Einstein equations for a Finsler-Larange space with canonical N-linear connections
OMS-Vol. 4 (2020), Issue 1, pp. 240 – 247 Open Access Full-Text PDF
Roopa M. K, Narasimhamurthy S. K
Abstract: This paper is devoted to study the geometry of Einstein equations of Finsler-Lagrange with \((\alpha, \beta)\)-metrics. We characterized the Einstein equations of Finsler Lagrange space with Randers metric, by using canonical N-metrical connection.
Valuations and their generalizations for UP-algebras
OMS-Vol. 4 (2020), Issue 1, pp. 220 – 239 Open Access Full-Text PDF
Siriwan Pawai, Tararat Khamsang, Aiyared Iampan
Abstract: In this paper, we introduce the notions of a weak pseudo-valuation, a \(0\)-weak pseudo-valuation, a weak valuation, a near pseudo-valuation, a near valuation, a pseudo-valuation, and a valuation and induce a pseudo-metric without triangle inequality, a quasi pseudo-metric, a pseudo-metric, and a metric by some these mappings on a UP-algebra. We also prove that the binary operation defined on a UP-algebra is uniformly continuous under the induced metric by a valuation in some conditions.
Existence of the golden ratio in Tanjavur Brihadeeshwarar temple
OMS-Vol. 4 (2020), Issue 1, pp. 211 – 219 Open Access Full-Text PDF
C. Velmurugan, R. Kalaivanan
Abstract: In this study, we discussed the existence of golden ratio in Brihadeeshwarar temple, Tanjavur, Tamil Nadu, India, built in 1010 AD. It is listed on the UNESCO’s world heritage site of the Chola temples in southern India. This temple represents an outstanding creative achievement in the architectural idea of the pure form of the Dravida temples. Golden ratio has great influence in architecture, mathematics and art. We analyzed existence of the Golden ratio in structural design of Tanjavur Brihadeeshwarar temple prakaram. We used the Phi Grid and Phi Spiral software to measure the golden ratio and verified our result.
On a generalization of KU-algebras pseudo-KU algebras
OMS-Vol. 4 (2020), Issue 1, pp. 200 – 210 Open Access Full-Text PDF
Daniel A. Romano
Abstract: As a generalization of KU-algebras, the notion of pseudo-KU algebras is introduced in 2020 by the author (D. A. Romano. Pseudo-UP algebras, An introduction. Bull. Int. Math. Virtual Inst., 10(2)(2020), 349-355). Some characterizations of pseudo-KU algebras are established in that article. In addition, it is shown that each pseudo-KU algebra is a pseudo-UP algebra. In this paper it is a concept developed of pseudo-KU algebras in more detail and it has identified some of the main features of this type of universal algebras such as the notions of pseudo-subalgebras, pseudo-ideals, pseudo-filters and pseudo homomorphisms. Also, it has been shown that every pseudo-KU algebra is a pseudo-BE algebra. In addition, a congruence was constructed on a pseudo-KU algebra generated by a pseudo-ideal and shown that the corresponding factor-structure is and pseudo-KU algebra as well.
Intuitionistic fuzzy subgroups with respect to norms (\(T,S\))
EASL-Vol. 3 (2020), Issue 2, pp. 40 – 53 Open Access Full-Text PDF
Rasul Rasuli
Abstract: The purpose of this paper is introduce the notion of intuitionistic fuzzy subgroups with respect to norms (\(t\)-norm \(T\) and \(s\)-norm \(S\)). Also we introduce intersection and normality of them and investigate some properties of them. Finally, we provide some results of them under group homomorphisms.
On Caputo fractional derivatives via exponential \((s,m)\)-convex functions
EASL-Vol. 3 (2020), Issue 2, pp. 32 – 39 Open Access Full-Text PDF
Saad Ihsan Butt, Mehroz Nadeem, Ghulam Farid
Abstract: In this paper, we establish several integral inequalities including Caputo fractional derivatives for exponential \((s,m)\)-convex functions. By using convexity for exponential \((s,m)\)-convex functions of any positive integer order differentiable function some novel results are obtained.
