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Abstract: In the present paper we studied the Voronovskaya type theorem for modified Gamma operators presented by A. İzgi in the paper “Voronovskaya type asymptotic approximation by modified Gamma operators” [Applied Mathematics and Computation 217 (2011) 8061–8067]. We show that this theorem is not true. We present a correct form of this theorem and its proof. Furthermore, we obtain an error estimate for modified Gamma operators. [Copyright &y& Elsevier]

Abstract: Comment on the paper “A class of methods based on non-polynomial spline functions for the solution of a special fourth-order boundary-value problems with engineering applications” in Applied Mathematics and Computation 174 (2006) 1169–1180. The paper considered a class of two-point boundary-value problems of the form where f(x) and g(x) are continuous on [a, b], and A i and B i (i =1,2) are finite real constants. Here we correct some mistake in derivation of non-polynomial spline, boundary formulas, truncation errors, convergence analysis and computational experiments. [Copyright &y& Elsevier]

Abstract: In this paper, we establish new Lyapunov-type inequalities for two classes of one-dimensional quasilinear elliptic systems of resonant type, which improve the recent results of Tang and He [X.H. Tang, X. He, Lower bounds for generalized eigenvalues of the quasilinear systems, J. Math. Anal. Appl. 385 (2012) 72–85] when 1< p i <2 for i =1,2,…, n. [Copyright &y& Elsevier]

Abstract: In this paper, some sufficient conditions are established for the oscillation of second-order neutral differential equations where and . On the other hand, some new oscillation criteria are established for the second-order nonlinear neutral delay differential equations where . The results obtained here complement and correct some known results in . Some examples are given to illustrate the main results. [Copyright &y& Elsevier]

Abstract: In this short note an addition to the paper [A.G. Bratsos, M. Ehrhardt, I.Th. Famelis, A discrete Adomian decomposition method for discrete nonlinear Schrödinger equations, Appl. Math. Comput. 197(1) (2008) 190–205] using the modulus of the terms evaluated from the Adomian decomposition method on p. 194 and their relation to the convergence of the resulting series is presented. Conclusions for the accuracy of the approximated solution are derived. [Copyright &y& Elsevier]

Abstract: The aim of this note is to show that the optimization algorithm proposed in may not lead to the optimal solution in some cases. In fact, the optimization problem remains open if we do not apply the branch-and-bound method to solve it or compute all the objective values of minimal solutions of the feasible domain. [Copyright &y& Elsevier]

Abstract: A counterexample is provided in this short note to show that some of local convergence theorems established in [D.K.R. Babajee, M.Z. Dauhoo, An analysis of the properties of the variants of Newton’s method with third order convergence, Appl. Math. Comput. 183 (2006) 659–684] are not always true. Some mistakes in the proofs of these theorems are pointed out. [Copyright &y& Elsevier]

Abstract: In this technical note, we give a short extension application for nonlinear sum of ratios problem (P) considered in [Y.J. Wang, K.C. Zhang, Global optimization of nonlinear sum of ratios problem, Applied Mathematics and Computation 158 (2004) 319–330]. Actually our result is slightly more general, since we do not specify additional positive coefficient for each ratio. In this note, we use different equivalent problem as done in Wang and Zhang (2004). Our method introduce p variables less than other method (Wang and Zhang, 2004), and our approach need not additional special program to obtain the upper and lower bound of numerator and denominator for each ratio in the objective function. [Copyright &y& Elsevier]

Abstract: In this note, we will modify several gaps in Gurudwan and Sharma [N. Gurudwan, B.K. Sharma, Convergence theorem for the common solution for a finite family of -strongly accretive operator equations, Appl. Math. Comput. 217 (2011) 6748–6754]. [Copyright &y& Elsevier]

