On separability criteria for continuous Bitopological spaces
OMA-Vol. 5 (2021), Issue 2, pp. 31 – 45 Open Access Full-Text PDF
O. Ogola, N. B. Okelo, O. Ongati
Abstract:In this paper, we give characterizations of separation criteria for bitopological spaces via \(ij\)-continuity. We show that if a bitopological space is a separation axiom space, then that separation axiom space exhibits both topological and heredity properties. For instance, let \((X, \tau_{1}, \tau_{2})\) be a \(T_{0}\) space then, the property of \(T_{0}\) is topological and hereditary. Similarly, when \((X, \tau_{1}, \tau_{2})\) is a \(T_{1}\) space then the property of \(T_{1}\) is topological and hereditary. Next, we show that separation axiom \(T_{0}\) implies separation axiom \(T_{1}\) which also implies separation axiom \(T_{2}\) and the converse is true.
Integrated interpretive structural modeling (ISM) and MICMAC diagram for analysis of infrastructure influence in supporting submarine operations
EASL-Vol. 4 (2021), Issue 3, pp. 8 – 18 Open Access Full-Text PDF
Moelyanto, Marsetio, A. Octavian, R.O. Bura, I. N. Putra
Abstract:The strategic value of the Navy’s submarine capabilities is greatly influenced by the ability of its supporting infrastructure to be able to maintain the confidentiality of submarine operations. Based on these conditions, this study aims to identify and analyze the operational readiness of submarines to increase the deterrence of the state defense system at sea. This study uses Interpretive Structural Modeling (ISM) and MIC-MAC diagrams. The ISM method is used to analyze the effect on the criteria. MICMAC diagrams are used as criteria for determining the related variables. Based on the results of the ISM and MICMAC diagram analysis, it was found that fifteen elements were divided into \(4\) (four) quadrants. Quadrant I (Autonomous) consists of six elements, such as \((C_1)\), \((C_2)\), \((C_3)\), \((C_4)\), \((C_{13)}\), \((C_{15})\). Quadrant II (Dependent) consists of six elements, such as \((C_5)\), \((C_6)\), \((C_7)\), \((C_{11})\), \((C_{12})\), \((C_{14})\). Quadrant IV (Independent) consists of three elements, such as \((C_8)\), \((C_9)\), \((C_{10})\). This research is expected to provide benefits to both academics and practitioners in the field of submarines and defense strategy.
Generalized orthopair fuzzy matrices
OMS-Vol. 5 (2021), Issue 2, pp. 288 – 299 Open Access Full-Text PDF
I. Silambarasan
Abstract:A q-rung orthopair fuzzy matrix (q-ROFM), an extension of the Pythagorean fuzzy matrix (PFM) and intuitionistic fuzzy matrix (IFM), is very helpful in representing vague information that occurs in real-world circumstances. In this paper we define some algebraic operations, such as max-min, min-max, complement, algebraic sum, algebraic product, scalar multiplication \((nA)\), and exponentiation \((A^n)\). We also investigate the algebraic properties of these operations. Furthermore, we define two operators, namely the necessity and possibility to convert q-ROFMs into an ordinary fuzzy matrix, and discuss some of their basic algebraic properties. Finally, we define a new operation(@) on q-ROFMs and discuss distributive laws in the case where the operations of \(\oplus_{q}, \otimes_{q}, \wedge_{q}\) and \(\vee_{q}\) are combined each other.
Generalized fractional differential ring
OMS-Vol. 5 (2021), Issue 1, pp. 279 – 287 Open Access Full-Text PDF
Zeinab Toghani, Luis Gaggero-Sager
Abstract: There are many possible definitions of derivatives, here we present some and present one that we have called generalized that allows us to put some of the others as a particular case of this but, what interests us is to determine that there is an infinite number of possible definitions of fractional derivatives, all are correct as differential operators each of them must be properly defined its algebra. We introduce a generalized version of fractional derivative that extends the existing ones in the literature. To those extensions it is associated a differentiable operator and a differential ring and applications that shows the advantages of the generalization. We also review the different definitions of fractional derivatives and it is shown how the generalized version contains the previous ones as a particular cases.
Spectral conditions for the Bipancyclic Bipartite graphs
ODAM-Vol. 4 (2021), Issue 2, pp. 48 – 51 Open Access Full-Text PDF
Rao Li
Abstract:Let \(G = (X, Y; E)\) be a bipartite graph with two vertex partition subsets \(X\) and \(Y\). \(G\) is said to be balanced if \(|X| = |Y|\) and \(G\) is said to be bipancyclic if it contains cycles of every even length from \(4\) to \(|V(G)|\). In this note, we present spectral conditions for the bipancyclic bipartite graphs.
Repeated sums and binomial coefficients
ODAM-Vol. 4 (2021), Issue 2, pp. 30 – 47 Open Access Full-Text PDF
Roudy El Haddad
Abstract:Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial coefficient identities will be shown in order to prove this definition. Using this new definition, we simplify some particular sums such as the repeated Harmonic sum and the repeated Binomial-Harmonic sum. We derive formulae for simplifying general repeated sums as well as a variant containing binomial coefficients. Additionally, we study the \(m\)-th difference of a sequence and show how sequences whose \(m\)-th difference is constant can be related to binomial coefficients.
