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Nonlinear Kawarada equations have been used to model solid fuel combustion processes in the oil industry. An effective way to approximate solutions of such equations is to take advantage of the finite difference configurations. Traditionally, the nonlinear term of the equation is linearized while the numerical stability of a difference scheme is investigated. This leaves certain ambiguity and uncertainty in the analysis. Based on nonuniform grids generated through a quenching-seeking moving mesh method in space and adaptation in time, this paper introduces a completely new stability analysis of the approximation without freezing the nonlinearity involved. Pointwise orders of convergence are investigated numerically. Simulation experiments are carried out to accompany the mathematical analysis to strengthen our conclusions. [ABSTRACT FROM AUTHOR]

The generalized minimal residual (GMRES) method is widely used to solve a linear system. This paper establishes upper and lower bounds for GMRES residuals for solving antridiagonal Toeplitz linear system. For normal matrixA, this problem has been studied previously by Li [Convergence of CG and GMRES on a tridiagonal Toeplitz linear system, BIT 47(3) (2007), 577–599.]. Also, Li and Zhang [The rate of convergence of GMRES on a tridiagonal Toeplitz linear system, Numer. Math. 112 (2009), pp. 267–293.] for non-symmetric matrixA, presented upper bound for GMRES residuals. In fact, our main goal in this paper is to find the upper and lower bounds for GMRES residuals on normal tridiagonal Toeplitz linear systems, and lower bounds for residuals of GMRES on solving non-normal tridiagonal Toeplitz linear systems. [ABSTRACT FROM PUBLISHER]

In the literature, rank-constrained Hermitian nonnegative-definite solutions to the matrix equation AXAH=B have been investigated, under the conditions that B is Hermitian and nonnegative-definite, and the matrix equation is consistent. In this paper, we discuss rank-constrained Hermitian nonnegative-definite least squares solutions to this matrix equation, in which the above conditions may not hold. We derive the rank range and expression of these least squares solutions. Therefore, the results obtained in this paper generalize those in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we give the comments on the article ‘Inversion of a Generalized Vandermonde Matrix’ by M.E.A. El Mikkawy, Int. J. Computer Math. 80 (2003), pp. 759–765. The article gives an algorithm for the elementary symmetric function's calculation which contains a severe error. In these comments, we have proposed necessary corrections of that algorithm. [ABSTRACT FROM PUBLISHER]

This paper is concerned with numerical solution of the nonlinear fractional diffusion equation with multi-delay. The studied model plays a significant role in population ecology. A linearized Crank-Nicolson method for such problem is proposed by combing the Crank-Nicolson approximation in time with the fractional centred difference formula in space. Using the discrete energy method, the suggested scheme is proved to be uniquely solvable, stable and convergent with second-order accuracy in both space and time for sufficiently small space and time increments. Several numerical experiments for solving the delay fractional Hutchinson equation and two real problems in population dynamics are provided to verify our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we analyse the iterated collocation method for the nonlinear Urysohn operator equation x=y+K(x) with K a singular kernel. The paper extends the study [H. Kaneko, R.D. Noren, and P.A. Padilla, J. Comput. Appl. Math. 80 (1997), pp. 335-349] in which the convergence of the iterated collocation method for Urysohn equations is considered. [ABSTRACT FROM AUTHOR]

Dupin cyclides, their applications in geometric modelling and their parametrization using bi-quadratic patches bounded by lines of curvature, have been investigated in recent years by a number of authors such as Martin, de Pont and Sharrock in 1986, Boehm in 1990, Pratt in 1990, and Degen in 1994. However, no completely reliable and general algorithm for the determination of bi-quadratic cyclide patches has appeared in the literature. This paper presents a new approach that produces any required bi-quadratic patch, bounded by lines of curvature, without non-intrinsic geometric constraints or restrictions. Specifically, if a bi-quadratic parametrization exists for the specified region of the cyclide, then it is correctly determined. Explicit formulae are given for the Bernstein weights and vectors of the parametrizations. The method is neither cyclide specific nor specific to the construction of bi-quadratic rational parametrizations - it may therefore be applied to other surfaces and to higher degree rational constructions. [ABSTRACT FROM AUTHOR]

