http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/328479.htmlThis paper is concerned with the second-order Hamiltonian system on time scales 𝕋 of the form uΔΔ(ρ(t))+μb(t)|u(t)|μ−2u(t)+∇¯H(t,u(t))=0, Δ-a.e. t∈[0,T]𝕋 , u(0)−u(T)=uΔ(ρ(0))−uΔ(ρ(T))=0, where 0,T∈𝕋. By using the minimax methods in critical theory, an existence theorem of periodic solution for the above system is established. As an application, an example is given to illustrate the result. This is probably the first time the existence of periodic solutions for second-order Hamiltonian system on time scales has been studied by critical theory.You-Hui Su and Wan-Tong Li© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/475320.htmlWe determine the weakly asymptotically orders for the average errors of the Grünwald interpolation sequences based on the Tchebycheff nodes in the Wiener space. By these results we know that for the Lp-norm (2≤q≤4) approximation, the p-average (1≤p≤4) error of some Grünwald interpolation sequences is weakly equivalent to the p-average errors of the best polynomial approximation sequence.Yingfang Du and Huajie Zhao© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/608976.htmlThis paper studies the dynamic behavior of the positive solutions to the difference equation xn=A+xn−kp/xn−1r, n=1,2,…, where A,p, and r are positive real numbers, and the initial conditions are arbitrary positive numbers. We establish some results regarding the stability and oscillation character of this equation for p∈(0,1).Fangkuan Sun, Xiaofan Yang, and Chunming Zhang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/325296.htmlWe study the behavior of the solutions of the following system of difference equations xn+1=max⁡{A/xn,yn/xn}, yn+1=max⁡{A/yn,xn/yn} where the constant A and the initial conditions are positive real numbers.Dağistan Simsek, Bilal Demir, and Cengiz Cinar© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/143019.htmlWe present a set of difference equations which generalizes that proposed in the work of G. Izzo and A. Vecchio (2007) and represents the discrete counterpart of a larger class of continuous model concerning the dynamics of an infection in an organism or in a host population. The limiting behavior of this new discrete model is studied and a threshold parameter playing the role of the basic reproduction number is derived.Giuseppe Izzo, Yoshiaki Muroya, and Antonia Vecchio© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/140369.htmlWe give new and very general characterizations for uniform exponential dichotomy of variational difference equations in terms of the admissibility of pairs of sequence spaces over ℕ with respect to an associated control system. We establish in the variational case the connections between the admissibility of certain pairs of sequence spaces over ℕ and the admissibility of the corresponding pairs of sequence spaces over ℤ. We apply our results to the study of the existence of exponential dichotomy of linear skew-product flows.Bogdan Sasu© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/863178.htmlWe establish sufficient conditions for the convergence of solutions of a certain third-order nonlinear differential equations. By constructing a Lyapunov function as the basic tool, some results which exist in the relevant literature are generalized.Ercan Tunç© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/323065.htmlBy constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the discrete predator-prey system with Hassell-Varley type functional response are obtained. Example together with its numerical simulation shows that the main results are verifiable.Runxin Wu and Lin Li© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/315713.htmlThis paper investigates the stability properties of a class of switched systems possessing several linear time-invariant parameterizations (or configurations) which are governed by a switching law. It is assumed that the parameterizations are stabilized individually via an appropriate linear state or output feedback stabilizing controller whose existence is first discussed. A main novelty with respect to previous research is that the various individual parameterizations might be continuous-time, discrete-time, or mixed so that the whole switched system is a hybrid continuous/discrete dynamic system. The switching rule governs the choice of the parameterization which is active at each time interval in the switched system. Global asymptotic stability of the switched system is guaranteed for the case when a common Lyapunov function exists for all the individual parameterizations and the sampling period of the eventual discretized parameterizations taking part of the switched system is small enough. Some extensions are also investigated for controlled systems under decentralized or mixed centralized/decentralized control laws which stabilize each individual active parameterization.M. De la Sen and A. Ibeas© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/670560.htmlThis