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This paper identifies a previously undiscovered behavior of uniformly distributed data points or vectors in high dimensional ellipsoidal models. Such models give near normal distributions for each of its dimensions. Converse of this may also be true; that is, for a normal-like distribution of an observed variable, it is possible that the distribution is a result of uniform distribution of data points in a high dimensional ellipsoidal model, to which the observed variable belongs. Given the currently held notion of normal distributions, this new behavior raises many interesting questions. This paper also attempts to answer some of those questions. We cover both volume based (filled) and surface based (shell) ellipsoidal models. The phenomenon is demonstrated using statistical as well as mathematical approaches. We also show that the dimensionality of the latent model, that is, the number of hidden variables in a system, can be calculated from the observed distribution. We call the new distribution “Tanazur” and show through experiments that it is at least observed in one real world scenario, that of the motion of particles in an ideal gas. We show that the Maxwell-Boltzmann distribution of particle speeds can be explained on the basis of Tanazur distributions.

Copyright © 2015 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this special issue, we have solicited submissions from electrical engineers, control engineers, computer scientists, and mathematicians. After a rigorous peer review process, 18 papers have been selected that provide overviews, solutions, or early promises, to manage, analyse, and interpret dynamical behaviours of networked systems. These papers have covered both the theoretical and practical aspects of networked system with incomplete information in the broad areas of dynamical systems, mathematics, statistics, operational research, and engineering.

This special volume was originally conceived to provide authors and readers a publication to present the most recent advances in the study of applications of various fixed point theorems. Since 1909, when Luitzen Brouwer proved the first fixed point theorem named after him, fixed point theory has played very important roles in many different fields. We can find a lot of demonstrations in optimization theory, approximation theory, differential equations, variational inequalities, complementary problems, equilibrium theory, game theory, economics theory, and so forth. Fixed point theorems are developed for single-valued or set-valued mappings of metric spaces, topological vector spaces, posets and lattices, Banach lattices, . . .. Among the themes of fixed point theory, the topic of approximation of fixed points of mappings is particularly important because it is useful for proving the existence of fixed points ofmappings. It can be applied to prove the solvability of optimization problems, differential equations, variational inequalities, and equilibrium problems. Due to the importance of and the high volume of active research in the nonlinear analysis and optimization and, in particular, many new tools in studying them involving fixed point approximations, it is worthwhile to publish a special issue on this topic to highlight the recent advances in this field. The selection of the papers included in this volume, which has been based on a strict international peer review procedure, contains a representative list of papers with newfangled results which covers the different topics considered in our original proposal. In the papers in this special issue, the following topics are discussed.

Anderson's inequality (Anderson, 1958) as well as its improved version given by Fink (2003) is known to provide interesting examples of integral inequalities. In this paper, we establish local fractional integral analogue of Anderson's inequality on fractal space under some suitable conditions. Moreover, we also show that the local fractional integral inequality on fractal space, which we have proved in this paper, is a new generalization of the classical Anderson's inequality.

This paper presents a tube-based model predictive control (MPC) algorithm with piecewise affine control laws for discrete-time linear systems in the presence of bounded disturbances. By solving the standard multiparametric quadratic programming (mp-QP), the explicit piecewise affine control laws for tube-based MPC are obtained. Each control law is piecewise affine with respect to the corresponding region (one of the partitions of the feasible set). Due to the fact that the above-mentioned procedures are totally offline, the online computation time is short enough for stabilizing those systems with fast dynamics. In this paper, all the involved constraint sets are assumed to be polytopes. An illustrative example is utilized to verify the feasibility and efficiency of the proposed algorithm.

The stock market has the huge effect and influence on a country or region’s economic and financial activities. But we have found that it is very hard for the prediction and control. This illustrates a critical need for new and fundamental understanding of the structure and dynamics of stock markets. Previous research and analysis on stock markets often focused on some assumptions of the game of competition and cooperation. Under the condition of these assumptions, the conclusions often reflect just part of the problem. The stock price is the core reflections of a stock market. So, in this paper, the authors introduce a methodology for constructing stock networks based on stock prices in a stock market and detecting dynamic communities in it. This strategy will help us from a new macroperspective to explore and mine the characteristics and laws hiding in the big data of stock markets. Through statistical analysis of many characteristics of dynamic communities, some interesting phenomena are found in this paper. These results are new findings in finance data analysis field and will potentially contribute to the analysis and decision-making of a financial market. The method presented in this paper can also be used to analyze other similar financial systems.