In this paper, we analyse the iterated collocation method for the nonlinear operator equation x = y+K(x) with K a smooth kernel. The paper expands the study begun by H. Kaneko and Y. Xu concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. Let x* denote an isolated fixed point of K. Let Xn, n≥1, denote a sequence of finite-dimensional approximating subspaces, and let Pn be a projection of X onto Xn. The projection method for solving x = y+K(x) is given by xn = Pny+PnK(xn), and the iterated projection solution is defined as [image omitted] . We analyse the convergence of {xn} and {[image omitted] } to x*, giving a general analysis that includes the collocation method. A detailed analysis is then given for a large class of Urysohn integral operators in one variable, showing the superconvergence of {[image omitted] } to x*. [ABSTRACT FROM AUTHOR]

A vertex-coloured graphGis said to berainbow vertex-connectedif every two vertices ofGare connected by a path whose internal vertices have distinct colours, such a path is called a rainbow path. Therainbow vertex-connection numberof a connected graphG, denoted by, is the smallest number of colours that are needed in order to makeGrainbow vertex-connected. In this paper, we study the rainbow vertex-connection number on the lexicographical, strong, Cartesian and direct product and present several upper bounds for these products of graphs. The rainbow vertex-connection number of some product networks is also investigated in this paper. [ABSTRACT FROM AUTHOR]

The conditional diagnosis is a very important measure of the reliability and the fault-tolerance of networks. The ‘condition’ means that no faulty set contains all neighbours of any node. Under this assumption, for any systemG, every component ofhas more than 1 node, whereFis the faulty set ofG. Theg-extra conditional diagnosability is defined under the assumption that every component ofhas more thannodes. ‘A system with at mosttfaulty nodes is defined as sequentiallyt-diagnosable if at least one faulty node can be repaired, so that the testing can be continued using the repaired node to eventually diagnose all faulty nodes’ [E.P. Duarte Jr., R.P. Ziwich, and L.C.P. Albini,A survey of comparison-based system-level diagnosis, ACM Comput. Surv. 43(3) (2011), article 22]. To increase the degree of the sequentialt-diagnosability of a system, sequential-diagnosis strategy is proposed in this paper. It is allowed that there are at mostkmisdiagnosed nodes. In this paper, we determine theg-extra conditional diagnosability of hypercubes and propose sequential-diagnosis algorithms for hypercubes with low time complexities under the Preparata, Metze, and Chien (PMC) model and the MM* model which is a special case of the Maeng and Malek (MM) model. [ABSTRACT FROM PUBLISHER]

This paper concerns modified Two-Derivative Runge–Kutta–Nyström (TDRKN) methods for solving second-order initial value problems. Compromised with the deduced order and symmetry criteria, two implicit and forth-order two-stage TDRKN schemes are derived through a mixed collocation approach. Phase and periodic stability features are examined. Numerical experiments are carried out to illustrate the effectiveness and competence of our new methods. Comparisons with existing highly accurate and efficient numerical methods are given. [ABSTRACT FROM AUTHOR]

LetGbe a simple connected graph with vertex set. The connective eccentricity index (CEI) of a graph is defined as, where,denote the eccentricity and the degree ofv, respectively. In this paper, we further study the CEI of trees and unicyclic graphs with several graph constraints, we also determine the extremal graphs. [ABSTRACT FROM AUTHOR]

In this paper, we present many new fourth-order optimal families of Jarratt's method and Ostrowski's method for computing simple roots of nonlinear equations numerically. The proposed families of Jarratt's method having the same scaling factor of functions as that of Jarratt's method (i.e. quadratic scaling factor of functions in the numerator and denominator of the correction factor) are the main finding of this paper. It is observed that the body structures of our proposed families of Jarratt's method are simpler than those of the original families of Jarratt's method. The efficiency of these methods is tested on a number of relevant numerical problems. Furthermore, numerical examples suggest that each member of the proposed families can be competitive to other similar robust methods available in the literature. [ABSTRACT FROM PUBLISHER]

