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Abstract: In this paper, we apply a complete pivoting strategy to compute the left-looking version of AINV preconditioner for linear systems. As the preprocessing, the MultiLevel Nested Dissection reordering has also been applied. We have used this preconditioner as the right preconditioner for several linear systems where the coefficient matrices have been downloaded from the University of Florida Sparse Matrix Collection. Numerical experiments presented in this paper indicate the effectiveness of such a complete pivoting on the quality of left-looking version of AINV preconditioner. [Copyright &y& Elsevier]

Abstract Given a finite group G , we say that G has property P n if for every prime integer p , G has at most n − 1 irreducible characters whose degrees are multiples of p. In this paper, we classify all finite groups that have property P 4. We show that the groups satisfying property P 4 are exactly the finite groups with at most three nonlinear irreducible characters, one solvable group of order 168, SL 2 (3) , A 5 , S 5 , PSL 2 (7) and A 6. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we use the exp-function method to construct some new soliton solutions of the Benjamin–Bona–Mahony and modified Benjamin–Bona–Mahony equations. These equations have important and fundamental applications in mathematical physics and engineering sciences. The exp-function method is used to find the soliton solution of a wide class of nonlinear evolution equations with symbolic computation. This method provides the concise and straightforward solution in a very easier way. The results obtained in this paper can be viewed as a refinement and improvement of the previously known results. [Copyright &y& Elsevier]

Abstract: This paper investigates the problem of chaos and hyper-chaos control, and proposes a simple adaptive feedback control method for chaos control under a reasonable assumption. In comparison with previous methods, the present control technique is simple both in the form of the controller and its application. Several illustrative examples with numerical simulations are studied by using the results obtained in this paper. Study of examples shows that our control method works very well in chaos control. [Copyright &y& Elsevier]

Abstract: In this paper, high-resolution finite volume schemes are combined with an adaptive mesh technique inspired by multiresolution analysis to improve the computational efficiency for two-dimensional hyperbolic conservation laws. The method is conservative. Moreover, it is stable which is proven numerically in this paper. The computational grid is dynamically adapted so that higher spatial resolution is automatically allocated to regions where strong gradients are observed. Using this proposed scheme, we compute several two-dimensional model problems and a compressive rate ranging from about 5–10 is observed in all simulations. [Copyright &y& Elsevier]

Abstract: Recently, Shen et al. has published a paper concerning the properties and computations of matrix pseudospectra. However, some of the main results seem to be incomplete. As a complement of the paper, in this note we first make several examples to show the incompleteness of that results, then we give the modified results through giving more appropriate definitions replacing the one given in [Y. Shen, J. Zhao, H. Fan, Properties and computations of matrix pseudospectra, Applied Mathematics and Computation 161 (2005) 385–393]. An interesting inclusion theorem for pseudospectra is given, which provides preferable bounds for standard pseudospectra. Some other properties are also explored. [Copyright &y& Elsevier]

Abstract: This paper is devoted to the study of the internal stabilization of the Bernoulli–Euler plate equation in a square. The continuous and the space semi-discretized problems are successively considered and analyzed using a frequency domain approach. For the infinite-dimensional problem, we provide a new proof of the exponential stability result, based on a two-dimensional Ingham''s type result. In the second and main part of the paper, we propose a finite difference space semi-discretization scheme and we prove that this scheme yields a uniform exponential decay rate (with respect to the mesh size). [Copyright &y& Elsevier]

The spectrum of a first order sentence is the set of all α such that G ( n , n − α ) does not obey zero–one law with respect to this sentence. In this paper, we prove that the minimal number of quantifier alternations of a first order sentence with infinite spectrum equals 3. We have also proved that the spectrum of a first-order sentence with quantifier depth 4 has no limit points except possibly the points 1 ∕ 2 and 3 ∕ 5 . [ABSTRACT FROM AUTHOR]