This paper deals with approximating properties of the newly defined $q$ -generalization of the genuine Bernstein-Durrmeyer polynomials in the case $q>1$ , which are no longer positive linear operators on $C[0,1]$ . Quantitative estimates of the convergence, the Voronovskaja-type theorem, and saturation of convergence for complex genuine $q$ -Bernstein-Durrmeyer polynomials attached to analytic functions in compact disks are given. In particular, it is proved that, for functions analytic in $\{z\in \Bbb C:|z|q$ , the rate of approximation by the genuine $q$ -Bernstein-Durrmeyer polynomials $(q>1)$ is of order ${q}^{-n}$ versus $1/n$ for the classical genuine Bernstein-Durrmeyer polynomials. We give explicit formulas of Voronovskaja type for the genuine $q$ -Bernstein-Durrmeyer for $q>1$ . This paper represents an answer to the open problem initiated by Gal in (2013, page 115).

Fractional Brownian motion with Hurst exponentH∈(1/2,1)is a good candidate for modeling financial time series with long-range dependence and self-similarity. The main purpose of this paper is to address the valuation of equity indexed annuity (EIA) designs under the market driven by fractional Brownian motion. As a result, this paper presents an explicit pricing expression for point-to-point EIA design and bounds for the pricing of high-water-marked EIA design. Some numerical examples are given to illustrate the impact of the parameters involved in the pricing problems.

We introduce a new iterative method for finding a common element of the set of solutions of an equilibrium problem and the set of all common fixed points of a nonexpansive semigroup and prove the strong convergence theorem in Hilbert spaces. Our result extends the recent result of Zegeye and Shahzad (2013). In the last part of the paper, by the way, we point out that there is a slight flaw in the proof of the main result in Shehu's paper (2012) and perfect the proof.

In the first part of the paper, following the works of Pehlivan et al. (2004), we study the set of allA-statistical cluster points of sequences inm-dimensional spaces and make certain investigations on the set of allA-statistical cluster points of sequences inm-dimensional spaces. In the second part of the paper, we apply this notion to study an asymptotic behaviour of optimal paths and optimal controls in the problem of optimal control in discrete time and prove a general version of turnpike theorem in line of the work of Mamedov and Pehlivan (2000). However, all results of this section are presented in terms of a more general notion ofℐ-cluster points.

The reconstruction of destroyed paper documents is of more interest during the last years. This topic is relevant to the fields of forensics, investigative sciences, and archeology. Previous research and analysis on the reconstruction of cross-cut shredded text document (RCCSTD) are mainly based on the likelihood and the traditional heuristic algorithm. In this paper, a feature-matching algorithm based on the character recognition via establishing the database of the letters is presented, reconstructing the shredded document by row clustering, intrarow splicing, and interrow splicing. Row clustering is executed through the clustering algorithm according to the clustering vectors of the fragments. Intrarow splicing regarded as the travelling salesman problem is solved by the improved genetic algorithm. Finally, the document is reconstructed by the interrow splicing according to the line spacing and the proximity of the fragments. Computational experiments suggest that the presented algorithm is of high precision and efficiency, and that the algorithm may be useful for the different size of cross-cut shredded text document.

This paper deals with a research question raised by Jentzen and Röckner (A Milstein scheme for SPDEs, arXiv:1001.2751v4 (2012)), whether the exponential term in their introduced scheme can be replaced by a simpler mollifier. This replacement can lead to more simplification and computational reduction in simulation. So, in this paper, we essentially replace the exponential term with a Padé approximation of order 1 and denote the resulting scheme by simplified Milstein scheme. The convergence analysis for this scheme is carried out and it is shown that even with this replacement the order of convergence is maintained, while the resulting scheme is easier to implement and slightly more efficient computationally. Some numerical tests are given that confirm the order of accuracy and also computational cost reduction.

This paper deals with the mathematical analysis of a retarded partial integrodifferential equation that belongs to the class of thermostatted kinetic equations with time delay. Specifically, the paper is devoted to the proof of the existence and uniqueness of mild solutions of the related Cauchy problem. The main result is obtained by employing integration along the characteristic curves and successive approximations sequence arguments. Applications and perspective are also discussed within the paper.

