Different Approaches for the Synthesis of Zinc Oxide Nanoparticles

OJC-Vol. 1 (2018), Issue 1, pp. 19–25 | Open Access Full-Text PDF
Zaheer Ahmad, Farman Ullah Khan, Sajid Mahmood, Tariq Mahmood, Aisha Shamim
Abstract:In this work we have described the synthesis of Zinc Oxide nanoparticles through chemical and biological methods. For biological synthesis Aspargillus niger was used. The product obtained was characterized through different analytical techniques like XRD, SEM and EDX. The obtained results were matched with the literature. It was confirmed that the Zinc Oxide nanoparticles can also be prepared from Aspargillus niger.Which may be more ecofriendly and economical compared to other commonly used methods.
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Zero-Sum Flow Number of Some Grid Graphs

ODAM-Vol. 1 (2018), Issue 1, pp. 16–25 | Open Access Full-Text PDF
Muhammad Kamran Siddiqui, Muhammad Naeem, Muhammad Imran
Abstract:For an undirected graph \(G\), a zero-sum flow is an assignment of nonzero integers to the edges such that the sum of the values of all edges incident with each vertex is zero, and we call it a zero-sum \(k\)-flow if the absolute values of edges are less than \(k\). We define the zero-sum flow number of \(G\) as the least integer \(k\) for which \(G\) admitting a zero sum \(k\)-flow. In this paper we gave complete zero-sum flow and zero sum number for octagonal grid, generalized prism and book graph.
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Distance-based Indices Computation of Symmetry Molecular Structures

OMS-Vol. 2 (2018), Issue 1, pp. 323–337 Open Access Full-Text PDF
Li Yan, Mohammad Reza Farahani, Wei Gao
Abstract:Most of molecular structures have symmetrical characteristics. It inspires us to calculate the topological indices by means of group theory. In this paper, we present the formulations for computing the several distance-based topological indices using group theory. We solve some examples as applications of our results.
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On Graph Invariants of Oxide Network

EASL-Vol. 1 (2018), Issue 1, pp. 23–28 | Open Access Full-Text PDF
Muhammad Imran, Asima Asghar, Abdul Qudair Baig
Abstract:The application of graph theory in chemical and molecular structure research far exceeds people’s expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. In this report, we study the several Zagreb polynomials and Redefined Zagreb indices of Oxide Network.
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Computing Degree-Based Topological Indices of Jahangir Graph

EASL-Vol. 1 (2018), Issue 1, pp. 16–22 | Open Access Full-Text PDF
Wei Gao, Asima Asghar, Waqas Nazeer
Abstract:Topological indices are numerical numbers associated with a graph that helps to predict many properties of underlined graph. In this paper we aim to compute multiplicative degree based topological indices of Jahangir graph.
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\(L^p-\) boundedness for integral transforms associated with singular partial differential operators

OMA-Vol. 2 (2018), Issue 2, pp. 53–77 | Open Access Full-Text PDF
Lakhdar T. Rachdi, Samia Sghaier
Abstract:We define fractional transforms \(\mathscr{R}_\mu\) and \(\mathscr{H}_\mu\), \(\mu>0\) on the space \(\mathbb{R}\times\mathbb{R}^n\). First, we study these transforms on regular function spaces and we establish that these operators are topological isomorphisms and we give the inverse operators as integro differential operators. Next, we study the \(L^p\)-boundedness of these operators. Namely, we give necessary and sufficient condition on the parameter \(\mu\) for which the transforms \(\mathscr{R}_\mu\) and \(\mathscr{H}_\mu\) are bounded on the weighted spaces \(L^p([0,+\infty[\times\mathbb{R}^n,r^{2a}dr\otimes dx)\) and we give their norms.
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Oscillation Criteria for Nonlinear Dynamic Equations on Time Scales

OMS-Vol. 2 (2018), Issue 1, pp. 307–322 Open Access Full-Text PDF
Merve Zingil, Fatma Serap Topal
Abstract:The main goal of this article is to study the oscillation criteria of the second-order neutral differential equations on time scales. We give several theorems and related examples to illustrate the applicability of these theorems. Our results extend some recent work in the literature.
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Remarks on Fractional Locally Harmonious Coloring

OMS-Vol. 2 (2018), Issue 1, pp. 301–306 Open Access Full-Text PDF
Wei Gao
Abstract:Locally harmonious coloring is a relax version of standard harmonious coloring which only needs that the color pairs for adjacent edges are different. In this remark, we introduce the concept of fractional locally harmonious coloring, and present some basic facts for this coloring.
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