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Computational & Applied Mathematics, Volume: 30, Número: 3, Publicado: 2011
  • Arithmetic fuchsian groups and space time block codes

    Carvalho, E.D.; Andrade, A.A.; Palazzo Jr., R.; Vieira Filho, J.

    Resumo em Inglês:

    In the context of space time block codes (STBCs) the theory of arithmetic Fuchsian groups is presented. Additionally, in this work we present a new class of STBCs based on arithmetic Fuchsian groups. This new class of codes satisfies the property full-diversity, linear dispersion and full-rate. Mathematical subject classification: 18B35, 94A15, 20H10.
  • A modified parametric iteration method for solving nonlinear second order BVPs

    Ghorbani, Asghar; Gachpazan, Morteza; Saberi-Nadjafi, Jafar

    Resumo em Inglês:

    The original parametric iteration method (PIM) provides the solution of a nonlinear second order boundary value problem (BVP) as a sequence of iterations. Since the successive iterations of the PIM may be very complex so that the resulting integrals in its iterative relation may not be performed analytically. Also, the implementation of the PIM generally leads to calculation of unneeded terms, which more time is consumed in repeated calculations for series solutions. In order to overcome these difficulties, in this paper, a useful improvement of the PIM is proposed. The implementation of the modified method is demonstrated by solving several nonlinear second order BVPs. The results reveal that the new developed method is a promising analytical tool to solve the nonlinear second order BVPs and more promising because it can further be applied easily to solve nonlinear higher order BVPs with highly accurate. Mathematical subject classification: Primary: 34B15; Secondary: 41A10.
  • On a nonstationary nonlinear coupled system

    Li, Gang; Wang, Hui; Zhu, Jiang

    Resumo em Inglês:

    In this paper, a strongly nonlinear coupled elliptic-parabolic system modelling a class of engineering problems with heat effect is studied. Existence of a weak solution is first established by Schauder fixed point theorem, where the coupled functions σ(s), k(s) are assumed to be bounded. The uniqueness of the solution is obtained by applying Meyers' theorem and assuming that σ(s), k(s) are Lipschitz continuous. The regularity of the solution is then analyzed in dimension d < 2 under the assumptions on σ(s), k(s) ∈ C2(R) and the boundedness of their derivatives of second order. Finally, the blow-up phenomena of the system are studied. Mathematical subject classification: 35J60, 35K55.
  • Closed balls for interpolating quasi-polynomials

    Wen, Jiajin; Cheng, Sui Sun

    Resumo em Inglês:

    The classic interpolation problem asks for polynomials to fit a set of given data. In this paper, quasi-polynomials are considered as interpolating functions passing through a set of spatial points. Existence and uniqueness is obtained by means of generalized Vandermonde determinants. By means of several estimates related to these determinants, we are also able to find closed balls for any given centers that enclose the approximating curves. By choosing proper centers based on the observed spatial points, these balls may lead us to applications such as satellite tracking and control. Mathematical subject classification: 41A05.
  • A smoothing Newton-type method for second-order cone programming problems based on a new smoothing Fischer-Burmeister function

    Fang, Liang; Feng, Zengzhe

    Resumo em Inglês:

    A new smoothing function of the well known Fischer-Burmeister function is given. Based on this new function, a smoothing Newton-type method is proposed for solving second-order cone programming. At each iteration, the proposed algorithm solves only one system of linear equations and performs only one line search. This algorithm can start from an arbitrary point and it is Q-quadratically convergent under a mild assumption. Numerical results demonstrate the effectiveness of the algorithm. Mathematical subject classification: 90C25, 90C30, 90C51, 65K05, 65Y20.
  • Block triangular preconditioner for static Maxwell equations

    Wu, Shi-Liang; Huang, Ting-Zhu; Li, Liang

    Resumo em Inglês:

    In this paper, we explore the block triangular preconditioning techniques applied to the iterative solution of the saddle point linear systems arising from the discretized Maxwell equations. Theoretical analysis shows that all the eigenvalues of the preconditioned matrix arestrongly clustered. Numerical experiments are given to demonstrate the efficiency of the presented preconditioner. Mathematical subject classification: 65F10.
  • Solutions to the recurrence relation u n+1 = v n+1 + u n ⊗ v n in terms of Bell polynomials

