Search

Abstract: In this paper, we present some sixth-order class of modified Ostrowski’s methods for solving nonlinear equations. Per iteration each class member requires three function and one first derivative evaluations, and is shown to be at least sixth-order convergent. Several numerical examples are given to illustrate the performance of some of the presented methods. [Copyright &y& Elsevier]

• The proposed method is applicable to Cohen-Grossberg neural networks that can or can not be written as the vector-matrix form. • The second and third terms in the Lyapunov-Krasovskii functionals are introduced for the first time. • The algebraic criteria are given for the first time. This paper aims at establishing global exponential stability criteria for multiple time-varying delay Cohen–Grossberg neural networks (CGNNs). The considered network models cannot be expressed as the vector-matrix form, which yields that many methods in literature are unavailable. By constructing novel Lyapunov–Krasovskii functionals, two novel algebraic criteria guaranteeing global exponential stability of CGNNs under consideration are given. A pair of numerical examples are used to explain the effectiveness of the obtained algebra criteria relative to the previously stability conditions. It is worth emphasizing that the approach applied in this paper is applicable to CGNNs that may or may not be represented in vector-matrix form. [ABSTRACT FROM AUTHOR]

In this paper we study an asymptotic behavior of solutions of nonlinear dynamic systems on time scales of the form y Δ ( t ) = f ( t , y ( t ) ) , where f : T × R n → R n , and T is a time scale. For a given set Ω ⊂ T × R n , we formulate conditions for function f which guarantee that at least one solution y of the above system stays in Ω . Unlike previous papers the set Ω is considered in more general form, i.e., the time section Ω t is an arbitrary closed bounded set homeomorphic to the disk (for every t ∈ T ) and the boundary ∂ T Ω does not contain only egress points. Thanks to this, we can investigate a substantially wider range of equations with various types of bounded solutions. A relevant example is considered. The results are new also for non-autonomous systems of difference equations and the systems of impulsive differential equations. [ABSTRACT FROM AUTHOR]

There are few optimal fourth-order methods for solving nonlinear equations when the multiplicity m of the required root is known in advance. Therefore, the first focus of this paper is on developing new fourth-order optimal families of iterative methods by a simple and elegant way. Computational and theoretical properties are fully studied along with a main theorem describing the convergence analysis. Another main focus of this paper is the dynamical analysis of the rational map associated with our proposed class for multiple roots; as far as we know, there are no deep study of this kind on iterative methods for multiple roots. Further, using Mathematica with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm the theoretical development. [ABSTRACT FROM AUTHOR]

• In this paper, we present a new method for solving linear neutral delay differential equations. • We derive and illustrate the main features of this novel approach that combines the Laplace transform method with (harmonic) Fourier series theory. • We rely on computer algebra and numerical methods to implement the method. • We derive an approximate formula for the location of the complex poles, which are required for computing the inverse Laplace transform. • We include several examples where we compare the solutions generated by the standard Laplace method and the proposed Laplace-Fourier approach. • It is shown that the Laplace-Fourier solution provides more accurate solutions than the conventional Laplace transform solution. In this paper, we present a new method for solving linear neutral delay differential equations. We derive and illustrate the main features of this novel approach, that combines the Laplace transform method with (harmonic) Fourier series theory. Linear neutral delay differential equations are generally more difficult to solve because the time delay appears in the derivative of the state variable. We rely on computer algebra and numerical methods to implement the method. In addition, we derive an approximate formula for the location of the complex poles, which are required for computing the inverse Laplace transform. The form of the resulting solution, when only the Laplace method is used is a non-harmonic Fourier series. The accuracy of this solution can be improved by including more terms in the associated truncated series, but the convergence to the correct solution is slow. The main goal of this paper is to present a modified method which enables us to account for the terms which are excluded from these truncated Laplace series. That is, the terms in the tail of the infinite series. We include several examples where we compare the solutions generated by the standard Laplace method and the proposed Laplace-Fourier approach. Both solutions require using Cauchy's residue theorem and finding the real and complex poles. It is shown that the Laplace-Fourier solution provides more accurate solutions than the conventional Laplace transform solution. Finally, since the Laplace-Fourier method generates a solution which is valid for all times, it allows us to accurately approximate the solution at any point with a single calculation. [ABSTRACT FROM AUTHOR]

Abstract A graph Γ is symmetric or arc-transitive if its automorphism group Aut(Γ) is transitive on the arc set of the graph. Let p be an odd prime. Pentavalent symmetric graphs of order 2 pn with n ≥ 2 have been considered by Pan et al. in [Algebra Colloq. 22 (2015) 383-394] and by Feng et al. in [Discrete Math. 339 (2016) 2640-2651]. This paper gives a depiction of pentavalent symmetric graphs of order 2 m pn for any integers m ≥ 2 and n ≥ 1. As an application, connected pentavalent symmetric graphs of order 16 p , 8 p 2 and 8 p 3 are classified. [ABSTRACT FROM AUTHOR]

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 The restricted version of the overlapping Schur complement (SchurRAS) preconditioner was introduced by Li and Saad (2006) for the solution of linear system A x = b , and numerical results have shown that the SchurRAS method outperforms the restricted additive Schwarz (RAS) method both in terms of iteration count and CPU time. In this paper, based on meticulous derivation, we give an algebraic representation of the SchurRAS preconditioner, and prove that the SchurRAS method is convergent under the condition that A is an M -matrix and it converges faster than the RAS method. [ABSTRACT FROM AUTHOR]

Abstract: Probably the popular form of binary genetic algorithms for function optimization use tournament selection (TS) or roulette wheel selection (RS) for function optimization. Also single point crossover (SC) and uniform crossover (UC) are most popular and effective crossover operators. In an earlier paper we had considered all four combinations of these crossover and mutation operators along with bit-wise mutation, called GA1 (TS+SC), GA2 (TS+UC), GA3 (RS+SC) and GA4 (RS+UC). In this paper, an attempt is made to hybridize these four GAs by incorporating the quadratic approximation (QA) operator into them. The four resultant hybrid GAs, called HGA1, HGA2, HGA3 and HGA4, are compared with the four simple GAs on a set of 22 test problems taken from literature. Based on the extensive numerical and graphical analysis of results it is concluded that the HGA3 outperforms all rest 7 versions. Further, we study the depth and frequency of the QA should be applied for better performance for the particular problem suite. [Copyright &y& Elsevier]

Abstract: This paper presents a survey of error-free algorithms to solve various systems of linear equations. The presented algorithms do not introduce computational errors into the solution and thus they are well suited to solve ill-conditioned linear systems. The error-free algorithms are based on modulo arithmetic. Two basic approaches have been investigated in the paper. The first one is based on iterative scheme using one modulus only. The other one is parallel and uses several moduli and the Chinese theorem. It is based on polynomial algebra operations that allow to express the operation of deconvolution as a sequence of convolutions of both response and output signals. [Copyright &y& Elsevier]

Abstract: In this paper, we formulate a new robust two-species nonautonomous predator–prey model with multi-delays and impulsive effects and perform a systematic mathematical and ecological study. Our results in this paper indicate that under the appropriate linear periodic impulsive perturbations, the system is permanent and has a unique positive globally attractive semi-trivial periodic solution. By using the Brouwer fixed point theorem, we prove that if the periodic system is permanent, then there is at least one positive periodic solution of the system. We show that the conditions for global attractivity of the positive semi-trivial periodic solution and permanence of the population of the model depend on time delay, so, we call it “profitless”. In this paper, the main feature is that we introduce multi-delays and impulses into the predator–prey model, exhibit a new modeling method which is applied to investigate multi-species impulsive multi-delays differential equations. [Copyright &y& Elsevier]

Abstract: In this paper, we first define some generalized Schur complements, then we study the representation of M–P inverse group inverse and Drazin for the partitioned matrix . Based on this, we give three kind quotient identities of generalized Schur complement about the partitioned matrix and develops the results in paper [M. Redivo-Zaglia, Pseudo-Schur complement and their applications, Appl. Num. Math. 50 (2004) 511–519; K. Jbilou, A. Messaoudi, K. Tabaâ, Some Schur complement identities and applications to matrix exatrapolation methods, Linear Algebra Appl. 392 (2004) 195–210]. In the end of the paper, we give the application of these generalized Schur complement in solution of linear equation, and give numerical example to show our results. [Copyright &y& Elsevier]

Abstract: A detailed, comparative study of the numerical stability of the recursive algorithms, widely used to calculate the Zernike moments of an image, is presented in this paper. While many papers, introducing fast algorithms for the computation of Zernike moments have been presented in the literature, there is not any work studying the numerical behaviour of these methods. These algorithms have been in the past compared to each other only according to their computational complexity, without been given the appropriate attention, as far as their numerical stability is concerned, being the most significant part of the algorithms’ reliability. The present contribution attempts to fill this gap in the literature, since it mainly demonstrates that the usefulness of a recursive algorithm is defined not only by its low computational complexity, but most of all by its numerical robustness. This paper exhaustively compares some well known recursive algorithms for the computation of Zernike moments and sets the appropriate conditions in which each algorithm may fall in an unstable state. The experiments show that any of these algorithms can be unstable under some conditions and thus the need to develop more stable algorithms is of major importance. [Copyright &y& Elsevier]

Abstract: In this paper, our main purpose is to establish the existence of singular positive radial solutions of second order quasilinear elliptic equations. The main results of the present paper are new and extend the previously known results. [Copyright &y& Elsevier]

Abstract: This paper develops an Improved harmony search (IHS) algorithm for solving optimization problems. IHS employs a novel method for generating new solution vectors that enhances accuracy and convergence rate of harmony search (HS) algorithm. In this paper the impacts of constant parameters on harmony search algorithm are discussed and a strategy for tuning these parameters is presented. The IHS algorithm has been successfully applied to various benchmarking and standard engineering optimization problems. Numerical results reveal that the proposed algorithm can find better solutions when compared to HS and other heuristic or deterministic methods and is a powerful search algorithm for various engineering optimization problems. [Copyright &y& Elsevier]

Abstract: Network managers wish to optimize control parameters such as signal setting which are very related to the traffic assignment models. On the other hand traffic assignment patterns as an important instrument for predicting the amount of flow on network links are dependent to control decisions. According to the significance of this concept, some important papers about this mutually relation are reviewed in this paper. Then we implement a nonlinear algorithm on a minimal cost multicommodity flow (MCMF) problem to optimize some control policies subject to optimal flows. Although we take signal times into account, but this approach has a far more reaching application in urban network control and design. We employ a hybrid intelligent algorithm integrating decent direction algorithm and an interior point algorithm in a mutually consistent scheme for obtaining optimal signals and equilibrium flows. An example is given to illustrate the effectiveness of our scheme. [Copyright &y& Elsevier]

Abstract: This paper is an extension of the work (J. Rimas, On computing of arbitrary positive integer powers for one type of odd order skew-symmetric tridiagonal matrices with eigenvalues on imaginary axis-I, Appl. Math. Comput., in press), in which the general expression of the lth power (l ∈ N) for one type of tridiagonal matrices of order n =2p +1 (p ∈ N) is given. In this new paper we present the complete derivation of this general expression. Expressions of eigenvectors and Jordan’s form of the matrix and of the transforming matrix and its inverse are given, too. [Copyright &y& Elsevier]

Abstract: This paper presents an outcome-space finite algorithm for solving linear multiplicative programming, in each iteration of which a convex quadratic programming is only solved. In the paper, we give a global optimization condition on a class of multiplicative programming problems and prove that the proposed algorithm is finite terminative and gain a global optimal solution of the former problem when it stops. It can be shown by the numerical results that the proposed algorithm is effective and the computational results can be gained in short time. [Copyright &y& Elsevier]

Abstract: In this paper, our main purpose is to establish the existence of positive bounded entire solutions of second order quasilinear elliptic equations under new conditions. The main results of the present paper are new and extend the previously known results. [Copyright &y& Elsevier]

