Annular structures in perturbed low mass disc-shaped gaseous nebulae: general, standard and polytropic models

OMS-Vol. 8 (2024), Issue 1, pp. 55-82 Open Access Full-Text PDF
Vladimir Pletser

Abstract:We study analytical solutions of a bi-dimensional low-mass gaseous disc slowly rotating around a central mass and submitted to small radial periodic perturbations. Hydrodynamics equations are solved for the equilibrium and perturbed configurations. A wave-like equation for the gas-perturbed specific mass is deduced and solved analytically for several cases of exponents of the power law distributions of the unperturbed specific mass and sound speed. It is found that, first, the gas perturbed specific mass displays exponentially spaced maxima, corresponding to zeros of the radial perturbed velocity; second, the distance ratio of successive maxima of the perturbed specific mass is a constant depending on disc characteristics and, following the model, also on the perturbation’s frequency; and, third, inward and outward gas flows are induced from zones of minima toward zones of maxima of perturbed specific mass, leading eventually to the possible formation of gaseous annular structures in the disc. The results presented may be applied in various astrophysical contexts to slowly rotating thin gaseous discs of negligible relative mass, submitted to small radial periodic perturbations.

Read more

A version of the Hermite-Hadamard inequality for Quasi \(F-(h,g,m)\)-convex functions

OMS-Vol. 8 (2024), Issue 1, pp. 46-54 Open Access Full-Text PDF
Ghulam Farid and Josip Pečarić

Abstract:This paper aims to present Hermite-Hadamard type inequalities for a new class of functions, which will be denoted by \(Q_m^{h,g}(F;I)\) an and called class of quasi \(F-(h,g;m)\)-convex functions defined on interval \(I\). Many well known classes of functions can be recaptured from this new quasi convexity in particular cases. Also, several publish results are obtained along with new kinds of inequalities.

Read more

On the robustness of the Olanrewaju-Olanrewaju regression kernel-based to nonparametric kernels for Support Vector Regressor (SVR)

EASL-Vol. 7 (2024), Issue 2, pp. 42 – 54 Open Access Full-Text PDF
Rasaki Olawale Olanrewaju, Toyin Omoyeni Oguntola, Lukman Abiodun Nafiu and Sodiq Adejare Olanrewaju

Abstract:{In this article we studied and juxtaposed nonparametric Least Square and the Olanrewaju-Olanrewaju regression-type \({L_{(O – O){\lambda _{\gamma (\left| \theta \right|)}}}}\) kernels for supervised Support Vector Regressor (SVR) machine learning of hyperplane regression in a bivariate setting. The nonparametric kernels used to expound the SVR were Bisquare, Gaussian, Triweight, Uniform, Epanechnikov, and Triangular. Lagrangian multiplier estimation technique was adopted in estimating the involved SVR hyperplane regression coefficients as well as other embedded coefficients in each of the stated kernels. In addition, point estimate of the Euclidean distance (\(r\)) and error margin (\(d\)) in each of the SVR kernels were carved-out. In demonstration to the annual birthrate and its percentage change (\(\Delta \% \)) of the Nigeria populace from 1950 to 2023, the Olanrewaju-Olanrewaju regression-type kernel for SVR robustly outperformed the nonparametric and Least Square kernel-based SVRs with a miniature Cross-Validation index of -1205.49. 5.9% and 3.2% hyperplane estimated regression coefficients from the Olanrewaju-Olanrewaju kernel-based SVR were recorded for the annual birthrate and its percentage change (\(\Delta \% \)) respectively. Interpretably, this connotes that for every one percent increment in the annual birthrate per 1000, the mean rate of the Nigeria populace from 1950 to 2023 increased by 5.9% while other variables were held constant. Similarly, its percentage change per 1000 increased by 3.2% while other variables were held constant. In recommendation, the nonparametric and Olanrewaju-Olanrewaju regression-type SVRs as well as the Least Square SVR were pinpointed for future consideration of categorical, missing and zero bivariate observations.

