http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2010/978137.htmlThe existence of multiple periodic solutions of the following differential delay equation x′(t)=−f(x(t−r)) is established by applying variational approaches directly, where x∈ℝ, f∈C(ℝ,ℝ) and r>0 is a given constant. This means that we do not need to use Kaplan and Yorke's reduction technique to reduce the existence problem of the above equation to an existence problem for a related coupled system. Such a reduction method introduced first by Kaplan and Yorke in (1974) is often employed in previous papers to study the existence of periodic solutions for the above equation and its similar ones by variational approaches.Rong Cheng and Jianhua Hu© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2010/278962.htmlWe study necessary and sufficient conditions for the oscillation of the third-order nonlinear ordinary differential equation with damping term and deviating argument x‴(t)+q(t)x′(t)+r(t)f(x(φ(t)))=0. Motivated by the work of Kiguradze (1992), the existence and asymptotic properties of nonoscillatory solutions are investigated in case when the differential operator ℒx=x‴+q(t)x′ is oscillatory.Miroslav Bartušek, Mariella Cecchi, Zuzana Došlá, and Mauro Marini© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2010/734126.htmlThe purpose of this paper is to introduce a new hybrid projection method for finding a common element of the set of common fixed points of two relatively quasi-nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone, and the set of solutions of the generalized equilibrium problem in the framework of a real Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Base on this result, we also get some new and interesting results. The results in this paper generalize, extend, and unify some well-known strong convergence results in the literature.Siwaporn Saewan, Poom Kumam, and Kriengsak Wattanawitoon© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/957475.htmlBy the continuation theorem of coincidence degree and M-matrix theory, we obtain some sufficient conditions for the existence and exponential stability of periodic solutions for a class of generalized neural networks with arbitrary delays, which are milder and less restrictive than those of previous known criteria. Moreover our results generalize and improve many existing ones.Yimin Zhang, Yongkun Li, and Kuohui Ye© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/128624.htmlThis paper concerns solutions for the Hamiltonian system: z˙=𝒥Hz(t,z). Here H(t,z)=(1/2)z⋅Lz+W(t,z), L is a 2N×2N symmetric matrix, and W∈C1(ℝ×ℝ2N,ℝ). We consider the case that 0∈σc(−(𝒥(d/dt)+L)) and W satisfies some superquadratic condition different from the type of Ambrosetti-Rabinowitz. We study this problem by virtue of some weak linking theorem recently developed and prove the existence of homoclinic orbits.Jian Ding, Junxiang Xu, and Fubao Zhang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/907167.htmlLee, An and Park introduced the quadratic functional equation f(2x+y)+f(2x−y)=8f(x)+2f(y) and proved the stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation in Banach spaces.Choonkil Park and Ji-Hye Kim© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/103723.htmlWe study the policy iteration algorithm (PIA) for continuous-time jump Markov decision processes in general state and action spaces. The corresponding transition rates are allowed to be unbounded, and the reward rates may have neither upper nor lower bounds. The criterion that we are concerned with is expected average reward. We propose a set of conditions under which we first establish the average reward optimality equation and present the PIA. Then under two slightly different sets of conditions we show that the PIA yields the optimal (maximum) reward, an average optimal stationary policy, and a solution to the average reward optimality equation.Quanxin Zhu, Xinsong Yang, and Chuangxia Huang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/780287.htmlWe show that the p-convexified Tsirelson space 𝒯(p) for 0<p<1 and all its complemented subspaces with unconditional basis have unique unconditional basis up to permutation. The techniques involved in the proof are different from the methods that have been used in all the other uniqueness results in the nonlocally convex setting.F. Albiac and C. Leránoz© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/725846.htmlThe passivity problem is investigated for a class of stochastic uncertain neural networks with time-varying delay as well as generalized activation functions. By constructing appropriate Lyapunov-Krasovskii functionals, and employing Newton-Leibniz formulation, the free-weighting matrix method, and stochastic analysis technique, a delay-dependent criterion for checking the passivity of the addressed neural networks is established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. An example with simulation is given to show the effectiveness and less conservatism of the proposed criterion. It is noteworthy that the traditional assumptions on the differentiability of the time-varying delays and the boundedness of its derivative are removed.Jianting Zhou, Qiankun Song, and Jianxi Yang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/297565.htmlWe prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006) and Nakajo and Takahashi (2003).Watcharaporn Cholamjiak and Suthep Suantai© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/243604.htmlThis paper is devoted to the following question: how to characterize convex nowhere dense subsets of normed linear spaces in terms of porosity? The motivation for this study originates from papers of V. Olevskii and L. Zajíček, where it is shown that convex nowhere dense subsets of normed linear spaces are porous in some strong senses.Filip Strobin© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/481712.htmlWe study the permanence of periodic predator-prey system with general nonlinear functional responses and stage structure for both predator and prey and obtain that the predator and the prey species are permanent.Xuming Huang, Xiangzeng Kong, and Wensheng Yang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/341679.htmlWe consider a higher-order three-point boundary value problem on time scales. A new existence result is first obtained by using a fixed point theorem due to Krasnoselskii and Zabreiko. Later, under certain growth conditions imposed on the nonlinearity, several sufficient conditions for the existence of a nonnegative and nontrivial solution are obtained by using Leray-Schauder nonlinear alternative. Our conditions imposed on nonlinearity are all very easy to verify; as an application, some examples to demonstrate our results are given.Yanbin Sang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/931020.htmlA bounded linear operator T on a Hilbert space ℋ, satisfying ‖T2h‖2+‖h‖2≥2‖Th‖2 for every h∈ℋ, is called a convex operator. In this paper, we give necessary and sufficient conditions under which a convex composition operator on a large class of weighted Hardy spaces is an isometry. Also, we discuss convexity of multiplication operators.Karim Hedayatian and Lotfollah Karimi© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/149367.htmlIn this work we use analytical tools—Schauder bases and Geometric Series theorem—in order to develop a new method for the numerical resolution of the linear Volterra integral equation of the second kind.M. I. Berenguer, D. Gámez, A. I. Garralda-Guillem, M. Ruiz Galán, and M. C. Serrano Pérez© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/467342.htmlWe abstract the definition of the Costas property in the context of a group and study specifically dense Costas sets (named Costas clouds) in groups with the topological property that they are dense in themselves: as a result, we prove the existence of nowhere continuous dense bijections that satisfy the Costas property on ℚ2, ℝ2, and ℂ2, the latter two being based on nonlinear solutions of Cauchy's functional equation, as well as on ℚ, ℝ, and ℂ, which are, in effect, generalized Golomb rulers. We generalize the Welch and Golomb construction methods for Costas arrays to apply on ℝ and ℂ, and we prove that group isomorphisms on and tensor products of Costas sets result to new Costas sets with respect to an appropriate set of distance vectors. We also give two constructive examples of a nowhere continuous function that satisfies a constrained form of the Costas property (over rational or algebraic displacements only, i.e.), based on the indicator function of a dense subset of ℝ.Konstantinos Drakakis© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/294845.htmlThe problem of robust stability for a class of neutral control systems with mixed delays is investigated. Based on Lyapunov stable theory, by constructing a new Lyapunov-Krasovskii function, some new stable criteria are obtained. These criteria are formulated in the forms of linear matrix inequalities (LMIs). Compared with some previous publications, our results are less conservative. Simulation examples are presented to illustrate the improvement of the main results.Zixin Liu, Shu Lü, Shouming Zhong, and Mao Ye© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/723236.htmlWe investigate the stochastic 3D Navier-Stokes-α model which arises in the modelling of turbulent flows of fluids. Our model contains nonlinear forcing terms which do not satisfy the Lipschitz conditions. The adequate notion of solutions is that of probabilistic weak solution. We establish the existence of a such of solution. We also discuss the uniqueness.Gabriel Deugoue and Mamadou Sango© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/624798.htmlWe consider a hybrid projection algorithm based on the shrinking projection method for two families of quasi-ϕ-nonexpansive mappings. We establish strong convergence theorems for approximating the common element of the set of the common fixed points of such two families and the set of solutions of the variational inequality for an inverse-strongly monotone operator in the framework of Banach spaces. As applications, at the end of the paper we first apply our results to consider the problem of finding a zero point of an inverse-strongly monotone operator and we finally utilize our results to study the problem of finding a solution of the complementarity problem. Our results improve and extend the corresponding results announced by recent results.Rabian Wangkeeree and Rattanaporn Wangkeeree© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/430452.htmlThe author establishes some identities involving the D numbers, Bernoulli numbers, and central factorial numbers of the first kind. A generating