In this paper, we present a fast numerical algorithm for solving nearly penta-diagonal linear systems and show that the computational cost is less than those of three algorithms in El-Mikkawy and Rahmo, [Symbolic algorithm for inverting cyclic penta-diagonal matrices recursively–Derivation and implementation, Comput. Math. Appl. 59 (2010), pp. 1386–1396], Lv and Le [A note on solving nearly penta-diagonal linear systems, Appl. Math. Comput. 204 (2008), pp. 707–712] and Neossi Nguetchue and Abelman [A computational algorithm for solving nearly penta-diagonal linear systems, Appl. Math. Comput. 203 (2008), pp. 629–634.]. In addition, an efficient way of evaluating the determinant of a nearly penta-diagonal matrix is also discussed. The algorithm is suited for implementation using computer algebra systems (CAS) such as MATLAB, MACSYMA and MAPLE. Some numerical examples are given in order to illustrate the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we consider a kernel-based online learning algorithm for regression when the sampling process is unbounded. Under a moment hypothesis on the sampling outputs, we provide a confidence-based bound for the error in the corresponding reproducing kernel Hilbert space. [ABSTRACT FROM AUTHOR]

Communication networks are immensely important today, since both companies and individuals use numerous services that rely on them. This paper considers the design of hierarchical (communication) networks. We consider the survivability of asymmetrical hierarchical network flows (AHNF), when arcs failure and, hence, flow destruction is probable. In such networks, it is supposed that the remaining arc capacities are known and the guaranteed evaluation of the functional capability assumes finding the worst distribution of flow in the destructed network. Since, in the network flows, a unique efficiency criterion is not generally known or defined, we assess the quality of the network functioning by a measure of demands satisfaction, i.e. the fraction of satisfied demands at the sink nodes. With regard to this criterion, we construct the mathematical model of the network regardless of the design structure. Then, by defining a measure of satisfying the demands, we compute and compare the survivability of two well-known reserve designs, namely radial and circular reserves. [ABSTRACT FROM AUTHOR]

In this paper, we present the general bounds of multiplicative relative perturbation for diagonalizable matrices, which are the improvement of recent results. The bounds gained here are sharper than those in related literatures. In addition, we obtain the multiplicative relative bounds for normal matrices, which are discussed first. [ABSTRACT FROM AUTHOR]

The domination polynomial of a graph G of order n is the polynomial [image omitted] , where d(G, i) is the number of dominating vertex sets of G with cardinality i. A root of D(G, x) is called a domination root of G. In this paper, we characterize graphs with exactly four distinct domination roots [image omitted] . [ABSTRACT FROM AUTHOR]

This paper deals with the mean-square (MS) stability of the Euler-Maruyama method for stochastic differential delay equations (SDDEs) with jumps. First, the definition of the MS-stability of numerical methods for SDDEs with jumps is established, and then the sufficient condition of the MS-stability of the Euler-Maruyama method for SDDEs with jumps is derived, finally a class scalar test equation is simulated and the numerical experiments verify the results obtained from theory. [ABSTRACT FROM AUTHOR]

For the global optimization problems with continuous variables, evolutionary algorithms (EAs) are often used to find the approximate solutions. The number of generations for an EA to find the approximate solutions, called the first hitting time, is an important index to measure the performance of the EA. However, calculating the first hitting time is still difficult in theory. This paper proposes some new drift conditions that are used to estimate the upper bound of the first hitting times of EAs for finding the approximate solutions. Two case studies are given to show how to apply these conditions to estimate the first hitting times. [ABSTRACT FROM AUTHOR]

The nonlinear Schrodinger's equation, which describes the electron (Langmuir) waves in plasmas, is studied in this paper in the presence of perturbation terms. The method of multiple-scale analysis is employed to perform this study. The perturbation terms that are considered here are both local and non-local. [ABSTRACT FROM AUTHOR]

Some factories use the cutting and stamping processes to divide stock plates into circles to make products. A guillotine machine cuts the plate into strips in the cutting process and then a stamping press punches out circles from the strips in the stamping process. The circles in a strip have the same size. The number of rows of circles in each strip is limited. Under these constraints, this paper addresses the following primary objective: to cut a plate by a guillotine method so that the maximal number of circles is obtained. Then the secondary objective should be optimized: the cutting layout should use a minimal number of strips. The problem is formulated as a bi-objective optimization problem and a recursive algorithm is presented for it. The computational results indicate that the algorithm can efficiently simplify the cutting process. [ABSTRACT FROM AUTHOR]

This paper presents an explicit representation for M-P inverse A†. Based on this, we can use Gauss-Jordan elimination to compute it, and get the upper bound of the total number of arithmetic operations about 21/4n3. Finally, a numerical example is demonstrated. [ABSTRACT FROM AUTHOR]

In this paper, a universal simulator for cellular neural network (CNN) is presented. This simulator is capable of performing Raster simulation for any size of input image, and thus is a powerful tool for researchers investigating potential applications of CNN. This paper reports the latency properties of CNNs along with popular numerical integration algorithms; results and comparisons are also presented. [ABSTRACT FROM AUTHOR]

Some preconditioners for accelerating the classical iterative methods are given in Zhang et al. [Y. Zhang and T.Z. Huang, A class of optimal preconditioners and their applications, Proceedings of the Seventh International Conference on Matrix Theory and Its Applications in China, 2006. Y. Zhang, T.Z. Huang, and X.P. Liu, Modified iterative methods for nonnegative matrices and M-matrices linear systems, Comput. Math. Appl. 50 (2005), pp. 1587-1602. Y. Zhang, T.Z. Huang, X.P. Liu, A class of preconditioners based on the (I+S(α))-type preconditioning matrices for solving linear systems, Appl. Math. Comp. 189 (2007), pp. 1737-1748]. Another kind of preconditioners approximating the inverse of a symmetric positive definite matrix was given in Simons and Yao [G. Simons, Y. Yao, Approximating the inverse of a symmetric positive definite matrix, Linear Algebra Appl. 281 (1998), pp. 97-103]. Zhang et al. 's preconditioners and Simons and Yao's are generalized in this paper. These preconditioners are all of low construction cost, which all could be taken as approximate inverse of M-matrices. Numerical experiments of these preconditioners applied with Krylov subspace methods show the effectiveness and performance, which also show that the preconditioners proposed in this paper are better approximate inverse for M-matrices than Simons'. [ABSTRACT FROM AUTHOR]

In this paper, the new short-term problems that are faced by a generation company in a deregulated electricity market are addressed and an optimization algorithm is proposed. Our model of the spot market explicitly represents the price of electricity as an uncertain exogenous variable. We consider a very complex problem of hydrothermal optimization with pumped-storage plants, so the problem deals with non-regular Lagrangian and non-holonomic inequality constraints. To obtain a necessary minimum condition, the problem was formulated within the framework of nonsmooth analysis using the generalized (or Clarke's) gradient and the Nonsmooth maximum principle. The optimal control problem is solved by means of an algorithm implemented in the commercial software package Mathematica. Results of the application of the method to a numerical example are presented. [ABSTRACT FROM AUTHOR]

This paper presents the nonlinear optimal control for the deployment process of an elastically tethered subsatellite model, which involves not only the usually addressed in-plane motion, but also the out-of-plane motion. All the nonlinearities in the system model and the mission-related state-control constraints are taken into consideration. Instead of the commonly used state-space model, a second-order differential inclusion formulation is exploited in this paper to achieve a significant reduction of the number of system variables. The optimal control is solved by discretizing the optimal control problem first and then solving the resulting large-scale optimization problem. The case studies in the paper demonstrate well the performance of the proposed strategy. [ABSTRACT FROM AUTHOR]

In an earlier paper, the author introduced new upper bounds for free linear and nonlinear vibration systems; to compute the best upper bounds, the differential calculus of norms was applied. In the present paper, this work is continued for the corresponding excited systems. Some new techniques and ideas are involved. The results in the applications cannot be obtained by the methods used so far. [ABSTRACT FROM AUTHOR]