Read more

Dose response Hill model for the arsenic contamination in the groundwater samples of the Lakhimpur district of Uttar Pradesh

EASL-Vol. 7 (2024), Issue 2, pp. 29 – 41 Open Access Full-Text PDF
Sudhanshu Aggarwal and Lalit Mohan Upadhyaya

Abstract:An experimental study conducted by Ankit Kumar and colleagues (Kumar, Gupta, Pandey, Govil, and Patel, “Status of Arsenic Contamination in District Lakhimpur, Uttar Pradesh, India,” in Emerging Trends in Science, Social Science and Engineering, edited by Aggarwal, Pandey, Naik, Mishra, Raj, Tripathi, and Shukla, pp. 60-73, ISBN 9789358380125, Astitva Prakashan, Bilaspur, Chhattisgarh) has identified significant levels of arsenic contamination in the groundwater of Lakhimpur district, Uttar Pradesh. Their findings indicate that arsenic levels are notably higher in the shallow regions compared to the deeper India Mark II regions across eight selected study sites. Building on these findings, this paper aims to apply a dose-response Hill model to analyze and explain the observed patterns of arsenic contamination in the groundwater resources of Lakhimpur district.

Read more

Emerging trends of nanomaterials synthesis using bos taurus urine

EASL-Vol. 7 (2024), Issue 2, pp. 14 – 28 Open Access Full-Text PDF
Sampada B. Warake, Prashant D Sarvalkar, Neeraj R. Prasad, Avinash A. Ramteke, Kiran K Sharma

Abstract:The ability of organisms or organic compounds to reduce metal ions and stabilize them into nanoparticles is known as green synthesis. Various synthesis methods have been developed, each with its own advantages and drawbacks. In recent years, nanomaterials have found extensive applications in biological sciences, particularly in health and veterinary medicine. For these applications, it is crucial that nanomaterials are biocompatible and non-toxic. Consequently, researchers have increasingly focused on biological synthesis routes. Drawing inspiration from the ancient Indian system of medicine, Ayurveda, some researchers have recently synthesized nanomaterials using Indian cow urine. This review aims to catalog the various nanomaterials produced using Indian cow urine and to discuss their catalytic and biological activities.

Read more

Mathematical algorithms for perpetual ethiopian calendar(e.c.)and similar calendars

EASL-Vol. 7 (2024), Issue 2, pp. 1 – 13 Open Access Full-Text PDF
Aschale Moges Belay and Snehashish Chakraverty

Abstract:This study focused on developing mathematical algorithms for the perpetual Ethiopian calendar and similar calendars. The primary objective was to demonstrate the methodology for creating these algorithms. The research identified that arithmetic progression, ceiling function, congruence modulo, floor function, and Bahre Hasabe are fundamental concepts necessary for this development. Utilizing these concepts, the study successfully developed mathematical algorithms for the perpetual Ethiopian calendar and analogous calendars.

Read more

On edge irregularity strength of some classes of Toeplitz graphs

ODAM-Vol. 7 (2024), Issue 2, pp. 23 – 34 Open Access Full-Text PDF
Noha Mohammad Seyam, Muhammad Faisal Nadeem

Abstract:An edge irregular \(k\)-labeling of a graph \(G\) is a labeling of vertices of \(G\) with labels from the set \(\{1,2,3,\dots,k\}\) such that no two edges of \(G\) have same weight. The least value of \(k\) for which a graph \(G\) has an edge irregular \(k\)-labeling is called the edge irregularity strength of \(G\). Ahmad et. al. [1] showed the edge irregularity strength of some particular classes of Toeplitz graphs. In this paper we generalize those results and finds the exact values of the edge irregularity strength for some generalize classes of Toeplitz graphs.

Read more

On the eccentric atom-bond sum-connectivity index

ODAM-Vol. 7 (2024), Issue 2, pp. 11 – 22 Open Access Full-Text PDF
Zaryab Hussain, Muhammad Ahsan Binyamin

Abstract: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.

Read more

The inverse degree conditions for Hamiltonian and traceable graphs

ODAM-Vol. 7 (2024), Issue 2, pp. 7 – 10 Open Access Full-Text PDF
Rao Li

Abstract:Let \(G = (V(G), E(G))\) be a graph with minimum degree at least \(1\). The inverse degree of \(G\), denoted \(Id(G)\), is defined as the sum of the reciprocals of degrees of all vertices in \(G\). In this note, we present inverse degree conditions for Hamiltonian and traceable graphs.

Read more

A direct proof of stability of nonnegative weak solution for fractional \(\mathbf{p}\)-Laplacian problem with concave nonlinearity

OMA-Vol. 8 (2024), Issue 1, pp. 76 – 79 Open Access Full-Text PDF
Salah A. Khafagy

Abstract: The present paper provides a direct proof of stability of nontrivial nonnegative weak solution for fractional \(p\)-Laplacian problem under concave nonlinearity condition. The main results of this work are extend the previously known results for the fractional Laplacian problem.

Read more