We obtain nearly sharp estimates for the L p (R 2) norms of certain convolution operators. For n 1 let n be the measure on R 2 obtained by multiplying normalized arclength measure on fjxj = 1g by the oscillating factor e inarg(x). For 1 p 1, let C(p; n) denoted the norm of the operator T n f : = n f on L p (R 2). The purpose of this note is to estimate the rate of decay of C(p; n) as n ! 1. By ...

There are three main types of numerical computations for the Bessel function second kind: series expansion, continued fraction, and asymptotic expansion. In addition, they combined in appropriate domain each. However, there some regions where combination these requires sufficient computation time to achieve accuracy, however, efficiency is significantly reduced when parallelized. proposed metho...

The lost of nonentun and stiffness due to ablation nay significantly influence the vibrations of a solid propellant grain. This paper presents an analytical study of the axial shear vibrations of a long hollow cylinder that is subjected to tine dependent body forces in the axial direction. The outer surface of the cylinder is bonded to a rigid case, and the inner radius increases monotonically ...

The bivariate confluent hypergeometric function kind 1 distribution is defined by the probability density function proportional to x1 1 x2 2 1 F1(α; β; −x1 − x2). In this article, we study several properties of this distribution and derive density functions of X1/X2, X1/(X1 + X2), X1 + X2 and 2 √ X1X2. The density function of 2 √ X1X2 is represented in terms of modified Bessel function of the s...