The aim of this paper is to determine the Fekete-Szegö inequalities for a normalized analytic function defined on the open unit disk lies in a region starlike with respect to 1 and it is symmetric with respect to the real axis by using the operator given recently by the authors. As a special case of this result, Fekete-Szegö inequality for a class of functions defined by fractional derivatives is also obtained.

Using a generalized derivative operator, we introduce and study a new class of harmonic univalent functions. In the present paper, we investigate some results for functions f belong to this class which include the necessary and sufficient coefficient bounds. Growth bounds and a closure property are also obtained.

Motivated by generalized derivative operator defined by the authors (El-Yagubi and Darus, 2013) and the technique of differential subordination, several interesting properties of the operator are given.

The aim of this paper is to introduce a new class of analytic functions in the unit disk, with negative coefficients, via a new generalized derivative operator. We prove coecient inequalities for the new class of functions and for a subclass of it, as well as distortion theorems for functions in this subclass and for their derivatives. We determine the extreme points of the newly introduced subclass.

Abstract:

The basic physical and mechanical properties of Libyan soil are analyzed through some experiments, including direct shear test, grading analysis test and compression test. According to the test results, the soil is named as low liquid limit silt featured by weak strength, high compressibility and permeability, which directly influences sub-grade stability, durability and pavement’s usability. In order to solve these problems, measures are discussed from two aspects, namely, soil improvement and construction method. The strength of the soil is apparently increased by the cement and lime adding, and the compressibility is decreased at the same time. And the rising height of capillary water reducing and protection forms for silt soil slope are also proved to be effective in the subgrade construction

A convenient method of preparing ultrafine polystyrene latex nano-particles with amino groups on the surface is developed. polystyrene latexes in the size range 50–400 nm were prepared via emulsion polymerization, using sodium dodecyl sulfate (SDS) as surfactant. The poly styrene with amino groups on the surface will be fine to use as organic filler to modify rubber. Transmission electron microscopy (TEM) was used to observe the morphology of silicon dioxide and functionalized polystyrene nanoparticles. The nature of bonding between the polymer and the reactive groups on the filler surfaces was analyzed using Fourier transform infrared spectroscopy (FTIR). Scanning electron microscopy (SEM) was employed to examine the filler surface.