Journals – Page 5

Arc coloring of odd graphs for hamiltonicity

ODAM-Vol. 6 (2023), Issue 2, pp. 14 – 31 Open Access Full-Text PDF

Italo Dejter

Abstract:Coloring the arcs of biregular graphs was introduced with possible applications to industrial chemistry, molecular biology, cellular neuroscience, etc. Here, we deal with arc coloring in some non-bipartite graphs. In fact, for \(1< k \in\mathbb{Z}\), we find that the odd graph \(O_k\) has an arc factorization with colors \(0,1,\ldots,k\) such that the sum of colors of the two arcs of each edge equals \(k\). This is applied to analyzing the influence of such arc factorizations in recently constructed uniform 2-factors in \(O_k\) and in Hamilton cycles in \(O_k\) as well as in its double covering graph known as the middle-levels graph \(M_k\).

More on second Zagreb energy of graphs

ODAM-Vol. 6 (2023), Issue 2, pp. 7 – 13 Open Access Full-Text PDF

Mitesh J. Patel, Kajal S. Baldaniya and Ashika Panicker

Abstract:Let \(G\) be a graph with \(n\) vertices. The second Zagreb energy of graph \(G\) is defined as the sum of the absolute values of the eigenvalues of the second Zagreb matrix of graph \(G\). In this paper, we derive the relation between the second Zagreb matrix and the adjacency matrix of graph \(G\) and derive the new upper bound for the second Zagreb energy in the context of trace. We also derive the second Zagreb energy of \(m-\)splitting graph and \(m-\)shadow graph of a graph.

On the product of Sombor and modified Sombor indices

ODAM-Vol. 6 (2023), Issue 2, pp. 1 – 6 Open Access Full-Text PDF

Ivan Gutman, Redžepović and Boris Furtula

Abstract:The Sombor index (\(SO\)) and the modified Sombor index (\(^mSO\)) are two closely related vertex-degree-based graph invariants. Both were introduced in the 2020s, and have already found a variety of chemical, physicochemical, and network-theoretical applications. In this paper, we examine the product \(SO \cdot {^mSO}\) and determine its main properties. It is found that the structure-dependence of this product is fully different from that of either \(SO\) or \(^mSO\). Lower and upper bounds for \(SO \cdot {^mSO}\) are established and the extremal graphs are characterized. For connected graphs, the minimum value of the product \(SO \cdot {^mSO}\) is the square of the number of edges. In the case of trees, the maximum value pertains to a special type of eclipsed sun graph, trees
with a single branching point.

Early prediction of non union tibia from post operative follow up 3rd month radiographic union status of tibial fracture (rust ) score: A systematic review and meta analysis

TCMS-Special issue: Recent developments of medical and surgical research (2023), pp. 693 – 697 Open Access Full-Text PDF

Govind Kumar Gupta, Subhankar Mandal, Sudha Rani, Tushar Kumar, Pancham Prasad and Ratnajeet Chakraborty

Abstract:Purpose: Early prediction of the non-union tibia by the RUST score (Radiographic union score for tibia fracture) at three months postoperatively. That will help with early detection of non-union, intervene to treat the non-union and help get back to normal daily life.
Materials and method: Systematic search was done in an electronic database (Google Scholar, PubMed , Chochrane library ) for articles published till 5th January 2022 investigating RUST score as a predictor for non union tibia . The new castle Ottowa scale (NOS) was used to determine risk of bias for each study.
Result: The search turned up 81 records. The final sample included three trials ( 2 cohorts and 1 case control study) involving 510 patients. Statistical analysis showed that if RUST score is >6 at 3rd month then there is 7.12 times more chance for union( OR -7.12, 95% CI-4.06 to 12.49). This meta analysis suggests that the RUST score at 3rd month has the potential to provide an early prediction of tibial non-union. Radiographic union scale in tibial fracture (RUST), the Newcastle ottowa scale (NOS), fracture tibia, non-union, intramedullary interlocking nail.

Cardiac manifestations and COVID-19- A review

TCMS-Special issue: Indian Medical Research Views and Findings on Last 5 years (2023), pp. 429 – 434 Open Access Full-Text PDF

Vikas Ashok Mishra, Suhel Siddiqui, Pradeep Kumar Jain and Shishir Soni

Abstract:The World Health Organization (WHO) classified the most recent coronavirus disease outbreak of 2019 (COVID-19) a pandemic on March 11, 2020. The cause of COVID-19, Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), largely affects the respiratory system, with viral pneumonia as a complication most common manifestation. Moreover, SARS-CoV-2 has a number of cardiovascular symptoms that raise COVID-19’s morbidity and fatality rates. Individuals are more likely to develop COVID-19 and have a worse prognosis if they have underlying cardiovascular illnesses and traditional cardiovascular risk factors. Endothelial dysfunction, widespread microangiopathy with thrombosis, and elevated angiotensin II levels are potential pathways of cardiovascular damage. Acute coronary syndrome, myocarditis, heart failure, cardiac arrhythmias, and sudden death can all be caused by myocardial hyperinflammation. The early stages of COVID-19 show a high level of cardiac troponins and natriuretic peptides, which indicates an acute myocardial damage. Given the intricate relationship between COVID-19 and cardiovascular symptoms, comprehensive knowledge for the proper management of these patients. Treatment is symptomatic until a particular antiviral medication for COVID-19 becomes available. Information about COVID-19’s cardiovascular risk factors and symptoms is provided in this review.

Coefficient bounds for \(p\)-valent functions

OMA-Vol. 7 (2023), Issue 1, pp. 83 – 90 Open Access Full-Text PDF

Olusegun Awoyale and Timothy Oloyede Opoola

Abstract: This present paper introduces two new subclasses of p-valent functions. The coefficient bounds and Fekete-Szego inequalities for the functions in these classes are also obtained.

Limit cycles obtained by perturbing a degenerate center

OMA-Vol. 7 (2023), Issue 1, pp. 56 – 70 Open Access Full-Text PDF

Nabil Rezaiki and Amel Boulfoul

Abstract: This paper deals with the maximum number of limit cycles bifurcating from the degenerate centre
\[ \dot{x}=-y(3x^2+y^2),\: \dot{y}=x(x^2-y^2), \]
when we perturb it inside a class of all homogeneous polynomial differential systems of degree \(5\). Using averaging theory of second order, we show that, at most, five limit cycles are produced from the periodic orbits surrounding the degenerate centre under quintic perturbation. In addition, we provide six examples that give rise to exactly \(5, 4, 3, 2, 1\) and \(0\) limit cycles.

Expansion of the Jensen \((\Gamma_{1},\Gamma_{2})\)-functional inequatities based on Jensen type \((\eta,\lambda)\)-functional equation with \(3k\)-Variables in complex Banach space

OMA-Vol. 7 (2023), Issue 1, pp. 56 – 70 Open Access Full-Text PDF

Ly Van An

Abstract: In this paper, we work on expanding the Jensen \((\Gamma_{1},\Gamma_{2})\)-function inequalities by relying on the general Jensen \((\eta,\lambda)\)-functional equation with \(3k\)-variables on the complex Banach space. That is the main result of this.

On norms of derivations implemented by self-adjoint operators

OMA-Vol. 7 (2023), Issue 1, pp. 42 – 55 Open Access Full-Text PDF

Obogi Robert Karieko

Abstract:In this paper, we concentrate on norms of derivations implemented by self-adjoint operators. We determine the upper and lower norm estimates of derivations implemented by self-adjoint operators. The results show that the knowledge of self-adjoint governs the quantum chemical system in which the eigenvalue and eigenvector of a self-adjoint operator represents the ground state energy and the ground state wave function of the system respectively.

A class of power series based modified newton method with high precision for solving nonlinear models

OMA-Vol. 7 (2023), Issue 1, pp. 32 – 41 Open Access Full-Text PDF

Oghovese Ogbereyivwe and Salisu Shehu Umar

Abstract:This manuscript proposed high-precision methods for obtaining solutions for nonlinear models. The method uses the Newton method as its predictor and an iterative function that involves the perturbed Newton method with the quotient of two power series as the corrector function. The theoretical analysis of convergence indicates that the methods class is of convergence order four, requiring three functions evaluation per cycle. The computation performance comparison with some existing methods shows that the developed methods class has perfect precision.

Category Archives: Journals