paper proposes a one-sector multigroup growth model with endogenous labor supply in discrete time. Proposing an alternative approach to behavior of households, we examine the dynamics of wealth and income distribution in a competitive economy with capital accumulation as the main engine of economic growth. We show how human capital levels, preferences, and labor force of heterogeneous households determine the national economic growth, wealth, and income distribution and time allocation of the groups. By simulation we demonstrate, for instance, that in the three-group economy when the rich group's human capital is improved, all the groups will economically benefit, and the leisure times of all the groups are reduced but when any other group's human capital is improved, the group will economically benefit, the other two groups economically lose, and the leisure times of all the groups are increased.Wei-Bin Zhang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/527385.htmlTotal transfer capability (TTC) is an important index in a power system with large volume of inter-area power exchanges. This paper proposes a novel technique to determine the TTC and its confidence intervals in the system by considering the uncertainties in the load and line parameters. The optimal power flow (OPF) method is used to obtain the TTC. Variations in the load and line parameters are incorporated using the interval arithmetic (IA) method. The IEEE 30 bus test system is used to illustrate the proposed methodology. Various uncertainties in the line, load and both line and load are incorporated in the evaluation of total transfer capability. From the results, it is observed that the solutions obtained through the proposed method provide much wider information in terms of closed interval form which is more useful in ensuring secured operation of the interconnected system in the presence of uncertainties in load and line parameters.Prabha Umapathy, C. Venkataseshaiah, and M. Senthil Arumugam© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/485412.htmlWe extend to random fields case, the results of Woyczynski, who proved Brunk's type strong law of large numbers (SLLNs) for 𝔹-valued random vectors under geometric assumptions. Also, we give probabilistic requirements for above-mentioned SLLN, related to results obtained by Acosta as well as necessary and sufficient probabilistic conditions for the geometry of Banach space associated to the strong and weak law of large numbers for multidimensionally indexed random vectors.Zbigniew A. Lagodowski© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/235038.htmlA kind of fourth-order delay differential equation is considered. Firstly, the linear stability is investigated by analyzing the associated characteristic equation. It is found that there are stability switches for time delay and Hopf bifurcations when time delay cross through some critical values. Then the direction and stability of the Hopf bifurcation are determined, using the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the analytic results.Xiaoqian Cui and Junjie Wei© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/812674.htmlWe investigate asymptotic behavior and periodic nature of positive solutions of the difference equation xn=max⁡{A/xn−1,1/xn−3α},n=0,1,…, where A>0 and 0<α<1. We prove that every positive solution of this difference equation approaches x¯=1 or is eventually periodic with period 2.Ali Gelişken and Cengiz Çinar© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/976406.htmlWe study the existence of positive solutions for the following nonlinear m-point boundary value problem for an increasing homeomorphism and homomorphism with sign changing nonlinearity: {(ϕ(u′(t)))′+a(t)f(t,u(t))=0, 0<t<1, u′(0)=∑i=1m−2aiu′(ξi), u(1)=∑i=1kbiu(ξi)−∑i=k+1sbiu(ξi)−∑i=s+1m−2biu′(ξi), where ϕ:R→R is an increasing homeomorphism and homomorphism and ϕ(0)=0. The nonlinear term f may change sign. As an application, an example to demonstrate our results is given. The conclusions in this paper essentially extend and improve the known results.Hua Su© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/329173.htmlThe batch split-complex backpropagation (BSCBP) algorithm for training complex-valued neural networks is considered. For constant learning rate, it is proved that the error function of BSCBP algorithm is monotone during the training iteration process, and the gradient of the error function tends to zero. By adding a moderate condition, the weights sequence itself is also proved to be convergent. A numerical example is given to support the theoretical analysis.Huisheng Zhang, Chao Zhang, and Wei Wu© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/760328.htmlThis paper deals with the second-order nonlinear systems of difference equations, we obtain the existence theorems of periodic solutions. The theorems are proved by using critical point theory.Shugui Kang and Bao Shi© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/205481.htmlThis