Abstract: In abstract of the paper [A. Rafiq, A note on “A family of methods for solving nonlinear equations”, Appl. Math. Comput. 195 (2008) 819–821] we can find the following sentences. We cite: Ujević et al. introduced a family of methods for solving nonlinear equations. However the main Algorithm 1 put forward by Ujević et al. (p. 7) is wrong. This is the main aim of this note. We also point out some major bugs in the results of Ujević et al. – the end of the citation. Here it is shown that all of the mentioned assertions are not true. In other words, the Algorithm 1 is correct (up to an obvious misprint, which is not mentioned in the above paper) and there are no major bugs in the paper by Ujević et al. In fact, these observations, which will be given in this note, show that the main aim of the paper by Rafiq is wrong. [Copyright &y& Elsevier]

This paper focuses on resolving the distributed formation containment control issue in general multi-agent systems (MASs) possessing multiple leader agents subject to limited communication resources. The unnecessary data transmissions among agents in MASs are reduced by utilizing a unique dynamic event-triggering communication mechanism (DETCM), which can build communication time sequences for each agent automatically. Based on the sampled states of agents at event-triggering instants, a novel distributed formation containment control protocol is proposed. By mathematical analysis, the formation containment control problem is turned into the problem of stability in a reduced-order system. The global formation containment of the MASs is finally achieved through the application of Lyapunov-Krasovskii functionals and general inequalities. Moreover, a valid example is also given to support the validity and effectiveness of the findings. • This paper considers MASs with multiple leader agents, which has a broad application range and significant value. • A distributed formation containment control is proposed, which benefits the containment of leader and promotes formation of followers. • The DETM proposed in this paper eliminates the need for real-time communication and reduces the communication load. • A dynamic parameter is introduced to the ETM, which makes the triggering conditions change according to the states of agents. [ABSTRACT FROM AUTHOR]

As a type of uncertain differential equations, uncertain spring vibration equation is driven by Liu process. This paper proposes a concept of α -path, and shows that the solution of an uncertain spring vibration equation can be expressed by a family of solutions of second-order ordinary differential equations. This paper also proves that the inverse uncertainty distribution of solution of uncertain spring vibration equation is just the α -path of uncertain spring vibration equation, and a numerical algorithm is designed. Moreover, a formula to calculate the expected value of solution of uncertain spring vibration equation is derived. Finally, several numerical examples are provided to illustrate the efficiency of the numerical method. [ABSTRACT FROM AUTHOR]

The problem of consistency of a solution over time remains an important issue in cooperative dynamic games. Payoffs to players prescribed by an inconsistent solution may not be achievable since such a solution is extremely sensitive to its revision in the course of a game developing along an agreed upon cooperative behavior. The paper proposes a strong time-consistent payment scheme which is stable to a revision of cooperative set solutions, e.g., the core. Using a linear transformation of the solution, it becomes possible to obtain non-negative payments to players. In the paper, we also deal with a limit linear transformation of the solution whose convergence is proved. Developing a non-negative strong time-consistent payment scheme in a closed form, we guarantee that the solution supported by the scheme will not be revised over time. [ABSTRACT FROM AUTHOR]

Convergence rate result for a modified steepest descent method and a modified minimal error method for the solution of nonlinear ill-posed operator equation have been proved with noisy data. To our knowledge, convergence rate result for the steepest descent method and minimal error method with noisy data are not known. We provide a convergence rate results for these methods with noisy data. The result in this paper are obtained under less computational cost when compared to the steepest descent method and minimal error method. We present an academic example which satisfies the assumptions of this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the delay-dependent stability problem of continuous neural networks with a bounded time-varying delay via Lyapunov–Krasovskii functional (LKF) method. This paper focuses on reducing the conservatism of stability criteria by estimating the derivative of the LKF more accurately. Firstly, based on several zero-value equalities, a generalized free-weighting-matrix (GFWM) approach is developed for estimating the single integral term. It is also theoretically proved that the GFWM approach is less conservative than the existing methods commonly used for the same task. Then, the GFWM approach is applied to investigate the stability of delayed neural networks, and several stability criteria are derived. Finally, three numerical examples are given to verify the advantages of the proposed criteria. [ABSTRACT FROM AUTHOR]

The paper proposes a new approach for function approximation by ‘estimating’ the second derivative, using Taylor series, where the samples of the function and its first derivatives at the sample points are known. Without such ‘estimation’, these initial data, can approximate the function traditionally using the first order Taylor approximation, but with more error. If we desire to improve the approximation via second order Taylor series, then we can estimate the ‘pseudo’ second derivatives of the function in three different ways. All these three ways are investigated in this paper. The pseudo second derivatives help in computing many more sample points of the function within each sampling interval. Thus, the approach acts like a mathematical ‘magnifying glass’. Two examples are treated to compare the efficiencies of the methods. Also, a qualitative study for upper bound of error of the approximations is studied in detail. [ABSTRACT FROM AUTHOR]

Let D = ( P , B ) be any nontrivial nonsymmetric 2-( v, k, λ ) design. In this paper we construct a connected, regular and bipartite graph, say IG v , b ( D ) , from D . Some graphic properties of IG v , b ( D ) are investigated. In particular, the results in the paper bridges the equivalency between edge-transitivity of IG v , b ( D ) and flag-transitivity of D . With the equivalency, it is obtained that IG v , b ( D ) is a semisymmetric graph as long as D is a nonsymmetric flag-transitive 2-( v, k, λ ) design. [ABSTRACT FROM AUTHOR]

In this paper we study and obtain the existence of a positive almost periodic solution to the nonlinear differential equation with delays that describes the so-called hematopoiesis model. The main tool utilized to establish our existence result consists of the fixed-point theorem in a cone. Two examples are given at the end of the paper to illustrate our main result. [ABSTRACT FROM AUTHOR]

For uncertain differential equations, we cannot always obtain their analytic solutions. Early researchers have described the Euler method and Runge–Kutta method for solving uncertain differential equations. This paper proposes a new numerical method—Adams method to solve uncertain differential equations. Some numerical experiments are given to illustrate the efficiency of our numerical method. Moreover, this paper also gives two numerical methods for calculating the extreme value and the time integral of solutions of uncertain differential equations. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to investigate some new integral inequalities of Grüss type for k - Riemann–Liouville fractional integrals. From our results, new weighted or classical Grüss type inequalities have been established for some special cases. Moreover, special cases of the integral inequalities in this paper have been obtained by Dahmani and Tabharit, 2010 in [5]. [ABSTRACT FROM AUTHOR]

In the present paper we will give some properties of the subclass of harmonic mappings which is related to m -fold starlike functions in the open unit disc D = { z | | z | < 1 } . Throughout this paper we restrict ourselves to the study of sense-preserving harmonic mappings. We also note that an elegant and complete treatment theory of the harmonic mapping is given in Durens monograph (Duren, 1983). The main aim of us to investigate some properties of the new class of us which represented as in the following form, S ∗ H ( m ) = f = h ( z ) + g ( z ) ‾ | f ∈ SH ( m ) , g ′ ( z ) h ′ ( z ) ≺ b 1 p ( z ) , h ( z ) ∈ S ∗ ( m ) , p ( z ) ∈ P ( m ) , where h ( z ) = z + ∑ n = 1 ∞ a mn + 1 z mn + 1 , g ( z ) = ∑ n = 0 ∞ b mn + 1 z mn + 1 , | b 1 | < 1 . [ABSTRACT FROM AUTHOR]

In this paper, we obtain some gap functions for generalized mixed quasi variational inequality problems in terms of regularized gap function and D -gap function. Further, by using these gap functions we obtain global error bounds for the solution of generalized mixed quasi variational inequality problems in Hilbert spaces. The results obtained in this paper generalize and improve some corresponding known results in literatures. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some new Lyapunov-type inequalities for a class of even-order linear differential equations. The results of this paper generalize and improve some earlier results in this field. [ABSTRACT FROM AUTHOR]

• A cholera infection model with vaccination strategy is studied. • The basic reproduction number is obtained. • A threshold dynamics is established by using Lyapunov function technique. • Several reasonable optimal control strategies are suggested to the prevention and control of the cholera infection. In this paper, a cholera infection model with vaccination strategy is investigated. By analyzing corresponding characteristic equations, the local stability of each of feasible equilibria is established. By means of Lyapunov functions and LaSalle's invariance principle, it is proved that if the basic reproduction number is less than unity, the disease-free equilibrium is globally asymptotically stable. If the basic reproduction number is greater than unity, the endemic equilibrium is globally asymptotically stable. In addition, by using Pontryagin's maximum principle, several reasonable optimal control strategies are suggested to the prevention and control of the cholera infection. Numerical simulations are carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

