109 results
Search Results
2. First order sentences about random graphs: Small number of alternations.
- Author
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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
3. Left-looking version of AINV preconditioner with complete pivoting strategy.
- Author
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Rafiei, A.
- Subjects
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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
4. Some new solitonary solutions of the modified Benjamin–Bona–Mahony equation
- Author
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Noor, Muhammad Aslam, Noor, Khalida Inayat, Waheed, Asif, and Al-Said, Eisa A.
- Subjects
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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
5. ON THE INTERPOLATION ERROR ESTIMATES FOR Q1 QUADRILATERAL FINITE ELEMENTS.
- Author
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Shipeng Mao, Nicaise, Serge, and Zhong-Ci Shi
- Subjects
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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
6. RAPID SOLUTION OF THE WAVE EQUATION IN UNBOUNDED DOMAINS.
- Author
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Banjai, L. and Sauter, S.
- Subjects
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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
7. A new bound on the number of special fibers in a pencil of curves.
- Subjects
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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
8. A multiresolution finite volume scheme for two-dimensional hyperbolic conservation laws
- Author
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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
9. The sub-elliptic obstacle problem: regularity of the free boundary in Carnot groups of step two
- Author
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Danielli, Donatella, Garofalo, Nicola, and Petrosyan, Arshak
- Subjects
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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
10. Internal stabilization of the plate equation in a square: the continuous and the semi-discretized problems
- Author
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Ramdani, K., Takahashi, T., and Tucsnak, M.
- Subjects
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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
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11. On fuzzy implications determined by aggregation operators
- Author
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Ouyang, Yao
- Subjects
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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
12. Design-Oriented Analysis of Circuits With Equality Constraints.
- Author
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Vytyaz, Igor, Hanumolu, Pavan Kumar, Moon, Un-Ku, and Mayaram, Kartikeya
- Subjects
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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
13. ANALYSIS OF VELOCITY-FLUX FIRST-ORDER SYSTEM LEAST-SQUARES PRINCIPLES FOR THE NAVIER-STOKES EQUATIONS: PART I.
- Author
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Bochev, P., Cai, Z., Manteuffel, T. A., and McCormick, S. F.
- Subjects
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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
14. Design of Linear Phase FIR Filters in Subexpression Space Using Mixed Integer Linear Programming.
- Author
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Ya Jun Yu and Yong Ching Lim
- Subjects
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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
15. Wold-type decomposition for some regular operators.
- Author
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Ezzahraoui, H., Mbekhta, M., and Zerouali, E.H.
- Subjects
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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
16. The blow-up solutions of the heat equations in [formula omitted].
- Author
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Ru, S. and Chen, Jiecheng
- Subjects
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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
17. An internal characterisation of radiality.
- Author
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Leek, Robert
- Subjects
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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
18. Asymptotic Properties of Solutions of Two Dimensional Neutral Difference Systems.
- Author
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Revathi, Thiagarajan
- Subjects
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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
19. A Tricky Linear Algebra Example.
- Author
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Sprows, David
- Subjects
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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
20. On symmetric neighborhood assignments
- Author
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Yu, Zuoming, Shi, Guohua, and Yun, Ziqiu
- Subjects
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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
21. New pre-dual space of Morrey space
- Author
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Gogatishvili, A. and Mustafayev, R.Ch.
- Subjects
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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
22. An Enhanced Matrix-Free Secant Method via Predictor-Corrector Modified Line Search Strategies for Solving Systems of Nonlinear Equations.
- Author
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Waziri, M. Y. and Majid, Z. A.
