In this paper, we present some new dynamic Opial-type diamond alpha inequalities on time scales. The obtained results are related to the function [Formula: see text].

Let $\mathbb F$ be a finite field. Consider direct sum $V$ of an infinite number copies F$, consider the dual space $V^\diamond$, i.~e., product F$. ${\mathbb V}=V\oplus V^\diamond$. The object paper is group $\mathbf{GL}$ continuous linear operators in V$. We reduce theory unitary representations to projective certain category whose morphisms are relations finite-dimensional spaces over In fac...

Assume that $mathbb{D}$ is the open unit disk. Applying Ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{G}(alpha)$ and $mathcal{F}(mu)$ as follows begin{equation*}  mathcal{G}(alpha):=left{fin mathcal{A}:mathfrak{Re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right) <1+frac{alpha }{2},quad 0<alphaleq1right}, end{equation*} and begin{equation*}  ma...

The goal of this article is to study the box dimension mixed Katugampola fractional integral two-dimensional continuous functions on $$[0,1]\times [0,1]$$ . We prove that having order $$(\alpha =(\alpha _1,\alpha _2);~ \alpha _1>0, _2>0)$$ still two. Moreover, results are also established for Hadamard integral. Our new improve existing studies. pose some open problems further research.

The charge collection properties of CVD diamond have been investigated with ionising radiation. In this study two CVD diamond samples, prepared with electrical contacts have been used as solid state ionisation chambers. The diamonds have been studied with beta particles and 10 keV photons, providing a homogeneous ionisation density and with protons and alpha particles which are absorbed in a th...

Let $C_0(alpha)$ denote the class of concave univalent functions defined in the open unit disk $mathbb{D}$. Each function $f in C_{0}(alpha)$ maps the unit disk $mathbb{D}$ onto the complement of an unbounded convex set. In this paper, we study the mapping properties of this class under integral operators.