This note presents some upper bounds for the size of the upper deg-centric grapg \(G_{ud}\) of a simple connected graph G. Amongst others, a result for graphs for which a compliant graph \(G\) has \(G_{ud} \cong \overline G\) is presented. Finally, results for size minimality in respect upper deg-centrication and minimum size of such graph \(G\) are presented.

Squares of odd index Fibonacci polynomials are used to define a new function \(\Phi\left(10^{n}\right)\) to approximate the number \(\pi\left(10^{n}\right)\) of primes less than \(10^{n}\). Multiple of 4 index Fibonacci polynomials are further used to define another new function \(\Psi\left(10^{n}\right)\) to approximate the number \(\Delta\left(\pi\left(10^{n}\right)\right)\) of primes having \(n\) digits and compared to a third function \(\Psi’\left(10^{n}\right)\) defined as the difference of the first function \(\Phi\left(10^{n}\right)\) based on odd index Fibonacci polynomials. These three functions provide better approximations of \(\pi\left(10^{n}\right)\) than those based on the classical \(\left(\frac{x}{log\left(x\right)}\right)\), Gauss’ approximation \(Li\left(x\right)\), and the Riemann \(R\left(x\right)\) functions.

We show that Euler’s relation and the Taxi-Cab relation are both solutions of the same equation. General solutions of sums of two consecutive cubes equaling the sum of two other cubes are calculated. There is an infinite number of relations to be found among the sums of two consecutive cubes and the sum of two other cubes, in the form of two families. Their recursive and parametric equations are calculated.

This study introduces theorems concerning matrix products, which delineate the transformations of sequences or series into other sequences or series, ensuring either the preservation of limits or the guarantee of convergence. Previous literature has explored the properties of matrices facilitating transformations between sequences, series, and their combinations, with detailed insights available in references [1,2,3].

The concept of weak UP-algebras (shortly wUP-algebra) is an extension of the notion of UP-algebras introduced in 2021 by Iampan and Romano. In this report, an effective extension of a (weak) UP-algebra to a wUP-algebra is created. In addition to the previous one, the concept of atoms in wUP-algebras is introduced and their important properties are registered. Finally, the concept of wUP-filters in wUP-algebras was introduced and its connections with other substructures in wUP-algebras were analyzed.

In normed spaces, Birkhoff orthogonality and isosceles orthogonality can be used to characterize space structures, and many scholars have introduced geometric constants to quantitatively describe the relationship between these two types of orthogonality. This paper introduces a new orthogonal relationship – Skew orthogonality – and proposes a new geometric constant to measure the “distance” of difference between skew orthogonality and Birkhoff orthogonality in normed spaces. In the end, we provide some examples of specific spaces.

Entropy patterns typically transfer actions of two-state relations in nonlinear systems. Here, multivalent logic is applied from autowave fields to selected Quantum Neurophysical systems.

Enhancement of heat and mass transfer heat over rotating plates in industrial processes is a major area of research recently due to several attempts to find cost-effective means. In this study, the flow of Williamson fluid is considered because of its ability to exhibit pseudo-plastic and shear-thinning properties. A theoretical analysis of the effect of Coriolis force and the angle inclination on the magnetohydrodynamic flow of Williamson fluid is considered. The flow is modelled by including Coriolis force and angle of inclination in the Navier-Stokes equation. By adopting a suitable similarity transformation, the system of governing partial differential equations is reduced to a system of ordinary differential equations which are solved using bvp4c solver in MATLAB. The simulations are depicted as graphs and it is found that velocity increases with increasing Coriolis force while it decreases as the magnetic field strength and inclination angle increases. Also, the local skin friction reduces as the rotation increases. Hence, to boost heat and mass transfer in the flow of fluid over a rotating inclined plate in a magnetic field, it is recommended that rotation should be increased and magnetic field strength should be reduced.

This study investigates contemporary and emerging transportation problems in North-central Nigeria. Its primary objective is to identify and characterize the major challenges facing passengers within the region and to propose a sustainable institutional framework for improved transportation management. The study draws upon data collected through field audits in three North-central states: the Federal Capital Territory (FCT) Abuja, Nasarawa, and Niger. Key findings highlight the lack of developed transit connections to major activity centers. The study concludes that these challenges stem from inefficiencies within the existing institutional mechanisms for transportation management. To address this, the study proposes the establishment of an effective, innovative transport system, such as an intercity train network within the North-central zone, as a sustainable transportation management strategy for the region.

The purpose of this paper is to introduce and evaluate novel iterative methods for approximating solutions to nonlinear equations, which leverage the power of the variational iteration technique. Specifically, we present a comprehensive analysis of the proposed methods and demonstrate their effectiveness through various examples. Moreover, we provide a comparative analysis with other existing methods and conclude that the newly developed methods offer a competitive alternative. Our results highlight the potential of this approach in generating a diverse set of iterative methods for solving nonlinear equations. Therefore, this study contributes to the ongoing efforts to improve the efficiency and accuracy of nonlinear equation solving techniques.