263 results
Search Results
2. Some inequalities involving quadratic forms of operator means.
- Author
-
Raïssouli, Mustapha
- Subjects
- *
QUADRATIC forms , *MATHEMATICS , *MATHEMATICAL analysis , *NUMERICAL analysis , *HILBERT space - Abstract
Let T and S be two self-adjoint positive invertible operators of a complex Hilbert space H. In this paper, we investigate some inequalities involving the quadratic forms of the weighted arithmetic and harmonic means of T and S. Application for operator entropies is also discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
3. On Genocchi Operational Matrix of Fractional Integration for Solving Fractional Differential Equations.
- Author
-
Abdulnasir Isah and Chang Phang
- Subjects
- *
FRACTIONAL integrals , *MATHEMATICS , *POLYNOMIALS , *MATHEMATICAL analysis , *NUMERICAL analysis , *EQUATIONS , *ALGEBRA - Abstract
In this paper we present a new numerical method for solving fractional differential equations (FDEs) based on Genocchi polynomials operational matrix through collocation method. The operational matrix of fractional integration in Riemann-Liouville sense is derived. The upper bound for the error of the operational matrix of fractional integration is also shown. The properties of Genocchi polynomials are utilized to reduce the given problems to a system of algebraic equations. Illustrative examples are finally given to show the simplicity, accuracy and applicability of the method. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
4. The Computation of Zeros of Ahlfors Map for Multiply Connected Regions.
- Author
-
Nazar, Kashif, Murid, Ali H. M., and Sangawi, Ali W. K.
- Subjects
- *
MATHEMATICAL analysis , *MATHEMATICS , *INTEGRAL equations , *FUNCTIONAL equations , *FREDHOLM equations , *NUMERICAL analysis , *INTEGERS - Abstract
The relation between the Ahlfors map and Szegö kernel S (z, a) is classical. The Szegö kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman-Stein kernel. The exact zeros of the Ahlfors map are known for a particular family of doubly connected regions and a particular triply connected region. This paper presents a numerical method for computing the zeros of the Ahlfors map of any bounded multiply connected regions with smooth boundaries. The method depends on the values of S (z(t), a), S'(z(t), a) and θ'(t), where θ(t) is the boundary correspondence function of Ahlfors map. A formula is derived for computing S'(z(t), a). An integral equation for θ'(t) is used for finding the zeros of Ahlfors map. The numerical examples presented here demonstrate the method. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
5. On the oscillation of impulsive vector partial differential equations with distributed deviating arguments.
- Author
-
Chatzarakis, George E., Sadhasivam, Vadivel, and Raja, Thangaraj
- Subjects
- *
NUMERICAL analysis , *MATHEMATICAL analysis , *DIFFERENTIAL equations , *ADJOINT differential equations , *MATHEMATICS - Abstract
In this paper, we consider a class of nonlinear impulsive neutral partial functional differential equations with continuous distributed deviating arguments. For this class, we establish sufficient conditions for the
H -oscillation of the solutions, using impulsive differential inequalities and an averaging technique with two different boundary conditions. We provide an example to illustrate the main result. [ABSTRACT FROM AUTHOR]- Published
- 2018
- Full Text
- View/download PDF
6. First order sentences about random graphs: Small number of alternations.
- Author
-
Matushkin, A.D. and Zhukovskii, M.E.
- Subjects
- *
RANDOM graphs , *GRAPH theory , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICS - Abstract
The spectrum of a first order sentence is the set of all α such that G ( n , n − α ) does not obey zero–one law with respect to this sentence. In this paper, we prove that the minimal number of quantifier alternations of a first order sentence with infinite spectrum equals 3. We have also proved that the spectrum of a first-order sentence with quantifier depth 4 has no limit points except possibly the points 1 ∕ 2 and 3 ∕ 5 . [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
7. Some D-optimal chemical balance weighing designs: theory and examples.
- Author
-
ław Ceranka, Bronis and Graczyk, Małgorzata
- Subjects
- *
OPTIMAL designs (Statistics) , *WEIGHT measurement , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICS - Abstract
In this paper we study a certain kind of experimental designs called chemical balance weighing designs. We consider issues with regard to determining optimality conditions. We give new classes of designs in which we are able to determine an optimal design. Moreover, examples are given for the presented cases. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
8. Left-looking version of AINV preconditioner with complete pivoting strategy.
- Author
-
Rafiei, A.
- Subjects
- *
LINEAR systems , *MATRICES (Mathematics) , *GEOMETRIC dissections , *NUMERICAL analysis , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we apply a complete pivoting strategy to compute the left-looking version of AINV preconditioner for linear systems. As the preprocessing, the MultiLevel Nested Dissection reordering has also been applied. We have used this preconditioner as the right preconditioner for several linear systems where the coefficient matrices have been downloaded from the University of Florida Sparse Matrix Collection. Numerical experiments presented in this paper indicate the effectiveness of such a complete pivoting on the quality of left-looking version of AINV preconditioner. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
9. ROUNDING IN THE PROBLEM OF THE ALLOCATION OF INDIVISIBLE GOODS.
- Author
-
Cegiełka, Katarzyna and Łyko, Janusz
- Subjects
- *
NUMERICAL analysis , *MATHEMATICAL analysis , *ALLOCATION (Accounting) , *MATHEMATICS , *LOGIC - Abstract
Using approximate, rounded values implies, in a sense, that an exact numerical value may be ignored. In many cases the difference between the exact and approximate values is not important, and replacing exact numbers by their approximate values does not result in undesired consequences. Yet in certain circumstances, rounding significantly influences the solutions of given problems. This is the case, among others, when we allocate indivisible goods. It may happen that the rounding mode affects the result of allocation so much that the rounding differences cannot be neglected by the agents participating in distribution. This paper presents the classic problem of distributing mandates in representative bodies along with different rounding modes in respective solution procedures. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
10. Some new solitonary solutions of the modified Benjamin–Bona–Mahony equation
- Author
-
Noor, Muhammad Aslam, Noor, Khalida Inayat, Waheed, Asif, and Al-Said, Eisa A.