Recent work has shown that designing absorbing boundary conditions through algebraic approaches may be a nice alternative to the continuous approaches based on a Fourier analysis. In this paper, an original algebraic technique based on the computation of small patches is presented for the Helmholtz equation. This new technique is not directly linked to the continuous equations of the problem, nor to the numerical scheme. These properties make this technique very convenient to implement in a domain decomposition context. The proposed algebraic absorbing boundary conditions are used in a non-overlapping domain decomposition method and are defined on the interface between the subdomains. An additional coarse grid correction is then applied to ensure full scalability of the domain decomposition method upon the number of subdomains. This coarse grid correction involves trigonometric functions defined on the interface between the subdomains. Numerical experiments are presented and illustrate the robustness and parallel efficiency of the proposed method for acoustics applications. [ABSTRACT FROM AUTHOR]

In this paper, a finite filter is used in the structure of the Barzilai–Browein (BB) gradient method in order to propose a new modified BB algorithm for solving large-scale unconstrained optimization problems. Our algorithm is equipped with a relaxed nonmonotone line search technique which allows the algorithm to enjoy the nonmonotonicity properties from scratch. Under some suitable conditions, the global convergence property of the new proposed algorithm is established. Numerical results on some test problems in CUTEr library show the efficiency and effectiveness of the new algorithm in practice too. [ABSTRACT FROM PUBLISHER]

In the paper, basing on the structure of Nekrasov matrices, the authors first obtain several practical criteria for judgingH-matrices, then provide some criteria for identifying that a given matrix is not anH-matrix. The effectiveness of the proposed results is illustrated by numerical examples. [ABSTRACT FROM PUBLISHER]

This paper is devoted to the construction of two-Lee weight codes overwith typebased on a distance-preserving Gray map fromto. The necessary conditions for a code overto have only two different nonzero weights are given. The existence of two-Lee weight projective codes is also presented. Finally, some examples are also presented to illustrate the algebraic structure of two-Lee weight codes over. [ABSTRACT FROM PUBLISHER]

Based on the mixed finite element method, we consider the decoupled Crank-Nicolson/Adams-Bashforth scheme for the Boussinesq equations with smooth initial data in this paper. The temporal treatment of the spatial discrete Boussinesq equations is based on the implicit Crank-Nicolson scheme for the linear terms and the explicit Adams-Bashforth scheme for the nonlinear terms. Thanks to the decoupled method, the considered problem is split into two subproblems and these subproblems can be solved in parallel. Under some restriction on the time step, we present the stability and convergence results of numerical solutions, Finally, some numerical experiments are provided to test the performance of the developed numerical scheme and verify the established theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method to construct cryptographically significant (vectorial) Boolean functions overby using the decomposition of the multiplicative group of, and give a generalized description for constructing a class of vectorial Boolean functions with high algebraic immunity. Moreover, for evenn, we introduce two special classes of vectorial Boolean functions with high algebraic immunity: one is hyper-bent and the other is balanced with optimal algebraic degree. [ABSTRACT FROM AUTHOR]

In this paper, we use a good technique to construct a high-order numerical scheme for the impulsive fractional ordinary differential equations (IFODEs). This technique is based on the so-called block-by-block method, which is a common method for the integral equations. In our approach, the classical block-by-block method is improved so as to avoid the coupling of the unknown solutions at each block step with an exception in the first two steps between two adjacent pulse points. The convergence and stability analysis of the scheme are given. It proves that the numerical solution converges to the exact solution with order 3+q for , where q is the order of the fractional derivative. A series of numerical examples are provided to support the theoretical results. [ABSTRACT FROM AUTHOR]

For any graphG, let α′(G) and α′min(G) be the maximum cardinality and minimum cardinality among all maximal matchings inG, respectively, and let γ′(G) and γt′(G) be the edge domination number and edge total domination number ofG, respectively. In this paper, we first show some properties of maximal matchings and further determine the exact values of α′(G) and α′min(G) for a complete multipartite graphG. Then, we disclose relationships between maximal matchings and minimal edge dominating sets, and thus obtain the exact values of γ′(G) and γt′(G) for a complete multipartite graphG. [ABSTRACT FROM AUTHOR]