• SIS-type system of equations coupled by impulses at fixed times is analyzed. • Dynamics and structure's interdependence constitute network damping of infection. • Network suppression of pathogen spread indicates units prone to high prevalence. • Based on analytical results a scheme for network R 0 reduction is proposed. • Theoretical results are illustrated by simulations for the patient hospital records. In the paper, we describe the transfer of patients in the healthcare system by SIS-type equations coupled by impulses at fixed times. The first aim for these considerations is to provide a rigorous mathematical analysis of a general theoretical model, which incorporates the structure of patients' transfers. Based on theoretical results, we disprove the intuitions taken from decoupled systems, showing a damping of infection in the case when the transmission rate is locally higher than the recovery rate. Observations on network suppression of pathogen spread allow us to indicate units prone to the high prevalence and propose, possibly low-cost, interventions reducing the infection spread in a whole system. Core results combine the dynamical and structural properties of a system. Finally, we consider a model of the transmission of hospital-acquired multidrug-resistant bacteriae infections, based on real patient hospital records provided by the German insurance company – AOK Lower Saxony, to ilustrate the theoretical considerations. [ABSTRACT FROM AUTHOR]

The paper presents a new semi-analytic numerical method for solving multi-point boundary value problems with linear and nonlinear equations of the second and higher orders. The method is based on the use of the particular solutions of the linearized equation. Presented in the paper examples include the solution of equations with differential operators of the second, third and fourth orders. [ABSTRACT FROM AUTHOR]

Abstract: Li and Lim (2011) [8] proposed a three-dimensional system of ordinary differential equations modeling the role of Tax expression in the persistence of Human T-lymphotropic virus Type I and presented a mathematical analysis and its immunovirological explanation. The previous paper shows that three-dimensional system is a cooperative system if a sharp condition is satisfied. By means of the theory of cooperative dynamical systems, they studied the global dynamics. If the sharp condition is not satisfied, they leave it an open problem. The present paper is to provide a complete classification of global dynamics for this ODE model. In particular, our global analysis establishes that the dynamics of the HTLV-I infection are completely determined by a basic reproductive number, which completely solves the open problem above. [Copyright &y& Elsevier]

Abstract: This paper presents methods for solving the polynomial system which is called the composite sum of powers. It is shown that these polynomial equation can be reduced to a single-variable polynomial equations by exploiting the modified Newton’s identities. In this paper we generalize this identity and solve it via Padé approximation theory and the related theory of formal orthogonal polynomials (FOPs). Because the solution forms the roots of FOPs we present several interesting computational procedures, such as the use of three-term reccurence formulas, determinantal formulations and the computation of the eigenvalues of tridiagonal matrices. The computation of this special polynomial system arise in practical engineering task of solving optimal odd symmetry single-phase pulse-width modulated (PWM) problem. [Copyright &y& Elsevier]

Abstract: The problem about cluster synchronization of fractional-order CDNs is studied via a pinning adaptive approach in this paper. Based on the stability theory of fractional differential equations, some sufficient criteria for local and global cluster synchronization of fractional-order CDNs are derived. In this paper, the coupling configuration matrix can be asymmetric as well as reducible and the inner coupling matrix can also be asymmetric. Moreover, the number of pinning nodes in each cluster can be evaluated. Especially, when the coupling strength is large enough and the coupling configuration matrix is symmetric, cluster synchronization can be achieved via pinning a single node in each cluster. Finally, some typical examples are given to illustrate the correctness and effectiveness of our results, a surprising finding is that the synchronization performance will become better as the fractional order decreases in this simulation. [Copyright &y& Elsevier]

Abstract: There are many evolutionary algorithms for numerical optimization problems. However, the universality and robustness of existing algorithms are still unsatisfactory, and the performance of these algorithms deteriorates significantly as the dimensionality of the optimization problems increases. In this paper, an ensemble of evolution algorithm based on self-adaptive learning population search techniques (EEA-SLPS) is presented to overcome these defects on the numerical optimization problems. The EEA-SLPS integrates three self-adaptive learning based stochastic search algorithms which are termed as sub-algorithms. In the EEA-SLPS, the population is divided into three sub-populations, and the sub-algorithms are employed to evolve the sub-populations in parallel. Among the three sub-algorithms, one is designed in this paper and the other two are proposed by relevant literature, and eighteen information exchanging manners (IEMs) between sub-populations are investigated in order to make use of the sub-algorithms efficiently. We have found the most suitable IEM for the EEA-SLPS according to experimental investigations. Finally, the EEA-SLPS is tested on a suite of 26 bound-constrained functions with low and high dimensionality. The experimental results indicate that the universality and robustness performance of EEA-SLPS is better. Meanwhile, the results clearly verify the advantages of EEA-SLPS on the numerical optimization problems with low or high dimensionality. [Copyright &y& Elsevier]

Abstract: In this paper we derive an explicit formula which uses the first two Hu moment invariants to compute a shape ellipticity measure, i.e. to evaluate how much a planar shape differs from an ellipse. The ellipticity measure computed by this formula is invariant with respect to translation, rotation and scaling transformations. Also, the highest possible value is obtained if and only if the shape considered is an ellipse. Several experiments are also provided to confirm the theoretical observations. A by product, of the derivations made in this paper, is an implicit interpretation of geometric/shape meaning of the second Hu moment invariant. A formula which connects the shape ellipticity and the first Hu moment invariant (both having a well understood behavior) and the second Hu moment invariant is derived. [Copyright &y& Elsevier]

Abstract: In this paper, we give some necessary and sufficient conditions for the solvability to the system of matrix equations and provide an expression of the general solution to (0.1). Furthermore, we obtain the maximal and minimal ranks of and in (0.1). The findings of this paper extend the known results in the literatures. [Copyright &y& Elsevier]

Abstract: This paper introduces a saturated treatment function into an SIS model with saturated incidence rate. The treatment function is a continuous and differential function which describes the effect of delayed treatment when the medical condition is limited and the number of infected individuals is large. Sufficient conditions for the existence and global asymptotical stability of the disease-free and endemic equilibria are given in this paper, and the nonexistence of limit cycles is also demonstrated. A backward bifurcation is found when the capacity of the treatment is low. It indicates that we should improve the efficiency and enlarge the capacity of the treatment to control the spread of diseases. By mathematical analysis and numerical simulations, it is shown that the system undergoes Hopf bifurcation and Bogdanov–Takens bifurcation. [Copyright &y& Elsevier]

Abstract: This paper discusses the dynamics of particles orbiting planetary rings under a general central potential. Starting with the mathematical description of the dynamical system, we analyze the motion of a particle with infinitesimal mass as attracted by a central body surrounded by a homogeneous circular annular disk. Throughout the paper we carry out an analytic search of the most relevant equilibria solutions and, based on that, we investigate numerically the stability matrix of the system to find stability inequalities. In this way, we describe the in-plane and out-of-plane motion by means of the numerical continuation of a wide number of uni-parametric families of planar and spatial periodic orbits. We present a description of the main families of periodic orbits encountered, their bifurcations and linear stability. With the aim of reproducing a more realistic scenario, we analyse different mass proportions between the annulus and the central body, we consider an oblate planet and we also include a composition of rings in the dynamical model. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the new notion which is more general than the previous works on the weakly isotone mappings in the case of single valued mappings and multivalued mappings in an ordered Banach space. We also extend some common fixed point theorems of Dhage et al. [4] and give some applications of the main results. Furthermore, at the end of this paper, we give an open problem for further investigation. [Copyright &y& Elsevier]