The purpose of this paper is using the viscosity approximation method to study the strong convergence problem for a family of nonexpansive mappings in CAT(0) spaces. Under suitable conditions, some strong convergence theorems for the proposed implicit and explicit iterative schemes to converge to a common fixed point of the family of nonexpansive mappings are proved which is also a unique solution of some kind of variational inequalities. The results presented in this paper extend and improve the corresponding results of some others.

As platform based on users’ relationship to acquire, share, and propagate knowledge, Wechat develops very rapidly and becomes an important channel to spread knowledge. This new way to propagate knowledge is quite different from the traditional media way which enables knowledge to be spread surprisingly in Wechat. Based on complex network theory and the analysis of the factors which influence the knowledge propagation in Wechat, this paper summarizes the behavior preferences of Wechat users in knowledge propagation and establishes a Wechat knowledge propagation model. By the simulation experiment, this paper tests the model established and finds some important thresholds in knowledge propagation in Wechat. The findings are valuable for further studying the knowledge propagation in Wechat and provide theoretical proof for forecasting the scale and influence of knowledge propagation.

Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/303575 Open Access The paper investigates the stability and passivity analysis problems for a class of uncertain neural networks with time-delay via delta operator approach. Both the parameter uncertainty and the generalized activation functions are considered in this paper. By constructing an appropriate Lyapunov-Krasovskii functional, some new stability and passivity conditions are obtained in terms of linear matrix inequalities (LMIs). The main characteristic of this paper is to obtain novel stability and passivity analysis criteria for uncertain neural networks with time-delay in the delta operator system framework. A numerical example is presented to demonstrate the effectiveness of the proposed results.

The relative order of growth gives a quantitative assessment of how different functions scale each other and to what extent they are self-similar in growth. In this paper for any two positive integers p and q, we wish to introduce an alternative definition of relative $(p,q)$ th order which improves the earlier definition of relative $(p,q)$ th order as introduced by Lahiri and Banerjee (2005). Also in this paper we discuss some growth rates of entire functions on the basis of the improved definition of relative $(p,q)$ th order with respect to another entire function and extend some earlier concepts as given by Lahiri and Banerjee (2005), providing some examples of entire functions whose growth rate can accordingly be studied.

In the paper by Mocanu (1980), Mocanu has obtained sufficient conditions for a function in the classesC1(U), respectively, andC2(U)to be univalent and to mapUonto a domain which is starlike (with respect to origin), respectively, and convex. Those conditions are similar to those in the analytic case. In the paper by Mocanu (1981), Mocanu has obtained sufficient conditions of univalency for complex functions in the classC1which are also similar to those in the analytic case. Having those papers as inspiration, we try to introduce the notion of subordination for nonanalytic functions of classesC1andC2following the classical theory of differential subordination for analytic functions introduced by Miller and Mocanu in their papers (1978 and 1981) and developed in their book (2000). LetΩbe any set in the complex planeC, letpbe a nonanalytic function in the unit discU,p∈C2(U),and letψ(r,s,t;z):C3×U→C. In this paper, we consider the problem of determining properties of the functionp, nonanalytic in the unit discU, such thatpsatisfies the differential subordinationψ(p(z),Dp(z),D2p(z)-Dp(z);z)⊂Ω⇒p(U)⊂Δ.

Many studies show that the relationship among income inequality, poverty, and income mobility needs to be further discussed. Meanwhile, some researches on Distribution Function offer new perspective and methods to analyze this issue. First, this paper expresses the relationship among the Gini coefficient, poverty ratio, and income mobility of 5 common Distribution Functions through math deduction; this finding cannot be found in relevant literatures. Furthermore, an empirical research result proves that the income distribution of urban residents in the period from 2005 to 2010 fits Log-Logistic Distribution. On the basis of the above analysis and empirical data, the paper explores the relations of income inequality, poverty, and income mobility of urban residents and draws some useful conclusions.

In the recent paper (B. Samet, C. Vetro, and P. Vetro, Fixed point theorems forα-ψ-contractive type mappings, Nonlinear Analysis. Theory, Methods and Applications, 75 (2012), 2154-2165.), the authors introduced the concept ofα-admissible maps on metric spaces. Using this new concept, they presented some nice fixed point results. Also, they gave an existence theorem for integral equation to show the usability of their result. Then, many authors focused on this new concept and obtained a lot of fixed point results, which are used for existence theorems. In this paper, we not only extend some of the recent results about this direction but also generalize them. Then, we give some examples to show our results are proper extensions. Furthermore, we use our results to obtain the existence and uniqueness result for a solution of fourth order two-point boundary value problem.

