Fixed point theorems for some generalized multivalued nonexpansive mappings

In this paper, we introduce a condition on multivalued mappings which is a multivalued version of condition (C_λ) defined by Garcia-Falset et al. (2011) [3]. It is shown here that some of the classical fixed point theorems for multivalued nonexpansive mappings can be extended to mappings satisfying this condition. Our results generalize the results in Lim (1974), Lami Dozo (1973), Kirk and Massa (1990), Garcia-Falset et al. (2011), Dhompongsa et al. (2009) and Abkar and Eslamian (2010) [4], [5], [6], [3], [7] and [8] and many others.     

Inexact Newton-type methods

We introduce the new idea of recurrent functions to provide a semilocal convergence analysis for an inexact Newton-type method, using outer inverses. It turns out that our sufficient convergence conditions are weaker than in earlier studies in many interesting cases (Argyros, 2004 [5] and [6], Argyros, 2007 [7], Dennis, 1971 [14], Deuflhard and Heindl, 1979 [15], Gutiérrez, 1997 [16], Gutiérrez et al., 1995 [17], Häubler, 1986 [18], Huang, 1993 [19], Kantorovich and Akilov, 1982 [20], Nashed and Chen, 1993 [21], Potra, 1982 [22], Potra, 1985 [23]).     

A posteriori error estimates for a finite element approximation of transmission problems with sign changing coefficients

We perform the a posteriori error analysis of residual type of transmission problem with sign changing coefficients. According to Bonnet-BenDhia et al. (2010) [9], if the contrast is large enough, the continuous problem can be transformed into a coercive one. We further show that a similar property holds for the discrete problem for any regular meshes, extending the framework from Bonnet-BenDhia et al. [9]. The reliability and efficiency of the proposed estimator are confirmed by some numerical tests.     

Improved utilization for joint HCCA–EDCA access in IEEE 802.11e WLANs

This paper presents a model for improving utilization in IEEE 802.11e wireless LAN via a Markov decision process (MDP) approach. A Markov chain tracking the utilized transmission window for two separate access mechanisms is devised. Subsequently, the action space and the rewards of the MDP are judiciously selected with the aim of improving overall utilization without explicit blocking. The proposed MDP model for 802.11e reveals that proportional allocation of access opportunities improve overall utilization compared to completely randomized access. Simulation results go on to show that a policy that limits HCCA access as a function of channel load improves utilization by an average 8 %. The optimization framework proposed in this paper is promising as a practical decision support tool for resource planning in 802.11e.     

The asymptotic behavior of an inertial alternating proximal algorithm for monotone inclusions

The aim of this paper is to investigate the asymptotic behavior of an inertial alternating algorithm based on the composition of resolvents of monotone operators. The proposed algorithm is a generalization of those proposed in Attouch et al. (2007) [3] and Bauschke et al. (2005) [1]. As a special case, we also recover the classical alternating minimization algorithm (Acker, 1980) [2], which itself is a natural extension of the alternating projection algorithm of von Neumann (1950) [4]. An application to equilibrium problems is also proposed.     

Regularity for the Harmonic-Einstein equation

We establish a regularity theorem for the Harmonic-Einstein equation. As a byproduct of the local regularity, we also have a compactness theorem on the Harmonic-Einstein equation. The method is mainly the Moser iteration technique which has been used and developed by Bando et al. (1989) [4], Tian (1990) [22], Tian and Viaclovsky (2005) [23] and others.     

The nonlinear boundary layer to the Boltzmann equation for cutoff soft potential with physical boundary condition

We consider the nonlinear boundary layer to the Boltzmann equation for cutoff soft potential with physical boundary condition, i.e., the Dirichlet boundary condition with weak diffuse effect. Under the assumption that the distribution function of gas particles tends to a global Maxwellian in the far field, we will show the boundary layer exist if the boundary data satisfy the solvability condition. Moreover, the codimensions of the boundary data which satisfies the solvability condition change with the Mach number of the far field Maxwellian like Chen et al. (2004) [5], Ukai et al. (2003) [6] and Wang et al. (2007) [7].     

Common fixed point results in CAT(0) spaces

Let X be a complete CAT(0) space, T be a generalized multivalued nonexpansive mapping, and t be a single valued quasi-nonexpansive mapping. Under the assumption that T and t commute weakly, we shall prove the existence of a common fixed point for them. In this way, we extend and improve a number of recent results obtained by Shahzad (2009) [7] and [12], Shahzad and Markin (2008) [6], and Dhompongsa et al. (2005) [5].     

