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Kar T.K.,Panskura Banamali College | Jana S.,Abhedananda Mahavidyalaya
Biophysical Reviews and Letters | Year: 2017

In this paper we have proposed and analyzed a simple three-dimensional mathematical model related to malaria disease. We consider three state variables associated with susceptible human population, infected human population and infected mosquitoes, respectively. A discrete delay parameter has been incorporated to take account of the time of incubation period with infected mosquitoes. We consider the effect of insecticide control, which is applied to the mosquitoes. Basic reproduction number is figured out for the proposed model and it is shown that when this threshold is less than unity then the system moves to the disease-free state whereas for higher values other than unity, the system would tend to an endemic state. On the other hand if we consider the system with delay, then there may exist some cases where the endemic equilibrium would be unstable although the numerical value of basic reproduction number may be greater than one. We formulate and solve the optimal control problem by considering insecticide as the control variable. Optimal control problem assures to obtain better result than the noncontrol situation. Numerical illustrations are provided in support of the theoretical results. © 2017 World Scientific Publishing Company.


Seth S.K.,M.G. Mahavidyalaya | Maity G.C.,Abhedananda Mahavidyalaya | Kar T.,Indian Association for The Cultivation of Science
Journal of Molecular Structure | Year: 2012

An anthrilidine derivative of arjunolic acid, namely, anthrylidene methyl arjunolate (1) have been synthesized and characterized by X-ray structural studies with a detailed analysis of Hirshfeld surfaces and fingerprint plots facilitating a comparison of intermolecular interactions in building self-assembled framework. The central six member fused ring, which is flattened due to the presence of a CC double bond, adopts a sofa conformation, whereas other fused six member rings assumes chair conformations. All the fused rings have trans fusion except one ring junction, which is in cis fusion. The crystal packing of (1) exhibits intermolecular OH⋯O and CH⋯O hydrogen bonds forming R33(7) ring motif and are further linked through CH⋯π (arene) bonds to generate a framework. The fingerprint plots enabled to decode intermolecular interaction types present in the title crystal structure and the structures retrieved from the Cambridge Structural Database (CSD). A comparison of Hirshfeld surface in the title compound with similar structure retrieved from the CSD has been presented. © 2012 Elsevier B.V. All rights reserved.


Jana S.,Abhedananda Mahavidyalaya | Nandi S.K.,Nayabasat P. M. Sikshaniketan | Kar T.K.,Indian Institute of Science
Acta Biotheoretica | Year: 2016

This paper describes a traditional SIR type epidemic model with saturated infection rate and treatment function. The dynamics of the model is studied from the point of view of stability and bifurcation. Basic reproduction number is obtained and it is shown that the model system may possess a backward bifurcation. The global asymptotic stability of the endemic equilibrium is studied with the help of a geometric approach. Optimal control problem is formulated and solved. Some numerical simulation works are carried out to validate our analytical results. © 2015, Springer Science+Business Media Dordrecht.


Seth S.K.,Indian Association for The Cultivation of Science | Maity G.C.,Abhedananda Mahavidyalaya | Kar T.,Indian Association for The Cultivation of Science
Journal of Molecular Structure | Year: 2011

A benzylidene derivative of arjunolic acid, namely, para-nitro benzylidene methyl arjunolate (3) have been synthesized and characterized by X-ray structural studies and the electronic structure was calculated at the DFT level with a detailed analysis of Hirshfeld surface and fingerprint plot facilitating a comparison of intermolecular interactions. The crystal packing of (3) exhibits intermolecular O-H⋯O and C-H⋯O hydrogen bonds forming linear chains propagating parallel to [1 0 0] and [0 1 0] directions, respectively, which are further linked through C-H⋯π (arene) bonds to generate two-dimensional framework. Investigation of intermolecular interactions and crystal packing via Hirshfeld surface analysis reveals that more than two-thirds of the close contacts are associated with weak interactions. Hirshfeld surface analysis for visually analyzing intermolecular interactions in crystal structures employing molecular surface contours and 2D fingerprint plots have been used to examine molecular shapes. The large HOMO-LUMO energy gap indicates a high kinetic stability for the title compound (3). © 2011 Elsevier B.V. All rights reserved.


Debsarma S.,University of Calcutta | Senapati S.,Abhedananda Mahavidyalaya | Das K.P.,University of Calcutta
Physics of Fluids | Year: 2014

The present work is motivated by the work of Leblanc ["Amplification of nonlinear surface waves by wind," Phys. Fluids 19, 101705 (2007)] which showed that Stokes waves grow super exponentially under fair wind as a result of modulational instability. Here, we have studied the effect of wind in a situation of crossing sea states characterized by two obliquely propagating wave systems in deep water. It is found that the wind-forced uniform wave solution in crossing seas grows explosively with a super-exponential growth rate even under a steady horizontal wind flow. This is an important piece of information in the context of the formation of freak waves. © 2014 AIP Publishing LLC.