The nonconvexregularization, which has superiority on sparsity-inducing over the convex counterparts, has been proposed in many areas of engineering and science. In this paper, we present an acceleratedregularization thresholding algorithm for sparse signal recovery, which can be viewed as an extension of the well-known Nesterov's accelerated gradient method from convex optimization to nonconvex case. It has shown numerically that the proposed algorithm keeps fast convergence, and also maintains high recovery precision. Extensive numerical experiments have been to demonstrate the effectiveness of the proposed algorithm. It is also mentioned that the proposed algorithm has much faster convergence and higher recovery precision in sparse signal recovery over the commonly non-acceleratedthresholding algorithm. [ABSTRACT FROM PUBLISHER]

Three of the most essential criteria for cryptographically strong Boolean functions are balancedness, high nonlinearity and high algebraic degree. In this paper, we give two methods for constructing balanced Boolean functions with high nonlinearity via modifying Maiorana–McFarland type bent functions. The algebraic immunity of the constructed functions is also considered. [ABSTRACT FROM AUTHOR]

In this paper, we present the Sherman–Morrison–Woodbury-type formula for the solution of the Sylvester equation of the formas well as for the solution of theT-Sylvester equation of the formwhereU1,U2,V1,V2are low-rank matrices. Although the matrix version of this formula for the Sylvester equation has been used in several different applications (but not for the case of aT-Sylvester equation), we present a novel approach using a proper operator representation. This novel approach allows us to derive a matrix version of the Sherman–Morrison–Woodbury-type formula for the Sylvester equation as well as for theT-Sylvester equation which seems to be new. We also present algorithms for the efficient calculation of the solution of structured Sylvester andT-Sylvester equations by using these formulas and illustrate their application in several examples. [ABSTRACT FROM PUBLISHER]

In practical applications of graph theory, due to some reasons, different types of uncertainties are frequently encountered. In this paper, we employ uncertainty theory to investigate an uncertain graph in which complete determination of whether two vertices are joined by an edge or not cannot be carried out. By means of uncertainty theory, the concepts of connectedness strength of two vertices in an uncertain graph and strength of an uncertain path are proposed. A method to calculate the connectedness strength of two vertices is also described. After that, we investigate the relationship between the connectedness strength of two vertices and the connectedness index of the uncertain graph. This relationship provides a new method to obtain the connectedness index of an uncertain graph. [ABSTRACT FROM PUBLISHER]

Ingeneralized one-sided forbidding grammars(GOFGs), each context-free rule has associated a finite set offorbidding strings, and the set of rules is divided into the sets ofleftandright forbidding rules. A left forbidding rule can rewrite a nonterminal if each of its forbidding strings is absent to the left of the rewritten symbol. A right forbidding rule is applied analogically. Apart from this, they work like any generalized forbidding grammar. This paper proves the following three results. (1) GOFGs where each forbidding string consists of at most two symbols characterize the family of recursively enumerable languages. (2) GOFGs where the rules in one of the two sets of rules contain only ordinary context-free rules without any forbidding strings characterize the family of context-free languages. (3) GOFGs with the set of left forbidding rules coinciding with the set of right forbidding rules characterize the family of context-free languages. [ABSTRACT FROM PUBLISHER]

The requirement of data security is an important parameter for all organizations for their survival in the world. Cryptography is the best method to avoid unauthorized access to data. It involves an encryption algorithm and the keys that are being used by the users. Multiple keys provide a more secure cryptographic model with a minimum number of overheads. There are various factors that affect the security pattern such as the number of keys and their length, encryption algorithm, latency, key shifting time, and users. In this paper, a new approach is proposed for generating keys from the available data. The analysis of various times, such as encryption, decryption, key setup, processing, and key shifting times, has been done. The model takes minimum time to replace the faulty keys with the fresh keys. In this paper, we consider all the above-mentioned factors and suggest an optimized way of using them. [ABSTRACT FROM AUTHOR]

