Multiplier properties for the \(AP\)-Henstock integral

OMA-Vol. 6 (2022), Issue 1, pp. 28 – 38 Open Access Full-Text PDF
Kwancheol Shin and JU Han Yoon

Abstract:In this paper, we investigate some properties of the \(AP\)-Henstock integral on a compact set and prove that the product of an \(AP\)-Henstock integrable function and a function of bounded variation is \(AP\)-Henstock integrable. Furthermore, we prove that the product of an \(AP\)-Henstock integrable function and a regulated function is also \(AP\)-Henstock integrable. We also define the \(AP\)-Henstock integral on an unbounded interval, investigate some properties, and show similar multiplier properties.

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Results of a perturbation theory generating a one-parameter semigroup

OMA-Vol. 6 (2022), Issue 1, pp. 21 – 27 Open Access Full-Text PDF
Akinola Yussuff Akinyele, Omotoni Ezekiel Jimoh, Jude Babatunde Omosowon, Liman Kinbokun Alhassan and Kareem Akanbi Bello

Abstract:This paper consists of the results about \(\omega\)-order preserving partial contraction mapping using perturbation theory to generate a one-parameter semigroup. We show that adding a bounded linear operator \(B\) to an infinitesimal generator \(A\) of a semigroup of the linear operator does not destroy A’s property. Furthermore, \(A\) is the generator of a one-parameter semigroup, and \(B\) is a small perturbation so that \(A+B\) is also the generator of a one-parameter semigroup.

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The \(q\)-Legendre inversions and balanced \(q\)-series identities

OMA-Vol. 6 (2022), Issue 1, pp. 7 – 14 Open Access Full-Text PDF
Xiaojing Chen and Wenchang Chu

Abstract:Two terminating balanced \(_4\phi_3\)-series identities are established by applying the bilateral \(q\)-Legendre inversions. Four variants of them are obtained by means of contiguous relations. According to the polynomial argument, four “dual” formulae for balanced \(_4\phi_3\)-series are deduced, that lead also to four non-terminating \(_2\phi_2\)-series identities.

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Long-time solutions for some mixed boundary value problems depicting motions of a class of Maxwell fluids with pressure dependent viscosity

OMS-Vol. 6 (2022), Issue 1, pp. 192 – 204 Open Access Full-Text PDF
Constantin Fetecau, Dumitru Vieru, Waqas Nazeer and Shehraz Akhtar

Abstract:Closed-form expressions are established for dimensionless long-tome solutions of some mixed initial-boundary value problems. They correspond to three isothermal unsteady motions of a class of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure. The fluid motion, between infinite horizontal parallel flat plates, is induced by the lower plate that applies time-dependent shear stresses to the fluid. As a check of the obtained results, the similar solutions corresponding to the classical incompressible Maxwell fluids performing same motions are recovered as limiting cases of present solutions. Finally, some characteristics of fluid motion as well as the influence of pressure-viscosity coefficient on the fluid motion are graphically presented and discussed.

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Critical and stable pendant domination

OMS-Vol. 6 (2022), Issue 1, pp. 187 – 191 Open Access Full-Text PDF
Purushothama S

Abstract:Let \(S\) be a dominating set of a graph \(G\). The set \(S\) is called a pendant dominating set of \(G\) if the induced subgraph of \(S\) contains a minimum of one node of degree one. The minimum cardinality of the pendant dominating set in \(G\) is referred to as the pendant domination number of \(G\), indicated by \(\gamma_{pe}(G)\). This article analyzes the effect of \(\gamma_{pe}(G)\) when an arbitrary node or edge is removed.

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Certain topological indices of Basava wheel windmill graph

OMS-Vol. 6 (2022), Issue 1, pp. 177 – 186 Open Access Full-Text PDF
B. Basavanagoud and Mahammad Sadiq Sayyed

Abstract:In this paper, we have proposed new windmill graph, that is Basava wheel windmill graph. The Basava wheel windmill graph \(W^{(m)}_{n+1}\) is the graph obtained by taking \(m\geq 2\) copies of the graph \(K_1+W_{n}\) for \(n\geq 4\) with a vertex \(K_1\) in common. Inspired by recent work on topological indices, proposed new degree-based topological indices namely, general \(SK_{\alpha}\) and \(SK^{\alpha}_1\) indices of a graph \(G\). We have obtained first and second Zagreb index, F-index, first and second hyper-Zagreb index, harmonic index, Randi\(\acute{c}\) index, general Randi\(\acute{c}\) index, sum connectivity index, general sum connectivity index, atom-bond connectivity index, geometric-arithmetic index, Symmetric division deg index, Sombor index, SK indices, general \(SK_{\alpha}\) and \(SK^{\alpha}_1\) indices of Basava wheel windmill graph. Further, we have computed exact values of these topological indices of chloroquine, hydroxychloroquine and remdesiver.

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On the sum of the cubes of generalized balancing numbers: The sum formula \(\sum\limits_{k=0}^{n}x^{k}W_{mk+j}^{3}\)

OMS-Vol. 6 (2022), Issue 1, pp. 152 – 167 Open Access Full-Text PDF
Yüksel Soykan, Erkan Tasdemir and Can Murat Dikmen

Abstract:In this paper, closed forms of the sum formulas \(\sum\limits_{k=0}^{n}x^{k}W_{mk+j}^{3}\) for generalized balancing numbers are presented. As special cases, we give sum formulas of balancing, modified Lucas-balancing and Lucas-balancing numbers.

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