PubMed | Abhedananda Mahavidyalaya, Indian Institute of Science and Nayabasat P. M. Sikshaniketan
Type: Journal Article | Journal: Acta biotheoretica | Year: 2016

This paper describes a traditional SIR type epidemic model with saturated infection rate and treatment function. The dynamics of the model is studied from the point of view of stability and bifurcation. Basic reproduction number is obtained and it is shown that the model system may possess a backward bifurcation. The global asymptotic stability of the endemic equilibrium is studied with the help of a geometric approach. Optimal control problem is formulated and solved. Some numerical simulation works are carried out to validate our analytical results.


Das N.S.,Jadavpur University | Ghosh P.K.,Abhedananda Mahavidyalaya | Mitra M.K.,Jadavpur University | Chattopadhyay K.K.,Jadavpur University
Physica E: Low-Dimensional Systems and Nanostructures | Year: 2010

Nanocrystalline cadmium sulfide thin films were deposited by the radio frequency magnetron sputtering technique on Si and glass substrates with different particle sizes and thicknesses by varying deposition time. X-ray diffraction and transmission electron microscopic studies confirmed the nanocrystalline cubic CdS phase formation. TEM micrographs of the films revealed the manifestation of nano-CdS phase with average particle size of 3.67.3 nm for different films. These nanocrystalline films were analyzed by spectroscopic ellipsometry. The optical constants and the fitting constants were obtained by fitting the ellipsometric parameter del and psi data using Forouhi and Bloomer models in the wavelength range 248825 nm. The optical band gaps of the films were also measured by spectrophotometric studies. It was found that the energy band gap decreased from 3.28 to 2.54 eV when the film thickness increased from 153 to 205 nm. © 2010 Elsevier B.V. All rights reserved.


Ghosh P.K.,Abhedananda Mahavidyalaya | Chattopadhyay K.K.,Jadavpur University
AIP Conference Proceedings | Year: 2013

Nanoparticles of ZnS have been synthesized via radio frequency magnetron sputtering technique. Selected area electron diffraction patterns confirmed the nanocrystalline cubic phase of ZnS. TEM micrographs of the thin films revealed the manifestation of ZnS nanoparticles (3.00-5.83 nm). UV-VIS-NIR spectrophotometric measurements showed that the films are highly transparent ∼ 90 % with a blue shift of absorption edge. The particle size calculated from the shift of direct bandgap (3.89-4.44 eV) due to quantum confinement of nanoparticles lying in the range 3.23-5.60 nm, which well support the TEM results. The photoluminescence spectra of the films showed sulfer vacancy in the films and the EDX results also supported these results. © 2013 AIP Publishing LLC.


Choudhuri A.,Visva Bharati | Talukdar B.,Visva Bharati | Das U.,Abhedananda Mahavidyalaya
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2010

We observe that the fully nonlinear evolution equations of Rosenau and Hymann, often abbreviated as K (n,m) equations, can be reduced to Hamiltonian form only on a zero-energy hypersurface belonging to some potential function associated with the equations. We treat the resulting Hamiltonian equations by the dynamical systems theory and present a phase-space analysis of their stable points. The results of our study demonstrate that the equations can, in general, support both compacton and soliton solutions. For the K (2,2) and K (3,3) cases one type of solutions can be obtained from the other by continuously varying a parameter of the equations. This is not true for the K (3,2) equation for which the parameter can take only negative values. The K (2,3) equation does not have any stable point and, in the language of mechanics, represents a particle moving with constant acceleration. © 2010 The American Physical Society.


Jana S.,Abhedananda Mahavidyalaya | Haldar P.,Sundarban Hazi Desarat College | Kar T.K.,Indian Institute of Science
International Journal of Computer Mathematics | Year: 2016

In this article, we consider a susceptible–infectious–recovered (SIR) type epidemic model with some isolation to the susceptible, treatment for infectives, and vaccination to the newly recruited individuals. The basic reproduction number (Formula presented.) is obtained, and both the existence and stability of the disease-free and endemic equilibrium are discussed. We study the influence of isolation on infected individuals. We also study the existence of optimal control for both vaccination and treatment to minimize both the infected population and the costs required to control the disease. All the theoretical results are verified through numerical simulations and some of the key findings are given at the end of the article. © 2016 Informa UK Limited, trading as Taylor & Francis Group

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