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Latest Published Articles

Small convective motions of a visco-elastic fluid filling completely a container when the fluid is heated from below

OMA-Vol. 3 (2019), Issue 1, pp. 30–41 Open Access Full-Text PDF
Hilal Essaouini, Pierre Capodanno
Abstract: In this paper, we study the small oscillations of a visco-elastic fluid that is heated from below and fills completely a rigid container, restricting to the more simple Oldroyd model. We obtain the operatorial equations of the problem by using the Boussinesq hypothesis. We show the existence of the spectrum, prove the stability of the system if the kinematic coefficient of viscosity and the coefficient of temperature conductivity are sufficiently large and the existence of a set of positive real eigenvalues having a point of the real axis as point of accumulation. Then, we prove that the problem can be reduced to the study of a Krein-Langer pencil and obtain new results concerning the spectrum. Finally, we obtain an existence and unicity theorem of the solution of the associated evolution problem by means of the semigroups theory.
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On further results of hex derived networks

ODAM-Vol. 2 (2019), Issue 1, pp. 32–40 Open Access Full-Text PDF
Haidar Ali, Ammara Sajjad
Abstract: Topological indices are real numbers associated with molecular graphs of compounds that help to guess properties of compounds. Hex-Derived networks has an assortment of valuable applications in drug store, hardware, and systems administration. Imran et al. [1] computed the general Randić, first Zagreb, ABC, GA, ABC\(_{4}\), and GA\(_{5}\) indices for these hex-derived networks. In this article, we extend the work of [1] and compute some new topological indices of these networks.
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General Zagreb index of some cactus chains

ODAM-Vol. 2 (2019), Issue 1, pp. 24–31 Open Access Full-Text PDF
Nilanjan De
Abstract: The mathematical chemistry deals with applications of graph theory to study the physicochemical properties of molecules theoretically. A chemical graph is a simple graph where hydrogen depleted atoms are vertices and covalent bonds between them represent the edges. A topological index of a graph is a numeric quantity obtained from the graph mathematically. A cactus graph is a connected graph in which no edges lie in more than one cycle. In this study, we derive exact expressions of general Zagreb index of some cactus chains.
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K Banhatti and K hyper-Banhatti indices of nanotubes

EASL-Vol. 2 (2019), Issue 1, pp. 19–37 Open Access Full-Text PDF
Muhammad Shahzad Anjum, Muhammad Usman Safdar
Abstract: Nanomaterials are compound substances or materials that are produced and utilized at an exceptionally little scale. Nanomaterials are created to display novel attributes contrasted with a similar material without nanoscale highlights, for example, expanded quality, synthetic reactivity or conductivity. Topological indices are numbers related to molecular graphs that catch symmetry of molecular structures and give it a scientific dialect to foresee properties, such as: boiling points, viscosity, the radius of gyrations and so on. In this paper, we aim to compute topological indices of \(TUC_4[m,n]\), \(TUZC_6[m,n]\), \(TUAC_6[m,n]\), \(SC_5C_7[p,q]\), \(NPHX[p,q]\), \(VC_5C_7[p,q]\) and \(HC_5C_7[p,q]\) nanotubes. We computed first and second K Banhatti indices, first and second K hyper-Banhatti indices and harmonic Banhatti indices of understudy nanotubes. We also computed multiplicative version of these indices. Our results can be applied in physics, chemical, material, and pharmaceutical engineering.
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Unsteady Casson nanofluid squeezing flow between two parallel plates embedded in a porous medium under the influence of magnetic field

OMS-Vol. 3 (2019), Issue 1, pp. 59–73 Open Access Full-Text PDF
Gbeminiyi Sobamowo, Lawrence Jayesimi, David Oke, Ahmed Yinusa, Oluwatoyin Adedibu
Abstract: This paper investigates the squeezing flow of an electrically conducting magnetohydrodynamic Casson nanofluid between two parallel plates embedded in a porous medium using differential transformation and variation of parameter methods. The accuracies of the approximate analytical methods for the small and large values of squeezing and separation numbers are investigated and established. Good agreements are established between the results of the approximate analytical methods are compared with the results numerical method using fourth-fifth order Runge-KuttaFehlberg method. However, the results of variation of parameter methods show better agreement with the results of numerical method than the results of differential transformation method. Thereafter, the developed approximate analytical solutions are used to investigate the effects of pertinent flow parameters on the squeezing phenomena of the nanofluids between the two moving parallel plates. The results established that the squeezing number and magnetic field parameters decrease as the flow velocity increases when the plates were coming together. Also, the velocity of the nanofluids further decreases as the magnetic field parameter increases when the plates move apart. However, the velocity is found to be directly proportional to the nanoparticle concentration during the squeezing flow i.e. when the plates are coming together and an inverse variation between the velocity and nanoparticle concentration is recorded when the plates are moving apart. As increased physical insights into the flow phenomena are provided, it is hope that this study will enhance the understanding the phenomena of squeezing flow in various applications such as power transmission, polymer processing and hydraulic lifts.
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BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC