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In this paper, we extend SMSNS [Pourbagher M, Salkuyeh DK. On the solution of a class of complex symmetric linear systems. Appl Math Lett. 2018;76:14–20.] iteration method for solving a class of complex symmetric system of linear equations. We propose a successive-overrelaxation (SOR) acceleration scheme for SMSNS (SMSNSSOR), discuss the convergence conditions of it and give the optimal parameters which make the fast convergence. Numerical results demonstrate that SMSNSSOR iteration method is feasible and effective for solving complex symmetric systems, and performs better than some other usually used iteration methods. [ABSTRACT FROM AUTHOR]

Recently, Chen and Ma [A generalized shift-splitting preconditioner for complex symmetric linear systems, J. Comput. Appl. Math., 344 (2018), pp. 691–700] have presented the generalized shift-splitting (GSS) method to solve complex symmetric linear systems. In this paper, we establish a class of modified GSS (MGSS) method to extend the existing GSS method. We prove the convergence of the proposed method under suitable restrictions on the iteration parameters. Lastly, numerical experiments are carried out, and experimental results show that the new iteration method is feasible and effective. [ABSTRACT FROM AUTHOR]

The wavelet method based on the Meyer wavelet function and scaling function is a rather effective regularization method for solving some illposed problems. Recently, there are many works on this method limited to the a priori choice rule. The typical paper [H. Cheng and C.L. Fu, Wavelets and numerical pseudodifferential operator, Appl. Math. Model. 40 (2016), pp. 1776-1787] has systematically considered the a priori choice rule in the framework of the pseudodifferential operator (ψDO). In this paper, we will systematically consider the a posteriori choice rule for two kinds of ill-posed problems in the framework of the ψDO, and construct the convergence error estimates between the exact solution and its regularized approximation. [ABSTRACT FROM AUTHOR]

In this paper, a new conjugate gradient-based projection method for solving a system of nonlinear monotone equations is proposed. The method can be viewed as an extension of a family of conjugate gradient methods for unconstrained optimization by Li et al. [A new family of conjugate gradient methods for unconstrained optimization, J. Appl. Math. Comput. 58 (2018), pp. 219–234]. The proposed method is derivative-free which makes it suitable for large-scale nonlinear monotone equations. We show that the method satisfies the descent condition independent of line searches and that the method is globally convergent. Numerical results indicate that the proposed method is efficient. [ABSTRACT FROM AUTHOR]

In this paper, we present two nonmonotone versions of adaptive cubic regularized (ARC) method for unconstrained optimization problems. The proposed methods are a combination of the ARC algorithm with the nonmonotone line search methods introduced by Zhang and Hager [A nonmonotone line search technique and its application to unconstrained optimization, SIAM J. Optim. 14 (2004), pp. 1043–1056] and Ahookhosh et al. [A nonmonotone trust-region line search method for large-scale unconstrained optimization, Appl. Math. Model. 36 (2012), pp. 478–487]. The global convergence analysis for these iterative algorithms is established under suitable conditions. Several numerical examples are given to illustrate the efficiency and robustness of the newly suggested methods. The obtained results show the satisfactory performance of the proposed algorithms when compared to the basic ARC algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the convergence for improved multi-point Chebyshev-like methods is considered. Compared to the results of Chebyshev method with second derivative in reference [M.A. Hernández, M.A. Salanova, J. Comput. Appl. Math. 126 (2000), pp. 131–143], the R-order is maximised and the Hölder continuity condition is also relaxed. Moreover, these improved methods do not need second derivatives, when the computation of second derivative is large, these improved methods will be more efficient than Chebyshev method. Under the relaxed condition, an existence-uniqueness theorem is proved. The R-order of convergence for these improved methods is also analysed. [ABSTRACT FROM AUTHOR]

The 0–1 test for chaos is increasingly used in applications where it is important to distinguish between chaotic and regular dynamics of the deterministic dynamical system. This test consists of translating the time series into (p , q) plane. Then the boundedness of the object created in the (p , q) plane is inspected by computing mean square displacement and its growth rate. The computation of the mean square displacement for various lag has high computational complexity. In this paper, the inspection of the boundedness using bounding box and centre of gravity is proposed. This method has linear computational complexity and provides more control over the precision of the test through multiple input parameters. [ABSTRACT FROM AUTHOR]

In this paper we design a family of cell-average nonlinear prediction operators that make use of the generalized harmonic means and we apply the resulting schemes to image processing. The new family of nonlinear schemes conserve the numerical properties of the linear schemes, such as the L 1 -stability, the order of accuracy or compression rate but avoiding Gibbs phenomenon close to the discontinuities. The generalized harmonic mean was introduced in the framework of point-values in [A. Guessab, M. Moncayo, and G. Schmeisser, A class of nonlinear four-point subdivision schemes. Properties in terms of conditions, Adv. Comput. Math. 37 (2012), pp. 151–190] in order to improve the results of the harmonic mean. However, in the cell-average setting our conclusion is that, from a numerical point of view, the advantage of using the new mean is not clear. [ABSTRACT FROM AUTHOR]

In this paper a singularly perturbed fourth-order ordinary differential equation is considered. The differential equation is transformed into a coupled system of singularly perturbed equations. A hybrid finite difference scheme on a Vulanović--Shishkin mesh is used to discretize the system. This hybrid difference scheme is a combination of a non-equidistant generalization of the Numerov scheme and the central difference scheme based on the relation between the local mesh widths and the perturbation parameter. We will show that the scheme is maximum-norm stable, although the difference scheme may not satisfy the maximum principle. The scheme is proved to be almost fourth-order uniformly convergent in the discrete maximum norm. Numerical results are presented for supporting the theoretical results. [ABSTRACT FROM AUTHOR]

Conjugate gradient methods are widely used for solving unconstrained optimization and nonlinear equations, specially in large-scale cases. Since they own the attractive practical factors of simple computation and low memory requirement, interesting theoretical features of curvature information and strong global convergence. In this paper, we present a modified conjugate gradient algorithm by line search method with acceleration scheme for nonlinear symmetric equations. Furthermore, the proposed method not only possess descent property but also owns global convergence in mild conditions. Numerical results also indicate that the presented method is much more effective than the other methods for the test problems. [ABSTRACT FROM PUBLISHER]

In this paper, a multiple-time-step decoupled algorithm for a non-stationary Stokes–Darcy problem is proposed and investigated. Under a modest time step restriction of physical parameters and the time step proportion, we give the stability analysis and convergence analysis of the decoupled scheme with different time step in fluid and porous subregions. Finally, a series of numerical experiments are provided to illustrate the accuracy, efficiency, and stability of the presented method for the coupled problem with the Beavers–Joseph–Saffman–Jones interface conditions. [ABSTRACT FROM PUBLISHER]

The traditional way to define the instantaneous frequency of a real-valued signal is based on the analytic signal obtained by means of the Hilbert transform. Vakman showed the justification of this method by proving that under some fundamental conditions the imaginary part signal operator I must be the Hilbert transform. This paper shows that his arguments are not valid in the finite-energy signal space L2() - an important space of signals. In this paper, we propose substitutive conditions and establish the L2() version of Vakman's analysis, which is a meaningful supplement to Vakman's theory. [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]

Chang and Wang discussed the consistent conditions for the symmetric solutions of the linear matrix equation (ATXA, BTXB)=(C, D) and obtained the general expressions for its symmetric solution and symmetric least-squares solution, but they could not give the minimum Frobenius norm symmetric solution for this equation or the related least-squares problem. In this paper, the explicit analytical expression of the symmetric optimal approximation solution (or the minimum Frobenius norm symmetric solution as a special case) for the least-squares problem of this linear matrix equation is obtained by using the projection theorem in the Hilbert space, the quotient singular value decomposition and the canonical correlation decomposition in the matrix theory for efficient tools; therefore, this result gives an answer to the open problem in Chang and Wang's paper in 1993. [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]

Nonlinear systems of time dependent partial differential equations of real life phenomena tend to be very complicated to solve numerically. One common approach to solve such problems is by applying operator splitting which introduces subproblems that are easier to handle. The solutions of the subsystems are usually glued together by either the Godunov method (first-order) or the Strang method (second-order). However, the accuracy of such an approach may be very hard to analyse because of the complexity of the equations involved. The purpose of the present paper is to introduce another line of reasoning concerning the accuracy of operator splitting. Let us assume that a fully coupled and implicit discretization of the complete system has been developed. Under appropriate conditions on the continuous problem, such discretizations provide reasonable and convergent approximations. As in the continuous case, operator splitting can be utilized to obtain tractable algebraic subsystems. The problem we address in the present paper is to obtain a bound on the difference between the fully coupled implicit discrete solutions, uh, and the solutions, uh, s, obtained by applying operator splitting to these discrete equations. Suppose we know that uh converges to the analytical solution u as the grid is properly refined and, applying the results from this paper, that uh, s converges toward uh under grid refinement. Then, by the triangle inequality, also the splitting approximation uh, s converges toward the analytical solution u and convergence is thus obtained for an approximation that, from a practical point of view, is easier to compute. [ABSTRACT FROM AUTHOR]

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]

The convergence of the inexact Uzawa method for stabilized saddle point problems was analysed in a recent paper by Cao, Evans and Qin. We show that this method converges under conditions weaker than those stated in their paper. [ABSTRACT FROM AUTHOR]

In a recent paper [4], Li et al . gave a generalized successive overrelaxation (GSOR) method for the least squares problems. In this paper, the connection between the GSOR method and the preconditioned conjugate gradient (PCG) method for the normal equations is investigated. It is shown that the PCG method is at least as fast as the GSOR method. Numerical examples demonstrates that the PCG method is much faster than the GSOR method. [ABSTRACT FROM AUTHOR]

Augmentedk-aryn-cubeis proposed as a new interconnection network model by Xiang and Steward [Augmented k-ary n-cubes, Inform. Sci. 181(1) (2011), pp. 239–256]. For a connected graphG, an edge-cut (vertex-cut)Sis called a restricted edge-cut (restricted vertex-cut) ifG–Scontains no isolated vertices. The restricted edge-connectivity (restricted connectivity) ofG, denoted by(), is the minimum cardinality over all restricted edge-cuts (vertex-cuts) ofG. In this paper, we completely determine the restricted (edge-)connectivity of. Precisely,for;for,for,forand, butdoes not have restricted vertex-cut. [ABSTRACT FROM AUTHOR]

Many problems in mathematics and engineering lead to Fredholm integral equations of the first kind, e.g. signal and image processing. These kinds of equations are difficult to solve numerically since they are ill-posed. Therefore, regularization is required to obtain a reasonable approximate solution. This paper presents a new regularization method based on a weightedH1seminorm. Details of numerical implementation are given. Numerical examples, including one-dimensional and two-dimensional integral equations, are presented to illustrate the efficiency of the proposed approach. Numerical results show that the proposed regularization method can restore edges as well as details. [ABSTRACT FROM AUTHOR]

In this paper, we give a review on rigorous and numerical results for amplitude equations. We focus on the Swift-Hohenberg equation and the Burgers' equation in order to determine the quality of the approximation and the impact of degenerate noise on the approximating equation. [ABSTRACT FROM AUTHOR]

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]

Huang and Liu [Generalized scrambling indices of primitive a digraph, Linear Algebra Appl. 433 (2010), pp. 1798–1808] gave the definitions of the generalized μ-scrambling indices and the generalized scrambling indices of a primitive digraph and also provided some exact lower and upper bounds for the generalized scrambling indices of various classes of primitive digraphs. In this paper, we give some exact lower and upper bounds for the generalized μ-scrambling indices of various classes of primitive digraphs. [ABSTRACT FROM PUBLISHER]

In this paper, a quadratic B-spline finite-element method is proposed for solving the coupled Schrodinger-Boussinesq equations numerically. A semi-discrete finite-element scheme is constructed for this system. The existence and uniqueness of the numerical solutions and the convergence of the discrete scheme are discussed. Numerical results indicate that the proposed method is accurate and efficient. [ABSTRACT FROM AUTHOR]

Let k1≥k2≥···≥km be positive integers. In this paper, we prove that every [0, k1+···+km-n+1]-graph G contains a subgraph R such that R has a [image omitted] -factorization orthogonal to any given subgraph H with n edges for every 1≤n≤m. [ABSTRACT FROM AUTHOR]

