Open Journal of Mathematical Sciences (OMS)

We introduce the generalized von Neumann-Jordan constant of a quasi-Banach space \(X\). Also, the quasi-Hilbert characteristic is introduced. An attempt has been made to investigate the relationship between them. At the end, a characterization of uniformly non-square is given.

We study the foreign measures in general by proving all operations possibilities with their characteristic relation \( \perp \) and deduce that the set of foreign vector measures is a subset of bounded vector measures; stable par linear combination.

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.

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.

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.

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.

In this article, modified difference-type estimator for the population mean in two-phase sampling scheme using two auxiliary variables has been proposed. The mean squared error of the proposed estimator has also been derived using large sample approximation. The efficiency comparison conditions for the proposed estimator in comparison with other existing estimators in which the proposed estimator performed better than the other relevant existing estimators have been given.

Let \(G = (V,E)\) be a simple connected undirected graph. In this paper, we define generalized the Liouville’s and Möbius functions of a graph \(G\) which are the sum of Liouville \(\lambda\) and Möbius \(\mu\) functions of the degree of the vertices of a graph denoted by \(\Lambda(G)=\sum\limits_{v\in V(G)}\lambda(deg(v))\) and \(M(G)=\sum\limits_{v\in V(G)}\mu(deg(v))\), respectively. We also determine the Liouville’s and Möbius functions of some standard graphs as well as determining the relationships between the two functions with their proofs. The sum of generalized the Liouville and Möbius functions extending over the divisor d of degree of vertices of graphs is also given.

In this paper, we introduce a symmetric function in order to derive a new generating functions of bivariate Pell Lucas polynomials. We define complete homogeneous symmetric functions and give generating functions for Gauss Fibonacci polynomials, Gauss Lucas polynomials, bivariate Fibonacci polynomials, bivariate Lucas polynomials, bivariate
Jacobsthal polynomials and bivariate Jacobsthal Lucas polynomials.

We establish the strong generalized solution of the second mixed problem for an Euler-Poisson-Darboux equation in which the free term has the form: \(\gamma(t) u(x_0,t_0)\) where \(u(x,t)\) is the unknown function sought at the point \((x_0,t_0).\)