Abstract: In this paper, we extend technique for order preference by similarity ideal solution (TOPSIS) for solving large scale multiple objective programming problems involving fuzzy parameters. These fuzzy parameters are characterized as fuzzy numbers. For such problems, the α-Pareto optimality is introduced by extending the ordinary Pareto optimality on the basis of the α-level sets of fuzzy numbers. An interactive fuzzy decision making algorithm for generating α-Pareto optimal solution through TOPSIS approach is provided where the decision maker (DM) is asked to specify the degree α and the relative importance of objectives. Finally, a numerical example is given to clarify the main results developed in the paper. [Copyright &y& Elsevier]

Abstract: In this paper, a new approach, the extend sinh–cosh method, is proposed, to investigate the exact solutions with solitary patterns of the Boussinesq-like equations with fully nonlinear dispersion, B(m, n) equations: u tt +(u m ) xx −(u n ) xxxx =0. The new exact special solutions with solitary patterns of the equations are found by our new method. The two special cases, B(2,2) and B(3,3), are chosen to illustrate the concrete scheme of our approach in B(m, n) equations. The nonlinear equations B(m, n) are addressed for two different cases, namely when m = n being odd and even integers. An entirely new general formulas for the solutions of B(n, n) equations are established. The general formulas for the solutions of B(n, n) equations with all integer n >1 can be extended to the case of B(m, n) equations with m = n being noninteger. Our results include not only some known results in literature as special cases but also some new exact special solutions with solitary patterns. The method presented by this paper is suitable for studying exact special solutions with solitary patterns of some other equations. [Copyright &y& Elsevier]

Abstract: This paper is an extension of the work [On computing of arbitrary positive integer powers for one type of tridiagonal matrices, Applied Mathematics and Computation, to appear], in which the general expression of the lth power (l∈N) for one type of tridiagonal matrices of order n=2p+1 (p∈N) is presented. In this new paper we derive the general expression of the lth power (l∈N) for the same type of tridiagonal matrices of order n=2p (p∈N). Expressions of eigenvectors and Jordan’s form of the matrix, and of transforming matrix and its inverse are given, too. [Copyright &y& Elsevier]

In this paper, by using the theories and methods of mathematical analysis and computer algebra, a new algorithm of symbolic integral was established, a new Maple procedure myint for it was established, too. And it was applied to the automatic proving the mean-value theorems for derivatives. The results indicated that the algorithm of symbolic integral had been established in this paper had advantage of simple idea, excellent property for operation and powerful competence. This would be useful for the problem of solving differential equations, automatic proving some mathematical theorems, and so on. [Copyright &y& Elsevier]

In this paper, our main purpose is to establish the existence of positive bounded entire solutions of second order quasilinear elliptic equations. The main results of the present paper are new and extend the previously known results. [Copyright &y& Elsevier]

Some new criteria have been obtained for the oscillation of the linear matrix Hamiltonian system X′=A(t)X+B(t)Y, Y′=C(t)X-A*(t)Y under the hypothesis: A(t), B(t)=B*(t)>0 and C(t)=C*(t) are n×n real continuous matrix functions on the interval [t0,∞)(t0>-∞). Our results are independent of the main results obtained in our recent paper [Appl. Math. Comput. 131 (2002) 357] in the sense that they are given in terms of the positive linear functional on the linear space of n×n matrices with real entries. At the same time, our results improve some previous results to a great extent, which can be seen by the examples given at the end of this paper. [Copyright &y& Elsevier]

In this paper we consider new representations of the analogue higher order Bernoulli numbers in p-adic analysis. Also, we prove Kummer-type congruence for these numbers using Ota’s method [J. Number Theory 92 (2002) 1], which is a solution to a part of the Question 2 in the paper by Jang and Kim [Appl. Math. Comput. 137 (2,3) (2003) 387]. [Copyright &y& Elsevier]

The mathematics of the new physics developed in the Series [11–14] that we summarize here is quite extensive. However, the reconstruction of the reals without the axiom of choice is the principle focus of this paper. Combined with the enrichment of the reals by completion in the standard metric, algebraic extension and admission of a topological axiom, the new reals is established and well-defined. It is further extended to the new nonstandard analysis which, together, has the following achievements developed in the Series:

In this paper we first write a proof of the perceptron convergence algorithm for the complex multivalued neural networks (CMVNNs). Our primary goal is to formulate and prove the perceptron convergence algorithm for the bicomplex multivalued neural networks (BMVNNs) and other important results in the theory of neural networks based on a bicomplex algebra. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the study of the diamond partial order in C * -algebras. We characterize linear maps preserving this partial order. [ABSTRACT FROM AUTHOR]

The edge-rupture degree of an incomplete connected graph G is defined as r ′ ( G ) = m a x { ω ( G − S ) − | S | − m ( G − S ) : S ⊆ E ( G ) , ω ( G − S ) > 1 } , where ω ( G − S ) and m ( G − S ) , respectively, denote the number of components and the order of a largest component in G − S . This is a reasonable parameter to measure the vulnerability of networks, as it takes into account both the amount of work done to damage the network and how badly the network is damaged. In this paper, firstly, the relationships between the edge-rupture degree and some other graph parameters, namely the edge-connectivity, edge-integrity, edge-toughness, edge-tenacity, diameter, the algebraic connectivity and the minimum degree are established. After that, the edge-rupture degree of the middle graphs of path and cycle are given. Then, we introduced the concept of r ′-maximal graph and give some basic results of such graphs. Finally, we introduce the concept of edge-ruptured and strictly edge-ruptured graph, and we establish necessary and sufficient conditions for a graph to be edge-ruptured and strictly edge-ruptured, respectively. [ABSTRACT FROM AUTHOR]

Finding the solution of the absolute value equation (AVE) A x − | x | = b has attracted much attention in recent years. In this paper, we propose a relaxed nonlinear PHSS-like iterative method, which is more efficient than the Picard-HSS iterative method for the AVE, and is a generalization of the nonlinear HSS-like iteration method for the AVE. By using the theory of nonsmooth analysis, we prove the convergence of the relaxed nonlinear PHSS-like iterative method for the AVE. Numerical experiments are given to demonstrate the feasibility, robustness and effectiveness of the relaxed nonlinear HSS-like method. [ABSTRACT FROM AUTHOR]

Recently, Cui and Wang (2014) constructed an algorithm for demicontractive operators that converges weakly, under mild assumptions, to some solution of the split common fixed point problem. In this paper, based on Halpern’s type method (1967), we construct an algorithm for demicontractive operators that produces sequences that always converge strongly to a specific solution of the split common fixed point problem. Particular cases of directed operators and quasi-nonexpansive mappings are also considered. [ABSTRACT FROM AUTHOR]

The paper discusses a large class of stochastic Volterra integral equations whose coefficients additively depend on small perturbations. Their solutions are compared in the L 2 -sense with the solutions of the appropriate unperturbed equations of the equal or simpler type. More precisely, we prove for an arbitrary η > 0 that there exists an interval [ t ¯ ( η ) , T ] ⊂ [ 0 , T ] on which the L 2 -difference between the solutions of the perturbed and unperturbed equations is less than η . [ABSTRACT FROM AUTHOR]

In this paper we study the generalized Emden–Fowler and the generalized isothermal spheres equations. We examine singularities of solutions which are analytic at the origin. We also find an asymptotic behaviour of these solutions at infinity. A correspondence between these equations when one of the parameters tends to infinity is presented. [ABSTRACT FROM AUTHOR]

In this paper, we extend the generalized product-type bi-conjugate gradient (GPBiCG) method for solving the generalized Sylvester-conjugate matrix equations A 1 X B 1 + C 1 Y ¯ D 1 = S 1 , A 2 X ¯ B 2 + C 2 Y D 2 = S 2 by the real representation of the complex matrix and the properties of Kronecker product and vectorization operator. Some numerical experiments demonstrate that the introduced iteration approach is efficient. [ABSTRACT FROM AUTHOR]

Ariyawansa and Zhu (2011) have derived volumetric barrier decomposition algorithms for solving two-stage stochastic semidefinite programs and proved polynomial complexity of certain members of the algorithms. In this paper, we utilize their work to derive volumetric barrier decomposition algorithms for solving two-stage stochastic convex quadratic second-order cone programming, and establish polynomial complexity of certain members of the proposed algorithms. [ABSTRACT FROM AUTHOR]

