PARTIAL SUMS OF GENERALIZED CLASS OF HARMONIC UNIVALENT FUNCTIONS INVOLVING A GAUSSIAN HYPERGEOMETRIC FUNCTION
The purpose of the present paper is to establish some new results giving the sharp bounds of the real parts of ratios of harmonic univalent functions to its sequences of partial sums by involving the Gaussian hypergeometric function. Relevant connections of the results presented here with various known results are briefly indicated. We also mention results which are associated with certain classical orthogonal polynomials (deduced from some of the main results) exhibiting the usefulness of the results presented in this paper.
Some properties of a new class of analytic functions defined in terms of a Hadamard product.
In this paper we introduce a new class H(φ, α, β) of analytic functions which is defined by means of a Hadamard product (or convolution) of two suitably normalized analytic functions. Several properties like, the coefficient bounds, growth and distortion theorems, radii of starlikeness, convexity and close-to-convexity are investigated. We further consider a subordination theorem, certain boundedness properties associated with partial sums, an integral transform of a certain class of functions, and some integral means inequalities. Several interesting consequnces of our main results are also pointed out.
Numerical Simulation of Thermal Sensitivity for Explosives
In order to compare the thermal sensitivity of several typical explosives, this article solved numerically one-dimensional transient heat conduction equation including thermal decomposition for explosives with finite difference method. The explicit difference equations under different boundary conditions were established, and the corresponding stability criterion was derived. The ignition times for typical explosives were calculated, which was used to evaluate thermal sensitivity of explosives.