respect to a discrete interval-valued capacity. In particular, we discuss the Choquet integral as an interval-valued aggregation operator and discuss an application of them.

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Topics: Mathematics

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Geodesic Effect Near an Elliptical Orbit (2012)

Alina-Daniela Vîlcu

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-21

Description: Using a differential geometric treatment, we analytically derived the expression for De Sitter (geodesic) precession in the elliptical motion of the Earth through the gravitational field of the Sun with Schwarzschild's metric. The expression obtained in this paper in a simple way, using a classical approach, agrees with that given in B. M. Barker and R. F. O'Connell (1970, 1975) in a different setting, using the tools of Newtonian mechanics and the Euler-Lagrange equations.

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Topics: Mathematics

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Three-Step Fixed Point Iteration for Generalized Multivalued Mapping in Banach Spaces (2012)

Zhanfei Zuo

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-21

Description: The convergence of three-step fixed point iterative processes for generalized multivalued nonexpansive mapping was considered in this paper. Under some different conditions, the sequences of three-step fixed point iterates strongly or weakly converge to a fixed point of the generalized multivalued nonexpansive mapping. Our results extend and improve some recent results.

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(λ,μ)-Fuzzy Version of Ideals, Interior Ideals, Quasi-Ideals, and Bi-Ideals (2012)

Yuming Feng and P. Corsini

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-21

Description: We introduced (λ,μ)-fuzzy ideals, (λ,μ)-fuzzy interior ideals, (λ,μ)-fuzzy quasi-ideals, and (λ,μ)-fuzzy bi-ideals of an ordered semigroup and studied them. When λ=0 and μ=1, we meet the ordinary fuzzy ones. This paper can be seen as a generalization of Kehayopulu and Tsingelis (2006), Kehayopulu and Tsingelis (2007), and Yao (2009).

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Periodic Points and Fixed Points for the Weaker (ϕ,φ)-Contractive Mappings in Complete Generalized Metric Spaces (2012)

Chi-Ming Chen and W. Y. Sun

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-21

Description: We introduce the notion of weaker (ϕ,φ)-contractive mapping in complete metric spaces and prove the periodic points and fixed points for this type of contraction. Our results generalize or improve many recent fixed point theorems in the literature.

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An Analytical Approach to the Analysis of Guard-Channel-Based Call Admission Control in Wireless Cellular Networks (2012)

Hyung; Man Kim, Agassi Melikov, Mehriban Fattakhova, and Che; Soong Kim

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-02-21

Description: We develop an analytical approach to the performance analysis and optimization of wireless cellular networks for which different types of calls are prioritized based on a channel reservation scheme. We assume that the channel occupancy time differs for new and handover calls. We obtain simple formulas for calculating quality of service (QoS) metrics and solve some problems related to finding the optimal values of guard channels as well as present the results of numerical experiments.

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Filtering-Based Fault Detection for Stochastic Markovian Jump System with Distributed Time-Varying Delays and Mixed Modes (2012)

Yucai Ding, Hong Zhu, Shouming Zhong, Yuping Zhang, and Jianwei Xia

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-26

Description: The problem of fault detection for stochastic Markovian jump system is considered. The system under consideration involves discrete and distributed time-varying delays, Itô-type stochastic disturbance, and different system and delay modes. The aim of this paper is to design a fault detection filter such that the fault detection system is stochastically stable and satisfies a prescribed disturbance attenuation level. By using a novel Lyapunov functional, a mix-mode-dependent sufficient condition is formulated in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed main results.

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Existence and Uniqueness of Homoclinic Solution for a Class of Nonlinear Second-Order Differential Equations (2012)

Lijuan Chen and Shiping Lu

Hindawi

In: Journal of Applied Mathematics

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Publication Date: 2012-12-26

Description: The authors study the existence and uniqueness of a set with -periodic solutions for a class of second-order differential equations by using Mawhin's continuation theorem and some analysis methods, and then a unique homoclinic orbit is obtained as a limit point of the above set of -periodic solutions.

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