Chemists often come across triangle domains - usually with the basic simplex in 2. A smooth surface is needed for approximating the chemical properties between the measured data for solving some model (differential) equations numerically. Our research group has been working on approximating ternary chemical surfaces of two special fields by smooth functions (vapour - Liquid equilibrium data and explosion-limit surfaces of ternary gas systems). A mathematical solution was given in both fields by special spline surfaces, and for visualization, our own software (TRIGON) was used. In this paper the summarized chemical background of each problem is provided, the mathematical solutions, the newest theoretical developments and their results are discussed. [ABSTRACT FROM AUTHOR]

The problem of counting rankings satisfying the collinearity condition with respect to two rankings over the metric spaces of rank distance is treated in this paper by transforming it into finding the number of systems of distinct representatives (abbreviated as SDR's) with respect to associated set systems. A formula for the chromatic list expression of graphs is then given in terms of the inclusion and exclusion principle, followed by a formula for the number of SDR's of set systems when the graphs are complete. [ABSTRACT FROM AUTHOR]

Let G be a connected graph. A spanning tree T of G is a tree t-spanner if the distance between any two vertices in T is at most t times their distance in G. If their distances in T and G differ by at most t, then T is an additive tree t-spanner of G. In this paper, we show that any permutation graph has an additive tree 2-spanner, and it can be found in O(n) time sequentially or in O(log n) time with O(n/log n) processors on the EREW PRAM computational model by using a previously published algorithm for finding a tree 3-spanner of a permutation graph. [ABSTRACT FROM AUTHOR]

The aim of this paper is to extend the concept of inverse of a matrix with fuzzy numbers as its elements, which may be used to model uncertain and imprecise aspects of real-world problems. We pursue two main ideas based on employing real scenarios and arithmetic operators. In each case, exact and inexact strategies are provided. In the first idea, we give some necessary and sufficient conditions for invertibility of fuzzy matrices based on regularity of their scenarios. And then Zadeh's extension principle and interpolation on Rohn's approach for inverting interval matrices are followed to compute fuzzy inverse. In the second idea, Dubois and Prade's arithmetic operators will be employed for the same purpose. But with respect to the inherent difficulties which are derived from the positivity restriction on spreads of fuzzy numbers, the concept of ε-inverse of a fuzzy matrix and its relaxation are generalized and some useful theorems will be revealed. Finally fuzzifying the defuzzified version of the original problem for introducing fuzzy inverse, which can be followed by each idea, will be presented. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the multiple-objective optimization problems, considering an improved definition of generalized type I univex function. Some optimality conditions as well as some duality relations are established. [ABSTRACT FROM AUTHOR]

The efficient and reliable control of an electric arc furnace (EAF) is a challenging problem, due to the strong intercorrelation among process variables, the large dimension of the input and output space, the strong interaction among process variables, a large time delay, and a highly nonlinear behaviour. This paper presents a model that allows us to optimize the control and, therefore, the electric power consumption in an EAF. The data used for this study were collected from Bizkaia Steel Mill (Arcelor Company). Neural network and fuzzy logic techniques have been applied on these data in order to get an improved model of the casting temperature inside the furnace's hearth. First, we developed some neural network models with different topologies and input variables. Then we used the best model obtained in the previous step to combine it with a fuzzy logic technique to get the final model. Comparison with experimental data and other models is carried out to validate the proposed model. Finally, the conclusions and future studies are exposed. [ABSTRACT FROM AUTHOR]

Bezier curves with n shape parameters and triangular Bezier surfaces with 3n(n+1)/2 shape parameters are presented in this paper. The geometric significance of the shape parameters and the geometric properties of these curves and surfaces are discussed. The shapes of the curves and the surfaces can be modified intuitively, foreseeably and precisely by changing the values of the shape parameters. [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]

In this paper, we present a mathematical model of the static pantograph/catenary interaction for high-speed railways, with an outline of the development of a computing algorithm which can be used to obtain the solution of the static equilibrium equation of the pantograph/catenary system which has been reached after an exhaustive study of the traditional mechanical approach based on a set of coupled strings. In order to obtain favourable behaviour in the pantograph/catenary system, it is necessary to obtain adequate conditions in the line; thus we need a precise mechanical calculus. The resulting stiffness matrix shows a high degree of sparsity. Hence, this result can be interpreted in two ways: less memory storage requirements as well as the use of suitable methods to solve the static equilibrium equation as projection methods. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a structure result on the infinite ω-limit sets of continuous triangular mappings defined on the unit square, i.e. maps of the form (x, y)→(f(x), g(x, y)) having zero topological entropy in the base map f and on the fibres defined over the periodic points of f. We show for this class of systems that the infinite ω-limit sets of the points of the form (x, y), where x is a periodic point of f, have a solenoidal distribution. It extends the results by Smital [J. Smital, Chaotic functions with zero topological entropy, Trans. Amer. Math. Soc. 297 (1986), pp. 269-282] on zero topological entropy of continuous interval maps. An application is presented. [ABSTRACT FROM AUTHOR]