We consider Fredholm–Hammerstein integral equations of the second kind over a rectangular region in plane. As in Kumar and Sloan (1987) [5], we reformulate it into an equivalent integral equation. For the alternative equation, we triangulate the rectangular domain and on each triangle use a collocation method based on constant spline approximation. We discuss the convergence of the approximate solutions and conclude the paper with numerical examples. [ABSTRACT FROM AUTHOR]

Let H m × n be the set of all m × n matrices over the real quaternion algebra H = { c 0 + c 1 i + c 2 j + c 3 k ∣ i 2 = j 2 = k 2 = i j k = − 1 , c 0 , c 1 , c 2 , c 3 ∈ R } . A ∈ H n × n is known to be η -Hermitian if A = A η * = − η A * η , η ∈ { i , j , k } and A * means the conjugate transpose of A . We mention some necessary and sufficient conditions for the existence of the solution to the system of real quaternion matrix equations including η -Hermicity A 1 X = C 1 , A 2 Y = C 2 , Y B 2 = D 2 , Y = Y η * , A 3 Z = C 3 , Z B 3 = D 3 , Z = Z η * , A 4 X + ( A 4 X ) η * + B 4 Y B 4 η * + C 4 Z C 4 η * = D 4 , and also construct the general solution to the system when it is consistent. The outcome of this paper diversifies some particular results in the literature. Furthermore, we constitute an algorithm and a numerical example to comprehend the approach established in this treatise. [ABSTRACT FROM AUTHOR]

Various problems of pure and applied sciences can be studied in the unified frame work of the nonlinear equations. In this paper, a new family of iterative methods for solving nonlinear equations is developed by using a new decomposition technique. The convergence of the proposed methods is proved. It is shown that the new family contains several well-known iterative methods as special case. For the implementation and performance of the new methods, a nonlinear equation arising in the population model and another one arising in the motion of a particle on inclined plane is solved. [ABSTRACT FROM AUTHOR]

In this paper we unify the system of functional equations defining a multi-additive-quadratic mapping to obtain a single equation. We also prove, using the fixed point method, the generalized Hyers–Ulam stability of this equation thus generalizing some known results. [ABSTRACT FROM AUTHOR]

Real options were firstly formulated by using traditional financial option models; however, an investor can confront in practice with exotic dynamics. Nowadays, approaches based on simulations have been gaining relevance for solving complex options. This paper proposes the application of the path integral approach (PI) to multivariate real option problems. We discuss the viability of the proposal by a mathematical analysis of the problem and an application to a case study of control chart decision (CCD). The proposal is compared with the traditional approaches for solving real option problems. The results present the proposal as a competitive alternative for the simulation in low dimensional problems. [ABSTRACT FROM AUTHOR]

Let Θ n be the digraph with vertex set V n = { 1 , 2 , … , n } and arc set E = ∪ l < k { ( k , l ) | k = 2 , … , n } ∪ { ( k , k + 1 ) | k = 1 , … , n − 1 } , and Θ n i , j the digraph obtained by deleting one arc ( i, j ) from Θ n where 1 ≤ j < i ≤ n ( n ≥ 2). We have solved the Laplacian spectra of digraphs Θ n i , j for i − j = 1 and i − j = 2 . In this paper, we further obtain the Laplacian spectra of Θ n i , j for the case i − j = 3 . Meanwhile, Θ n i , i − 4 is found to have completely real spectra as well. [ABSTRACT FROM AUTHOR]

In this paper we analyze the Riemann problem for the widely used drift-flux two-phase flow model. This analysis introduces the complete information that is attained in the representation of solutions to the Riemann problem. It turns out that the Riemann waves have rarefactions, a contact discontinuity and shocks. Within this respect, an exact Riemann solver is developed to accurately resolve and represent the complete wave structure of the gas-liquid two-phase flows. To verify the solver, a series of test problems selected from the literature are presented including validation against independent numerical simulations where the solution of the Riemann problem is fully numerical. In this framework the governing equations are discretized by finite volume techniques facilitating the application Godunov methods of centred-type. It is shown that both analytical and numerical results demonstrate the broad applicability and robustness of the new exact Riemann solver. [ABSTRACT FROM AUTHOR]