- Subjects
- *
NONLINEAR evolution equations , *SOLITONS , *MATHEMATICAL physics , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICS - Abstract
Abstract: In this paper, we use the exp-function method to construct some new soliton solutions of the Benjamin–Bona–Mahony and modified Benjamin–Bona–Mahony equations. These equations have important and fundamental applications in mathematical physics and engineering sciences. The exp-function method is used to find the soliton solution of a wide class of nonlinear evolution equations with symbolic computation. This method provides the concise and straightforward solution in a very easier way. The results obtained in this paper can be viewed as a refinement and improvement of the previously known results. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
11. A simple adaptive feedback control method for chaos and hyper-chaos control
- Author
-
Chen, Guoxin
- Subjects
- *
FEEDBACK control systems , *CHAOS theory , *NUMERICAL analysis , *MATHEMATICS , *ALGEBRA , *MATHEMATICAL analysis - Abstract
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]
- Published
- 2011
- Full Text
- View/download PDF
12. On Solving Games Constructed Using Both Short and Long Conjunctive Sums.
- Author
-
Kane, Daniel M.
- Subjects
- *
COMBINATORICS , *MATHEMATICS , *PERMUTATIONS , *ALGEBRA , *GAME theory , *DECISION theory , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICAL optimization - Abstract
In a 1966 paper by C.A.B. Smith, the short and long conjunctive sums of games are defined and methods are described for determining the theoretical winner of a game constructed using one type of these sums. In this paper, we develop a method for determining the winner of a game constructed using arbitrary combinations of these sums. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
13. A class of approximate inverse preconditioners for solving linear systems.
- Author
-
Zhang, Yong, Huang, Ting-Zhu, Liu, Xing-Ping, and Gu, Tong-Xiang
- Subjects
- *
MATRICES (Mathematics) , *LINEAR systems , *MATHEMATICS , *MATHEMATICAL ability , *NUMERICAL analysis , *MATHEMATICAL analysis , *EQUATIONS , *ALGEBRA , *MATHEMATICAL combinations , *LINEAR differential equations - Abstract
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]
- Published
- 2009
- Full Text
- View/download PDF
14. Supplement to: ‘Boundary stabilization of hyperbolic systems related to overhead cranes’ [H. Sano, IMA J. Math. Control Inf. (2008) vol. 25, 353–366, doi:10.1093/imamci/dnm031].
- Author
-
SANO, HIDEKI
- Subjects
- *
EQUATIONS , *NUMERICAL analysis , *SYMMETRY (Physics) , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
In the paper cited in the heading, we treated the problem of stabilizing a flexible cable with two rigid loads, which was described by two kinds of hyperbolic equations. To show the asymptotic stability of the closed-loop system with a controller derived there, we used the LaSalle's invariance principle. However, in that paper, we need to supplement the proof of Theorem 5.1 and to revise the proof of Theorem 5.2. Throughout this note, we use the same notation as in the paper cited in the heading. [ABSTRACT FROM PUBLISHER]
- Published
- 2009
- Full Text
- View/download PDF
15. ON THE FINE SPECTRUM OF THE GENERALIZED DIFFERENCE OPERATOR Δv OVER THE SEQUENCE SPACE C0.
- Author
-
Srivastava, P. D. and Kumar, Sudhanshu
- Subjects
- *
MATHEMATICAL analysis , *EQUATIONS , *REAL numbers , *MATHEMATICS , *NUMERICAL analysis - Abstract
The purpose of the paper is to determine fine spectrum of newly introduced operator Δν on the sequence space c0. The operator Δν on c0 is defined by Δνχ = (νnχn - νn-1χn-1)n=0∞ with χ-1 = 0, where ν = (νk) is either constant or strictly decreasing sequence of positive real numbers such that lim νk = L > 0 and sup νk ≤ 2L. In this paper, it is shown that spectrum (These equations cannot be represented into ASCII text), the point spectrum σp(Δν,c0) = ϕ if ν is a constant and σp(Δν,c0) = {νn} if ν is a strictly decreasing sequence. We have also obtained the results on continuous spectrum σc(Δν,c0), residual spectrum σr(Δν,c0) and fine spectrum of the operator Δν on c0. [ABSTRACT FROM AUTHOR]
- Published
- 2009
16. RAPID SOLUTION OF THE WAVE EQUATION IN UNBOUNDED DOMAINS.
- Author
-
Banjai, L. and Sauter, S.
