The goal of this article is to develop local discontinuous Galerkin (LDG) schemes for solving a time fractional equation describing the ultrasonic wave in homogeneous isotropic porous material. Two novel semi-discrete LDG are designed considered model. constructed by splitting original model into coupled system. first scheme follows traditional method second-order space derivative. second one s...

For many years, liquid-based cytology (LBC) has been developed for cervical cancer screening and not oral cancer, as it requires automated devices. The aim of this study was to compare the utility of centrifugated CLBC preparation with that of direct preparation in oral lesions, by Papanicolaou (Pap) and May Grünwald-Giemsa's (MGG) methods. A total of 100 consecutive cases of oral lesions were ...

The relation showing that the Grünwald-Letnikov and generalised Cauchy derivatives are equal is presented. This establishes a bridge between two different formulations and simultaneously between the classic integer order derivatives and the fractional ones. Starting from the generalised Cauchy derivative formula, new relations are obtained, namely a regularised version that makes the concept of...

The dynamics of the nonlinear Helmholtz Oscillator with fractional order damping is studied in detail. The discretization of the differential equations according to the Grünwald-Letnikov fractional derivative definition in order to get numerical simulations is reported. Comparison between solutions obtained through a fourth-order Runge-Kutta method and the fractional damping system is commented...

A 88-year old woman presented with malnutrition and depressive psychosis. No lymphadenopathy nor hepatomegaly or splenomegaly was noted on clinical examination. A blood count showed haemoglobin 12.6 g/dL, haematocrit 0.38, WBC 6.6×10/L with the lymphocyte count 1.6×10/L and platelet count 184×10/L. Twenty percent of the lymphocytes showed large cytoplasmic inclusions which appeared rectangular ...

In this paper, we presented a novel multi-strain TB model of variable-order fractional derivatives, which incorporates three strains: drug-sensitive, emerging multi-drug resistant (MDR) and extensively drug-resistant (XDR), as an extension for multi-strain TB model of nonlinear ordinary differential equations which developed in 2014 by Arino and Soliman [1]. Numerical simulations for this varia...

A. T. D. Grünwald,1 A. R. Wildes,2,* W. Schmidt,3 E. V. Tartakovskaya,1,4 J. Kwo,5 C. Majkrzak,6 R. C. C. Ward,7 and A. Schreyer1 1GKSS Research Centre, 21502 Geesthacht, Germany 2Institut Laue-Langevin, 38042 Grenoble, France 3IFF, JCNS at ILL, Forschungszentrum Jülich, 38042 Grenoble, France 4Institute for Magnetism of National Ukrainian Academy of Science, 03142 Kiev, Ukraine 5Department of ...

A simple, routine procedure for water miscible glycol methacrylate (GMA) embedding of undecalcified bone marrow cores, which preserves the activity of enzymes useful in diagnosing various haematopoietic disorders, is described. The GMA used in this study has a low acid content that eliminates background staining, and the modified May-Grünwald-Giemsa stain provides good definition and excellent ...

Abstract In this paper we propose a stable finite difference method to solve the fractional reaction–diffusion systems in two-dimensional domain. The space discretization is implemented by weighted shifted Grünwald (WSGD) which results stiff system of nonlinear ordinary differential equations (ODEs). This solved an efficient compact implicit integration factor (cIIF) method. stability second or...