In this paper we present a new class of memory gradient methods for unconstrained optimization problems and develop some useful global convergence properties under some mild conditions. In the new algorithms, trust region approach is used to guarantee the global convergence. Numerical results show that some memory gradient methods are stable and efficient in practical computation. In particular, some memory gradient methods can be reduced to the BB method in some special cases. [ABSTRACT FROM AUTHOR]

The objective is to combine the dynamical problem of multi-rigid-body systems under non-smooth constraints with linear complementary problem (LCP). For multibody systems under unilateral constraints, according to their unilateral property, the laws governing such situations can be formulated to a complementary problem. But for multibody systems under bilateral constraints with friction, it becomes more difficult to formulate the complementary conditions because normal contact force is no longer non-negative. The complementary conditions are derived by introducing new parameters according to the property of rigid bilateral constraints in a completely general way, so that the fundamental problem of multi-rigid-body systems with frictional bilateral constraints can be solved as a mixed problem of DAE and LCP. The example shows the realized process and possible singularity and validates the LCP formulations given in this paper indirectly. [ABSTRACT FROM AUTHOR]

In this paper we study the a one-dimensional reaction-diffusion-convection (R-D-C) equation with weak spatial non-uniformities to the diffusion and reaction rates. The convection is represented by a uniform flow field. Singular perturbation analysis will be used to compute the speed of the front as well as the asymptotic solution. [ABSTRACT FROM AUTHOR]

The paper presents a strict mathematical proof of the classifications of finite groups of symmetries of two-dimensional quasicrystals given by Hermisson, Richard and Baake in 1997. [ABSTRACT FROM AUTHOR]

An optimization problem for a Boussinesq equation system will be formulated. We are looking for a temperature profile or an appropriate velocity on the boundary of the considered region of the thermal coupled flow problem to induce a forced convection, which implies a velocity field close to a prescribed one. For such tracking type optimization problems with tracking type minimization functionals, the evaluation of the first-order necessary optimality condition leads to an optimality system consisting of the forward (primal) and adjoint (dual) mathematical model. Besides the derivation of the optimality system we discuss aspects of numerical solution, e.g. the spatial and time discretization and the iteration method for the solution of the resulting coupled nonlinear primal and dual problem in this paper. The optimization concept will be applied to a crystal growth flow and results of two-dimensional and three-dimensional model problems will be presented. [ABSTRACT FROM AUTHOR]

In this paper, we present a structure-preserving model-order reduction method for solving large-scale second-order MIMO dynamical systems. It is a projection method based on a block second-order Krylov subspace. We use the block second-order Arnoldi (BSOAR) method to generate an orthonormal basis of the projection subspace. The reduced system preserves the second-order structure of the original system. Some theoretical results are given. Numerical experiments report the effectiveness of this method. [ABSTRACT FROM AUTHOR]

In this paper, we split the 3-D linearly elastic shell problem into a 2-D problem by using the approach of formal asymptotic expansion. The approximate solution UKT(x, ξ) for the 3-D linearly elastic shell consists of [image omitted] , where u0, u1, u2 are independent of ξ. The leading term u0 satisfies a 2-D elliptic boundary value problem, and other terms u1, u2 will be derived using the algebraic expression for u0 without solving PDEs. We prove that the solution u0(x) exists and is unique, and give the error estimation for an elliptic membrane, which is smaller than the error with other models. [ABSTRACT FROM AUTHOR]

This paper studies a fully adaptive splitting method for the numerical solution of two-dimensional quenching differential equations. The non-uniform adaptive mesh is established in space and time via standard arc-length formulations. We concentrate on the monotonic property of the numerical algorithm developed since the issue is fundamental for this type of nonlinear singular differential equations. Numerical examples are given to illustrate our computational results as well as the quenching phenomena approximated. [ABSTRACT FROM AUTHOR]

