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Effective boost and "point-form" approach  [PDF]
B. Desplanques,L. Theu?l,S. Noguera
Physics , 2001, DOI: 10.1103/PhysRevC.65.038202
Abstract: Triangle Feynman diagrams can be considered as describing form factors of states bound by a zero-range interaction. These form factors are calculated for scalar particles and compared to point-form and non-relativistic results. By examining the expressions of the complete calculation in different frames, we obtain an effective boost transformation which can be compared to the relativistic kinematical one underlying the present point-form calculations, as well as to the Galilean boost. The analytic expressions obtained in this simple model allow a qualitative check of certain results obtained in similar studies. In particular, a mismatch is pointed out between recent practical applications of the point-form approach and the one originally proposed by Dirac.
Parity Transformation in the Front Form  [PDF]
M. Sawicki,D. V. Ahluwalia
Physics , 1993,
Abstract: By considering the parity-transformation properties of the $(1/2,\,0)$ and $(0,\,1/2)$ fields in the {\it front form} we find ourselves forced to study the front-form evolution both along $x^+$ and $x^-$ directions. As a by product, we find that half of the dynamical degrees of freedom of a full theory live on the $x^+=0$ surface and the other half on the $x^-=0$ surface. Elsewhere, Jacob shows how these results are required to build a satisfactory, and internally consistent, front-form quantum field theory.
Closed form expressions for moments of the beta Weibull distribution
Cordeiro, Gauss M;Simas, Alexandre B;Sto?ic, Borko D;
Anais da Academia Brasileira de Ciências , 2011, DOI: 10.1590/S0001-37652011000200002
Abstract: the beta weibull distribution was first introduced by famoye et al. (2005) and studied by these authors and lee et al. (2007). however, they do not give explicit expressions for the moments. in this article, we derive explicit closed form expressions for the moments of this distribution, which generalize results available in the literature for some sub-models. we also obtain expansions for the cumulative distribution function and rényi entropy. further, we discuss maximum likelihood estimation and provide formulae for the elements of the expected information matrix. we also demonstrate the usefulness of this distribution on a real data set.
Conditional Expressions for Blind Deconvolution: Derivative form  [PDF]
S. Aogaki,I. Moritani,T. Sugai,F. Takeutchi,F. M. Toyama
Computer Science , 2006,
Abstract: We developed novel conditional expressions (CEs) for Lane and Bates' blind deconvolution. The CEs are given in term of the derivatives of the zero-values of the z-transform of given images. The CEs make it possible to automatically detect multiple blur convolved in the given images all at once without performing any analysis of the zero-sheets of the given images. We illustrate the multiple blur-detection by the CEs for a model image
Closed form expressions for Bayesian sample size  [PDF]
B. Clarke,Ao Yuan
Mathematics , 2006, DOI: 10.1214/009053606000000308
Abstract: Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the data. Thus, when a sample size criterion is formalized in terms of a functional of the posterior, its value is a random variable. Generally, such functionals have means under the true distribution. We give asymptotic expressions for the expected value, under a fixed parameter, for certain types of functionals of the posterior density in a Bayesian analysis. The generality of our treatment permits us to choose functionals that encapsulate a variety of inference criteria and large ranges of error bounds. Consequently, we get simple inequalities which can be solved to give minimal sample sizes needed for various estimation goals. In several parametric examples, we verify that our asymptotic bounds give good approximations to the expected values of the functionals they approximate. Also, our numerical computations suggest our treatment gives reasonable results.
Compact form of expressions for inductance calculation of meander inductors  [PDF]
Stojanovi? Goran,?ivanov Ljiljana,Damjanovi? Mirjana
Serbian Journal of Electrical Engineering , 2004, DOI: 10.2298/sjee0403057s
Abstract: The quality of modeling and analyzing of RF IC with planar inductors extremely depends on accuracy of expression for inductance. In this paper efficient methods for total inductance calculation of meander inductor are given. By using proposed algorithm, we are able to predict correctly all inductance variations introduced by varying geometry parameters. Our. developed program gives possibility for fast and accurate inductance calculation for meander inductor, while new expression in monomial form is useful for optimization of this inductor. The results validations, given by proposed software tool are conformed by comparison with measured data from literature.
Analytical Form of the Deuteron Wave Function Calculated within the Dispersion Approach  [PDF]
A. F. Krutov,V. M. Muzafarov,V. E. Troitsky
Physics , 2006, DOI: 10.1103/PhysRevC.76.017001
Abstract: We present a convenient analytical parametrization of the deuteron wave function calculated within dispersion approach as a discrete superposition of Yukawa-type functions, in both configuration and momentum spaces.
$B -> πl ν$ Form Factors Calculated on the Light-Front  [PDF]
C. Y. Cheung,C. W. Hwang,W. M. Zhang
Physics , 1996, DOI: 10.1007/s002880050511
Abstract: A consistent treatment of $B\rightarrow \pi l \nu$ decay is given on the light-front. The $B$ to $\pi$ transition form factors are calculated in the entire physical range of momentum transfer for the first time. The valence-quark contribution is obtained using relativistic light-front wave functions. Higher quark-antiquark Fock-state of the $B$-meson bound state is represented effectively by the $|B^*\pi\rangle$ configuration, and its effect is calculated in the chiral perturbation theory. Wave function renormalization is taken into account consistently. The $|B^*\pi\rangle$ contribution dominates near the zero-recoil point ($q^2\simeq 25$ GeV$^2$), and decreases rapidly as the recoil momentum increases. We find that the calculated form factor $f_+(q^2)$ follows approximately a dipole $q^2$-dependence in the entire range of momentum transfer.
Lorentz Transformation Equations in Galilean Form  [PDF]
S. D. Agashe
Physics , 2010,
Abstract: Using the notion, developed in an earlier paper, of "representation" of "position" by a vector in a vector space with an inner product, we show that the Lorentz Transformation Equations relating positions in two different reference frames can be put in a particularly simple form which could be said to be "Galilean". We emphasize that two different reference frames can use a common vector space for representation but with two different inner products. The inner products are defined through the observational set-up of each frame.
Some General Expressions for the Coefficient of the 14th Chern Form  [PDF]
C. C. Briggs
Physics , 1999,
Abstract: Some general expressions are given for the coefficient of the 14th Chern form in terms of the Riemann-Christoffel curvature tensor and some of its concomitants (e.g., Pontrjagin's characteristic tensors) for n-dimensional differentiable manifolds having a general linear connection.
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