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Latest Published Articles

Global well-posedness and analyticity for generalized porous medium equation in critical Fourier-Besov-Morrey spaces

OMA-Vol. 3 (2019), Issue 2, pp. 71 – 80 Open Access Full-Text PDF
Mohamed Toumlilin
Abstract: In this paper, we study the generalized porous medium equations with Laplacian and abstract pressure term. By using the Fourier localization argument and the Littlewood-Paley theory, we get global well-posedness results of this equation for small initial data \(u_{0}\) belonging to the critical Fourier-Besov-Morrey spaces. In addition, we also give the Gevrey class regularity of the solution.
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The primary corrosiveness of crude oils and destructions of metals

OJC-Vol. 2 (2019), Issue 2, pp. 1 – 8 Open Access Full-Text PDF
Suresh Aluvihara, Jagath K. Premachandra
Abstract: Metals play predominant prefaces regarding most of industrial components such as the crude oil refining industry although corrosion performed some banes. In the current research it was expected to investigate to compare the effect of corrosive properties of two different crude oils on the rates of corrosion in seven different types of ferrous metals. The contents of sulfur, mercaptans, organic acids, salt in both crude oils and chemical compositions of ferrous metals were determined by standard methods and instruments. A batch of similar sized metal coupons was prepared and immersed in both crude oils separately. The corrosion rate of each metal coupon was determined by the weight loss method in order to after 15, 30 and 45 days while observing the corroded metal surfaces by the optical microscope. The decayed concentrations of copper and ferrous in each crude oil sample were tested and the both initial and final hardness of each metal coupon were tested. According to the results there were observed lower corrosion rates from stainless steels, relatively higher impact from salts on the corrosion, formation corrosion compounds, corrosion cracks, pitting corrosion on metal surfaces and there were observed a slight reduction of hardness in each metal coupon eventually.
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Random attractors for Stochastic strongly damped non-autonomous wave equations with memory and multiplicative noise

OMA-Vol. 3 (2019), Issue 2, pp. 50 – 70 Open Access Full-Text PDF
Abdelmajid Ali Dafallah, Qiaozhen MA, Ahmed Eshag Mohamed
Abstract: In this paper, we study the dynamical behavior of solutions for the stochastic strongly damped wave equation with linear memory and multiplicative noise defined on \(\mathbb{R}^{n}\). Firstly, we prove the existence and uniqueness of the mild solution of certain initial value for the above-mentioned equations. Secondly, we obtain the bounded absorbing set. Lastly, We investigate the existence of a random attractor for the random dynamical system associated with the equation by using tail estimates and the decomposition technique of solutions.
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Computing multiplicative topological indices of some chemical nenotubes and networks

ODAM-Vol. 2 (2019), Issue 3, pp. 7 – 18 Open Access Full-Text PDF
Zaryab Hussain, Ahsan, Shahid Hussain Arshad
Abstract: The aim of this paper is to calculate the multiplicative topological indices of Zigzag polyhex nanotubes, Armchair polyhex nanotubes, Carbon nanocone networks, two dimensional Silicate network, Chain silicate network, six dimensional Hexagonal network, five dimensional Oxide network and four dimensional Honeycomb network.
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A note on the Kirchhoff index of graphs

ODAM-Vol. 2 (2019), Issue 3, pp. 1 – 6 Open Access Full-Text PDF
Marjan M. Matejić, Emina I. Milovanović, Predrag D. Milošević, Igor Ž. Milovanović
Abstract: Let \(G\) be a simple connected graph with \(n\) vertices, \(m\) edges, and a sequence of vertex degrees \(\Delta=d_1\geq d_2\geq\cdots\geq d_n=\delta >0\). Denote by \(\mu_1\geq \mu_2\geq\cdots\geq \mu_{n-1}>\mu_n=0\) the Laplacian eigenvalues of \(G\). The Kirchhoff index of \(G\) is defined as \(Kf(G)=n\sum_{i=1}^{n-1} \frac{1}{\mu_i}\). A couple of new lower bounds for \(Kf(G)\) that depend on \(n\), \(m\), \(\Delta\) and some other graph invariants are obtained.
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Determination of the dynamic shearing force and bending moment of a tensioned single-walled carbon nanotube subjected to a uniformly distributed external pressure

EASL-Vol. 2 (2019), Issue 3, pp. 40 – 52 Open Access Full-Text PDF
A. A. Yinusa, M. G. Sobamowo, A. O. Adelaja
Abstract: The high strength-to-weight ratio and flexibility of single walled carbon nanotubes (SWCNT) make them of potential use in the control of nanoscale structures for thermal, electrical, structural and mechanical applications. This indicates that they will have a vital contribution to nanotechnology engineering. This paper presents an exact solution to the dynamic response of such CNTs considering the shear force and bending moment under uniformly distributed external pressure. The dynamic behaviour of the SWCNT is modeled by employing the theories of Euler-Bernoulli beam and thermal elasticity mechanics. The developed model that governs the physics of the behaviour of the SWCNT when excited by the aforementioned external agents is solved using Integral transforms. The results of the close form solution in this work were compared with results of past works and excellent agreements were achieved. Furthermore, the dynamic study revealed that a point of maximum shear force on the CNT produced the minimum bending moment at any mode and for any parameter value considered. It is envisaged that this work will enhance the application of SWCNT for structural, electrical and mechanical uses.
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BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC