On divisible and pure multigroups and their properties
OMS-Vol. 4 (2020), Issue 1, pp. 377 – 385 Open Access Full-Text PDF
P. A. Ejegwa, M. A. Ibrahim
Abstract: The theory of multigroups is a generalized group’s theoretic notions in multiset framework. Although myriad of researches have been done in multigroup theory, but some group’s analogue concepts have not been investigated in multigroup setting. In this paper we propose the notions of divisible and pure multigroups and characterize some of their properties. It is established that the image and preimage of homomorphism of divisible and pure multigroups are divisible and pure multigroups. The nexus between divisible and pure multigroups and that of divisible and pure groups are instituted using the concept of cuts of multigroups.
Coupled coincidence and coupled common fixed point theorem in dislocated quasi metric space
EASL-Vol. 3 (2020), Issue 4, pp. 11 – 18 Open Access Full-Text PDF
Mitiku Damene, Kidane Koyas, Solomon Gebregiorgis
Abstract: The objective of this paper is to establish a theorem involving a pair of weakly compatible mappings fulfilling a contractive condition of rational type in the context of dislocated quasi metric space. Besides we proved the existence and uniqueness of coupled coincidence and coupled common fixed point for such mappings. This work offers extension as well as considerable improvement of some results in the existing literature. Lastly, an illustrative example is given to validate our newly proved results.
On hyper-singular integrals
OMA-Vol. 4 (2020), Issue 2, pp. 100 – 103 Open Access Full-Text PDF
Alexander G. Ramm
Abstract: The integrals \(\int_{-\infty}^\infty t_+^{\lambda-1} \phi(t)dt\) and \(\int_0^t(t-s)^{\lambda -1}b(s)ds\) are considered, \(\lambda\neq 0,-1,-2…\), where \(\phi\in C^\infty_0(\mathbb{R})\) and \(0\le b(s)\in L^2_{loc}(\mathbb{R})\). These integrals are defined in this paper for \(\lambda\le 0\), \(\lambda\neq 0,-1,-2,…\), although they diverge classically for \(\lambda\le 0\). Integral equations and inequalities are considered with the kernel \((t-s)^{\lambda -1}_+\).
On odd prime labeling of graphs
ODAM-Vol. 3 (2020), Issue 3, pp. 33 – 40 Open Access Full-Text PDF
Maged Zakaria Youssef, Zainab Saad Almoreed
Abstract: In this paper we give a new variation of the prime labeling. We call a graph \(G\) with vertex set \(V(G)\) has an odd prime labeling if its vertices can be labeled distinctly from the set \(\big\{1, 3, 5, …,2\big|V(G)\big| -1\big\}\) such that for every edge \(xy\) of \(E(G)\) the labels assigned to the vertices of \(x\) and \(y\) are relatively prime. A graph that admits an odd prime labeling is called an odd prime graph. We give some families of odd prime graphs and give some necessary conditions for a graph to be odd prime. Finally, we conjecture that every prime graph is odd prime graph.
Anti complex fuzzy subgroups under \(s\)-norms
EASL-Vol. 3 (2020), Issue 4, pp. 1 – 10 Open Access Full-Text PDF
Rasul Rasuli
Abstract: In this study, we define anti complex fuzzy subgroups and normal anti complex fuzzy subgroups under $s$-norms and investigate some of characteristics of them. Later we introduce and study the intersection and composition of them. Next, we define the concept normality between two anti complex fuzzy subgroups by using \(s\)-norms and obtain some properties of them. Finally, we define the image and the inverse image of them under group homomorphisms.
Complex dynamics of a fractional-order predator-prey interaction with harvesting
ODAM-Vol. 3 (2020), Issue 3, pp. 24 – 32 Open Access Full-Text PDF
Rizwan Ahmed
Abstract: Harvesting has a strong impact on the dynamic evolution of a population subjected to it. In this paper, a fractional-order predator-prey interaction is studied with harvesting affecting both predator and prey populations. Local stability of the coexistence equilibrium point is discussed depending upon the harvesting of prey. Moreover, period-doubling and Neimark-Sacker bifurcations are studied for a wide range of constant harvesting effort of prey.