- Subjects
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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
23. Some constacyclic self-dual codes over the integers modulo
- Author
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Kai, Xiaoshan, Zhu, Shixin, and Tang, Yongsheng
- Subjects
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CODING theory , *INTEGERS , *MATHEMATICAL analysis , *NUMERICAL analysis , *RATIONAL numbers , *MATHEMATICS - Abstract
Abstract: In this paper, we explore constacyclic self-dual codes over . We first characterize constacyclic self-dual codes over of any length. Then we determine the structure of η-constacyclic self-dual codes over , where or . This structure is used to find some constacyclic self-dual codes over . [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
24. RENORMALIZED SOLUTIONS FOR A NON-UNIFORMLY PARABOLIC EQUATION.
- Author
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Chao Zhang and Shulin Zhou
- Subjects
- *
RENORMALIZATION group , *MATHEMATICAL proofs , *BOUNDARY value problems , *MATHEMATICAL analysis , *MATHEMATICS , *NUMERICAL analysis - Abstract
In this paper we prove the existence of nonnegative renormalized solutions for the initial-boundary value problem of a non-uniformly parabolic equation. Some well-known parabolic equations are the special cases of this equation. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
25. DJKM algebras I: Their universal central extension.
- Author
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Ben Cox and Vyacheslav Futorny
- Subjects
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INFINITE dimensional Lie algebras , *MATHEMATICAL analysis , *ALGEBRA , *MATHEMATICS , *NUMERICAL analysis - Abstract
The purpose of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, $ \mathfrak{g}\otimes \mathbb{C}[t,t^{-1},u\vert u^2=(t^2-b^2)(t^2-c^2)]$ [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
26. Perturbation of solutions of ordinary linear homogeneous differential equations of the second order
- Author
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Rajović, Miloje, Stojiljković, Rade, Dimitrovski, Dragan, and Radosavljević, Dragana
- Subjects
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PERTURBATION theory , *NUMERICAL solutions to linear differential equations , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICS , *ALGEBRA - Abstract
Abstract: In this paper we give a method for peturbation of solutions of linear homogeneous differential equation of the second order. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
27. Transitive closures and orderings on soft sets
- Author
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Babitha, K.V. and Sunil, Jacob John
- Subjects
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SET theory , *ALGORITHMS , *MATHEMATICAL proofs , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICS - Abstract
Abstract: In this paper an attempt is made to extend some standard results in set theory on the basis of soft set relations. Antisymmetric relation and transitive closure of a soft set relation are introduced and an analogue of Warshall’s algorithm is proposed for calculating the transitive closure of a soft set relation. Ordering on a soft set is defined and some set theoretical results based on this are proved. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
28. The periodicity and solutions of the rational difference equation with periodic coefficients
- Author
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Taskara, N., Uslu, K., and Tollu, D.T.
- Subjects
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DIFFERENCE equations , *MATHEMATICAL analysis , *GENERALIZATION , *NUMERICAL analysis , *MATHEMATICS , *ALGEBRA - Abstract
Abstract: In this paper, we give necessary and sufficient conditions for generalized solution and periodicity of the difference equation with -periodic coefficients, where , . Also, we obtain that the generalized solution is periodic with -period. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
29. What is a system of parameters?
- Author
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Louiza Fouli and Craig Huneke
- Subjects
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NOETHERIAN rings , *GENERALIZATION , *MATHEMATICAL analysis , *MATHEMATICS , *NUMERICAL analysis , *ALGEBRA - Abstract
In this paper we discuss various refinements and generalizations of a theorem of Sankar Dutta and Paul Roberts. Their theorem gives a criterion for $ d$-dimensional Noetherian Cohen-Macaulay local ring to be a system of parameters, i.e., to have height $ d$ [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
30. On subspace-hypercyclic operators.
- Subjects
- *
OPERATOR theory , *MATHEMATICS , *MATHEMATICAL analysis , *ALGEBRA , *NUMERICAL analysis ,QUESTIONS & answers - Abstract
In this paper we study an operator $ T$ which is $ M$ of $ E$-hypercyclic and use it to answer negatively two questions asked by Madore and Martínez-Avendaño. We also give a sufficient condition for $ T$-hypercyclic for all finite co-dimensional subspaces $ M$. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
31. A remark on the maximal operator for radial measures.
- Subjects
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OPERATOR theory , *MATHEMATICAL proofs , *MATHEMATICS , *MATHEMATICAL analysis , *ALGEBRA , *NUMERICAL analysis - Abstract
The purpose of this paper is to prove that there exist measures $ d\mu(x)=\gamma(x)dx$ $ \gamma(x)=\gamma_{0}(\vert x\vert)$ $ \gamma_{0}$ $ \mathcal{M}_{\mu}$ does not map $ L^{p}_{\mu}(\mathbb{R}^{n})$ $ L^{p}_{\mu}(\mathbb{R}^{n})$. This result answers an open question of P. Sjögren and F. Soria. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
32. Gradient-Type Methods: A Unified Perspective in Computer Science and Numerical Analysis.
- Author
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Fanelli, Stefano
- Subjects
- *
ALGORITHMS , *COMPUTER science , *MATHEMATICS , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
This paper presents a general and comprehensive description of Optimization Methods, and Algorithms from a novel viewpoint. It is shown, in particular, that Direct Methods, Iterative Methods, and Computer Science Algorithms belong to a well-defined general class of both Finite and Infinite Procedures, characterized by suitable descent directions. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
33. Some Sandwich Theorems for Certain Analytic Functions Defined by Convolution.
- Author
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Aouf, M. K. and Mostafa, A. O.
- Subjects
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DIFFERENTIAL calculus , *CALCULUS , *DIFFERENTIAL equations , *MATHEMATICAL convolutions , *MATHEMATICAL functions , *INTEGRALS , *MATHEMATICAL analysis , *MATHEMATICS , *NUMERICAL analysis - Abstract
Abstract. In this paper, we obtain some applications of first order differential subordination and superordination results for some analytic functions defined by convolution. [ABSTRACT FROM AUTHOR]
- Published
- 2010
34. GRAPHIC AND REPRESENTABLE FUZZIFYING MATROIDS.
- Author
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CHUN-E HUANG
- Subjects
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MATROIDS , *FUZZY graphs , *TREE graphs , *MATHEMATICAL analysis , *GRAPHIC methods , *NUMERICAL analysis , *MATHEMATICS - Abstract
In this paper, a fuzzifying matroid is induced respectively from a fuzzy graph and a fuzzy vector subspace. The concepts of graphic fuzzifying matroid and representable fuzzifying matroid are presented and some properties of them are discussed. In general, a graphic fuzzifying matriod can not be representable over any field. But when a fuzzifying matroid is isomorphic to a fuzzifying cycle matroid which is induced by a fuzzy tree, it is a representable over any field. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
35. SOME DIFFERENCE SEQUENCES DEFINED BY A SEQUENCE OF MODULUS FUNCTIONS.
- Author
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BATAINEH, AHMAD H. A. and SULAIMAN, IBRAHIM M. A.
- Subjects
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SEQUENCE spaces , *GENERALIZATION , *MATHEMATICAL functions , *MATHEMATICAL analysis , *ALGEBRA , *NUMERICAL analysis , *MATHEMATICS - Abstract
The idea of difference sequence spaces was introduced by Kizmaz [6], and this concept was generalized by Bektas and Colak [1]. In this paper, we define the sequence spaces c0(F, Δmu x) and l∞(F, Δmu x), where F = (fk) is a sequence of modulus functions, and examine some inclusion relations and properties of these spaces. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
36. A Filled Function Approach for Nonsmooth Constrained Global Optimization.
- Author
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Weixiang Wang, Youlin Shang, and Ying Zhang
- Subjects
- *
MATHEMATICAL optimization , *ALGORITHMS , *MATHEMATICS , *MATHEMATICAL analysis , *NUMERICAL analysis - Abstract
A novel filled function is given in this paper to find a global minima for a nonsmooth constrained optimization problem. First, a modified concept of the filled function for nonsmooth constrained global optimization is introduced, and a filled function, which makes use of the idea of the filled function for unconstrained optimization and penalty function for constrained optimization, is proposed. Then, a solution algorithm based on the proposed filled function is developed. At last, some preliminary numerical results are reported. The results show that the proposed approach is promising. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
37. Meromorphic functions in the unit disc that share values in an angular domain
- Author
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Mao, Zhiqiang and Liu, Huifang
- Subjects
- *
MEROMORPHIC functions , *BOREL sets , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: In this paper, we investigate the uniqueness of meromorphic functions in the unit disc and consider the relation between the Borel points and shared-values of meromorphic functions in an angular domain. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
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38. On the Semi-bounded Solution of Cauchy Type Singular Integral Equations of the First Kind.