In this paper, we will investigate how radiality occurs in topological spaces by considering neighbourhood bases generated by nests. We will define a new subclass of radial spaces that contains LOTS, GO-spaces and spaces with well-ordered neighbourhood bases, called the independently-based spaces. We show that first-countable spaces are precisely the independently-based, strongly Fréchet spaces and we give an example of a Fréchet–Urysohn space that is neither independently-based nor strongly Fréchet. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, properties of symmetric neighborhood assignments are discussed. We show that in some results of Balogh and Gruenhage, the family of spherical neighborhoods in a metric space can be generalized to a symmetric open neighborhood assignments in any topology space. By a simple example, we answer a question raised by Hung negatively. We also discuss two questions raised by Nagata about metrization and symmetric neighborhood assignments. By giving new characterizations of strongly paracompact metrizable spaces and orthocompact Moore spaces respectively, we show that answer of the first question is negative, while the second question is undecidable under ZFC. [Copyright &y& Elsevier]

Abstract: considered order preserving property of maximum likelihood estimators. In this paper there are given conditions under which the moment estimators have the property of preserving stochastic orders. The preserving property for the usual stochastic order as well as for likelihood ratio one is considered. Sufficient conditions are established for some parametric families of distributions. [Copyright &y& Elsevier]

Abstract: Mixed-level designs have become widely used in the practical experiments. When the levels of some factors are difficult to be changed or controlled, fractional factorial split-plot (FFSP) designs are often used. It is highly to know when a mixed-level FFSP design with resolution III or IV has clear effects. This paper investigates the conditions of a resolution III or IV FFSP design with both two-level and four-level factors to have various clear factorial effects, including two types of main effects and three types of two-factor interaction components. The structures of such designs are shown and illustrated with examples. [Copyright &y& Elsevier]

Abstract: In this paper, wave interaction with a bottom-mounted uniform porous cylinder of arbitrary shape is studied using SBFEM (Scaled Boundary Finite-element Method) and domain decomposition technique. The non-homogeneous equation due to the complex configuration of the structure is processed by introducing a porous effect parameter G. The resulting final scaled boundary finite-element equation is homogeneous and can be solved in conventional manners. Only the boundary is spatially discretized with curved surface finite elements, leading a reduction of the spatial dimension by one. The solution in the radial direction is analytical; while in the circumferential direction, the solution is numerical. High accuracy is achieved with a small number of surface finite elements. [Copyright &y& Elsevier]

Abstract: In this paper we give a method for peturbation of solutions of linear homogeneous differential equation of the second order. [Copyright &y& Elsevier]

Abstract: In this paper an attempt is made to extend some standard results in set theory on the basis of soft set relations. Antisymmetric relation and transitive closure of a soft set relation are introduced and an analogue of Warshall’s algorithm is proposed for calculating the transitive closure of a soft set relation. Ordering on a soft set is defined and some set theoretical results based on this are proved. [Copyright &y& Elsevier]

Abstract: In this paper, we give necessary and sufficient conditions for generalized solution and periodicity of the difference equation with -periodic coefficients, where , . Also, we obtain that the generalized solution is periodic with -period. [Copyright &y& Elsevier]

Abstract: In this paper, we are concerned with the oscillation of second order superlinear differential equations of the formA new oscillation criterion is established under quite general assumptions. Our results are based on the information on a sequence of subintervals of [t 0,∞) only, rather than on the whole half-line. Our methodology is somewhat different from that of previous authors . Our results generalize and extend some earlier results of Yu and Lu and Meng . An example is also given to illustrate the results. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a class of non-standard time optimal control problems involving a dynamical system consisting of multiple subsystems evolving over different time horizons. Different subsystems are required to reach their respective target sets at different termination times. The goal is to minimize the maximum of these termination times. By introducing a discrete variable to represent the system termination ordering, we reformulate this problem as a discrete optimization problem. A discrete filled function method is developed to solve this discrete optimization problem. For illustration, a numerical example is solved. [Copyright &y& Elsevier]

