Different treatment modalities in management of plantar fasciitis
TCMS-Vol. 1 (2021), Issue 3, pp. 1 – 5 Open Access Full-Text PDF
Fluorent Lucotte, Ehab Ahmed
Abstract:The aim of this paper is to compare different treatment modalities in management of plantar fasciitis. Forty- five patients with plantar fasciitis (males- 2- females- 20) were randomized into 3 groups. Group 1 patients received conventional treatment, group 2 patients received heat treatment with silicone heel pad and group 3 patients received active plantar fascia stretching with sham calf stretching. Patient was evaluated using foot function index (FFI) and the foot and ankle disability index (FADI). In group 1, foot function pre-intervention index score and post-intervention score was 68.2 and 43.5, in group 2 was 64.8 and 6.9 and in group 3 was 70.5 and 1.6 respectively. A significant difference was observed (P< 0.05). In group 1, pre-intervention foot and ankle disability score and post-intervention score was 61.5 and 76.4, in group 2 was 66.5 and 95.2 and in group 3 was 61.3 and 97.6 respectively. A significant difference was observed (P< 0.05). Active plantar fascia stretching with sham calf stretching exercise resulted in most significant improvement in FFI and FADI score followed by treatment with heat and silicone heel pad and conventional treatment.
On a generalized class of bi-univalent functions defined by subordination and \(q\)-derivative operator
OMA-Vol. 5 (2021), Issue 2, pp. 46 – 52 Open Access Full-Text PDF
Ayotunde O. Lasode, Timothy O. Opoola
Abstract:In this paper, the \(q\)-derivative operator and the principle of subordination were employed to define a subclass \(\mathcal{B}_q(\tau,\lambda,\phi)\) of analytic and bi-univalent functions in the open unit disk \(\mathcal{U}\). For functions \(f(z)\in\mathcal{B}_q(\tau,\lambda,\phi)\), we obtained early coefficient bounds and some Fekete-Szegö estimates for real and complex parameters.
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.
Some fixed point theorems for \(F\)-expansive mapping in generalized metric spaces
OMA-Vol. 5 (2021), Issue 2, pp. 17 – 30 Open Access Full-Text PDF
Mohamed Rossafi, Abdelkarim Kari
Abstract: In this paper, we present the notion of generalized \(F\)-expansive mapping in complete rectangular metric spaces and study various fixed point theorems for such mappings. The findings of this paper, generalize and improve many existing results in the literature.
The hyper order and fixed points of solutions of a class of linear differential equations
OMA-Vol. 5 (2021), Issue 2, pp. 1 – 16 Open Access Full-Text PDF
Nour el imane Khadidja CHERIET, Benharrat BELAÏDI
Abstract: In this paper, we precise the hyper order of solutions for a class of higher order linear differential equations and investigate the exponents of convergence of the fixed points of solutions and their first derivatives for the second order case. These results generalize those of Nan Li and Lianzhong Yang and of Chen and Shon.