- Subjects
- *
WAVE equation , *PARTIAL differential equations , *BOUNDARY element methods , *NUMERICAL analysis , *TOEPLITZ matrices , *HELMHOLTZ equation , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
In this paper we propose and analyze a new, fast method for the numerical solution of time domain boundary integral formulations of the wave equation. We employ Lubich's convolution quadrature method for the time discretization and a Galerkin boundary element method for the spatial discretization. The coefficient matrix of the arising system of linear equations is a triangular block Toeplitz matrix. Possible choices for solving the linear system arising from the above discretization include the use of fast Fourier transform (FFT) techniques and the use of data-sparse approximations. By using FFT techniques, the computational complexity can be reduced substantially while the storage cost remains unchanged and is, typically, high. Using data-sparse approximations, the gain is reversed; i.e., the computational cost is (approximately) unchanged while the storage cost is substantially reduced. The method proposed in this paper combines the advantages of these two approaches. First, the discrete convolution (related to the block Toeplitz system) is transformed into the (discrete) Fourier image, thereby arriving at a decoupled system of discretized Helmholtz equations with complex wave numbers. A fast data-sparse (e.g., fast multipole or panel-clustering) method can then be applied to the transformed system. Additionally, significant savings can be achieved if the boundary data are smooth and time-limited. In this case the right-hand sides of many of the Helmholtz problems are almost zero, and hence can be disregarded. Finally, the proposed method is inherently parallel. We analyze the stability and convergence of these methods, thereby deriving the choice of parameters that preserves the convergence rates of the unperturbed convolution quadrature. We also present numerical results which illustrate the predicted convergence behavior. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
17. ON THE INTERPOLATION ERROR ESTIMATES FOR Q1 QUADRILATERAL FINITE ELEMENTS.
- Author
-
Shipeng Mao, Nicaise, Serge, and Zhong-Ci Shi
- Subjects
- *
ERROR analysis in mathematics , *FINITE element method , *NUMERICAL analysis , *QUADRILATERALS , *ESTIMATION theory , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
In this paper, we study the relation between the error estimate of the bilinear interpolation on a general quadrilateral and the geometric characters of the quadrilateral. Some explicit bounds of the interpolation error are obtained based on some sharp estimates of the integral over 1/∣J∣p-1 for 1 ≤ p≤∞ on the reference element, where J is the Jacobian of the nonaffine mapping. This allows us to introduce weak geometric conditions (depending on p) leading to interpolation error estimates in the W1,p norm, for any p ϵ [1,∞), which can be regarded as a generalization of the regular decomposition property (RDP) condition introduced in [G. Acosta and R. G. Durán, SIAM J. Numer. Anal., 38 (2000), pp. 1073-1088] for p = 2 and new RDP conditions (NRDP) for p ≠ 2. We avoid the use of the reference family elements, which allows us to extend the results to a larger class of elements and to introduce the NRDP condition in a more unified way. As far as we know, the mesh condition presented in this paper is weaker than any other mesh conditions proposed in the literature for any p with 1 ≤ p≤∞. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
18. A new bound on the number of special fibers in a pencil of curves.
- Subjects
- *
CURVES , *MATHEMATICAL analysis , *PLANE curves , *NUMERICAL analysis , *ALGEBRA , *MATHEMATICS - Abstract
In a paper by J. V. Pereira and the author it was proved that any pencil of plane curves of degree $d>1$ with irreducible generic fiber can have at most five completely reducible fibers although no examples with five such fibers had ever been found. Recently Janis Stipins has proved that if a pencil has a base of $d^2$ points, then it cannot have five completely reducible fibers. In this paper we generalize Stipins' result to arbitrary pencils. We also include into consideration more general special fibers that are the unions of lines and non-reduced curves. These fibers are important for characteristic varieties of hyperplane complements. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
19. A multiresolution finite volume scheme for two-dimensional hyperbolic conservation laws
- Author
-
Tang, Lingyan and Song, Songhe
- Subjects
- *
FINITE volume method , *NUMERICAL analysis , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, high-resolution finite volume schemes are combined with an adaptive mesh technique inspired by multiresolution analysis to improve the computational efficiency for two-dimensional hyperbolic conservation laws. The method is conservative. Moreover, it is stable which is proven numerically in this paper. The computational grid is dynamically adapted so that higher spatial resolution is automatically allocated to regions where strong gradients are observed. Using this proposed scheme, we compute several two-dimensional model problems and a compressive rate ranging from about 5–10 is observed in all simulations. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
20. On the robustness of a multigrid method for anisotropic reaction-diffusion problems.
- Author
-
Reusken, A. and Soemers, M.
- Subjects
- *
MULTIGRID methods (Numerical analysis) , *NUMERICAL analysis , *MATHEMATICAL analysis , *ANISOTROPY , *GEOMETRY , *MATHEMATICS - Abstract
In this paper, we consider a reaction-diffusion boundary value problem in a three-dimensional thin domain. The very different length scales in the geometry result in an anisotropy effect. Our study is motivated by a parabolic heat conduction problem in a thin foil leading to such anisotropic reaction-diffusion problems in each time step of an implicit time integration method [7]. The reaction-diffusion problem contains two important parameters, namely ε >0 which parameterizes the thickness of the domain and μ >0 denoting the measure for the size of the reaction term relative to that of the diffusion term. In this paper we analyze the convergence of a multigrid method with a robust (line) smoother. Both, for the W- and the V-cycle method we derive contraction number bounds smaller than one uniform with respect to the mesh size and the parameters ε and μ. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
21. The sub-elliptic obstacle problem: regularity of the free boundary in Carnot groups of step two
- Author
-
Danielli, Donatella, Garofalo, Nicola, and Petrosyan, Arshak
- Subjects
- *
MATHEMATICAL analysis , *NUMERICAL analysis , *ASYMPTOTIC expansions , *MATHEMATICS - Abstract
Abstract: The sub-elliptic obstacle problem arises in various branches of the applied sciences, e.g., in mechanical engineering and robotics, mathematical finance, image reconstruction and neurophysiology. In the recent paper [Donatella Danielli, Nicola Garofalo, Sandro Salsa, Variational inequalities with lack of ellipticity. I. Optimal interior regularity and non-degeneracy of the free boundary, Indiana Univ. Math. J. 52 (2) (2003) 361–398; MR1976081 (2004c:35424)] it was proved that weak solutions to the sub-elliptic obstacle problem in a Carnot group belong to the Folland–Stein (optimal) Lipschitz class (the analogue of the well-known interior local regularity for the classical obstacle problem). However, the regularity of the free boundary remained a challenging open problem. In this paper we prove that, in Carnot groups of step , the free boundary is (Euclidean) near points satisfying a certain thickness condition. This constitutes the sub-elliptic counterpart of a celebrated result due to Caffarelli [Luis A. Caffarelli, The regularity of free boundaries in higher dimensions, Acta Math. 139 (3–4) (1977) 155–184; MR0454350 (56 #12601)]. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
22. Hybrid power flow analysis using coupling loss factor of SEA for low-damping system—Part II: Formulation of 3-D case and hybrid PFFEM
- Author
-
Park, Young-Ho and Hong, Suk-Yoon
- Subjects
- *
FINITE element method , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: The hybrid power flow analysis (PFA) is an analytic method proposed for the effective prediction of vibrational and acoustic responses of low-damping system in the medium-to-high frequency ranges by using the PFA algorithm and statistical energy analysis (SEA) coupling concepts. This paper presents the hybrid boundary condition on 3-D case for hybrid PFA in addition to 1-D and 2-D cases which are derived in the other companion paper, and formulates the hybrid power flow finite-element method (PFFEM) including coupling loss factor (CLF) of SEA to extend the application area of hybrid PFA to built-up structures. To verify the derived boundary condition and hybrid PFFEM, numerical analyses were successfully performed for various analytic models and reverberance factors. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
23. 3D HYBRID DEPTH MIGRATION AND FOUR-WAY SPLITTING SCHEMES.
- Author
-
Wen-Sheng Zhang and Guan-Quan Zhang
- Subjects
- *
NUMERICAL analysis , *MATHEMATICS , *FINITE differences , *EXTRAPOLATION , *APPROXIMATION theory , *MATHEMATICAL analysis - Abstract
The alternately directional implicit (ADI) scheme is usually used in 3D depth migration. It splits the 3D square-root operator along crossline and inline directions alternately. In this paper, based on the ideal of data line, the four-way splitting schemes and their splitting errors for the finite-difference (FD) method and the hybrid method are investigated. The wavefield extrapolation of four-way splitting scheme is accomplished on a data line and is stable unconditionally. Numerical analysis of splitting errors show that the two-way FD migration have visible numerical anisotropic errors, and that four-way FD migration has much less splitting errors than two-way FD migration has. For the hybrid method, the differences of numerical anisotropic errors between two-way scheme and four-way scheme are small in the case of lower lateral velocity variations. The schemes presented in this paper can be used in 3D post stack or prestack depth migration. Two numerical calculations of 3D depth migration axe completed. One is the four-way FD and hybrid 3D post-stack depth migration for an impulse response, which shows that the anisotropic errors can be eliminated effectively in the cases of constant and variable velocity variations. The other is the 3D shot-profile prestack depth migration for SEG/EAEG benchmark model with two-way hybrid splitting scheme, which presents good imaging results. The Message Passing Interface (MPI) programme based on shot number is adopted. [ABSTRACT FROM AUTHOR]
- Published
- 2006
24. A note on properties and computations of matrix pseudospectra
- Author
-
Du, Kui
- Subjects
- *
MATHEMATICS , *MATRICES (Mathematics) , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
Abstract: Recently, Shen et al. has published a paper concerning the properties and computations of matrix pseudospectra. However, some of the main results seem to be incomplete. As a complement of the paper, in this note we first make several examples to show the incompleteness of that results, then we give the modified results through giving more appropriate definitions replacing the one given in [Y. Shen, J. Zhao, H. Fan, Properties and computations of matrix pseudospectra, Applied Mathematics and Computation 161 (2005) 385–393]. An interesting inclusion theorem for pseudospectra is given, which provides preferable bounds for standard pseudospectra. Some other properties are also explored. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
25. Internal stabilization of the plate equation in a square: the continuous and the semi-discretized problems
- Author
-
Ramdani, K., Takahashi, T., and Tucsnak, M.
- Subjects
- *
FINITE differences , *MATHEMATICS , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
Abstract: This paper is devoted to the study of the internal stabilization of the Bernoulli–Euler plate equation in a square. The continuous and the space semi-discretized problems are successively considered and analyzed using a frequency domain approach. For the infinite-dimensional problem, we provide a new proof of the exponential stability result, based on a two-dimensional Ingham''s type result. In the second and main part of the paper, we propose a finite difference space semi-discretization scheme and we prove that this scheme yields a uniform exponential decay rate (with respect to the mesh size). [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