Nonuniform exponential dichotomy has been investigated extensively. The essential condition of these previous results is based on the assumption that the nonlinear term satisfies|f(t,x)|≤μe−ε|t|. However, this condition is very restricted. There are few functions satisfying|f(t,x)|≤μe−ε|t|. In some sense, this assumption is not reasonable enough. More suitable assumption should be|f(t,x)|≤μ. To the best of the authors' knowledge, there is no paper considering the existence and uniqueness of solution to the perturbed nonautonomous system with a relatively conservative assumption|f(t,x)|≤μ. In this paper, we prove that if the nonlinear term is bounded, the perturbed nonautonomous system with nonuniform exponential dichotomy has a unique solution. The technique employed to prove Theorem 4 is the highlight of this paper.

This note is concerned with the linear matrix equationX=AX⊤B + C, where the operator(·)⊤denotes the transpose (⊤) of a matrix. The first part of this paper sets forth the necessary and sufficient conditions for the unique solvability of the solutionX. The second part of this paper aims to provide a comprehensive treatment of the relationship between the theory of the generalized eigenvalue problem and the theory of the linear matrix equation. The final part of this paper starts with a brief review of numerical methods for solving the linear matrix equation. In relation to the computed methods, knowledge of the residual is discussed. An expression related to the backward error of an approximate solution is obtained; it shows that a small backward error implies a small residual. Just like the discussion of linear matrix equations, perturbation bounds for solving the linear matrix equation are also proposed in this work.Erratum to “A Note on the⊤-Stein Matrix Equation”

Recent advances in theory and applications of complex dynamical systems have contributed much to the successful handling of certain problems in biology, physics, economics, engineering, and so forth that until recently were thought too difficult to be analyzed. These complex systems may be characterized by systems with uncertainty, impulse, time delay, stochastic perturbation, hybrid dynamics, distributed dynamics, and chaotic dynamics. The overall aim of this special issue is to bring together the latest or innovative knowledge and advances in mathematics for handling complex systems, whichmay depend largely onmethods frommathematical analysis, artificial intelligence, statistics, and engineering, including nonlinear dynamics, time series analysis, neural networks, and evolutionary computation. The solicited papers in this special issue should provide solutions tomodeling, analysis, control, and applications of real-world complex systems. The topics in this special issue included, but are not limited to, modelling, analysis, and applications of complex systems such as impulsive systems, pulse-modulated systems, switching systems, delayed systems, discontinuous control system theory, bifurcation theory and chaotic dynamics. The response to this special issue on modelling, analysis, and applications of complex systemswas beyond our expectation. We received 39 papers in this research field.This special issue includes thirty-one high-quality peer-reviewed articles. These articles contain some new, novel, and innovative techniques and ideas that may stimulate further research in every branch of theory and applications of complex systems. Acknowledgments

This paper addresses discrete subspace multiwindow Gabor analysis. Such a scenario can model many practical signals and has potential applications in signal processing. In this paper, using a suitable Zak transform matrix we characterize discrete subspace mixed multi-window Gabor frames (Riesz bases and orthonormal bases) and their duals with Gabor structure. From this characterization, we can easily obtain frames by designing Zak transform matrices. In particular, for usual multi-window Gabor frames (i.e., all windows have the same time-frequency shifts), we characterize the uniqueness of Gabor dual of type I (type II) and also give a class of examples of Gabor frames and an explicit expression of their Gabor duals of type I (type II).

Dynamic systems abound in virtually all areas of science and engineering. The control and optimization of such systems are of paramount importance inmany applications, including batch chemical reactions, spacecraft and hypersonic vehicle control, and switching power converters. In recent years, control and optimization methodologies have also been successfully applied to study financial and biological systems. This special issue includes many high-quality papers discussing theoretical investigations, numerical experiments, and practical applications of dynamic systems, optimization, and control. These papers offer numerous exciting new insights and research developments. Moreover, with more researchers joining the community of dynamic systems, control, and optimization, these areas will continue to develop and flourish in the future.

The sequence space was introduced by Maddox (1967). Quite recently, the sequence space of nonabsolute type has been introduced and studied which is the domain of the double sequential band matrix in the sequence space by Nergiz and Başar (2012). The main purpose of this paper is to investigate the geometric properties of the space , like rotundity and Kadec-Klee and the uniform Opial properties. The last section of the paper is devoted to the conclusion.

