In this paper, wave propagation is considered in a medium described by fractional-order model, which formulated with the use of two-sided fractional derivative Ortigueira and Machado. Although relation to causality clearly specified its definition, there no obvious between transfer function induced derivative. Hence, system investigated; output an electromagnetic signal propagating media time-d...

Abstract In this work the Monte Carlo method, introduced recently by authors for orders of differentiation between zero and one, is further extended to higher than one. Two approaches have been developed on way. The first approach based interpreting coefficients Grünwald–Letnikov fractional differences as so called signed probabilities, which in case one can be negative or positive. We demonstr...

The purpose of this study is to evaluate the value of cytokeratin (CK) MNF116 and vimentin in the differential diagnosis of malignant pleural effusions. There were evaluated smears from 30 patients with pleural effusions stained with May-Grünwald Giemsa and Papanicolaou techniques for the routine cytological diagnosis. Additional smears were immunostained with CK MNF116 and vimentin using LSAB2...

Decoupled fractional Laplacian wave equation can describe the seismic wave propagation in attenuating media. Fourier pseudospectral implementations, which solve the equation in spatial frequency domain, are the only existing methods for solving the equation. For the earth media with curved boundaries, the pseudospectral methods could be less attractive to handle the irregular computational doma...

Fractional order partial differential equations, as generalizations of classical integer order partial differential equations, are increasingly used to model problems in fluid flow, finance and other areas of application. In this paper we discuss a practical alternating directions implicit method to solve a class of two-dimensional initial-boundary value fractional partial differential equation...

Fractional order diffusion equations are generalizations of classical diffusion equations, treating super-diffusive flow processes. In this paper, we examine a practical numerical method which is second-order accurate in time and in space to solve a class of initial-boundary value fractional diffusive equations with variable coefficients on a finite domain. An approach based on the classical Cr...

Special cases of this theorem have been proved by Erdös-Grünwald' and Webster2 (the cases a = 1/2 and a = 3/2) . If there is no danger of confusion we shall omit the upper index n in lk`, n ~ (x) . PROOF OF THE THEOREM . It clearly suffices to consider the lk(x) with -1 =< xk < 0 . From the differential equation of the ultraspherical polynomials' we obtain (") lk(xk) = {«~xk) _ axk z zP„ (xk) 1...

Abbreviations: A0: Cross-Section; BDNF: Brain Derived Growth Factor; BMP: Bone Morphogenetic Proteins: CGF: Concentrated Growth Factors: EGM: Endothelial Growth Medium:EBM-2: Endothelial Basal Medium 2; F: Load; FGM: Fibroblast Growth Medium; FBM: Fibroblast Basal Medium; H: Height; H0: Initial Height; HE: Hematoxylin And Eosin Staining; HOB: Human Osteoblasts; HRP: Horseradish Peroxidase; HUVE...