Schellekens [The Smyth completion: A common foundation for denotational semantics and complexity analysis, Electron. Notes Theor. Comput. Sci. 1 (1995), pp. 211–232.] introduced the theory of complexity (quasi-metric) spaces as a part of the development of a topological foundation for the asymptotic complexity analysis of programs and algorithms in 1995. The applicability of this theory to the asymptotic complexity analysis of divide and conquer algorithms was also illustrated by Schellekens in the same paper. In particular, he gave a new formal proof, based on the use of the Banach fixed-point theorem, of the well-known fact that the asymptotic upper bound of the average running time of computing of Mergesort belongs to the asymptotic complexity class of nlog 2 n. Recently, Schellekens’ method has been shown to be useful in yielding asymptotic upper bounds for a class of algorithms whose running time of computing leads to recurrence equations different from the divide and conquer ones reported in Cerdà-Uguet et al. [The Baire partial quasi-metric space: A mathematical tool for the asymptotic complexity analysis in Computer Science, Theory Comput. Syst. 50 (2012), pp. 387–399.]. However, the variety of algorithms whose complexity can be analysed with this approach is not much larger than that of algorithms that can be analysed with the original Schellekens method. In this paper, on the one hand, we extend Schellekens’ method in order to yield asymptotic upper bounds for a certain class of recursive algorithms whose running time of computing cannot be discussed following the techniques given by Cerdà-Uguet et al. and, on the other hand, we improve the original Schellekens method by introducing a new fixed-point technique for providing, contrary to the case of the method introduced by Cerdà-Uguet et al., lower asymptotic bounds of the running time of computing of the aforementioned algorithms and those studied by Cerdà-Uguet et al. We illustrate and validate the developed method by applying our results to provide the asymptotic complexity class (asymptotic upper and lower bounds) of the celebrated algorithms Quicksort, Largetwo and Hanoi. [ABSTRACT FROM PUBLISHER]

In this paper, we study the dynamical behaviour of a two-point iterative method with order of convergence five to solve nonlinear equations in the complex plane. In fact, we complement the dynamical study started in previous works with a more systematic analysis for polynomials with at most two different roots and different multiplicities. In addition, we characterize some polynomials of degree greater or equal to 4, such that the related methods are not generally convergent. We also analyse the degrees of the rational functions associated with two-point methods when they are applied to polynomials of degree n, showing their dependence on n 2 and how this fact considerably complicates the dynamical study. [ABSTRACT FROM AUTHOR]

This paper describes the generalized finite difference method to solve second-order partial differential equation systems and fourth-order partial differential equations. This method is applied to solve the problem of thin and thick elastic plates. [ABSTRACT FROM PUBLISHER]

System level diagnosis is an important technique for fault detection and location in multiprocessor computing systems. Adaptive diagnosis, proposed by Nakajima, is one of many practical approach system level diagnostic schemes. As far as we know, the adaptive approach under the MM model has only been discussed in relation to a completely connected system. In this paper, we consider the problem of adaptive fault diagnosis for systems modelled by a cycle and a torus under the MM model. For cycles, we give some useful properties for identifying faulty vertices, show the minimum number of test rounds and provide some efficient test assignments. We also present two adaptive diagnosis algorithms for tori and show the minimum number of tests for these algorithms. Moreover, the two algorithms take linear time both for overall testing and syndrome decoding. [ABSTRACT FROM PUBLISHER]

The r-component connectivity κ r (G) of the non-complete graph G is the minimum number of vertices whose deletion results in a graph with at least r components. So, κ2 is the usual connectivity. In this paper, we determine the r-component connectivity of the hypercube Q n for r=2, 3, …, n+1, and we classify all the corresponding optimal solutions. [ABSTRACT FROM PUBLISHER]

This paper focuses on the construction and properties of spline dyadic wavelet that equals its reconstruction wavelet. A general construction method of finite spline dyadic low-pass and high-pass filters is given. It proves that finite spline dyadic low-pass filters are symmetric about 0 or 1/2, but there are no finite spline high-pass filters possessing symmetry with respect to 0 or 1/2. It further shows that there exist infinite spline high-pass filters possessing symmetry with respect to 0 or 1/2, which can be constructed. Their energy is concentrated and so finite symmetric spline dyadic wavelet filter that equals its reconstruction filter can be obtained approximately. Construction examples for quadratic and cubic spline dyadic wavelet filters are given. [ABSTRACT FROM PUBLISHER]