Abstract: In this paper, Nicholson’s blowflies equation with diffusion and delay is investigated. By taking four different kinds of delay kernels and defining four corresponding characteristic equations, the existence of travelling wave solutions for Nicholson’ blowflies equation is obtained by employing the monotone iteration technique as well as the upper and lower solution method. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the oscillation of Third-order difference equation with impulses. Some sufficient conditions for the oscillatory behavior of the solutions of Third-order impulsive difference equations are obtained. [Copyright &y& Elsevier]

Abstract: A binary linear code in with dimension and minimum distance is called an code. A design is a set of points together with a collection of -subsets of (called a block) such that every -subset of is contained in exactly blocks. A constant length code which corrects different numbers of errors in different code words is called a non-uniform error correcting code. Parity sectioned reduction of a linear code gives a non-uniform error correcting code. In this paper a new code, , is developed. The error correcting capability of this code is . It is shown that this code holds a design. Also the parity sectioned reduction code after deleting the same positions of each code word of this code holds a design for and . [Copyright &y& Elsevier]

Abstract: In this paper, we study the superconvergence of the frictionless Signorini problem. When approximated by bilinear finite elements, by virtue of the information on the contact zone, we can derive a superconvergence rate of under a proper regularity assumption. Finally, a numerical test is given to verify our result. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze a single-server vacation queue with a general arrival process. Two policies, working vacation and vacation interruption, are connected to model some practical problems. The GI/M/1 queue with such two policies is described and by the matrix analysis method, we obtain various performance measures such as mean queue length and waiting time. Finally, using some numerical examples, we present the parameter effect on the performance measures and establish the cost and profit functions to analyze the optimal service rate η during the vacation period. [Copyright &y& Elsevier]

Abstract: In this paper, Volterra integral equations with separable kerenels are solved using the differential transform method. The approximate solution of this equation is calculated in the form of a series with easily computable terms. Exact solutions of linear and nonlinear integral equations have been investigated and the results illustrate the reliability and the performance of the differential transform method. [Copyright &y& Elsevier]

Abstract: In this paper, finite difference time domain (FDTD) method and perfect matching layer (PML) absorbing boundary condition are adopted to simulate and analyze a novel optical directional coupler (ODC) based on surface plasmon polaritons (SPPs). Transmittance at each output port of the novel ODC with different coupling region lengths shows it follows the general regulations of a conventional ODC. Especially, its transverse size is of nanoscale. The extreme power position offset between the two output ports is proved to be connected with the real part of Ag''s complex refractive index. The excess loss and isolation of the ODC are, respectively, 0.57 and 25.9dB for 1550nm telecommunication wavelength, when the length of the coupling region equals half of its coupling length. [Copyright &y& Elsevier]

Abstract: This paper presents a common fixed point theorem for a family of R-weakly commuting mappings satisfying nonlinear type contractive conditions. This result improves and unifies previous results due to O’Regan and Saadati [D. O’Regan, R. Saadati, Nonlinear contraction theorems in probabilistic spaces, Appl. Math. Comput. 195 (2008) 86–93]. Also, the following results will be probabilistic versions and improvements of the results given in [D.W. Boyd, J.S.W. Wong, On nonlinear contractions, Proc. Am. Math. Soc. 20 (1969) 458–464; G. Jungck, Commuting maps and fixed points, Am. Math. Month. 83 (1976) 261–263; R.P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994) 436–440] and many other. [Copyright &y& Elsevier]

Abstract: The shape optimization problem consists in looking for the geometry that minimizes an objective function, like mass or compliance, subject to mechanical constraints. The boundary element method (BEM) is used for the structural analysis. For linear elasticity problems, it needs only a mesh on the boundary of the structure. This characteristic makes the BEM a natural method for shape optimization, since only the boundary is needed to define the optimization problem and to carry out the structural analysis. The simultaneous analysis and design formulation (SAND) for structural optimization considers the state variables as unknowns of the optimization problem and includes the equilibrium equations as equality constraints. In this way, it is not necessary to solve the equilibrium equation per iteration; the equilibrium is only obtained at the end of the optimization process. In this paper, the shape optimization problem is dealt with using the BEM formulation to define a SAND optimization problem that is solved using an interior point algorithm. Numerical results for two-dimensional linear elasticity problems are presented to illustrate the efficacy of the proposed technique. [Copyright &y& Elsevier]