This paper is devoted to the convergence of the implicit Ishikawa iteration processes for approximating a common fixed point of nonexpansive semigroup in CAT(0) spaces. We obtain theΔ-convergence results of the implicit Ishikawa iteration sequences for a family of nonexpansive mappings in CAT(0) spaces. Under certain and different conditions, we also get the strong convergence theorems of implicit Ishikawa iteration sequences for nonexpansive semigroups in the CAT(0) spaces. The results presented in this paper extend and generalize some previous results.

The purpose of this paper is to deal with the shared set and uniqueness of meromorphic functions on annulus. The set of this paper is different from the set of the paper by Cao and Deng, and our theorems are improvement of the results given by Cao and Deng.

[EN] Plastic surgery practice grows continuously among the women in Western countries due to their body image dissatisfaction, aging anxiety, and an ideal body image propagated by the media. The consumption growth is so important that plastic surgery is becoming a normal practice among women, like any other cosmetic product, with the risk of suffering psychopathology disorders in the sense that plastic surgery could be employed as an instrument to recover personal self-esteem or even happiness. Plastic surgery practice depends on economic, demographic, and social contagion factors. In this paper, a mathematical epidemiological model to forecast female plastic surgery consumption in Spain is fully constructed. Overconsumer subpopulation is predicted and simulated. Robustness of the model versus uncertain parameters is studied throughout a sensitivity analysis., The authors would like to thank the European Union since this paper has been financed throughout the Project FP7-PEOPLE-2012-ITN Grant Agreement no. 304617 (FP7Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance). The authors also thank the Hadhramout University of Sciences and Technology of Yemen for financing the Ph.d. grant for M. S. S. Alkasadi.

This paper considers the problem of the convergence of the consensus algorithm for multiple agents in a directed network where each agent is governed by double-integrator dynamics and coupling time delay. The advantage of this protocol is that almost all the existing linear local interaction consensus protocols can be considered as special cases of the present paper. By combining algebraic graph theory and matrix theory and studying the distribution of the eigenvalues of the associated characteristic equation, some necessary and sufficient conditions are derived for reaching the second-order consensus. Finally, an illustrative example is also given to support the theoretical results.

The purpose of this paper is to introduce and analyze modified hybrid steepest-descent methods for a general system of variational inequalities (GSVI), with solutions being also zeros of an $m$ -accretive operator $A$ in the setting of real uniformly convex and 2-uniformly smooth Banach space $X$ . Here the modified hybrid steepest-descent methods are based on Korpelevich's extragradient method, hybrid steepest-descent method, and viscosity approximation method. We propose and consider modified implicit and explicit hybrid steepest-descent algorithms for finding a common element of the solution set of the GSVI and the set ${A}^{-\mathrm{1}}(\mathrm{0})$ of zeros of $A$ in $X$ . Under suitable assumptions, we derive some strong convergence theorems. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature.

Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic determinant where zeros cannot be explicitly computed. In this paper, we use the derivative sampling theorem “Hermite interpolations” to compute approximate values of the eigenvalues of Sturm-Liouville problems with eigenvalue parameter in one or two boundary conditions. We use recently derived estimates for the truncation and amplitude errors to compute error bounds. Also, using computable error bounds, we obtain eigenvalue enclosures. Also numerical examples, which are given at the end of the paper, give comparisons with the classical sinc method and explain that the Hermite interpolations method gives remarkably better results.

This paper deals with the construction of a discrete population mathematical model for the short-term forecast until January 2016 of the electoral support of extreme ideology parties in Spain. Firstly, the nontrivial concept of extreme ideology is stated. Then, the electoral register is split in three subpopulations: supporters of extremist parties, abstentions/blank voters, and supporters of establishment parties. The model takes into account the following variables: economy measured throughout the Spanish unemployment rate; demography quantified in terms of birth and death rates and emigration; sociopolitical situation measured by the Spanish poverty indicator, trust on the Government labor indicator (GLI), and the indicator of political trust. By considering the dynamic subpopulations transits built throughout data obtained from public and private prestigious institutions and sociopolitical analysis, a system of difference equations models the electoral population behavior in Spain allowing us to compute the expected electoral support in the time horizon of January 2016. Sensitivity analysis versus uncertain parameters is performed in order to improve the reliability of the model results., The authors of this paper would like to thank Phd. Pauwels from Universite Libre de Bruxelles and also Professor Eva Anduiza and her coworkers from Universidad Autonoma de Barcelona (UAB) for their valuable comments that have enriched our research. The authors would also thank the Universitat Poliecnica de Valencia since this paper has been financed through the Grant PAID06-11-2070.

