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Latest Published Articles

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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Numerical solution of boundary layer flow of MHD nanofluid over a stretching surface with chemical reaction and viscous dissipation effects

OMS-Vol. 3 (2019), Issue 1, pp. 289 – 299 Open Access Full-Text PDF
Santoshi Misra, G. Narender, K. Govardha
Abstract: A numerical study has been carried out in the analysis of two dimensional, incompressible and steady convective flow over a stretching surface in the presence of chemical reaction along with viscous dissipation. A mathematical model which resembles the physical flow problem has been developed. Similarity transformations are used to convert the fundamental partial differential equations into a system of nonlinear ordinary differential equations. The resulting system of nonlinear ordinary differential equations are then solved by using the shooting method along with Adams-Moultan method. The numerical solution obtained for the velocity, temperature and concentration profiles has been presented through graphs for different choice of the physical parameters.
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How to create satisfying high-resolution microscope stitched pictures with limited resources? A simple method applied to cross-sections of teeth

EASL-Vol. 2 (2019), Issue 3, pp. 30 – 39 Open Access Full-Text PDF
Maxime Bedez, Thomas Fasquelle, Cécile Olejnik
Abstract: By associating last progresses in photography, computer science and additive manufacturing, cost-effective planar stitching of non-structured photographs of microscope slides into high definition large pictures is achievable. The proposed method, inspired by previous works and state-of-the art equipment, uses non-professional camera, little pre-processing, no post processing, and little to no investment is needed. A total duration of 41 min was observed to create a high-quality, high-resolution full picture of a sagittal cross-section of a permanent maxillary central incisor, from 16 original photographs with a \(\times\)40 microscope optical magnification. Final pictures weights are in-between 60 Mo and 340 Mo, depending on the format and the number of initial photographs. Higher magnification does not seem to enhance pictures, but sensibly increases file weight. This method has numerous applications, such as research, sharing and teaching and will certainly be enhanced in the future thanks to the high speed development of smartphone abilities.
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A mathematical model for fish management in the Sundarbans ecosystem

OMA-Vol. 3 (2019), Issue 2, pp. 42 – 49 Open Access Full-Text PDF
Md. Nazmul Hasan, Md. Haider Ali Biswas, Md. Sharif Uddin
Abstract: With the establishment of 200-mile territorial zone in the Bay of Bengal for most countries having coastlines. The control of fishing in these zones has become highly regulated by these countries concerned. In this sense, fishing in territorial waters can be considered a sole owner fishery problem. If the people of a country are allowed to fish freely in the territorial zones, it can be termed as an open access fishery. In an open access fishery, the exploitation of fishing opportunity is completely uncontrolled. This study deals with the problem of harvesting in the prey-predator fishery model in the open access zones and seeks a plan for prey for sustainable fishing, particularly in Sundarbans ecosystem which is situated in the coastal area of the Bay of Bengal. The positive steady state of both local and global stability has been established. Optimal harvesting strategy is also studied for these purposes.
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On certain subclasses of p-valent functions with negative coefficients defined by a generalized differential operator

OMA-Vol. 3 (2019), Issue 2, pp. 32 – 41 Open Access Full-Text PDF
Bitrus Sambo, Gideon Benjamin Meller
Abstract: In this article, we introduce new subclasses of normalized analytic functions in the unit disk \(U\), defined by a generalized Raducanu-Orhan differential Operator. Various results are driven including coefficient inequalities, growth and distortion theorem, closure property, \(\delta\)-neighborhoods, extreme points, radii of close-to-convexity, starlikeness and convexity for these subclasses.
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BOOK-foundations-of-mathematical-analysis-and-semigroups-theory
BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC