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Latest Published Articles

A Note on the Zeroth-order General Randić Index of Polygonal Cacti

ODAM-Vol. 1 (2018), Issue 1, pp. 01–07 | Open Access Full-Text PDF
Jiachang Ye, Yuedan Yao
Abstract:The zeroth-order general Randić index of a simple connected graph G is defined as \(R_{\alpha}^{0}(G)=\sum_{u\in V(G)} \big(d(u)\big)^{\alpha}\), where \(d(u)\) is the degree of \(u\) and \(\alpha\not\in \{0,1\}\) is a real number. A \(k\)-polygonal cactus is a connected graph in which every edge lies in exactly one cycle of length \(k\). In this paper, we present the extremal \(k\)-polygonal cactus with \(n\) cycles for \(k\geq3\) with respect to the zeroth-order general Randić index.
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Viscosity methods for approximating solutions of variational inequalities for asymptotically nonexpansive mappings

OMA-Vol. 2 (2018), Issue 2, pp. 27–40 | Open Access Full-Text PDF
Muhammad Akmal, Muhammad Saqib Khan, Shahzad Ahmad Maitla
Abstract:The aim of this paper is to present a viscosity approximation method for asymptotically nonexpansive mappings in Banach spaces. The strong convergence of the viscosity rules is proved with some assumptions. This paper extend and improve results presented in [1, 2, 3, 4].
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The study of honey comb derived network via topological indices

OMA-Vol. 2 (2018), Issue 2, pp. 10–26 | Open Access Full-Text PDF
Wei Gao, Muhammad Asif, Waqas Nazeer
Abstract:Chemical reaction network theory is an area of applied mathematics that attempts to model the behavior of real world chemical systems. Since its foundation in the 1960s, it has attracted a growing research community, mainly due to its applications in biochemistry and theoretical chemistry. It has also attracted interest from pure mathematicians due to the interesting problems that arise from the mathematical structures involved. In this report, we compute newly defined topological indices, namely, Arithmetic-Geometric index (\(AG_{1}\) index), \(SK\) index, \(SK_{1}\) index, and \(SK_{2}\) index of the Honey Comb Derived Networks. We also compute sum connectivity index and modified Randić index. Moreover we give geometric comparison of our results.
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Oscillatory Behavior of Second Order Nonlinear Difference Equations with a Non-Positive Neutral Term

OMS-Vol. 2 (2018), Issue 1, pp. 240–252 Open Access Full-Text PDF
Said R. Grace, Shurong Sun, Limei Feng, Ying Sui
Abstract:We shall present new oscillation criteria of second order nonlinear difference equations with a non-positive neutral term of the form \(\Delta(a(t)(\Delta(x(t)-p(t)x(t-k)))^{\gamma})+q(t)x^{\beta}(t+1-m)=0,\) with positive coefficients. Examples are given to illustrate the main results.
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The Weighted Square Integral Inequalities for Smooth and Weak Subsolution of Fourth Order Laplace Equation

OMS-Vol. 2 (2018), Issue 1, pp. 228–239 Open Access Full-Text PDF
Muhammad Shoaib Saleem, J. Pečarič, Mubeen Munir, Asghar Ali, Muhammad Shahid Iqbal Tubssam
Abstract:In this work we develop the weighted square integral estimates for the second derivatives of weak subsolution of forth order Laplace equation. It is natural generalization of inequalities develop for the Superharmonic functions in [1].
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Ontology Similarity Computing Based on Stochastic Primal Dual Coordinate Technique

OMS-Vol. 2 (2018), Issue 1, pp. 221–227 Open Access Full-Text PDF
Guoshun Liu, Zhiyang Jia, Wei Gao
Abstract:With the extensive application of ontology in the fields of information retrieval and artificial intelligence, the ontology-based conceptual similarity calculation becomes a hot topic in ontology research. The essence of ontology learning is to obtain the ontology function through the learning of ontology samples, so as to map the vertices in each ontology graph into real numbers, and finally determine the similarity between corresponding concepts by the difference between real numbers. The essence of ontology mapping is to calculate concepts from different ontologies. In this paper, we introduce new ontology similarity computing in view of stochastic primal dual coordinate method, and two experiments show the effectiveness of our proposed ontology algorithm.
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BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC