A Piatetski-Shapiro sequence with exponent $\alpha$ is a of integer parts $n^\alpha$ $(n = 1,2,\ldots)$ non-integral $\alpha > 0$. We let $\mathrm{PS}(\alpha)$ denote the set those terms. In this article, we study so that equation $ax + by cz$ has infinitely many pairwise distinct solutions $(x,y,z) \in \mathrm{PS}(\alpha)^3$, and give lower bound for its Hausdorff dimension. As corollary, find...

Abstract In this paper, with the help of Green’s function and Hermite interpolating polynomial, an extension Jensen’s functional for n -convex functions is deduced from inequality involving diamond integrals. Special conditions, including Taylor two point formula Lagrange’s interpolation, are also deployed to find further extensions functional. This paper includes discussion on bounds Grüss ine...

In the paper, authors discuss some extended results involving Catalan numbers and establish an integral representation of in terms $(\alpha,k)$-gamma $(\alpha,k)$-beta function. We refer to available literature by giving special values parameters obtained theorems.

Evaluation and prediction of performance of diamond wire saw is one of the most important factors involved in planning the dimension stone quarries. The wear rate of diamond wire saw can be investigated as a major criterion to evaluate its performance. The wear rate of diamond wire saw depends upon non-controlled parameters related to rock characteristics and controlled parameters related to ch...

diamond like carbon (dlc) film was grown by hot filament chemical vapor deposition (hfcvd)technique. in the present work, we investigated the quality of the dlc films groew on the substratesthat were coated with various metal nanocatalysts (au and ni). a combination of ch4/ar/h2 rendersthe growth of carbon nanostructures technique (diamond like carbon). the utilized samples werecharacterized by...

We investigate the nonnegative solutions to nonlinear integral inequality $u \ge I_{\alpha}\ast\big((I_\beta \ast u^p)u^q\big)$ a.e. in $\mathbb{R}^N$, where $\alpha, \beta\in (0,N)$, $p, q>0$ and $I_\alpha$, $I_\beta$ denote Riesz potentials of order $\alpha$ $\beta$ respectively. Our approach relies on a nonlocal positivity principle which allows us derive optimal ranges for parameters $\alph...

We study structural, integral, differential, variational, and fractal properties of a function f whose argument $$ x={\Delta }_{\alpha_1{\alpha}_2\dots {\alpha}_n\dots}^{Q_s^{\ast }} is represented by polybasic s-symbol {Q}_s^{\ast } -representation (1 < s ∈ N) its corresponding value expressed as follows: f\left(x={\Delta }}\right)={a}^{\alpha_1{u}_1+{\alpha}_2{u}_2+\dots +{\alpha}_n{u}_n+\dot...