Abstract: This paper focuses on the developments of higher-order shell models by employing the new concept of interpolation surfaces (I-surfaces) inside the shell body. We introduce N (N ⩾3) I-surfaces and choose the values of displacements with correspondence to these surfaces as fundamental shell unknowns. Such choice allows, first, to develop various higher-order shell models in a very compact form and, second, to derive non-linear strain–displacement relationships, which are completely free for arbitrarily large rigid-body motions. The general 3N-parameter shell model is proposed in the framework of the Lagrangian description. The special 9, 12 and 15 parameters cases (corresponding to N =3, 4 and 5) have been dealt in detail. The proposed shell models account for thickness stretching and the complete 3D constitutive equations are utilized. The displacement vectors of equally located I-surfaces for each model are represented in a convected curvilinear coordinate system allowing one to develop directly finite deformation geometrically exact shell finite elements which could be discussed in future works. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze the spatial and spectral superconvergence properties of one-dimensional hyperbolic conservation law by a discontinuous Galerkin (DG) method. The analyses combine classical mathematical arguments with MATLAB experiments. Some properties of the DG schemes are discovered using discrete Fourier analyses: superconvergence of the numerical wave numbers, Radau structure of the X spatial error. [Copyright &y& Elsevier]

Abstract: In [S. Ahmad, I.M. Stamova, Almost necessary and sufficient conditions for survival of species, Nonlinear Anal. Real World Appl. 5 (2004)], implications of various inequalities involving interaction coefficients and averages of the growth rates were listed for a two-dimensional Lotka–Volterra system, and it was shown that the first condition can be extended to one that is almost necessary and sufficient for persistence of a three-dimensional Lotka–Volterra system. In this paper, we give similar extensions of all the cases. We also explore the relationship of the condition, a notion defined by Ahmad–Lazer recently (see [S. Ahmad, A.C. Lazer, Average growth and total permanence in a competitive Lotka–Volterra system, Ann. Mat. 185 (2006)]), to certain known conditions which imply persistence. [Copyright &y& Elsevier]

Abstract: The objective of this paper is to systematically study the qualitative properties of the solutions of the discrete nonlinear delay survival red blood cells model where , and are positive periodic sequences of period . First, by using the continuation theorem in coincidence degree theory, we prove that the equation has a positive periodic solution with strictly positive components. Second, we prove that the solutions are permanent and establish some sufficient conditions for oscillation of the positive solutions about . Finally, we give an estimation of the lower and upper bounds of the oscillatory solution and establish some sufficient conditions for global attractivity of . From applications point of view permanence guarantees the long term survival of mature cells, oscillation implies the prevalence of the mature cells around the periodic solution and the convergence implies the absence of any dynamical diseases in the population. Our results in the special case when the coefficients are positive constants involve and improve the oscillation and global attractivity results on the literature. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the nonautonomous Lotka–Volterra system with dispersion. Under the assumption that the intrinsic growth rates of the species may be negative, we show that certain average conditions imply the uniform persistence of all species. Some known result is improved. [Copyright &y& Elsevier]

Abstract: In this paper, we present numerical analysis for the generalized quadrature rule for , where is an oscillatory function, and derive higher order generalized quadrature rules. The results show that the generalized quadrature rules are efficient for Bessel-trigonometric transformations and the accuracy increases when oscillation becomes faster. [Copyright &y& Elsevier]

