Search

In this paper, we have investigated spatially homogeneous and anisotropic Kantowski–Sachs cosmological model in Lyra (Math. Z. 54:52, 1951) manifold in the presence of bulk viscous fluid containing one dimensional Cosmic strings. To obtain a determinate solution of the field equations, we have used some plausible physical conditions. The solution obtained represents a bulk viscous string cosmological model in Lyra geometry. Some physical and geometrical properties of the model are also discussed.

Given an integer n ≥ 2, let λ(n) := (log n)/(log γ(n)), where γ(n) = Πp|n p, stand for the index of composition of n, with λ(1) = 1. We study the distribution function of (λ(n) – 1) log n as n runs through particular sets of integers, such as the shifted primes, the values of a given irreducible cubic polynomial and the shifted powerful numbers.

The asymptotic expansion of ]]> ]]> ]]> \sum\limits_{n\le x}e^*(n)$ is given, where $e^*(n)$ is defined by $\sum{\frac{{e^*(n)}}{{n^s}}}\eg \prod\limits_{n=2}^\infty (1-1/n^s)$.

We give the asymptotics of the sum \(\sum\nolimits_{x \leqslant n \leqslant x + h} {f(n)}\), where \(h \gg x^{7/12 + \varepsilon }\), for the multiplicative functions \(f(n) = z^{\omega (n)} , z^{\omega (n)} |\mu (n)|, 1/d_k (n)\), and \(nd(n)\).

the following assertion is proved. If f is a completely multiplicative function taking values of modulus 1, such that the set e of limit points of \(f(n + 1)\bar f(n)\) has k ≨ 3 distinct values, then f(n) = nirF(n) with some r e R, and Fk(n) = 1 for every n.

The variations of the hybridh-parameters and the gain of the transistor with temperature have been studied by obtaining an analytical expression. The values of theh-parameters are calculated in the entire temperature range 213–473 K with the help of the expression obtained and the calculated values are in good agreement with the experimental data. The gain of the transistor extracted from the obtained values of the parameters is seen to be in excellent agreement with the experimental values.