26. ON RECOGNIZABLE LANGUAGES OF INFINITE PICTURES.
- Author
-
Finkel, Olivier
- Subjects
- *
MATHEMATICAL analysis , *NUMERICAL analysis , *INFINITE dimensional Lie algebras , *MACHINE theory , *MATHEMATICS - Abstract
In a recent paper, Altenbernd, Thomas and Wöhrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the Büchi and Muller ones, firstly used for infinite words. The authors asked for comparing the tiling system acceptance with an acceptance of pictures row by row using an automaton model over ordinal words of length ω2. We give in this paper a solution to this problem, showing that all languages of infinite pictures which are accepted row by row by Büchi or Choueka automata reading words of length ω2 are Büchi recognized by a finite tiling system, but the converse is not true. We give also the answer to two other questions which were raised by Altenbernd, Thomas and Wöhrle, showing that it is undecidable whether a Büchi recognizable language of infinite pictures is E-recognizable (respectively, A-recognizable). [ABSTRACT FROM AUTHOR]
- Published
- 2004
- Full Text
- View/download PDF
27. Error Estimates for a Variable Time-Step Discretization of a Phase Transition Model with Hyperbolic Momentum.
- Author
-
Segatti, Antonio
- Subjects
- *
NUMERICAL analysis , *EQUATIONS , *MATHEMATICAL optimization , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
This paper deals with a fully implicit time discretization scheme with variable time-step for a nonlinear system modelling phase transition and mechanical deformations in shape memory alloys. The model is studied in the non-stationary case and accounts for local microscopic interactions between the phases introducing the gradients of the phase parameters. The resulting initial-boundary value problem has already been studied by the author who proved existence, uniqueness and continuous dependence on data for a suitable weak solution along some regularity results. A careful and detailed investigation of the variable time-step discretization is the goal of this paper. Thus, we deduce some estimates for the discretization error. These estimates depend only on data, impose no constraints between consecutive time-steps and show an optimal order of convergence. Finally, we prove another regularity result for the solution under stronger regularity assumptions on data. [ABSTRACT FROM AUTHOR]
- Published
- 2004
- Full Text
- View/download PDF
28. Evaluating Gradients in Optimal Control: Continuous Adjoints versus Automatic Differentiation.
- Author
-
Griesse, R., Walther, A., and Pesch, H. J.
- Subjects
- *
MATHEMATICAL optimization , *MATHEMATICS , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICAL functions , *COMPUTER programming - Abstract
This paper deals with the numerical solution of optimal control problems for ODEs. The methods considered here rely on some standard optimization code to solve a discretized version of the control problem under consideration. We aim to make available to the optimization software not only the discrete objective functional, but also its gradient. The objective gradient can be computed either from forward (sensitivity) information or backward (adjoint) information. The purpose of this paper is to discuss various ways of adjoint computation. It will be shown both theoretically and numerically that methods based on the continuous adjoint equation require a careful choice of both the integrator and gradient assembly formulas in order to obtain a gradient consistent with the discretized control problem. Particular attention is given to automatic differentiation techniques which generate automatically a suitable integrator. [ABSTRACT FROM AUTHOR]
- Published
- 2004
- Full Text
- View/download PDF
29. A TRUST REGION METHOD FOR SOLVING DISTRIBUTED PARAMETER IDENTIFICATION PROBLEMS.
- Author
-
Yan-fei Wang, L. F. and Ya-xiang Yuan
- Subjects
- *
EQUATIONS , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICAL statistics , *MATHEMATICS - Abstract
This paper is concerned with the ill-posed problems of identifying a parameter in an elliptic equation which appears in may applications in science and industry. Its solution is obtained by applying trust region method to a nonlinear least squares error problem. Trust region method has long been a popular method for well-posed problems. This paper indicates that it is also suitable for all-posed problems. Numerical experiment is given to compare the trust region method with the Tikhonov regularization method. It seems that the trust region method is more promising. [ABSTRACT FROM AUTHOR]
- Published
- 2003
30. New Lyapunov-type inequalities for a class of even-order linear differential equations.
- Author
-
Yang, Xiaojing and Lo, Kueiming
- Subjects
- *
DIFFERENTIAL equations , *NUMERICAL analysis , *MATHEMATICAL analysis , *ALGEBRA , *MATHEMATICS - Abstract
In this paper, we obtain some new Lyapunov-type inequalities for a class of even-order linear differential equations, the results are new and generalize and improve some early results in this field. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
31. Wold-type decomposition for some regular operators.
- Author
-
Ezzahraoui, H., Mbekhta, M., and Zerouali, E.H.
- Subjects
- *
MATHEMATICAL decomposition , *OPERATOR theory , *MATHEMATICAL analysis , *MATHEMATICS , *NUMERICAL analysis - Abstract
This paper is concerned with Wold-type decomposition for regular operators whose orbits under any vector satisfy some growth conditions. Several results on left invertible operators close to isometries are extended. We also give numerous results on the Moore–Penrose inverse for regular operators in this particular setting. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
32. The blow-up solutions of the heat equations in [formula omitted].
- Author
-
Ru, S. and Chen, Jiecheng
- Subjects
- *
NUMERICAL solutions to heat equation , *NUMERICAL solutions to nonlinear evolution equations , *MATHEMATICAL analysis , *MATHEMATICS , *NUMERICAL analysis - Abstract
In this paper, we give a formal solution of some nonlinear evolution equations. By the formal solution, we can obtain the blow-up solution of the heat equations, even in the supercritical case. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
33. TRANSFORMATION OF FAMILIES OF MATRICES TO NORMAL FORMS AND ITS APPLICATION TO STABILITY THEORY.
- Author
-
Mailybaev, Alexei A.