    Withers, Christopher S.; Nadarajah, Saralees

    Resumo em Inglês:

    Motivated by time series analysis, we consider the problem of solving the recurrence relation u n+1 = v n+1 +u n⊗v n for n ≠ 0 and u n, given the sequence v n. A solution is given as a Bell polynomial. When v n can be written as a weighted sum of nth powers, then the solution u n also takes this form. Mathematical subject classification: 33E99.
  • The quotient of gamma functions by the psi function

    Mortici, Cristinel

    Resumo em Inglês:

    The aim of this paper is to construct the asymptotic series of the ratio of gamma functions by Kershaw then to deduce some sharp estimates. Mathematical subject classification: 33B15, 05A16, 26D15.
  • Differential transformation method for solving one-space-dimensional telegraph equation

    Soltanalizadeh, B.

    Resumo em Inglês:

    In this research, the Differential Transformation Method (DTM) has been utilized to solve the hyperbolic Telegraph equation. This method can be used to obtain the exact solutions of this equation. In the end, some numerical tests are presented to demonstrate the effectiveness and efficiency of the proposed method. Mathematical subject classification: 35Lxx, 35Qxx.
  • Operational Tau approximation for a general class of fractional integro-differential equations

    Vanani, S. Karimi; Aminataei, A.

    Resumo em Inglês:

    In this work, an extension of the algebraic formulation of the operational Tau method (OTM) for the numerical solution of the linear and nonlinear fractional integro-differential equations (FIDEs) is proposed. The main idea behind the OTM is to convert the fractional differential and integral parts of the desired FIDE to some operational matrices. Then the FIDE reduces to a set of algebraic equations. We demonstrate the Tau matrix representation for solving FIDEs based on arbitrary orthogonal polynomials. Some advantages of using the method, errorestimation and computer algorithm are also presented. Illustrative linear and nonlinear experiments are included to show the validity and applicability of the presented method. Mathematical subject classification: 65M70, 34A25, 26A33, 47Gxx.
  • Weak Allee effect in a predator-prey system involving distributed delays

    Tabares, Paulo C.C.; Ferreira, Jocirei D.; Rao, V. Sree Hari

    Resumo em Inglês:

    In this paper we study the influence of weak Allee effect in a predator-prey system model. This effect is included in the prey equation and we determine conditions for the occurrence of Hopf bifurcation. The stability properties of the system and the biological issues of the memory and Allee models on the coexistence of the two species are studied. Finally we present some simulations which allow one to verify the analytical conclusions obtained. Mathematical subject classification: Primary: 34C25; Secondary: 92B05.
  • Mimetic finite difference methods in image processing

    Bazan, C.; Abouali, M.; Castillo, J.; Blomgren, P.

    Resumo em Inglês:

    We introduce the use of mimetic methods to the imaging community, for the solution of the initial-value problems ubiquitous in the machine vision and image processing and analysis fields. PDE-based image processing and analysis techniques comprise a host of applications such as noise removal and restoration, deblurring and enhancement, segmentation, edge detection, inpainting, registration, motion analysis, etc. Because of their favorable stability and efficiency properties, semi-implicit finite difference and finite element schemes have been the methods of choice (in that order of preference). We propose a new approach for the numerical solution of these problems based on mimetic methods. The mimetic discretization scheme preserves the continuum properties of the mathematical operators often encountered in the image processing and analysis equations. This is the main contributing factor to the improved performance of the mimetic method approach, as compared to both of the aforementioned popular numerical solution techniques. To assess the performance of the proposed approach, we employ the Catté-Lions-Morel-Coll model to restore noisy images, by solving the PDE with the three numerical solution schemes. For all of the benchmark images employed in our experiments, and for every level of noise applied, we observe that the best image restored by using the mimetic method is closer to the noise-free image than the best images restored by the other two methods tested. These results motivate further studies of the application of the mimetic methods to other imaging problems. Mathematical subject classification: Primary: 68U10; Secondary: 65L12.
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