‎There are a few finite groups that are determined up to isomorphism solely by their order, such as $mathbb{Z}_{2}$ or $mathbb{Z}_{15}$. Still other finite groups are determined by their order together with other data, such as the number of elements of each order, the structure of the prime graph, the number of order components, the number of Sylow $p$-subgroups for each prime $p$, etc. In this...

Fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order. The purpose of this work is to use Hadamard fractional integral to establish some new integral inequalities of Gruss type by using one or two parameters which ensues four main results . Furthermore, other integral inequalities of reverse ...

A convex polyhedron P is k-equiprojective if all of its orthogonal projections, i.e., shadows, except those parallel to the faces of P are k-gon for some fixed value of k. Since 1968 it is an open problem to construct all equiprojective polyhedra. Recently, Hasan and Lubiw [8] have given a characterization of equiprojective polyhedra. Based on their characterization, in this paper we discover s...

In our laboratories some 200 compounds, including phenylacetic acid derivatives, have been studied as possible precursors for new penicillins, and several of these appeared to give rise to new penicillins. In this report, five new penicillins, four of which were obtained in crystalline form, are described and their production, isolation, and characterization discussed. The methods employed in o...

In this study, by a non-negative homogeneous kernel k we prove some extensions of Hardy's inequalityin two and three dimensions