paper discusses a discrete periodic Volterra model with mutual interference and Holling II type functional response. Firstly, sufficient conditions are obtained for the permanence of the system. After that, we give an example to show the feasibility of our main results.Lijuan Chen and Liujuan Chen© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/973714.htmlWe study the boundedness, the attractivity, and the stability of the positive solutions of the rational difference equation xn+1=(pnxn−2+xn−3)/(qn+xn−3), n=0,1,…, where pn,qn, n=0,1,… are positive sequences of period 2.G. Papaschinopoulos, G. Stefanidou, and C. J. Schinas© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/793732.htmlIn recent years, the impulsive population systems have been studied by many researchers. However, seasonal effects on prey are rarely discussed. Thus, in this paper, the dynamics of the Holling-type IV two-competitive-prey one-predator system with impulsive perturbations and seasonal effects are analyzed using the Floquet theory and comparison techniques. It is assumed that the impulsive perturbations act in a periodic fashion, the proportional impulses (the chemical controls) for all species and the constant impulse (the biological control) for the predator at different fixed time but, the same period. In addition, the intrinsic growth rates of prey population are regarded as a periodically varying function of time due to seasonal variations. Sufficient conditions for the local and global stabilities of the two-prey-free periodic solution are established. It is proven that the system is permanent under some conditions. Moreover, sufficient conditions, under which one of the two preys is extinct and the remaining two species are permanent, are also found. Finally, numerical examples and conclusion are given.Hunki Baek© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2008/467972.htmlThe paper presents a nonlinear discrete game model for two oligopolistic firms whose products are adnascent. (In biology, the term adnascent has only one sense, “growing to or on something else,” e.g., “moss is an adnascent plant.” See Webster's Revised Unabridged Dictionary published in 1913 by C. & G. Merriam Co., edited by Noah Porter.) The bifurcation of its Nash equilibrium is analyzed with Schwarzian derivative and normal form theory. Its complex dynamics is demonstrated by means of the largest Lyapunov exponents, fractal dimensions, bifurcation diagrams, and phase portraits. At last, bifurcation and chaos anticontrol of this system are studied.Baogui Xin, Junhai Ma, and Qin Gao© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2008/740845.htmlThe ongoing subprime mortgage crisis (SMC) and implementation of Basel II Capital Accord regulation have resulted in issues related to bank valuation and profitability becoming more topical. Profit is a major indicator of financial crises for households, companies, and financial institutions. An SMC-related example of this is the U.S. bank, Wachovia Corp., which reported major losses in the first quarter of 2007 and eventually was bought by Citigroup in September 2008. A first objective of this paper is to value a bank subject to Basel II based on premiums for market, credit, and operational risk. In this case, we investigate the discrete-time dynamics of banking assets, capital, and profit when loan losses and macroeconomic conditions are explicitly considered. These models enable us to formulate an optimal bank valuation problem subject to cash flow, loan demand, financing, and balance sheet constraints. The main achievement of this paper is bank value maximization via optimal choices of loan rate and supply which leads to maximal deposits, provisions for deposit withdrawals, and bank profitability. The aforementioned loan rates and capital provide connections with the SMC. Finally, OECD data confirms that loan loss provisioning and profitability are strongly correlated with the business cycle.C. H. Fouche, J. Mukuddem-Petersen, M. A. Petersen, and M. C. Senosi© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2009/189768.htmlWe study the one-dimensional p-Laplacian m-point boundary value problem (φp(uΔ(t)))Δ+a(t)f(t,u(t))=0, t∈[0,1]T, u(0)=0, u(1)=∑i=1m−2aiu(ξi), where T is a time scale, φp(s)=|s|p−2s, p>1, some new results are obtained for the existence of at least one, two, and three positive solution/solutions of the above problem by using Krasnosel′skll′s fixed point theorem, new fixed point theorem due to Avery and Henderson, as well as Leggett-Williams fixed point theorem. This is probably the first time the existence of positive solutions of one-dimensional p-Laplacian m-point boundary value problem on time scales has been studied.Ying Zhang and ShiDong Qiao© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2008/150163.htmlThis paper is concerned with nonoscillation of second-order neutral delay differential equation with forcing term. By using contraction mapping principle, some sufficient conditions for