Abstract: This paper reviews three articles, namely “A note on the inventory model for deteriorating items with trapezoidal type demand rate” by Cheng and Wang (2009) [1], “Inventory models with managerial policy independent of demand” by Lin (2011) [7], and “Optimal policy for deteriorating items with trapezoidal type demand and partial backlogging” by Chen et al. (2011) [2]. This paper extends their models with a generalized demand, a generalized deteriorated rate, and an extended backlogged rate. The findings of this study can provide references on important inventory models. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a Lotka–Volterra model with birth pulse and impulsive catching or poisoning for the prey at different moment and stage structure on the predator. We prove that all solutions of the system are uniformly ultimately bounded. Sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system are obtained. These results show that impulsive effects on the prey play an important role for the permanence of the system. In this paper, the main feature is to introduce birth pulse and impulse catching into Lotka–Volterra model and to give pest management strategies. [Copyright &y& Elsevier]

Abstract: There is an abundant literature on inequalities for the (Euler’s) Gamma function Γ and its various related functions. Yet, only very recently, several authors began to study inequalities for the (Barnes’) double Gamma function . Here, in this paper, we aim at presenting several two-sided inequalities for the multiple Gamma functions . In our investigation of these two-sided inequalities for the multiple Gamma functions , we employ and extend a method based upon Taylor’s formula and express as series involving the Zeta functions. We also give a more convenient explicit form of the multiple Gamma functions being the set of positive integers. The main two-sided inequalities for the multiple Gamma functions (which we have presented in this paper) are presumably new and their derivations provide a fruitful insight into the corresponding problem for the multiple Gamma functions when . [Copyright &y& Elsevier]

Abstract: In the present paper, the authors derive several sharp coefficient estimates for the function class consisting of the inverses of functions in a certain class of spirallike functions in the open unit disk , which was introduced by Libera. They also obtain a number of sharp coefficient bounds of functions in the more general classes and , each of which is introduced here. Some of the results derived in this paper would generalize those in a recent work of Kapoor and Mishra. [Copyright &y& Elsevier]

Abstract: In a recent paper, Srivastava et al. (2012) [23] introduced and studied some fundamental properties and characteristics of a family of potentially useful incomplete hypergeometric functions. The main object of this paper is to investigate several generating functions for a certain class of incomplete hypergeometric polynomials associated with them. Various (known or new) special cases and consequences of the results presented in this paper are also considered. [Copyright &y& Elsevier]

Abstract: Decision making in engineering is becoming increasingly complex due to the large number of alternatives and multiple conflicting goals. Powerful decision-support expert systems powered by suitable software are increasingly necessary. In this paper, the multiple attribute decision method known as analytical hierarchy process (AHP), which uses pairwise comparisons with numerical judgments, is considered. Since judgments may lack a minimum level of consistency, mechanisms to improve consistency are necessary. A method to achieve consistency through optimisation is described in this paper. This method has the major advantage of depending on just n decision variables – the number of compared elements – and so is less computationally expensive than other optimisation methods, and can be easily implemented in virtually any existing computer environment. The proposed approach is exemplified by considering a simplified version of one of the most important problems faced by water supply managers, namely, the minimisation of water loss. [Copyright &y& Elsevier]

Abstract: In this paper, we give a generalization of the well-known Lyapunov-type inequality to a class of linear differential systems, the result of this paper is new and generalizes many early results in this topic. [Copyright &y& Elsevier]

Abstract: This paper is an extension to a recent paper by Zhu and Lian (2011) [1], in which a closed-form exact solution was presented for the price of variance swaps with a particular definition of the realized variance. Here, we further demonstrate that our approach is quite versatile and can be used for other definitions of the realized variance as well. In particular, we present a closed-form formula for the price of a variance swap with the realized variance in the payoff function being defined as a logarithmic return of the underlying asset at some pre-specified discretely sampling points. The simple formula presented here is a result of successfully finding an exact solution of the partial differential equation (PDE) system based on the Heston (1993)’s [2] two-factor stochastic volatility model. A distinguishable feature of this new solution is that the computational time involved in pricing variance swaps with discretely sampling time has been substantially improved. [Copyright &y& Elsevier]

Abstract: In this paper, we establish some new determinantal representations of the generalized inverses and over the quaternion skew field by the theory of the column and row determinants. In addition, we derive a condensed Cramer rule for the unique solution of some restricted quaternion matrix equations. The findings of this paper extend some known results in the literature. [Copyright &y& Elsevier]

