International Journal of Mathematics And its Applications

2-12

Authors: V. R. Kulli

A graph index is a real number that is derived from molecular graphs of chemical compounds. In this paper, we introduce the multiplicative total reduced index, multiplicative reduced inverse degree, multiplicative reduced zeroth order index, general multiplicative reduced first Zagreb index of a graph and compute exact formulas for certain networks for chemical importance such as silicate networks, chain silicate networks, hexagonal networks, oxide networks and honeycomb networks.

17-25

Authors: M. Prasad, S. R. Nayaka and K. V. Prasad

Let $B_{2, 5}(n)$ denote the number of $(2, 5)$-regular bipartitions of a positive integer $n$ into distinct parts . In this paper, we establish several infinite families of congruences modulo powers of $2$ for $B_{2, 5}(n)$. For example, \begin{equation*} \sum_{n=0}^{\infty}B_{2, 5}\left(2^{2\alpha+1}\cdot5^{2\beta}n+\frac{2^{2\alpha+2}\cdot5^{2\beta}-1}{3}\right)q^n \equiv 2f_1f_{5}^3 \pmod{2^2}, \end{equation*} for $\alpha, \beta \geq 0$.

39-48

Authors: Dragan Obradovic, Lakshmi Narayan Mishra and Vishnu Narayan Mishra

The main factor in the development of human resources is knowledge and modern knowledge, through the application of which the individual and the company survive as competitive on the market. We acquire knowledge both during the formal educational process and through non-formal learning, in schools and colleges, and later in companies, in a traditional and online environment. Today, in science, great attention is paid to e-learning (e-learning) and e-education (e-education) using modern information and communication technologies. Nowadays, with the daily expansion of scientific knowledge there is also a huge progression of technology. In parallel, they developed technology in the field of education. Unfortunately, in our area this development and applications are flowing at a much slower pace (than needs dictate) in relation to the developed countries of the world and their educational systems. The main intention and goal of this paper is to point out on this occasion as well the importance, need and necessity of far broader and deeper study, and the application of modern educational technology at all levels of education, with special with an analytical review of contemporary university education.

55-62

Authors: Shradha Dwivedi, Sabir Ali Siddiqui, Peeyush Dwivedi and Sanjay Jain

The present paper deals in Bayesian analysis of the new distribution which is renamed here as SD-distribution. Bayesian estimates of the expected life, reliability function, hazard rate function is studied mathematically for the distribution, which is already established as a failure model. Similarly Bayesian estimates for the order statistics is also found here. The scale and shape parameters had been considered as random variables separately with certain prior distribution for the purpose of Bayesian estimation.

69-80

Authors: Ashok V. Bingi

In this paper, we introduce $\phi$-$\delta$-primary elements in a compactly generated multiplicative lattice $L$ and obtain its characterizations. We prove many of its properties and investigate the relations between these structures. By a counter example, it is shown that a $\phi$-$\delta$-primary element of $L$ need not be $\delta$-primary and found conditions under which a $\phi$-$\delta$-primary element of $L$ is $\delta$-primary.

91-95

Authors: Pradeep Kumar Dwivedi

In this paper we have to prove a common fixed point theorem for two pairs of compatible maps in dislocated metric space which generalizes and improves similar fixed point results.

101-104

Authors: Wanjala Victor and A. M. Nyongesa

In this paper, we introduce the class of (n,m)-metrically equivalent operators which is a generilazation of metrically equivalent operators and n-metrically equivalent operators. We then look at some properties of this class and its relation to some higher classes like quasi-isometries and the (n,m)-class (Q) operators. we also look at the relationship between this class and other equivalence relations like metrically equivalent and n-metrically equivalent operators.

111-113

Authors: Wanjala Victor and A. M. Nyongesa

In this paper, we introduce a new class of operator, the class of $(\alpha,\beta)$-Class (Q) operator acting on a complex Hilbert space $H$. An operator $T \in B(H)$ is said to be $(\alpha,\beta)$-Class (Q) if $\alpha^{2}T^{*2}T^{2}\leq (T^{*}T)^{2}\leq \beta^{2}T^{*2}T^{2}$ for $ 0 \leq \alpha\leq 1 \leq \beta$. We look at some properties that this class are priviledged to enjoy.