Recently, a new treatment based on Taylor’s expansion to give the estimate of the convergence radius of iterative method for multiple roots has been presented. It has been successfully applied to enlarge the convergence radius of the modified Newton’s method and Osada’s method for multiple roots. This paper re-investigates the convergence radius of Halley’s method under the condition that the derivative f ( m + 1 ) of function f satisfies the center-Hölder continuous condition. We show that our result can be obtained under much weaker condition and has a wider range of application than that given by Bi et. al.(2011) [21]. [ABSTRACT FROM AUTHOR]

In this paper, we consider the analytical solution and numerical approximation of the celebrated steady states Allen–Cahn equation. We present a computer code to solve and plot the solutions using Maxima software. [ABSTRACT FROM AUTHOR]

In this paper, we introduce some particular families of graphicable algebras obtained by following a relatively new line of research, initiated previously by some of the authors. It consists of the use of certain objects of Discrete Mathematics, mainly graphs and digraphs, to facilitate the study of graphicable algebras, which are a subset of evolution algebras. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we prove two theorems on , summability of orthogonal series. Also, several known and new results are deduced as corollaries of the main results. [Copyright &y& Elsevier]

Abstract: Nanotechnology is yet to come, but even now, in early stage of development it is clear that defect and fault levels will be much higher than current CMOS technology. The exact level of defect densities is unknown, but it is assumed that % on-chip resources will be defective. Novel techniques and architectures have to be devised in order for nanoelectronics to become a viable replacement for current VLSI processes. With defect rates for current VLSI processes in the range of 1 part per billion, manufacturers can afford to discard any chip that is found to be defective. However, in order to increase fabrication yield, nanotechnology requires extensive and computationally demanding analysis of defect significance. In order to simplify the analysis, in this paper we propose a mathematical framework based on tropical algebra for circuit analysis. It is more descriptive and convenient to use in graph analysis than traditional algebra. In tropical algebra, we will derive a simple iterative algorithm for error propagation analysis of systolic arrays. It will be shown that the computational complexity of the proposed algorithm is reduced from to , where T is the number of array cells. An example of tropical algebra analysis and design of partially defect tolerant hexagonal systolic multiplier will be given, too. [Copyright &y& Elsevier]

• In this paper, we proposed an algorithm to solve mixed solutions of the matrix Equation ∑ i = 1 t A i X i B i = E with sub-matrix constraints. We also prove that the iterative solution sequence generated by the algorithm is convergent. Moreover, for a given matrix, its best approximation is obtained, which is the mixed solution of the matrix equation with sub-matrix constraints. Finally, a large number of numerical experiments are carried out, and results show that the algorithm is effective not only in image restoration, but also in the general case, for both small-scale and large-scale matrices. The work belongs to the field of numerical algebra, and has been widely concerned. We put forward and analyze in details an iterative method to find the mixed solutions of a matrix equation with sub-matrix constraints. The convergence of the approximated solution sequence generated by the iterative method is investigated, showing that if the constrained matrix equation is consistent, the mixed solution group can be obtained after a finite number of iterations. Moreover, for a given matrix, its best approximation is obtained, which is the mixed solution of the matrix equation with sub-matrix constraints. Finally, a large number of numerical experiments are carried out, and results show that the algorithm is effective not only in image restoration, but also in the general case for both small-scale and large-scale matrices. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we apply the idea of Dixon resultant to algebraic differential equations and introduce the Dixon differential resultant. We prove that a necessary condition for the existence of a common solution of two algebraic differential equations is that the differential resultant is equal to zero, which actually provides a method of elimination and reduces a system of multi-variate differential equations to a system of single-variate differential equations. This result is also generalized to the system of n differential polynomials. We give algorithms to realize our method of elimination for systems of differential equations. Our results and algorithms are demonstrated by some examples. [Copyright &y& Elsevier]