the existence of nonoscillatory solution are established. The criteria obtained in this paper complement and extend several known results in the literature. Some examples illustrating our main results are given.Jin-Zhu Zhang, Zhen Jin, Tie-Xiong Su, Jian-Jun Wang, Zhi-Yu Zhang, and Ju-Rang Yan© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2008/310425.htmlWe study the dynamic behaviors of a general discrete nonautonomous system of plankton allelopathy with delays. We first show that under some suitable assumption, the system is permanent. Next, by constructing a suitable Lyapunov functional, we obtain a set of sufficient conditions which guarantee the global attractivity of the two species. After that, by constructing an extinction-type Lyapunov functional, we show that under some suitable assumptions, one species will be driven to extinction. Finally, two examples together with their numerical simulations show the feasibility of the main results.Yaoping Chen, Fengde Chen, and Zhong Li© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2008/903678.htmlAn epidemic model of HIV infection of CD4+ T-cells with cure rate and delay is studied. We include a baseline ODE version of the model, and a differential-delay model with a discrete time delay. The ODE model shows that the dynamics is completely determined by the basic reproduction number R0<1. If R0<1, the disease-free equilibrium is asymptotically stable and the disease dies out. If R0>1, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region. In the DDE model, the delay stands for the incubation time. We prove the effect of that delay on the stability of the equilibria. We show that the introduction of a time delay in the virus-to-healthy cells transmission term can destabilize the system, and periodic solutions can arise through Hopf bifurcation.Junyuan Yang, Xiaoyan Wang, and Fengqin Zhang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2008/143040.htmlWe study the following third-order p-Laplacian m-point boundary value problems on time scales: (ϕp(uΔ∇))∇+a(t)f(t,u(t))=0, t∈[0,T]T, βu(0)−γuΔ(0)=0, u(T)=∑i=1m−2aiu(ξi), ϕp(uΔ∇(0))=∑i=1m−2biϕp(uΔ∇(ξi)), where ϕp(s) is p-Laplacian operator, that is, ϕp(s)=|s|p−2s, p>1,  ϕp−1=ϕq, 1/p+1/q=1,  0<ξ1<⋯<ξm−2<ρ(T). We obtain the existence of positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.Fuyi Xu© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2008/636153.htmlAn SIR epidemic model with incubation time and saturated incidence rate is formulated, where the susceptibles are assumed to satisfy the logistic equation and the incidence term is of saturated form with the susceptible. The threshold value ℜ0 determining whether the disease dies out is found. The results obtained show that the global dynamics are completely determined by the values of the threshold value ℜ0 and time delay (i.e., incubation time length). If ℜ0 is less than one, the disease-free equilibrium is globally asymptotically stable and the disease always dies out, while if it exceeds one there will be an endemic. By using the time delay as a bifurcation parameter, the local stability for the endemic equilibrium is investigated, and the conditions with respect to the system to be absolutely stable and conditionally stable are derived. Numerical results demonstrate that the system with time delay exhibits rich complex dynamics, such as quasiperiodic and chaotic patterns.Jin-Zhu Zhang, Zhen Jin, Quan-Xing Liu, and Zhi-Yu Zhang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2008/179589.htmlFor nonlinear difference equations of the form xn=F(n,xn−1,…,xn−m), it is usually difficult to find periodic solutions. In this paper, we consider a class of difference equations of the form xn=anxn−1+bnf(xn−k), where {an},  {bn} are periodic sequences and f is a nonlinear filtering function, and show how periodic solutions can be constructed. Several examples are also included to illustrate our results.Chengmin Hou and Sui Sun Cheng© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2008/384346.htmlSegmentation, a new method, for color, gray-scale MR medical images, and aerial images, is proposed. The method is based on gray-scale morphology. Edge detection algorithm includes function edge and marker-controlled watershed segmentation. It features the simple algorithm implemented in MATLAB. The watershed segmentation has been proved to be a powerful and fast technique for both contour detection and region-based segmentation. In principle, watershed segmentation depends on ridges to perform a proper segmentation, a property that is often fulfilled in contour detection where the boundaries of the objects are expressed as ridges. For region-based segmentation, it is possible to convert the edges of the objects into ridges by calculating an edge map of the image. Watershed is normally implemented by region growing, based on a set of markers to avoid oversegmentation.K. Parvati, B. S. Prakasa Rao, and M. Mariya Das© 2009, Hindawi Publishing Corporation. All rights reserved.