University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Applied Mathematics

World University root node

arXiv preprint arXiv:2111.

Nonlocality without entanglement: Party asymmetric case

Within the framework of linearised theory of water waves, a model of oblique wave scattering by obstacles in the form of thin multiple surface-piercing porous barriers having non-uniform porosity is analysed. Herein, we consider a flexible base in an ocean of uniform finite depth. The flexible base surface is modelled as a thin elastic plate under the acceptance of Euler–Bernoulli beam equation. With the aid of eigenfunction expansion method along with mode-coupling relations, four Fredholm-type integral equations are obtained from the boundary value problem. The multi-term Galerkin approximations in terms of Chebychev polynomials multiplied by suitable weight functions are used for solving those integral equations. Analytic solutions for different hydrodynamic quantities (viz. reflection coefficients, transmission coefficients, dissipated wave energy and non-dimensional wave force) are determined, and those quantities are displayed graphically for various values of the dimensionless parameters. It is observed from the graphical representations that the permeability of the barriers and thickness of the bottom surface play a crucial role in modelling of efficient breakwaters. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Zeitschrift fur Angewandte Mathematik und Physik

Effects of flexible bed on oblique wave interaction with multiple surface-piercing porous barriers

Wave interaction with a thin porous barrier submerged in the lower layer of an infinite depth fluid are analyzed based on plane wave approximations. By employing Greens integral theorem, we formulate a hypersingular integral equation in terms of unknown potential difference across the porous barrier. A collocation method using a finite series of Chebyshev polynomials of the second kind has been introduced to get the unknown difference potential numerically. The reflection and transmission coefficients and hydrodynamic forces on a porous barrier are analyzed for various physical parameters associated with the problem. The present study will be of significant importance in the design of various types of coastal structures used in the marine environment for the reflection and dissipation of wave energy. © Springer Nature Singapore Pte Ltd. 2021.

Lecture Notes in Mechanical Engineering

Interface wave diffraction by a permeable thin barrier

The most commonly developed inventory models are the classical economic order quantity model, is governed by the integer order differential equations. We want to come out from the traditional thought i.e. classical order inventory model where the memory phenomena are absent. Here, we want to incorporate the memory effect that is based on the fact economic agents remember the history of changes of exogenous and endogenous variables. In this paper, we have proposed and solved a fractional order economic order quantity model with constant demand rate where the demand is fully backlogged during shortage time. Finally, a numerical example has been illustrated for this model to show the memory dependency of the system. The numerical example clears that for the considered system the profit is maximum in long memory affected system compared to the low memory affected or memory less system. © 2021 NSP Natural Sciences Publishing Cor. All Rights Reserved.

Progress in Fractional Differentiation and Applications

Study of Memory Effect in an Economic Order Quantity Model for Completely Backlogged Demand During Shortage

Fractional one-dimensional Schrödinger equation is considered within fractional position-dependent mass formalism. Fractional Coulomb type interaction is taken for the study. The entire work is composed of Katugampola fractional derivative. Point canonical transformation (PCT) is used as an analytical tool. The energy spectrum of the bound states and their eigenfunctions are written explicitly for different position-dependent mass profiles. Finally, we furnish a few wave function variations for different fractional parameter values and two separate mass profiles. © 2021 Tsing Hua University. All rights reserved.

Applied Mathematics E - Notes

Point canonical transformation and the time independent fractional schrödinger equation with position dependent mass

Waves in Random and Complex Media

Interactions in a nonlocal thermoelastic hollow sphere with voids due to harmonically varying heat sources

In the present paper we have investigated the impact of predator harvesting in a two-dimensional prey–predator model with Holling type III functional response. The main objective of this paper is to study the change of dynamical behaviour of the prey–predator model in the presence of non-linear predator harvesting. The model system shows complex dynamics with the change of different system parameters. We have established the positivity and boundedness of the solutions under a certain parametric condition with non-negative initial conditions. The existence and stability criterion of different equilibrium points are investigated in terms of system parameters. We have shown that the system undergoes through saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation under different parametric conditions. The structural changes or the system bifurcations predict the global dynamics of the model system. We have computed the first Lyapunov number to find the direction of the Hopf-bifurcating periodic solution of the system. Using numerical simulation we have studied here the effect of conversion efficiency, protection of the environment to the prey population and non-linear predator harvesting on the model dynamics. Finally the paper is ended with some conclusions. © 2021 Informa UK Limited, trading as Taylor &amp; Francis Group.

International Journal of Modelling and Simulation

The Complex Dynamical Behavior of a Prey-Predator Model with Holling Type-III Functional Response and Non-Linear Predator Harvesting

The present work looks for new spherically symmetric wormhole solutions of the Einstein field equations based on the well-known embedding class 1, i.e. Karmarkar condition. The embedding theorems have an interesting property that connects an n-dimensional space-time to the higher-dimensional Euclidean flat space-time. The Einstein field equations yield the wormhole solution by violating the null energy condition (NEC). Here, wormholes solutions are obtained corresponding to three different redshift functions: rational, logarithm, and inverse trigonometric functions, in embedding class 1 space-time. The obtained shape function in each case satisfies the flare-out condition after the throat radius, i.e. good enough to represents wormhole structure. In cases of WH1 and WH2, the solutions violate the NEC as well as strong energy condition (SEC), i.e. here the exotic matter content exists within the wormholes and strongly sustains wormhole structures. In the case of WH3, the solution violates NEC but satisfies SEC, so for violating the NEC wormhole preserve due to the presence of exotic matter. Moreover, WH1 and WH2 are asymptotically flat while WH3 is not asymptotically flat. So, indeed, WH3 cutoff after some radial distance r = r1 > rs, the Schwarzschild radius, and match to the external vacuum solution. © 2021 World Scientific Publishing Company.

International Journal of Modern Physics A

Wormhole solutions in embedding class 1 space-time

This paper deals with a system of two fractional order differential equations for prey-predator interaction with intra-specific competition among predators. The fractional order differential equation is considered in the sense of Caputo derivative and the derivation of the fractional order model is explained in terms of memory effect on population growth. Detailed mathematical results are provided to establish the positiveness, existence–uniqueness and boundedness of the solutions. The conditions required for local asymptotic stability of various equilibrium points and global stability of coexistence equilibrium are derived along with the Hopf-bifurcation condition for coexistence equilibrium. The effect of memory on the system dynamics through the shift of Hopf-bifurcation threshold is demonstrated with the help of exhaustive numerical simulations. This study also reveals the effect of memory based growth on global bifurcation threshold. © 2020

Chaos, Solitons and Fractals

Memory effect on Bazykin's prey-predator model: Stability and bifurcation analysis

A dynamical model has been developed to envisage the star formation scenario in filamentary molecular clouds. In the present work a double well potential has been considered to find the number of stable stationary points as the origin of field star, binary stars or stellar associations. It is found that low density structure can lead to the formation of field stars while an intermediate density structure is favourable for formation of binary stars. Stellar associations are generally prevalent in dense filamentary molecular clouds. © 2021, The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature.