Let β > 1 be a real number and M : R → GL(C) be a uniformly almost periodic matrix-valued function. We study the asymptotic behavior of the product Pn(x) = M(β x) · · ·M(βx)M(x). Under some condition we prove a theorem of Furstenberg-Kesten type for such products of non-stationary random matrices. Theorems of Kingman and Oseledec type are also proved. The obtained results are applied to multipl...

Following recent predictions that the geometric scaling properties of deep inelastic scattering data in inclusive γp collisions are expected also in exclusive diffractive processes, we investigate the diffractive production of vector mesons. Using analytic results in the framework of the BK equation at non-zero momentum transfer, we extend the QCD-inspired saturation model to parametrise the mo...

To determine the universality class of critical phenomena, we propose a method of statistical inference in the scaling analysis of critical phenomena. The method is based on Bayesian statistics, most specifically, the Gaussian process regression. It assumes only the smoothness of a scaling function, and it does not need a form. We demonstrate this method for the finite-size scaling analysis of ...

In this work, we proposed an effective method based on cubic and pantic B-spline scaling functions to solve partial differential equations of fractional order. Our method is based on dual functions of B-spline scaling functions. We derived the operational matrix of fractional integration of cubic and pantic B-spline scaling functions and used them to transform the mentioned equations to a syste...

This paper proposes an effective approach for the scaling registration of m-D point sets. Different from the rigid transformation, the scaling registration can not be formulated into the common least square function due to the ill-posed problem caused by the scale factor. Therefore, this paper designs a novel objective function for the scaling registration problem. The appearance of this object...

We show that recent data from HERA on the proton structure function F2 at small x and large Q 2 provide a direct confirmation of the double asymptotic scaling prediction of perturbative QCD. A linear rise of lnF2 with the scaling variable σ is observed throughout the kinematic region probed at HERA, and the measured slope is in excellent agreement with the QCD prediction. This provides a direct...

introduction: the aim of this study was to evaluate the influence of different levels of external irrigation during irradiation with an erbium, chromium: yttrium-scandium-gallium-garnet (er,cr:ysgg) laser on the roughness and wear of dental tissue during scaling procedures. methods: twenty-five uniradicular bovine teeth had the proximal surfaces planed and divided into 3 regions: upper, middle ...