This paper is concerned with the mathematical modeling of complex systems characterized by particles refuge. Specifically the paper focuses on the derivation and moments analysis of thermostatted kinetic frameworks with conservative and nonconservative interactions for closed and open complex systems at nonequilibrium. Applications and future research perspectives are discussed in the last section of the paper.

The purpose of this paper is to give a new modified Ishikawa type iteration algorithm for common fixed points of total asymptotically strict pseudocontractive semigroups. Under the reduction of some conditions, both strong convergence and weak convergence of the iteration algorithm are proved in Banach spaces with new methods of proofs, respectively. The main results presented in this paper extend and improve the corresponding recent results of many others.

This paper considers the locations of multiple facilities in the space ${R}^{p}$ , with the aim of minimizing the sum of weighted distances between facilities and regional customers, where the proximity between a facility and a regional customer is evaluated by the closest distance. Due to the fact that facilities are usually allowed to be sited in certain restricted areas, some locational constraints are imposed to the facilities of our problem. In addition, since the symmetry of distances is sometimes violated in practical situations, the gauge is employed in this paper instead of the frequently used norms for measuring both the symmetric and asymmetric distances. In the spirit of the Cooper algorithm (Cooper, 1964), a new location-allocation heuristic algorithm is proposed to solve this problem. In the location phase, the single-source subproblem with regional demands is reformulated into an equivalent linear variational inequality (LVI), and then, a projection-contraction (PC) method is adopted to find the optimal locations of facilities, whereas in the allocation phase, the regional customers are allocated to facilities according to the nearest center reclassification (NCR). The convergence of the proposed algorithm is proved under mild assumptions. Some preliminary numerical results are reported to show the effectiveness of the new algorithm.

The aim of this paper is to establish an extension of Kummer's second theorem in the form e-x/2F22[a,2+d;x2a+2,d;]=F10[-;x2/16a+3/2;]+((a/d-1/2)/(a+1))x F10[-;x2/16a+3/2;]+(cx2/2(2a+3))F10[-;x2/16a+5/2;], where c=1/a+11/2-a/d+a/d(d+1), d≠0,-1,-2,…. Ford=2a, we recover Kummer's second theorem. The result is derived with the help of Kummer's second theorem and its contiguous results available in the literature. As an application, we obtain two general results for the terminatingF23(2)series. The results derived in this paper are simple, interesting, and easily established and may be useful in physics, engineering, and applied mathematics.