Abstract: This paper investigates the effect of rotation in split and recombination (SAR) mixing, one of the specific cases in which chaotic advection is applied to lamination, in a microchannel. Three types of SAR micromixers were designed: No-R, Co-R, and Count-R. They are defined by their rotation effect and by the direction of the rotation. The mixing efficiency for the rotation effect was compared at various flow rates between 1μl/min (Re 0.12) and 100μl/min (Re 12) in an experiment and between 100μl/min (Re 12) and 1000μl/min (Re 120) for numerical analysis. It is concluded that there are three regions, SAR dominant, mixed, and rotation dominant regions, following mixed regimes for the Reynolds number when rotation is applied to SAR. In the mixed region, the SAR is distorted by rotation and the efficiency rapidly decreases as the Reynolds number increases. In order to increase the mixing efficiency for a wide range of Reynolds numbers in a microchannel, the second region (mixed region) must be diminished by optimizing the intensity of the rotation. [Copyright &y& Elsevier]

Abstract: This paper presents computable lower bounds of the penalty parameters for stable and convergent symmetric interior penalty Galerkin methods. In particular, we derive the explicit dependence of the coercivity constants with respect to the polynomial degree and the angles of the mesh elements. Numerical examples in all dimensions and for different polynomial degrees are presented. We show the numerical effects of loss of coercivity. [Copyright &y& Elsevier]

Abstract: This paper presents new families of Newton-type iterative methods (Newton, Halley and Chebyshev methods) for finding simple zero of univariate non-linear equation, permitting in the vicinity of the root. Newton-type iterative methods have well-known geometric interpretation and admit their geometric derivation from a parabola. These algorithms are comparable to the well-known powerful classical methods of Newton, Halley and Chebyshev respectively, and these can be seen as special cases of these families. The efficiency of the presented methods is demonstrated by numerical examples. [Copyright &y& Elsevier]

Abstract: In this paper, we suggest and analyze a new three-step iterative method for solving nonlinear equations involving only first derive of the function using a new decomposition technique which is due to Noor [M. Aslam Noor, Numerical Analysis and Optimization, Lecture Notes, COMSATS Institute of Information Technology, Islamabad, Pakistan, 2006; M. Aslam Noor, New iterative schemes for nonlinear equations, Appl. Math. Comput., in press] and Noor and Noor [M. Aslam Noor, K. Inayat Noor, Some iterative schemes for nonlinear equations, Appl. Math. Comput., in press]. We show that this new iterative method has fourth-order convergence. Several numerical examples are given to illustrate the efficiency and performance of the new method. [Copyright &y& Elsevier]

Abstract: In this paper, by using the theories and methods of mathematical analysis and computer algebra, a reliable algorithm of finite difference method for solving singular perturbation problems was established, a new matlab procedure ehssp was implemented, too. Several linear and non-linear problems are presented to illustrate the implementation of the program. [Copyright &y& Elsevier]

This article focuses on the Polish structure NUM+ na ‘out of’+NUM (e. g. Trzy na sto ‘three out of one hundred’). We explore the idea that, in most cases, the construction in question consists of a Determiner Phrase (DP) and an adjunct Prepositional Phrase (PP) – i. e. That it does not occupy a single numerical slot. We further postulate that this complex expression includes two occurrences of the quantified noun, one of them being subject to PF-ellipsis (deletion under identity). However, if the PP-internal (lower) numeral is a Q-type numeral (such as pięć ‘five’), the construction may be reanalysed as ‘mono-phrasal’. In such cases, the whole expression forms only one DP and the lower Q-numeral becomes the head of the numerical complex. The analysis we put forward in the present paper is based on the assumption that Polish is a DP-type language. We also take Q-numerals to be functional heads which occupy Q° and take NPs as their complements. [Copyright &y& Elsevier]