- Subjects
- *
MATRICES (Mathematics) , *NORMAL forms (Mathematics) , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICS , *MATHEMATICAL models - Abstract
Families of matrices smoothly depending on a vector of parameters are considered. Arnold [Russian Math. Surveys, 26 (1971), pp. 29–43] and Galin [Uspekhi Mat. Nauk, 27 (1972),pp. 241–242] have found and listed normal forms of families of complex and real matrices (miniversal deformations), to which any family of matrices can be transformed in the vicinity of a point in the parameter space by a change of basis, smoothly dependent on a vector of parameters, and by a smooth change of parameters. In this paper a constructive method of determining functions describing a change of basis and a change of parameters, transforming an arbitrary family to the miniversal deformation, is suggested. Derivatives of these functions with respect to parameters are determined from a recurrent procedure using derivatives of the functions of lower orders and derivatives of the family of matrices. Then the functions are found as Taylor series. Examples are given. The suggested method allows using efficiently miniversal deformations for investigation of different properties of matrix families. This is shown in the paper where tangent cones (linear approximations) to the stability domain at the singular boundary points are found. [ABSTRACT FROM AUTHOR]
- Published
- 1999
34. CONVERGENCE OF SUBDIVISION SCHEMES ASSOCIATED WITH NONNEGATIVE MASKS.
- Author
-
Jia, Rong-Qing and Zhou, Ding-Xuan
- Subjects
- *
STOCHASTIC matrices , *EQUATIONS , *STOCHASTIC processes , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICS - Abstract
This paper is concerned with refinement equations of the type [This symbol cannot be presented in ASCII format] where f is the unknown function defined on the s-dimensional Euclidean space Rs, a is a finitely supported sequence on Zs, and M is an s × s dilation matrix with m := | det M|. The solution of a refinement equation can be obtained by using the subdivision scheme associated with the mask. In this paper we give a characterization for the convergence of the subdivision scheme when the mask is nonnegative. Our method is to relate the problem of convergence to m column-stochastic matrices induced by the mask. In this way, the convergence of the subdivision scheme can be determined in a finite number of steps by checking whether each finite product of those column-stochastic matrices has a positive row. As a consequence of our characterization, we show that the convergence of the subdivision scheme with a nonnegative mask depends only on the location of its positive coefficients. Several examples are provided to demonstrate the power and applicability of our approach. [ABSTRACT FROM AUTHOR]
- Published
- 1999
35. On fuzzy implications determined by aggregation operators
- Author
-
Ouyang, Yao
- Subjects
- *
AGGREGATION operators , *FUZZY sets , *MATHEMATICAL analysis , *SET theory , *OPERATOR theory , *ALGEBRA , *MATHEMATICS , *NUMERICAL analysis - Abstract
Abstract: Fuzzy implication operators play important roles in both theoretical and applied aspects of fuzzy sets theory. Many papers investigated various properties of different types of implications and the interrelationships among these properties. In this paper, we exploit the minimal conditions which must be satisfied for a binary operation A to generate a residual implication with additional properties. It includes several examples to clarify the situation. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
36. Design-Oriented Analysis of Circuits With Equality Constraints.
- Author
-
Vytyaz, Igor, Hanumolu, Pavan Kumar, Moon, Un-Ku, and Mayaram, Kartikeya
- Subjects
- *
ELECTRONIC circuit design , *LOGIC design , *NUMERICAL analysis , *MATHEMATICAL analysis , *FINITE differences , *MATHEMATICS - Abstract
This paper presents a design-oriented circuit analysis that is augmented with design constraints. This analysis computes the circuit response and also finds the values of circuit parameters (equal to the number of design specifications) that result in a specified circuit performance. An application of this approach is demonstrated for the periodic steady-state analysis with shooting and finite difference formulations. The new analysis with design equality constraints is several times faster than search-based techniques that employ conventional analysis methods. [ABSTRACT FROM PUBLISHER]
- Published
- 2011
- Full Text
- View/download PDF
37. Acceleration of the Steepest Descent Method for the Real Symmetric Eigenvalue Problem.
- Author
-
Ozeki, Takashi and Iijima, Taizo
- Subjects
- *
EIGENVALUES , *MATRICES (Mathematics) , *METHOD of steepest descent (Numerical analysis) , *NUMERICAL analysis , *MATHEMATICAL analysis , *ELECTRONICS , *MATHEMATICS - Abstract
This paper discusses the eigenvalue problem for the real symmetric matrix, especially the determination of the largest eigenvalue. The largest eigenvalue is the maximum extremum of the objective function called the Rayleigh quotient and can be determined by the steepest descent method. It is known, however, that the steepest descent method suffers from slow convergence because it converges linearly. Especially, when the largest and the nest largest eigenvalues have very close values, the convergence is particularly slow. This paper analyzes this situation and shows that the convergence can be accelerated by combining the steepest descent method with a technique called shaking. Finally, it is demonstrated by a numerical example that the convergence is accelerated drastically by the proposed technique. [ABSTRACT FROM AUTHOR]
- Published
- 1996
- Full Text
- View/download PDF
38. ANALYSIS OF VELOCITY-FLUX FIRST-ORDER SYSTEM LEAST-SQUARES PRINCIPLES FOR THE NAVIER-STOKES EQUATIONS: PART I.
- Author
-
Bochev, P., Cai, Z., Manteuffel, T. A., and McCormick, S. F.