In this paper, we study the solution of a certain non-smooth eigenvalue problem, using operator-splitting methods to solve an equivalent, constrained minimization problem. We present the Marchuk-Yanenko and Peaceman-Rachford schemes for solving the problem and compare their performance numerically on some model problems. The Peaceman-Rachford scheme turns out to be superior to the Marchuk-Yanenko scheme in terms of accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]

In this paper a Petrov–Galerkin method is used to derive a numerical solution for the K (2, 2) equation, where we have chosen cubic B-splines as test functions and piecewise linear functions as trial functions. The product approximation technique is applied to the nonlinear terms. A Crank–Nicolson scheme is used to discertize in time. A nonlinear pentadiagonal system is obtained. We solve this system by Newton’s method and a linearization technique. The accuracy and stability of the scheme have been investigated. The single compacton solution and the conserved quantities are used to assess the accuracy of the scheme. The interaction of two compactons are displayed and the numerical results have shown that this compacton exhibits a soliton-like solution. [ABSTRACT FROM AUTHOR]

This paper presents a rationalization of a class of space B-spline curves whose base functions can be arbitrary (algebraic polynomial or non-algebraic polynomial). Based on the theory of the three-dimensional projective transform and the construction of an appropriate sequence of projective transforms, we perform a piecewise rationalization of this class of space B-spline curves such that the resulting generalized rational B-spline curves preserve piecewise geometric invariance in the sense of projective transform. By introducing a geometric point (called the weight centre) composed of weight coefficients and using it as the basic point and four control vertexes as coordinate points, a projective coordinate system is constructed piecewise. Thus a non-homogeneous coordinate ( i.e . rational coordinate) representation of the curve in the projective coordinate system is also obtained, where the weight coefficient groups are the gravity centre coordinates of the weight centre about the coordinate quadri-point figure and the base function groups are homogeneous projective coordinates of the curve. Furthermore, we give the curve’s projective coordinate sequence corresponding to a new weight coefficient sequence when the weight coefficients are changed, show that the new rational curve preserves piecewise projective invariance and finally conclude that space cubic non-uniform rational B-spline (NURBS) curves are special case of the above conclusions. [ABSTRACT FROM AUTHOR]

This paper deals with a discrete monotone iterative algorithm for solving a non-linear singularly perturbed parabolic reaction–diffusion problem. The monotone iterative method, which is based on a weighted average difference scheme, is applied to computing a non-linear difference scheme obtained after discretization of the continuous problem. This method solves only linear discrete systems at each iterative step of the iterative process. The uniform convergence of the method is established and numerical experiments are presented. [ABSTRACT FROM AUTHOR]

Let G =( V , E ) be a graph with vertex set V of size n and edge set E of size m . A vertex v ? V is called a hinge vertex if there exist two vertices in V \{ v } such that their distance becomes longer when v is removed. In this paper, we present a distributed algorithm that finds all hinge vertices on an arbitrary graph. The proposed algorithm works for named static asynchronous networks and achieves O ( n 2 ) time complexity and O ( m ) message complexity. In particular, the total messages exchanged during the algorithm are at most 2 m (log n + n log n +1) bits. [ABSTRACT FROM AUTHOR]

Although there are many text classification techniques depending on the vector space, it is difficult to detect the meaning related to the user’s intention (complaint, encouragement, request, invitation, etc.). The approach be discussed in this paper is very useful for understanding focus points in conversation. We present a technique for determining the speaker’s intention for sentences in conversation. Intention association expressions are introduced, and formal descriptions with weights are defined using these expressions to construct an intention classification. A deterministic multi-attribute pattern-matching algorithm is used to determine the intention class efficiently. In simulation results for 681 email messages of 5859 sentences, the multi-attribute pattern-matching algorithm is about 44.5 times faster than the Aho and Corasick method. The precision and recall of intention classification of sentences are 91% and 95%, respectively. The precision and recall of extraction of unnecessary sentences are 98% and 96%, respectively. The precision and recall of the classification of each email are 88% and 89%, respectively. [ABSTRACT FROM AUTHOR]