Abstract: The combined CFD-PBE (population balance models) are computationally intensive requiring efficient numerical methods for solving practical problems. In this paper, a high order method is presented based on the least-squares method (LSM) for the solution of a spatial-dependent population balance equation which includes advective processes. Numerical experiments are performed in order to study the behavior of the proposed method for one-dimensional cases using model problems with analytical solutions. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce and analyze the continuous finite element method for a class of delay-differential equation with a variable term. At first for the case of the constant delay and based on an orthogonal expansion in an element we derive optimal superconvergence u − U =O(h p+2), p ⩾2 at the (p +1)-order Lobatto points and u − U =O(h 2p ) at the integer nodal points. Next we prove the stability of linear and quadratic finite element schemes for the case of constant delay. For the case of variable delay, by use of the approximative to the continuous delay in every subinterval we decompose the original problem into a series of subproblems with constant delay. Finally we give a recursive schemes which can be compute by every subproblem. [Copyright &y& Elsevier]

Abstract: By means of variational iteration method the solution of generalized Huxley equation are obtained, comparison with the Adomian decomposition method is made, showing that the former is more effective than the later. In this paper, He’s variational iteration method is introduced to overcome the difficulty arising in calculating Adomian polynomials. [Copyright &y& Elsevier]

Abstract: In the present paper, we introduce the generic extension graph G of a Dynkin or cyclic quiver Q and then compare this graph with the crystal graph C for the quantized enveloping algebra associated to Q via two maps ℘ Q , Q : Ω → ΛQ induced by generic extensions and Kashiwara operators, respectively, where Λ Q is the set of isoclasses of nilpotent representations of Q, and Ω is the set of all words on the alphabet I, the vertex set of Q. We prove that, if Q is a (finite or infinite) linear quiver, then the intersection of the fibres ℘ Q −1 (λ) and KQ −1 (λ) is non-empty for every λ ∈ Λ Q . We will also show that this non-emptyness property fails for cyclic quivers. [Copyright &y& Elsevier]

Abstract: This paper provides a method for the decomposition of total factor productivity into partial measures of productivity. The proposed decomposition model measures the capacity productivity change and variable input productivity change. The latter can further be decomposed into partial factor technical efficiency change and partial factor technical change. This new decomposition isolates various sources of total factor productivity, and avoids providing a misleading indication of overall productivity. [Copyright &y& Elsevier]

Abstract: Analytic Hierarchy Process is a well-known method that is only able to rank different alternatives according to their AHP weights, but it does not determine the necessary threshold for discriminate between acceptable and unacceptable alternatives. In the other words, it does not lead the DM to choose the alternatives that have higher weights than the threshold. In this paper, we introduce a new method by which we are able to accept/reject alternatives based on AHP weights. The proposed method determines the necessary threshold by comparing the anticipated status with the desired status of alternatives and using LP and AHP combination for it. [Copyright &y& Elsevier]

Abstract: In this paper we revisit the solution of ill-posed problems by preconditioned iterative methods from a Bayesian statistical inversion perspective. After a brief review of the most popular Krylov subspace iterative methods for the solution of linear discrete ill-posed problems and some basic statistics results, we analyze the statistical meaning of left and right preconditioners, as well as projected-restarted strategies. Computed examples illustrating the interplay between statistics and preconditioning are also presented. [Copyright &y& Elsevier]

Abstract: Let m and t be positive integers with . An -splitting system is a pair where and is a collection of subsets of X called blocks such that for every with , there exists a block such that . An -splitting system is uniform if every block has size . In this paper, we give several constructions and bounds for splitting systems, concentrating mainly on the case . We consider uniform splitting systems as well as other splitting systems with special properties, including disjunct and regular splitting systems. Some of these systems have interesting connections with other types of set systems. [Copyright &y& Elsevier]

Abstract: Let be a compactification of an affine 3-fold into a smooth projective 3-fold such that the (reduced) boundary divisor is SNC. In this paper, as an affine counterpart to the work due to S. Mori (cf. [S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982) 133–176]), we shall classify -negative extremal rays on . In particular, if such an extremal ray intersects non-negatively, we shall describe the log flips and divisorial contractions appearing explicitly. [Copyright &y& Elsevier]