- Author
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Abdulkawi, M., Eshkuvatov, Z. K., and Nik Long, N. M. A.
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APPROXIMATION theory , *INTEGRAL equations , *FUNCTIONAL equations , *CHEBYSHEV polynomials , *FUNCTIONAL analysis , *DENSITY functionals , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
This paper presents an efficient approximate method to obtain a numerical solution, which is bounded at the end point x = -1, for Cauchy type singular integral equations of the first kind on the interval [-1,1]. The solution is derived by approximating the unknown density function using the weighted Chebyshev polynomials of the third kind, and then computing the Cauchy singular integral which is obtained analytically. The known force function is interpolated using the Chebyshev polynomials of the fourth kind. The exactness of this approximate method is shown for characteristic equation when the force function is a cubic. Particular result is also given to show the exactness of this method. [ABSTRACT FROM AUTHOR]
- Published
- 2009
39. Equivalence of Pepin's and the Lucas-Lehmer Tests.
- Author
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Jaroma, John H.
- Subjects
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FERMAT numbers , *PRIME numbers , *NATURAL numbers , *NUMBER theory , *FACTORS (Algebra) , *ALGEBRA , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Pepin's test provides a necessary and sufficient condition for a Fermat number to be prime. The Lucas-Lehmer test does similarly for a Mersenne number. These tests share a common nature. However, this is evident neither by their usual statements nor their usual treatment in the literature. Furthermore, it is unusual to even find a proof of the latter result in elementary textbooks. The intent of this paper is to bring to light the equivalent structure of these two primality tests [ABSTRACT FROM AUTHOR]
- Published
- 2009
40. A computational method for a class of non-standard time optimal control problems involving multiple time horizons
- Author
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Farhadinia, B., Teo, K.L., and Loxton, R.C.
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CALCULUS of variations , *MATHEMATICAL optimization , *MATHEMATICAL analysis , *NUMERICAL analysis , *MAXIMA & minima , *MATHEMATICS - Abstract
Abstract: In this paper, we consider a class of non-standard time optimal control problems involving a dynamical system consisting of multiple subsystems evolving over different time horizons. Different subsystems are required to reach their respective target sets at different termination times. The goal is to minimize the maximum of these termination times. By introducing a discrete variable to represent the system termination ordering, we reformulate this problem as a discrete optimization problem. A discrete filled function method is developed to solve this discrete optimization problem. For illustration, a numerical example is solved. [Copyright &y& Elsevier]
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- 2009
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41. A Linear Relaxation Technique for the Position Analysis of Multiloop Linkages.
- Author
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Porta, Josep M., Ros, Lluís, and Thomas, Federico
- Subjects
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RELAXATION methods (Mathematics) , *NUMERICAL analysis , *EQUATIONS , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
This paper presents a new method to isolate all configurations that a multiloop linkage can adopt. The problem is tackled by means of formulation and resolution techniques that fit particularly well together. The adopted formulation yields a system of simple equations (only containing linear, bilinear, and quadratic monomials, and trivial trigonometric terms for the helical pair only) whose structure is later exploited by a branch-and-prune method based on linear relaxations. The method is general, as it can be applied to linkages with single or multiple loops with arbitrary topology, involving lower pairs of any kind, and complete, as all possible solutions get accurately bounded, irrespective of whether the linkage is rigid or mobile. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
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42. Oscillatory criteria for Third-Order difference equation with impulses
- Author
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Li, Qiaoluan, Zhang, Zhenguo, Guo, Fang, Liu, Zhiyong, and Liang, Haiyan
- Subjects
- *
OSCILLATION theory of difference equations , *OSCILLATIONS , *MATHEMATICAL analysis , *MATHEMATICS , *NUMERICAL analysis - Abstract
Abstract: In this paper, we investigate the oscillation of Third-order difference equation with impulses. Some sufficient conditions for the oscillatory behavior of the solutions of Third-order impulsive difference equations are obtained. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
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43. On a new code,
- Author
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Basu, M., Rahaman, Md.M., and Bagchi, S.
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ERROR analysis in mathematics , *MATHEMATICAL analysis , *MATHEMATICS , *NUMERICAL analysis , *MATHEMATICAL statistics , *STATISTICS - Abstract
Abstract: A binary linear code in with dimension and minimum distance is called an code. A design is a set of points together with a collection of -subsets of (called a block) such that every -subset of is contained in exactly blocks. A constant length code which corrects different numbers of errors in different code words is called a non-uniform error correcting code. Parity sectioned reduction of a linear code gives a non-uniform error correcting code. In this paper a new code, , is developed. The error correcting capability of this code is . It is shown that this code holds a design. Also the parity sectioned reduction code after deleting the same positions of each code word of this code holds a design for and . [Copyright &y& Elsevier]
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- 2009
- Full Text
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44. SUPERCONVERGENCE OF SOME PROJECTION APPROXIMATIONS FOR WEAKLY SINGULAR INTEGRAL EQUATIONS USING GENERAL GRIDS.
- Author
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Amosov, Andrey, Ahues, Mario, and Largillier, Alain
- Subjects
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STOCHASTIC convergence , *INTEGRAL equations , *FUNCTIONAL equations , *GALERKIN methods , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
This paper deals with superconvergence phenomena in general grids when projectionbased approximations are used for solving Fredholm integral equations of the second kind with weakly singular kernels. Four variants of the Galerkin method are considered. They are the classical Galerkin method, the iterated Galerkin method, the Kantorovich method, and the iterated Kantorovich method. It is proved that the iterated Kantorovich approximation exhibits the best superconvergence rate if the right-hand side of the integral equation is nonsmooth. All error estimates are derived for an arbitrary grid without any uniformity or quasi-uniformity condition on it, and are formulated in terms of the data without any additional assumption on the solution. Numerical examples concern the equation governing transfer of photons in stellar atmospheres. The numerical results illustrate the fact that the error estimates proposed in the different theorems are quite sharp, and confirm the superiority of the iterated Kantorovich scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2009
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45. REHABILITATION OF THE LOWEST-ORDER RAVIART-THOMAS ELEMENT ON QUADRILATERAL GRIDS.
- Author
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Bochev, Pavel B. and Ridzal, Denis
- Subjects
- *
STOCHASTIC convergence , *FINITE element method , *NUMERICAL analysis , *EQUATIONS , *GALERKIN methods , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
A recent study [D. N. Arnold, D. Boffi, and R. S. Falk, SIAM J. Numer. Anal., 42 (2005), pp. 2429-2451] reveals that convergence of finite element methods using H(div , O)-compatible finite element spaces deteriorates on nonaffine quadrilateral grids. This phenomena is particularly troublesome for the lowest-order Raviart-Thomas elements, because it implies loss of convergence in some norms for finite element solutions of mixed and least-squares methods. In this paper we propose reformulation of finite element methods, based on the natural mimetic divergence operator [M. Shashkov, Conservative Finite Difference Methods on General Grids, CRC Press, Boca Raton, FL, 1996], which restores the order of convergence. Reformulations of mixed Galerkin and leastsquares methods for the Darcy equation illustrate our approach. We prove that reformulated methods converge optimally with respect to a norm involving the mimetic divergence operator. Furthermore, we prove that standard and reformulated versions of the mixed Galerkin method lead to identical linear systems, but the two versions of the least-squares method are veritably different. The surprising conclusion is that the degradation of convergence in the mixed method on nonaffine quadrilateral grids is superficial, and that the lowest-order Raviart-Thomas elements are safe to use in this method. However, the breakdown in the least-squares method is real, and there one should use our proposed reformulation. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
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46. NEW INTERIOR PENALTY DISCONTINUOUS GALERKIN METHODS FOR THE KELLER-SEGEL CHEMOTAXIS MODEL.