On the comparison of the pre-test and shrinkage phi-divergence test estimators for the symmetry model of categorical data

The estimation problem of the parameters in a symmetry model for categorical data has been considered for many authors in the statistical literature (for example, Bowker (1948) [1], Ireland et al. (1969) [2], Quade and Salama (1975) [3], Cressie and Read (1988) [4], Menéndez et al. (2005) [5]) without using uncertain prior information. It is well known that many new and interesting estimators, using uncertain prior information, have been studied by a host of researchers in different statistical models, and many papers have been published on this topic (see Saleh (2006) [9] and references therein). In this paper, we consider the symmetry model of categorical data and we study, for the first time, some new estimators when non-sample information about the symmetry of the probabilities is considered. The decision to use a “restricted” estimator or an “unrestricted” estimator is based on the outcome of a preliminary test, and then a shrinkage technique is used. It is interesting to note that we present a unified study in the sense that we consider not only the maximum likelihood estimator and likelihood ratio test or chi-square test statistic but we consider minimum phi-divergence estimators and phi-divergence test statistics. Families of minimum phi-divergence estimators and phi-divergence test statistics are wide classes of estimators and test statistics that contain as a particular case the maximum likelihood estimator, likelihood ratio test and chi-square test statistic. In an asymptotic set-up, the biases and the risk under the squared loss function for the proposed estimators are derived and compared. A numerical example clarifies the content of the paper.     

On recent developments in the theory of abstract differential equations with fractional derivatives

This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. (2009) [1], Belmekki and Benchohra (2010) [2], Darwish et al. (2009) [3], Hu et al. (2009) [4], Mophou and N’Guérékata (2009) [6] and [7], Mophou (2010) [8] and [9], Muslim (2009) [10], Pandey et al. (2009) [11], Rashid and El-Qaderi (2009) [12] and Tai and Wang (2009) [13]] are incorrect since the considered variation of constant formulas is not appropriate. In this note, we also consider a different approach to treat a general class of abstract fractional differential equations.     

An upper bound for the competition numbers of graphs

A hole of a graph is an induced cycle of length at least 4. Kim (2005) [2] conjectured that the competition number k(G) is bounded by h(G)+1 for any graph G, where h(G) is the number of holes of G. In Lee et al. [3], it is proved that the conjecture is true for a graph whose holes are mutually edge-disjoint. In Li et al. (2009) [4], it is proved that the conjecture is true for a graph, all of whose holes are independent. In this paper, we prove that Kim’s conjecture is true for a graph G satisfying the following condition: for each hole C of G, there exists an edge which is contained only in C among all induced cycles of G.     

A new approach to relative asymptotic behavior for discrete Sobolev-type orthogonal polynomials on the unit circle

In Foulquié et al. (1999) [2], Li and Marcellán (1996) [4], Marcellán and Moral (2002) [5], the relative asymptotic behavior of orthogonal polynomials with respect to a discrete Sobolev-type inner product on the unit circle was studied. In this paper, we propose an alternative approach to this problem based on the Uvarov spectral transformation.     

The wavelet transform method applied to a coupled chaotic system with asymmetric coupling schemes

The wavelet transform method originated by Wei et al. (2002) [19] is an effective tool for enhancing the transverse stability of the synchronous manifold of a coupled chaotic system. Much of the theoretical study on this matter is centered on networks that are symmetrically coupled. However, in real applications, the coupling topology of a network is often asymmetric; see Belykh et al. (2006)  [23], [24], Chavez et al. (2005)  [25], Hwang et al. (2005)  [26], Juang et al. (2007)  [17], and Wu (2003)  [13]. In this work, a certain type of asymmetric sparse connection topology for networks of coupled chaotic systems is presented. Moreover, our work here represents the first step in understanding how to actually control the stability of global synchronization from dynamical chaos for asymmetrically connected networks of coupled chaotic systems via the wavelet transform method. In particular, we obtain the following results. First, it is shown that the lower bound for achieving synchrony of the coupled chaotic system with the wavelet transform method is independent of the number of nodes. Second, we demonstrate that the wavelet transform method as applied to networks of coupled chaotic systems is even more effective and controllable for asymmetric coupling schemes as compared to the symmetric cases.     

Remarks on a Strongly Nonlinear Model for Two‐Layer Flows with a Top Free Surface

We revisit in this paper the strongly nonlinear long wave model for large amplitude internal waves in two‐layer flows with a free surface proposed by Choi and Camassa [1] and Barros et al. [2]. Its solitary‐wave solutions were the object of the work by Barros and Gavrilyuk [3], who proved that such solutions are governed by a Hamiltonian system with two degrees of freedom. A detailed analysis of the critical points of the system is presented here, leading to some new results. It is shown that conjugate states for the long wave model are the same as those predicted by the fully nonlinear Euler equations. Some emphasis will be given to the baroclinic mode, where interfacial waves are known to change polarity according to different values of density and depth ratios. A critical depth ratio separates these two regimes and its analytical expression is derived directly from the model. In addition, we prove that such waves cannot exist throughout the whole range of speeds.     