- Subjects
- *
NAVIER-Stokes equations , *STOKES equations , *LEAST squares , *MATHEMATICS , *MATHEMATICAL statistics , *NUMERICAL analysis , *MULTIGRID methods (Numerical analysis) , *MATHEMATICAL analysis - Abstract
This paper develops a least-squares approach to the solution of the incompressible NavierStokes equations in primitive variables. As with our earlier work on Stokes equations, we recast the NavierStokes equations as a first-order system by introducing a velocity-flux variable and associated curl and trace equations. We show that a least-squares principle based on L2 norms applied to this system yields optimal discretization error estimates in the H1 norm in each variable, including the velocity flux. An analogous principle based on the use of an H-1 norm for the reduced system (with no curl or trace constraints) is shown to yield similar estimates, but now in the L2 norm for velocity-flux and pressure. Although the H-1 least-squares principle does not allow practical implementation, these results are critical to the analysis of a practical least-squares method for the reduced system based on a discrete equivalent of the negative norm. A practical method of this type is the subject of a companion paper. Finally, we establish optimal multigrid convergence estimates for the algebraic system resulting from the L2 norm approach. [ABSTRACT FROM AUTHOR]
- Published
- 1998
- Full Text
- View/download PDF
39. Design of Linear Phase FIR Filters in Subexpression Space Using Mixed Integer Linear Programming.
- Author
-
Ya Jun Yu and Yong Ching Lim
- Subjects
- *
MATHEMATICAL optimization , *DIGITAL filters (Mathematics) , *FILTERS (Mathematics) , *DIGITAL electronics , *ALGORITHMS , *FUNCTIONAL analysis , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
In this paper, a novel optimization technique is proposed to optimize filter coefficients of linear phase finite-impulse response (FIR) filter to share common subexpressions within and among coefficients. Existing approaches of common subexpression elimination optimize digital filters in two stages: first, an FIR filter is designed in a discrete space such as finite wordlength space or signed power-of-two (SPT) space to meet a given specification; in the second stage, an optimization algorithm is applied on the discrete coefficients to find and eliminate the common subexpressions. Such a two-stage optimization technique suffers from the problem that the search space in the second stage is limited by the finite wordlength or SPT coefficients obtained in the first stage optimization. The new proposed algorithm overcomes this problem by optimizing the filter coefficients directly in subexpression space for a given specification. Numerical examples of benchmark filters show that the required number of adders obtained using the proposed algorithm is much less than those obtained using two-stage optimization approaches. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
40. A stability theory for model systems.
- Author
-
Y. Villacampa, F. Verdú, and A. Pérez
- Subjects
- *
MATHEMATICAL models , *SIMULATION methods & models , *MATHEMATICS , *MATHEMATICAL analysis , *NUMERICAL analysis - Abstract
Purpose - The purpose of this paper is to carry out a theoretical study of the stability of the mathematical models defined in a class of systems. Furthermore, it will be supposed that the models have been obtained from experimental data and by means of the application of a methodology. The studies carried out in this paper are, on one hand, the theoretical framework for an analysis of the sensitivity and stability of a type of systems; on the other hand, they supplement the studies carried out by the authors, in which, using a computational program, the sensitivity of the mathematical models is analyzed with respect to a type of perturbation. Design/methodology/approach - Initially, a class of systems is considered that are denominated quantifiable systems, in which model systems are defined that are determined by a set and a family of relationships. An initial study of the sensitivity of the mathematical models to perturbations in the experimental data lead to a concept of sensitive and stable models that forms the basis of the theory of stability developed in this paper. Furthermore, this permits a definition of the stability function for the set of the perturbations and, consequently, a determination of stable models according to the defined theoretical structure. Findings - An analysis of the sensitivity and stability of mathematical models in quantifiable systems from a systems theory perspective will be fundamental for the determination of mathematical model stability in environmental systems. Originality/value - The studies carried out in this paper supposes an advance in the study and modeling of a type of systems that the authors have denominated as quantifiable systems, applicable to the study of environmental systems and supplementing the numeric studies carried out by the authors. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
41. An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps
- Author
-
Chen, Guo, Chen, Yong, and Liao, Xiaofeng
- Subjects
- *
MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICS , *ALGEBRA - Abstract
Abstract: Tang et al. proposed a novel method for obtaining S-boxes based on the well-known two-dimensional chaotic Baker map. Unfortunately, some mistakes exist in their paper. The faults are corrected first in this paper and then an extended method is put forward for acquiring cryptographically strong S-boxes. The new scheme employs a three-dimensional chaotic Baker map, which has more intensive chaotic characters than the two-dimensional one. In addition, the cryptographic properties such as the bijective property, the nonlinearity, the strict avalanche criterion, the output bits independence criterion and the equiprobable input/output XOR distribution are analyzed in detail for our S-box and revised Tang et al.’s one, respectively. The results of numerical analysis show that both of the two boxes can resist several attacks effectively and the three-dimensional chaotic map, a stronger sense in chaotic characters, can perform more smartly and more efficiently in designing S-boxes. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
42. An internal characterisation of radiality.
- Author
-
Leek, Robert
- Subjects
- *
TOPOLOGICAL spaces , *INDEPENDENCE (Mathematics) , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICS - Abstract
In this paper, we will investigate how radiality occurs in topological spaces by considering neighbourhood bases generated by nests. We will define a new subclass of radial spaces that contains LOTS, GO-spaces and spaces with well-ordered neighbourhood bases, called the independently-based spaces. We show that first-countable spaces are precisely the independently-based, strongly Fréchet spaces and we give an example of a Fréchet–Urysohn space that is neither independently-based nor strongly Fréchet. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