- Author
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Epshteyn, Yekaterina and Kurganov, Alexander
- Subjects
- *
GALERKIN methods , *NUMERICAL analysis , *MATHEMATICAL models , *REACTION-diffusion equations , *PARABOLIC differential equations , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
We develop a family of new interior penalty discontinuous Galerkin methods for the Keller-Segel chemotaxis model. This model is described by a system of two nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction-diffusion equation for the chemoattractant concentration. It has been recently shown that the convective part of this system is of a mixed hyperbolic-elliptic-type, which may cause severe instabilities when the studied system is solved by straightforward numerical methods. Therefore, the first step in the derivation of our new methods is made by introducing the new variable for the gradient of the chemoattractant concentration and by reformulating the original Keller-Segel model in the form of a convection-diffusionreaction system with a hyperbolic convective part. We then design interior penalty discontinuous Galerkin methods for the rewritten Keller-Segel system. Our methods employ the central-upwind numerical fluxes, originally developed in the context of finite-volume methods for hyperbolic systems of conservation laws. In this paper, we consider Cartesian grids and prove error estimates for the proposed high-order discontinuous Galerkin methods. Our proof is valid for pre-blow-up times since we assume boundedness of the exact solution. We also show that the blow-up time of the exact solution is bounded from above by the blow-up time of our numerical solution. In the numerical tests presented below, we demonstrate that the obtained numerical solutions have no negative values and are oscillation-free, even though no slope-limiting technique has been implemented. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
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47. STABILITY PRESERVATION ANALYSIS FOR FREQUENCY-BASED METHODS IN NUMERICAL SIMULATION OF FRACTIONAL ORDER SYSTEMS.
- Author
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Tavazoei, Mohammad Saleh, Haeri, Mohammad, Bolouki, Sadegh, and Siami, Milad
- Subjects
- *
NUMERICAL analysis , *CURVES , *STABILITY (Mechanics) , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
In this paper, the frequency domain-based numerical methods for simulation of fractional order systems are studied in the sense of stability preservation. First, the stability boundary curve is exactly determined for these methods. Then, this boundary is analyzed and compared with an accurate (ideal) boundary in different frequency ranges. Also, the critical regions in which the stability does not preserve are determined. Finally, the analytical achievements are confirmed via some numerical illustrations. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
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48. DISCONTINUOUS DISCRETIZATION FOR LEAST-SQUARES FORMULATION OF SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS IN ONE AND TWO DIMENSIONS.
- Author
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Runchang Lin
- Subjects
- *
LEAST squares , *DIMENSIONS , *BOUNDARY value problems , *DIFFERENTIAL equations , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
In this paper, we consider the singularly perturbed reaction-diffusion problem in one and two dimensions. The boundary value problem is decomposed into a first-order system to which a suitable weighted least-squares formulation is proposed. A robust, stable, and efficient approach is developed based on local discontinuous Galerkin (LDG) discretization for the weak form. Uniform error estimates are derived. Numerical examples are presented to illustrate the method and the theoretical results. Comparison studies are made between the proposed method and other methods. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
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49. Superconvergence of finite element method for the Signorini problem
- Author
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Li, Ming-xia, Lin, Qun, and Zhang, Shu-hua
- Subjects
- *
FINITE element method , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: In this paper, we study the superconvergence of the frictionless Signorini problem. When approximated by bilinear finite elements, by virtue of the information on the contact zone, we can derive a superconvergence rate of under a proper regularity assumption. Finally, a numerical test is given to verify our result. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
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50. Distinguishing properties of Arens irregularity.
- Author
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Zhiguo Hu and Matthias Neufang
- Subjects
- *
IRREGULARITIES of distribution (Number theory) , *BANACH algebras , *COMMUTATIVE algebra , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICS - Abstract
In this paper, we present a number of examples of commutative Banach algebras with various Arens irregularity properties. These examples illustrate in particular that strong Arens irregularity and extreme non-Arens regularity, the two natural concepts of ``maximal'' Arens irregularity for general Banach algebras as introduced by Dales-Lau and Granirer, respectively, are indeed distinct. Thereby, an open question raised by several authors is answered. We also link these two properties to another natural Arens irregularity property. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
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