Performance enhancement and validation of the open-source software for modeling of ship infrared signatures (OSMOSIS)

Designing stealth technologies for modern warships requires methods for signatures reduction (radar, infrared, etc). First, we have to model these signatures. In Lapierre et al. (2006), Lapierre et al. (2007) [3] and [4], we proposed an infrared (IR) ship signature simulation software (OSMOSIS) that can manage parametric emissivity. OSMOSIS comprises a smart computation time and memory management. Evaluating the effectiveness of an IR signature reduction method implies simulating the evolution of the IR signature with time. This requires a huge computation time. In this paper, we propose a novel hierarchical meshing strategy leading to an important reduction of the computation time. The time complexity of the algorithm is shown to be , where N is the requested number of facets of the mesh of the ship’s surface. Then, we validate OSMOSIS on temperature measurements performed on an “L-shape” object.     

Multivariate measures of skewness for the skew-normal distribution

The main objective of this work is to calculate and compare different measures of multivariate skewness for the skew-normal family of distributions. For this purpose, we consider the Mardia (1970) [10], Malkovich and Afifi (1973) [9], Isogai (1982) [17], Srivastava (1984) [15], Song (2001) [14], Móri et al. (1993) [11], Balakrishnan et al. (2007) [3] and Kollo (2008) [7] measures of skewness. The exact expressions of all measures of skewness, except for Song’s, are derived for the family of skew-normal distributions, while Song’s measure of shape is approximated by the use of delta method. The behavior of these measures, their similarities and differences, possible interpretations, and their practical use in testing for multivariate normal are studied by evaluating their power in the case of some specific members of the multivariate skew-normal family of distributions.     

Weaker conditions for the convergence of Newton’s method

Newton’s method is often used for solving nonlinear equations. In this paper, we show that Newton’s method converges under weaker convergence criteria than those given in earlier studies, such as Argyros (2004) [2, p. 387], Argyros and Hilout (2010)[11, p. 12], Argyros et al. (2011) [12, p. 26], Ortega and Rheinboldt (1970) [26, p. 421], Potra and Pták (1984) [36, p. 22]. These new results are illustrated by several numerical examples, for which the older convergence criteria do not hold but for which our weaker convergence criteria are satisfied.     

M/D^{[y]}/1 Periodically gated vacation model and its application to IEEE 802.16 network

In this paper we consider the analysis of an \(M/D^{[y]}/1\) vacation queue with periodically gated discipline. The motivation of introducing the new periodically gated discipline lies in modeling a kind of contention-based bandwidth reservation mechanism applied in wireless networks. The analysis approach applied here consists of two steps and it is based on appropriately chosen characteristic epochs of the system. We provide approximate expressions for the probability-generating function of the number of customers at arbitrary epoch as well as for the Laplace–Stieljes transform and for the mean of the steady-state waiting time. Several numerical examples are also provided. In the second part of the paper we discuss how to apply the periodically gated vacation model to the non real-time uplink traffic in IEEE 802.16-based wireless broadband networks.     

Stability and convergence of staggered Runge-Kutta schemes for semilinear wave equations

A staggered Runge-Kutta (staggered RK) scheme is a Runge-Kutta type scheme using a time staggered grid, as proposed by Ghrist et al. in 2000 [6]. Afterwards, Verwer in two papers investigated the efficiency of a scheme proposed by Ghrist et al. [6] for linear wave equations. We study stability and convergence properties of this scheme for semilinear wave equations. In particular, we prove convergence of a fully discrete scheme obtained by applying the staggered RK scheme to the MOL approximation of the equation.     

Supply chain network downsizing with product line pruning using a new demand substitution

This paper presents an optimization model for downsizing a multi-product supply chain facing bankruptcy risk, where multi-functional production facilities are shared for producing a group of substitutable products. In order to determine the potential demand after discontinuation of certain product types, the proposed mixed integer programming model incorporates a new general formulation of demand substitution, which allows arbitrary demand diversion and arbitrary replacement rates between products under investigation. The new substitution formulation enables considering uneven substitutions for supply chain network design and therefore it extends currently used substitution approaches. A series of systematically generated downsizing cases confirm the validity of the here proposed approach, and illustrate how downsized chains can successfully adopt to the new circumstances.