Abstract: By suitably combining the investigations by Ghare and Schrader (1963) , Dolan (1987) and Huang and Chung (2003) , Kreng and Tan (2011) consider and analyze the optimal inventory policies with order-size dependent trade credit under delayed payment and cash discount. The mathematical analysis of Kreng and Tan (2011) is based upon an inventory model for deteriorating items with trade credit and cash discount linked to the order quantity. Motivated by the potential for practical applications of such inventory models as those that are considered in (for example) the aforecited works, we address some shortcomings in the 2011 paper by Kreng and Tan (2011) . We emphasize upon the invalidity of an important assumption by Kreng and Tan (2011) , namely that the deterioration rate is small, provide a counterexample to Kreng and Tan’s and question the results of Kreng and Tan’s . We present our own observations and results as theorems and proofs. We thus have not only removed the aforementioned shortcomings in the paper by Kreng and Tan (2011) , but we have also provided the complete solution procedures for some of the aforementioned models. Finally, some numerical examples are used to compare the results, which are presented in this paper, with those of the aforecited earlier investigations. [Copyright &y& Elsevier]

Abstract: This paper describes an algorithm designed for the automatic coarsening of three-dimensional unstructured simplicial meshes. This algorithm can handle very anisotropic meshes like the ones typically used to capture the boundary layers in CFD with Low Reynolds turbulence modeling that can have aspect ratio as high as 104. It is based on the concept of mesh generation governed by metrics and on the use of a natural metric mapping the initial (fine) mesh into an equilateral one. The paper discusses and compares several ways to define node based metric from element based metric. Then the semi-coarsening algorithm is described. Several application examples are presented, including a full three-dimensional complex model of an aircraft with extremely high anisotropy. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a class of fractional neutral control systems governed by abstract nonlinear fractional neutral differential equations. This paper deals with the exact controllability for fractional differential neutral control systems. First, we establish a new set of sufficient conditions for the controllability of nonlinear fractional systems by using a fixed point analysis approach. Further, we extend the result to study the controllability concept with nonlocal conditions. In particular, the controllability of nonlinear systems is established under the natural assumption that the associated linear control system is exactly controllable. [Copyright &y& Elsevier]

Abstract: In a recent paper, Hernández and Salanova proposed an interesting Newton-like method for the solution of nonlinear Fredholm integral equations. The aim of the present paper is to carry over this method to nonlinear operator equations of similar type. By using a functional analytic approach, the presentation becomes much clearer and more general. Apart from this, some new results in the Banach space setting as well as in the applications are obtained. [Copyright &y& Elsevier]

Abstract: The alternating group graph was proposed as an interconnection network topology for computing systems. In this paper we study fault tolerant edge k-pancyclicity of . A graph is edge k-pancyclic if for every edge there is a cycle going through e of every length from k to . Xue and Liu [Z.-J. Xue, S.-Y. Liu, An optimal result on fault-tolerant cycle-embedding in alternating group graphs, Inform. Proc. Lett. 109 (2009) 1197–1201] put the conjecture that is -fault-tolerant edge 4-pancyclic, which means that if the number of faults , then is still edge 4-pancyclic. Chang and Yang [J.-M. Chang, J.-S. Yang, Fault-tolerant cycle-embedding in alternating group graphs, Appl. Math. Comput. 197 (2008) 760–767] showed that for the shortest cycles the fault-tolerance of is much lower. They noted that with faults one can cut all 4-cycles going through a given edge e. On the other hand they showed that is -fault-tolerant edge 4-pancyclic. In this paper we show that the optimal upper bound of fault tolerance of edge 5-pancyclicity is equal to and it jumps up to for edge 6-pancyclicity (and edge k-pancyclicity, for every possible ). [Copyright &y& Elsevier]

Abstract: In this paper, several explicit parametric solutions to the generalized Sylvester-conjugate matrix equation are given. The proposed solutions can provide all the degrees of freedom which are represented by a free parameter matrix. In addition, the approaches adopted in this paper do not require that the coefficient matrices are in any canonical forms. [Copyright &y& Elsevier]