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Kjell Eriksson - One of the best experts on this subject based on the ideXlab platform.
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a domain independent Integral Expression for the crack extension force of a curved crack in three dimensions
Journal of The Mechanics and Physics of Solids, 2002Co-Authors: Kjell ErikssonAbstract:An Integral Expression that is domain independent in curvilinear coordinates and compatible with zero divergence of Eshelby's (Phil. Trans. Roy. Soc. (London) 244 (1951) 87.) energy momentum tensor was obtained from the principle of virtual work. By applying Eshelby's definition of the force on a material defect a general Expression of the crack extension force for a curved crack in three dimensions, here called the F-Integral, was derived from the domain independent Integral Expression. The F-Integral is given explicitly for a number of curved cracks and found to be in agreement with previously known solutions, when available. The influence of crack surface and crack front curvature upon the various forms of the F-Integral is discussed. The F-Integral presented in this work is a generalisation of the J-Integral (Rice, J. Appl. Mech. 35 (1968) 379.) to curved cracks in orthogonal curvilinear coordinates.
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a path independent Integral for the crack extension force of the circular arc crack
Engineering Fracture Mechanics, 2000Co-Authors: Maria Lorentzon, Kjell ErikssonAbstract:Abstract A path independent Integral Expression for the crack extension force of a two-dimensional circular arc crack is presented. The Integral Expression, which consists of a contour and an area Integral, is derived from the principle of virtual work. It is implemented into a FEM post-processing program and the crack extension force is calculated for a circular arc crack in a linear elastic material. Comparison with exact solutions by Cotterell and Rice [10] for the effective elastic stress intensity factor shows acceptable accuracy for the numerical procedure used.
Tibor K. Pogány - One of the best experts on this subject based on the ideXlab platform.
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Integral form of the com poisson renormalization constant
Statistics & Probability Letters, 2016Co-Authors: Tibor K. PogányAbstract:In this brief note an Integral Expression is presented for the COM–Poisson renormalization constant Z(λ,ν) on the real axis.
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Integral form of the com poisson normalization constant
arXiv: Statistics Theory, 2016Co-Authors: Tibor K. PogányAbstract:In this brief note an Integral Expression is presented for the COM-Poisson renormalization constant $Z(\lambda, \nu)$ on the real axis.
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laplace type Integral Expressions for a certain three parameter family of generalized mittag leffler functions with applications involving complete monotonicity
Journal of The Franklin Institute-engineering and Applied Mathematics, 2014Co-Authors: živorad Tomovski, Tibor K. Pogány, H M SrivastavaAbstract:Abstract In this paper, we derive a Laplace type Integral Expression for the function e α , β γ ( t ; λ ) defined by e α , β γ ( t ; λ ) ≔ t β − 1 E α , β γ ( − λ t α ) , where E α , β γ ( z ) stands for the generalized three-parameter Mittag–Leffler function occurring in many interesting applied problems involving fractional differential equations. Our result is shown to enable us to extend certain findings by Mainardi (2010) [21] and others. As an application of the obtained Laplace type Integral representation, we prove the complete monotonicity of the function e α , β γ ( t ; λ ) . We also establish several related positivity results and some uniform upper bounds for the function e α , β γ ( t ; λ ) .
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Integral representation for neumann series of bessel functions
Proceedings of the American Mathematical Society, 2009Co-Authors: Tibor K. Pogány, Endre SuliAbstract:A closed Integral Expression is derived for Neumann series of Bessel functions ― a series of Bessel functions of increasing order ― over the set of real numbers.
Jerry A Hausman - One of the best experts on this subject based on the ideXlab platform.
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using a laplace approximation to estimate the random coefficients logit model by nonlinear least squares laplace approximation of the random coefficients logit model
International Economic Review, 2007Co-Authors: Matthew Harding, Jerry A HausmanAbstract:Current methods of estimating the random coefficients logit model employ simulations of the distribution of the taste parameters through pseudo-random sequences. These methods suffer from difficulties in estimating correlations between parameters and computational limitations such as the curse of dimensionality. This article provides a solution to these problems by approximating the Integral Expression of the expected choice probability using a multivariate extension of the Laplace approximation. Simulation results reveal that our method performs very well, in terms of both accuracy and computational time.
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using a laplace approximation to estimate the random coefficients logit model by nonlinear least squares
International Economic Review, 2006Co-Authors: Matthew Harding, Jerry A HausmanAbstract:Current methods of estimating the random coefficients logit model employ simulations of the distribution of the taste parameters through pseudo-random sequences. These methods suffer from difficulties in estimating correlations between parameters and computational limitations such as the curse of dimensionality. This article provides a solution to these problems by approximating the Integral Expression of the expected choice probability using a multivariate extension of the Laplace approximation. Simulation results reveal that our method performs very well, in terms of both accuracy and computational time.
Guy A E Vandenbosch - One of the best experts on this subject based on the ideXlab platform.
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the expansion wave concept i efficient calculation of spatial green s functions in a stratified dielectric medium
IEEE Transactions on Antennas and Propagation, 1998Co-Authors: Filip Demuynck, Guy A E Vandenbosch, A Van De CapelleAbstract:A procedure is given to perform the inverse Fourier transformation relating a spatial Green's function to its spectral equivalent. The procedure is applied to the spectral Green's functions of the double scalar mixed-potential Integral Expression formulation of the electromagnetic field in a stratified dielectric medium. The extraction technique is used to annihilate every type of "problematic" behavior of the spectral Green's functions. Every annihilating function is inverse Fourier transformed analytically. It is shown that the annihilation of both the surface wave poles and the singularities at the branch point results in a set of analytical spatial functions, which are a very good approximation of the exact spatial Green's function down to relatively small lateral distances.
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mixed potential Integral Expression formulation of the electric field in a stratified dielectric medium application to the case of a probe current source
IEEE Transactions on Antennas and Propagation, 1992Co-Authors: Guy A E Vandenbosch, A Van De CapelleAbstract:The well-known procedure for determining the electric field in a structure consisting of an arbitrary number of planar dielectric layers is modified in order to obtain a form specially suited for the analysis of multiprobe multipath configurations. In general, the field is generated by arbitrary currents in the layers and arbitrary sheet currents in the transitions between the layers. The currents may be electric as well as magnetic, and the dielectric layers are isotropic, homogeneous, and lossy. The procedure results in Green's functions especially suited for the analysis of multiprobe multipatch configurations. They can be used in an efficient mixed-potential Integral Expression formulation. The theoretical procedure is applied in the case of a probe current source situated in one of the dielectric layers of the structure. For this probe current a highly efficient attachment current distribution is derived. Comparison of measured and calculated results for example structures proves the accuracy of both the approach and the attachment mode. >
A Van De Capelle - One of the best experts on this subject based on the ideXlab platform.
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the expansion wave concept i efficient calculation of spatial green s functions in a stratified dielectric medium
IEEE Transactions on Antennas and Propagation, 1998Co-Authors: Filip Demuynck, Guy A E Vandenbosch, A Van De CapelleAbstract:A procedure is given to perform the inverse Fourier transformation relating a spatial Green's function to its spectral equivalent. The procedure is applied to the spectral Green's functions of the double scalar mixed-potential Integral Expression formulation of the electromagnetic field in a stratified dielectric medium. The extraction technique is used to annihilate every type of "problematic" behavior of the spectral Green's functions. Every annihilating function is inverse Fourier transformed analytically. It is shown that the annihilation of both the surface wave poles and the singularities at the branch point results in a set of analytical spatial functions, which are a very good approximation of the exact spatial Green's function down to relatively small lateral distances.