function and several computational formulas for D-Nörlund numbers are also presented.Guodong Liu© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/649831.htmlWe establish strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of two relatively nonexpansive mappings in a Banach space by using a new hybrid method. Moreover we apply our main results to obtain strong convergence for a maximal monotone operator and two nonexpansive mappings in a Hilbert space.Chakkrid Klin-eam, Suthep Suantai, and Wataru Takahashi© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/694394.htmlWe establish two optimal inequalities among power mean Mp(a,b)=(ap/2+bp/2)1/p, arithmetic mean A(a,b)=(a+b)/2, logarithmic mean L(a,b)=(a−b)/(log⁡a−log⁡b), and geometric mean G(a,b)=ab.Ming-yu Shi, Yu-ming Chu, and Yue-ping Jiang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/165194.htmlThe present paper discusses in the metric Lp S. N. Bernstein type inequalities of the most general kind on very general accessible classes of curves in a complex plane. The obtained estimations, generally speaking, are not improvable.J. I. Mamedkhanov and I. B. Dadashova© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/307404.htmlIf F is a continuous function on the real line and f=F′ is its distributional derivative, then the continuous primitive integral of distribution f is ∫abf=F(b)−F(a). This integral contains the Lebesgue, Henstock-Kurzweil, and wide Denjoy integrals. Under the Alexiewicz norm, the space of integrable distributions is a Banach space. We define the convolution f∗g(x)=∫−∞∞f(x−y)g(y)dy for f an integrable distribution and g a function of bounded variation or an L1 function. Usual properties of convolutions are shown to hold: commutativity, associativity, commutation with translation. For g of bounded variation, f∗g is uniformly continuous and we have the estimate ‖f∗g‖∞≤‖f‖‖g‖ℬ𝒱, where ‖f‖=supI|∫If| is the Alexiewicz norm. This supremum is taken over all intervals I⊂ℝ. When g∈L1, the estimate is ‖f∗g‖≤‖f‖‖g‖1. There are results on differentiation and integration of convolutions. A type of Fubini theorem is proved for the continuous primitive integral.Erik Talvila© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/897058.htmlA class of second-order nonlinear differential equations with damping term (r(t)|x′(t)|σ−1x′(t))′+p(t)|x′(t)|σ−1x′(t)+q(t)f(x(t))=0 are investigated in this paper. By using a new method, we obtain some new sufficient conditions for the oscillation of the above equation, and some references are extended in this paper. Examples are inserted to illustrate this result.Zigen Ouyang, Jichao Zhong, and Shuliang Zou© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/695121.htmlWe study a Beddington-DeAngelis type predator-prey system with impulsive perturbation and seasonal effects. First, we numerically observe the influence of seasonal effects on the system without impulsive perturbations. Next, we find the conditions for the local and global stabilities of prey-free periodic solutions by using Floquet theory for the impulsive equation and small amplitude perturbation skills, and for the permanence of the system via comparison theorem. Finally, we show that seasonal effects and impulsive perturbation can give birth to various kinds of dynamical behavior of the system including chaotic phenomena by numerical simulations.Hunki Baek and Younghae Do© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/613524.htmlWe introduce and study a new hybrid projection algorithm for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points of relatively quasi-nonexpansive mappings, and the set of solutions of the variational inequality for an inverse-strongly-monotone operator in a Banach space. Under suitable assumptions, we show a strong convergence theorem. Using this result, we obtain some applications in a Banach space. The results obtained in this paper extend and improve the several recent results in this area.Wariam Chuayjan and Sornsak Thianwan© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/934905.htmlWe obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and quasiperiodic boundary conditions. Then by using these asymptotic formulas, we find conditions on the coefficients for which the number of gaps in the spectrum of the self-adjoint differential operator with the periodic matrix coefficients is finite.O. A. Veliev© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/728510.htmlWe introduce a general iteration scheme for a finite family of generalized asymptotically quasi-nonexpansive mappings in Banach spaces. The new iterative scheme includes the multistep Noor iterations with errors, modified Mann and Ishikawa iterations, three-step iterative scheme of Xu and Noor, and Khan and Takahashi scheme as special cases. Our results generalize and improve the recent ones announced by Khan et al. (2008), H. Fukhar-ud-din and S. H. Khan (2007), J. U. Jeong and S. H. Kim (2006), and many others.S. Imnang and S. Suantai© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/537963.htmlWe solve the inhomogeneous Euler differential equations of the form x2y′′(x)+αxy′(x)+βy(x)=∑m=0∞amxm and apply this result to the approximation of analytic functions of a special type by the solutions of Euler differential equations.Soon-Mo Jung and Seungwook Min© 2010, Hindawi Publishing Corporation. All rights reserved.