July 14, 2012 Tags: ABELIAN groups, FUNCTIONAL analysis, Haar, INTEGRALS, LORENTZ spaces, MATHEMATICAL models, MULTIPLIERS (Mathematical analysis), NUMERICAL analysis
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The purpose of this paper is to introduce and study a new class of nonlinear mixed family of random fuzzy and crisp operator equation couples in fuzzy normed spaces based on the random version of the theory of (φ, ψ)-contractor due to Mihet. Further, some new random iterative algorithms for solving this kind of nonlinear operator equation couples in fuzzy normed spaces are constructed and the convergence of iterative sequences generated by the algorithms under joint orbitally complete conditions is proved. As applications, some new common fixed point theorems for a mixed family of fuzzy and crisp operators in fuzzy normed spaces are also given. The results presented in this paper improve and generalize the corresponding results of recent works. [ABSTRACT FROM AUTHOR]
Read MoreFor the large sparse system of weakly nonlinear equations, based on separable property and strong dominance between the linear and the nonlinear terms and on the asymmetric Hermitian and skew-Hermitian splitting (AHSS) of the coefficient matrix, we establish two nonlinear composite iteration schemes, called Picard-AHSS and nonlinear AHSS-like methods. The advantage of these methods is that they only need to solve the linear sub-systems of constant coefficient matrices. In addition, these methods can also take full advantage of the dominance of Hermitian part. Therefore, computational workloads and computer storage may be saved in actual implementations. Theoretical analysis show that these new iteration methods are local convergent under suitable conditions. Numerical results show that both Picard-AHSS and nonlinear AHSS-like iteration methods are feasible and effective for the large scale system of weakly nonlinear equations, especially when the Hermitian part of the coefficient matrix is dominant. [ABSTRACT FROM AUTHOR]
Read MoreJuly 12, 2012 Tags: BINOMIAL coefficients, HERMITIAN operators, ITERATIVE methods (Mathematics), MATRIX inequalities, NONLINEAR models (Statistics), NONLINEAR systems, NUMERICAL analysis
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The one-dimensional fractional diffusion equation is studied systematically using the non-polynomial spline method. The Caputo fractional derivative is used for formulation. An example is solved to assess the accuracy of the method. The numerical results are obtained for different values (n) of equation. An effective and easy-to-use method for solving such equations is needed. [ABSTRACT FROM AUTHOR]
Read MoreJuly 12, 2012 Tags: EQUATIONS -- Numerical solutions, FRACTIONAL integrals, HEAT equation, NUMERICAL analysis, POLYNOMIALS, PROBLEM solving, SPLINE theory
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The boundedness and compactness of the integral-type operator Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. where g is a holomorphic function on the unit disk and n ∈ ℕ0, between weighted Bergman spaces are characterized. [ABSTRACT FROM AUTHOR]
Read MoreJuly 10, 2012 Tags: BERGMAN spaces, EQUATIONS -- Numerical solutions, FACULTY integration, HOLOMORPHIC functions, LINEAR operators, MATHEMATICAL models, NUMERICAL analysis
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Eshaghi Gordji and Bodaghi [2] proved the Hyers-Ulam stability of quadratic double centralizers on Banach algebras for the system of the functional equations f(kx + y) + f(kx – y) = 2k² f(x) + 2f(y) & f(xy) = f(x)y for a fixed integer k greater than 1. One can easily show that all the quadratic double centralizers (L, R) in the results are (0,0). The results are trivial. In this paper, we correct the results. Using the direct method, we prove the Hyers-Ulam stability of quadratic double centralizers on Banach algebras for the system of the functional equations f(kx + y) + f(kx – y) = 2k² f(x) + 2f(y) & f(xy) = f(x)y² for a fixed integer k greater than 1. [ABSTRACT FROM AUTHOR]
Read MoreJuly 9, 2012 Tags: BANACH algebras, EQUATIONS, FUNCTION algebras, FUNCTIONAL equations, MATHEMATICAL proofs, Natural, NUMBERS, NUMERICAL analysis, Quadratic
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A new weighted bivariate blending rational spline with parameters is constructed based on function values of a function only. The interpolation is C¹ in the whole interpolating region under the condition which free parameters is not limited. This paper deals with the properties of the interpolation surface, including the properties of basis function, the properties of integral weighted coefficients and bounded property of the interpolation. In order to meet the needs of practical design, an interpolation technique is employed to control the shape of surfaces. The method of value control of the interpolation at any point in the interpolating region is developed. This control method can be applied to modify the local shape of an interpolating surface by selecting suitable parameters simply. [ABSTRACT FROM AUTHOR]
Read MoreJuly 8, 2012 Tags: BINOMIAL coefficients, COMPUTER-aided design, FUNCTIONAL equations, INTERPOLATION, MATHEMATICAL models, MATHEMATICAL proofs, NUMERICAL analysis
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Laser forming has attracted considerable attention as a viable technique to form sheet metal by thermal residual stresses. Many numerical and experimental investigations of laser forming processes were carried out to understand the mechanisms and the effects of various parameters on the characteristics of the formed parts. The objective of this work is to investigate the effect of different beam geometries on laser bending process of metal sheets, which is dominated by temperature gradient mechanism (TGM). In this paper a comprehensive thermal and structural finite element analysis is conducted to investigate the effect that these laser beam geometries have on the process and the final product characteristics. To achieve this, the temperature distribution, deformation, plastic strains and stresses produced by different beam geometries are compared numerically. The findings suggest that beam geometry could be an important controlling parameter for bending angle, edge effect and bend radius. [ABSTRACT FROM AUTHOR]
Read MoreJuly 8, 2012 Tags: BENDING, DEFORMATIONS (Mechanics), FINITE element method, LASER beams, NUMERICAL analysis, STRAINS & stresses, TEMPERATURE distribution
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This paper presents the stress and displacement fields in a functionally graded material (FGM) caused by a load. The FGM is a graded material of Si3N4-based ceramics and is assumed to be of semi-infinite extent. The load is a distributed loading over a rectangular area that is parallel to the external surface of the FGM and either on its external surface or within its interior space. The point-load analytical solutions or so-called Yue’s solutions are used for the numerical integration over the distributed loaded area. The loaded area is discretized into 200 small equal-sized rectangular elements. The numerical integration is carried out with the regular Gaussian quadrature. Weak and strong singular integrations encountered when the field points are located on the loaded plane, are resolved with the classical methods in boundary element analysis. The numerical integration results have high accuracy. [ABSTRACT FROM AUTHOR]
Read MoreJune 1, 2012 Tags: MATERIALS -- Dynamic testing, NUMERICAL analysis, NUMERICAL integration, STRAINS & stresses, STRENGTH of materials, STRUCTURAL analysis (Engineering)
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A numerical finite element method (FEM) model for studying laser cladding of a pre-placed powder bed under a pulse mode condition was developed, which takes into account the phenomenon of partial remelting of the clad track, the effect of heat accumulation resulting from successive pulses, and the geometries of the clad coating. The model was used to study the cladding behaviour of an Al-Si alloy on magnesium alloy WE43. Both the theoretical predictions and experimental results showed that it is possible to obtain a clad coating on magnesium alloys, with a relatively low dilution level, under the pulse mode condition. In this respect, the model provides a sound basis for the determination of the process operation window for achieving a low dilution level. [ABSTRACT FROM AUTHOR]
Read MoreMay 19, 2012 Tags: DILUTION, FINITE element method, MAGNESIUM alloys, METAL cladding, METAL coating, NUMERICAL analysis, PULSE modulation (Electronics)
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