and Applied Analysis 3 1-homogeneous operator in a Banach space and then demonstrate its application in establishing the existence of positive solutions for p-Laplacian boundary value problems under certain conditions. (xi) In the paper titled “Existence of solutions for nonhomogeneous A-harmonic equations with variable growth,” the authors establish a theorem for the existence of weak solutions for nonhomogeneous A-harmonic equations in subspace and then give three examples to demonstrate its application. (xii) In the paper titled “Multiple solutions for degenerate elliptic systems near resonance at higher eigenvalues,” the authors study the degenerate semilinear elliptic system in an open bounded domain with smooth boundary, and some multiplicity results of solutions are obtained for the system near resonance at certain eigenvalues by the classical saddle point theorem and a local saddle point theorem in critical point theory. (xiii) In the paper titled “A regularity criterion for the Navier-Stokes equations in the multiplier spaces,” the authors establish a regularity criterion in terms of the pressure gradient for weak solutions to the NavierStokes equations in a special class. The third set of papers, including four papers, deal with several boundary value problems for highly nonlinear ordinary differential equations. (i) In the paper titled “Positive solutions for second-order singular semipositone differential equations involving Stieltjes integral conditions,” the authors investigate the existence of positive solutions for second-order singular differential equations with a negatively perturbed term, by means of the fixed-point theory in cones. (ii) In the paper titled “Positive solutions for Sturm-Liouville boundary value problems in a Banach Space,” the sufficient conditions for the existence of single and multiple positive solutions for a second-order SturmLiouville boundary value problem are established in a Banach space, by using the fixed-point theorem of strict set contraction operators in the frame of the ODE technique. (iii) In the paper titled “Positive solutions of a nonlinear fourth-order dynamic eigenvalue problem on time scales,” the authors study a nonlinear fourth-order dynamic eigenvalue problem on time scales and obtain the existence and nonexistence of positive solutions when 0 λ, respectively, for some λ, by using the Schauder fixed-point theorem and the upper and lower solution method. (iv) In the paper titled “Bifurcation analysis for a predatorprey model with time delay and delay-dependent parameters,” a class of stage-structured predator-prey model with time delay and delay-dependent parameters is considered. By using the normal form theory and center manifold theory, some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifur-cating from Hopf bifurcations are obtained. The fourth set of papers focus on finding the approximate and numerical solutions of various complex nonlinear boundary value problems. (i) In the paper titled “On spectral homotopy analysis method for solving linear Volterra and Fredholm integrodifferential equations,” a spectral homotopy analysis method (SHAM) is proposed to solve linear Volterra integrodifferential equations, and some examples are given to test the efficiency and the accuracy of the proposed method. (ii) In the paper titled “The solution of a class of singularly perturbed two-point boundary value problems by the iterative reproducing kernel method,” the authors establish an iterative reproducing kernel method (IRKM) for solving singular perturbation problems with boundary layers and give two numerical examples to demonstrate the effectiveness of the method. (iii) In the paper titled “A Galerkin solution for Burgers’ equation using cubic B-spline finite elements,” a Galerkin method using cubic B-splines is set up to find the numerical solutions of Burgers’ equation, and the method is shown to be capable of solving Burgers’ equation accurately for values of viscosity ranging from very small to very large. (iv) In the paper titled “Forward-backward splitting methods for accretive operators in Banach spaces,” the authors introduce two iterative forward-backward splitting methods with relaxations to find zeros of the sum of two accretive operators in Banach spaces and prove the weak and strong convergence of these methods under mild conditions, and also discuss applications of these methods to variational inequalities, the split feasibility problem, and a constrained convex minimization problem. Yong Hong Wu Lishan Liu Benchawan Wiwatanapataphee Shaoyong Lai Submit your manuscripts at http://www.hindawi.com Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Mathematics Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Mathematical Problems in Engineering Hindawi Publishing Corporation http://www.hindawi.com Differential Equations International Journal of Volume 2014 Applied Mathematics Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Probability and Statistics Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Mathematical Physics Advances in Complex Analysis Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Optimization Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Combinatorics Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 International Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Operations Research Advances in

The nonlinear boundary value problem describing the nanoboundary-layer flow with linear Navier boundary condition is investigated theoretically and numerically in this paper. TheG′/G-expansion method is applied to search for the all possible exact solutions, and its results are then validated by the Chebyshev pseudospectral differentiation matrix (ChPDM) approach which has been recently introduced and successfully used. This numerical technique is firstly applied and, on comparing with the other recent work, it is found that the results are very accurate and effective to deal with the current problem. It is then used to examine and validate the present analytical analysis. Although theG′/G-expansion method has been used widely to solve nonlinear wave equations, its application for nonlinear boundary value problems has not been discussed yet, and the present paper may be the first to address this point. It is clarified that the exact solutions obtained via theG′/G-expansion method cannot be obtained by using some of the other methods. In addition, the domain of the physical parameters involved in the current boundary value problem is also discussed. Furthermore, the convex, vicinity of zero, and asymptotic solutions are deduced.

This paper discusses highly finite element algorithms for the eigenvalue problem of electric field. Combining the mixed finite element method with the Rayleigh quotient iteration method, a new multi-grid discretization scheme and an adaptive algorithm are proposed and applied to the eigenvalue problem of electric field. Theoretical analysis and numerical results show that the computational schemes established in the paper have high efficiency.

This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this paper are first appeared.

We provide some new type of mappings associated with pseudocontractions by introducing some actual examples in smooth and strictly convex Banach spaces. Moreover, we also find the significant inequality related to the mappings mentioned in the paper and the mappings defined from generalized mixed equilibrium problems on Banach spaces. We propose an iterative shrinking projection method for finding a common solution of generalized mixed equilibrium problems and fixed point problems of closed and ϕ-quasi-strict pseudo-contractions. Our results hold in reflexive, strictly convex, and smooth Banach spaces with the property (K). The results of this paper improve and extend the corresponding results of Zhou and Gao (2010) and many others.

This paper presents a combined mathematical treatment for a special automatic music transcription system. This system is specially made for computer-synthesized music. The combined mathematical treatment includes harmonic selection, matrix analysis, and probability analysis method. The algorithm reduces dimension by PCA and selects candidates first by human auditory model and harmonic structures of notes. It changes the multiple-F0 estimation question into a mathematical problem and solves it in a mathematical way. It can be shown in this paper that the experimental results indicate that this method has very good recognition results.