43. Proximity Queries between Interval-Based CSG Octrees.
- Author
-
Dyllong, Eva and Grimm, Cornelius
- Subjects
- *
ALGORITHMS , *INTERVAL analysis , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICS - Abstract
This short paper is concerned with a new algorithm for collision and distance calculation between CSG octrees, a generalization of an octree model created from a Constructive Solid Geometry (CSG) object. The data structure uses interval arithmetic and allows us to extend the tests for classifying points in space as inside, on the boundary, or outside a CSG object to entire sections of the space at once. Tree nodes with additional information about relevant parts of the CSG object are introduced in order to reduce the depth of the required subdivision. The new data structure reduces the input complexity and enables us to reconstruct the CSG object. We present an efficient algorithm for computing the distance between CSG objects encoded by the new data structure. The distance algorithm is based on a distance algorithm for classical octrees but, additionally, it utilizes an elaborated sort sequence and differentiated handling of pairs of octree nodes to enhance its efficiency. Experimental results indicate that, in comparison to common octrees, the new representation has advantages in the field of proximity query. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
44. Asymptotic Properties of Solutions of Two Dimensional Neutral Difference Systems.
- Author
-
Revathi, Thiagarajan
- Subjects
- *
TWO-dimensional models , *MATHEMATICAL analysis , *NUMERICAL analysis , *SYSTEMS theory , *MATHEMATICS - Abstract
In this paper we obtain sufficient conditions for the asymptotic properties of solutions of two dimensional neutral difference systems. Our result extends some existing results in the literature. An example is given to illustrate the result. [ABSTRACT FROM AUTHOR]
- Published
- 2013
45. Analytic invariant curves for an iterative equation related to Pielou's equation.
- Author
-
Zhao, Houyu
- Subjects
- *
DIFFERENTIAL invariants , *NUMERICAL solutions to difference equations , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
In this paper, we study the existence of analytic invariant curves of an iterative equationwhich is from Pielou's equation. By reducing the equation with the Schröder transformation to an auxiliary equation, the author discusses not only that the constantat resonance, i.e. at a root of the unity, but also thosenear resonance under the Brjuno condition. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
46. A Tricky Linear Algebra Example.
- Author
-
Sprows, David
- Subjects
- *
MATHEMATICAL analysis , *MATHEMATICAL ability , *LINEAR algebra , *NUMERICAL analysis , *RECREATIONAL mathematics , *PSYCHIC ability , *MATHEMATICS teachers , *MATHEMATICS education , *MATHEMATICS - Abstract
The article presents an example of a tricky linear algebra. It states that the trick starts when the instructor writes the number 65 on a paper and the instructor announces his psychic ability to predict sums in advance. Moreover, the numbers from 1-25 are then written consecutively in a 5-by-5 arrangement and a student is asked to choose any five numbers from this with the restriction that no two numbers can lie in the same column or row. It is further instructed that these numbers are then added together by the student before the instructor shows the paper with the number 65 written on it.
- Published
- 2008
47. On symmetric neighborhood assignments
- Author
-
Yu, Zuoming, Shi, Guohua, and Yun, Ziqiu
- Subjects
- *
MATHEMATICAL symmetry , *TOPOLOGY , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICAL models , *MATHEMATICS - Abstract
Abstract: In this paper, properties of symmetric neighborhood assignments are discussed. We show that in some results of Balogh and Gruenhage, the family of spherical neighborhoods in a metric space can be generalized to a symmetric open neighborhood assignments in any topology space. By a simple example, we answer a question raised by Hung negatively. We also discuss two questions raised by Nagata about metrization and symmetric neighborhood assignments. By giving new characterizations of strongly paracompact metrizable spaces and orthocompact Moore spaces respectively, we show that answer of the first question is negative, while the second question is undecidable under ZFC. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
48. New pre-dual space of Morrey space
- Author
-
Gogatishvili, A. and Mustafayev, R.Ch.
- Subjects
- *
MATHEMATICAL proofs , *MATHEMATICAL analysis , *NUMERICAL analysis , *PARAMETERS (Statistics) , *MATHEMATICS , *ALGEBRAIC spaces - Abstract
Abstract: In this paper, we give new characterization of the classical Morrey space. Complementary global Morrey-type spaces are introduced. It is proved that for particular values of parameters these spaces give new pre-dual space of the classical Morrey space. We also show that our new pre-dual space of the Morrey space coincides with known pre-dual spaces. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
49. An Enhanced Matrix-Free Secant Method via Predictor-Corrector Modified Line Search Strategies for Solving Systems of Nonlinear Equations.
- Author
-
Waziri, M. Y. and Majid, Z. A.
- Subjects
- *
NONLINEAR equations , *SECANT function , *TRIGONOMETRIC functions , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Diagonal updating scheme is among the cheapest Newton-like methods for solving system of nonlinear equations. Nevertheless, the method has some shortcomings. In this paper, we proposed an improved matrix-free secant updating scheme via line search strategies, by using the steps of backtracking in the Armijo-type line search as a step length predictor and Wolfe-Like condition as corrector. Our approach aims at improving the overall performance of diagonal secant updating scheme. Under mild assumptions, the global convergence results have been presented. Numerical experiments verify that the proposed approach is very promising. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
50. Numerical study of amplitude equations for SPDEs with degenerate forcing.
- Author
-
Blömker, Dirk, Mohammed, WaelW., Nolde, Christian, and Wöhrl, Franz
- Subjects
- *
NUMERICAL solutions to stochastic partial differential equations , *NUMERICAL analysis , *BURGERS' equation , *APPROXIMATION theory , *MATHEMATICS , *MATHEMATICAL analysis , *FORCING (Model theory) - Abstract
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]
- Published
- 2012
- Full Text
- View/download PDF
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.