This paper studies the following third order neutral delay discrete equationΔ(anΔ2(xn+pnxn-τ))+f(n,xn-d1n,…,xn-dln)=gn,n≥n0, whereτ,l∈ℕ,n0∈ℕ∪{0},{an}n∈ℕn0,{pn}n∈ℕn0,{gn}n∈ℕn0are real sequences withan≠0forn≥n0,{din}n∈ℕn0⊆ℤwithlim n→∞(n-din)=+∞fori∈{1,2,…,l}andf∈C(ℕn0×ℝl,ℝ). By using a nonlinear alternative theorem of Leray-Schauder type, we get sufficient conditions which ensure the existence of bounded positive solutions for the equation. Three examples are given to illustrate the results obtained in this paper.

This paper describes an index for judging the severity of transient events of power systems in simulation. The proposed transient stability index, known as the area-based COI-referred rotor angle index, is developed by considering the fact that a large-sized power system is divided into several areas according to the coherency of generators in a particular area. It can be assumed that an equivalent single large machine can represent all the generators in that area. Thus, the assessment of rotor angles for all generators can be simplified by only assessing the index of areas in a power system. The effectiveness of the proposed index in assessing the stability of power systems and its ability in pinpointing the weakest area in the power system is analyzed. Furthermore, this paper developed an emergency control scheme known as the combined UFLS and generator tripping in order to stabilize the system when unstable faults occurred in a power system. The proposed index is used to identify the generator to be tripped when the developed emergency control scheme operates. The performance of the proposed index and the combined UFLS and generator tripping scheme are evaluated on the IEEE 39-bus test system.

This paper investigates the guaranteed cost control of chaos problem in permanent magnet synchronous motor (PMSM) via Takagi-Sugeno (T-S) fuzzy method approach. Based on Lyapunov stability theory and linear matrix inequality (LMI) technique, a state feedback controller is proposed to stabilize the PMSM systems. An illustrative example is provided to verify the validity of the results developed in this paper.

The aim of this paper is to present new results related to the convergence of the sequence of the 𝑞 -Bernstein polynomials { 𝐵 𝑛 , 𝑞 ( 𝑓 ; 𝑥 ) } in the case 𝑞 > 1 , where 𝑓 is a continuous function on [ 0 , 1 ] . It is shown that the polynomials converge to 𝑓 uniformly on the time scale 𝕁 𝑞 = { 𝑞 − 𝑗 } ∞ 𝑗 = 0 ∪ { 0 } , and that this result is sharp in the sense that the sequence { 𝐵 𝑛 , 𝑞 ( 𝑓 ; 𝑥 ) } ∞ 𝑛 = 1 may be divergent for all 𝑥 ∈ 𝑅 ⧵ 𝕁 𝑞 . Further, the impossibility of the uniform approximation for the Weierstrass-type functions is established. Throughout the paper, the results are illustrated by numerical examples.

The purpose of this paper is to study solvability of the second-order nonlinear neutral delay difference equationΔ(a(n,ya1n,…,yarn)Δ(yn+bnyn-τ))+f(n,yf1n,…,yfkn)=cn, ∀n≥n0. By making use of the Rothe fixed point theorem, Leray-Schauder nonlinear alternative theorem, Krasnoselskill fixed point theorem, and some new techniques, we obtain some sufficient conditions which ensure the existence of uncountably many bounded positive solutions for the above equation. Five nontrivial examples are given to illustrate that the results presented in this paper are more effective than the existing ones in the literature.

This paper presents sufficient conditions for the existence of positive solutions for a class of integral inclusions. Our results are obtained via a new fixed point theorem for multivalued operators developed in the paper, in which some nonnegative function is used to describe the cone expansion and compression instead of the classical norm-type, and lead to new existence principles.

The purpose of this paper is to prove strong convergence theorems for common fixed points of two countable families of relatively quasi nonexpansive mappings in a uniformly convex and uniformly smooth real Banach space using the properties of generalized $f$ -projection operator. In order to get the strong convergence theorems, a new iterative scheme by monotone hybrid method is presented and is used to approximate the common fixed points. Then, two examples of countable families of uniformly closed nonlinear mappings are given. The results of this paper modify and improve the results of Li et al. (2010), the results of Takahashi and Zembayashi (2008), and many others.