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

Local distinguishability of orthogonal product states is an area of active research in quantum information theory. However, most of the relevant results about local distinguishability are found in bipartite quantum systems and very few are known in multipartite cases. In this paper, we construct a locally indistinguishable subset in C2d⨂ C2d⨂ C2d, d≥ 2 that contains 18 (d- 1 ) orthogonal product states. Further, we generalize our method to arbitrary tripartite quantum systems Ck⨂ Cl⨂ Cm. This result helps us to understand the role of nonlocality without entanglement in multipartite quantum systems. Finally, we prove that a three-qubit GHZ state is sufficient as a resource to distinguish each of the above classes of states. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.

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Quantum Information Processing

Nonlocality of tripartite orthogonal product states

Recently, a new class of monogamy relations (actually, exponentially many) was provided by Christopher Eltschka et al. in terms of squared concurrence. Their approach is restricted to the distribution of bipartite entanglement shared between different subsystems of a global state. We have critically analysed those monogamy relations in three as well as in four-qubit pure states using squared negativity. We have been able to prove that in the case of pure three-qubit states those relations are always true in terms of squared negativity. However, if we consider the pure four-qubit states, the results are not always true. Rather, we find opposite behaviour in some particular classes of four-qubit pure states where some of the monogamy relations are violated. We have provided analytical and numerical evidences in support of our claim. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.

New monogamy relations for multiqubit systems

The Role of Harvesting in Population Control in Presence of Multiple Stochastic Noise Sources

This paper considers the reflection and transmission of flexural gravity waves by a pair of bottom-mounted rectangular barriers of arbitrary height and width. Depth of the fluid considered here is finite but not necessarily uniform. The fluid region is bounded by an infinite long thin ice sheet of homogeneous properties. Using linearized water wave theory the velocity potential associated with the motion is formulated. Eigenfunction matching technique is used to convert the boundary value problem to a set of integral equations which are solved by using multi-term Galerkin method. The reflection and transmission coefficients are calculated and represented graphically. An expression for the energy balance relation is given and checked carefully. A model of the problem in which the fluid is bounded by a free surface is recovered. For a set of physical parameters the results are analyzed through a number of figures. The convergence and correctness of the method is confirmed by comparing the results with the one available in the literature. It is shown that a pair of thick bottom-mounted barriers have significant impact on reflected and transmitted flexural gravity waves. Resonance effects are observed and verified for different parameters of the current problem. © 2020 Elsevier Ltd

Ocean Engineering

Interaction of flexural gravity wave in ice cover with a pair of bottom-mounted rectangular barriers

In this paper we have studied Left and Right ventricular hypertrophy of heart from ECGs using fractional calculus. An ECG is a rough or unreachable curve which is continuous everywhere but nondifferentiable at some points or all points where classical calculus fails. Our purpose of this paper is to find left and right fractional derivatives at those non-differentiable points and then predict LVH and RVH by calculating the phase transition values (absolute difference of left and right fractional derivatives). Our investigation shows that for LVH patients the phase transition values at the non-differentiable points of V1, V2, V5 and V6 leads are higher than those for normal ECG. For RVH ECG the phase transition values at S are smaller than those of R in V1 leads which are just opposite to the case of normal ECGs. Fractal dimension and Hurst Exponents of V1, V2, V5 and V6 leads of the ECGs have been calculated for both problematic and normal ECGs. All such measures may help doctors to diagnose LVH and RVH from ECG more accurately than the technique they use. ©2020 L&amp;H Scientific Publishing, LLC. All rights reserved. Email address: uttam math@yahoo.co.in

Journal of Applied Nonlinear Dynamics

Prediction of Ventricular Hypertrophy of Heart Using Fractional Calculus

Scattering of surface waves by two permeable vertical walls having apertures at different depths in uniform finite depth water has been studied assuming linear theory. The problem is reduced to a set of coupled integral equations involving the difference of velocity potentials across each wall as unknown function. A multi-term Galerkin's technique is employed to approximate these unknown functions and to obtain approximate solution of the integral equations. Numerical estimates for the reflection and transmission coefficients are then obtained by solving a linear system. It is observed from graphical representations of the reflection coefficient that in comparison with non-identical walls the minima of the reflection coefficient become very close to zero at discrete frequencies in case of identical walls. Very good agreement between some earlier known results and our present results is established. © 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group.

Waves in Random and Complex Media

Oblique wave scattering by two thin non-uniform permeable vertical walls with unequal apertures in water of uniform finite depth

The problem of oblique scattering of surface waves by a thick partially immersed rectangular barrier or a thick submerged rectangular barrier extending infinitely downwards in deep water is studied here to obtain the reflection and transmission coefficients semi-analytically. Use of Havelock’s expansion of water wave potential function reduces each problem to an integral equation of first kind on the horizontal component of velocity across the gap above or below the barrier. Multi-term Galerkin approximations involving polynomials as basis functions multiplied by appropriate weight functions are used to solve these equations numerically. Evaluated numerical results for the reflection coefficients are plotted graphically for both the barriers. The study reveals that the reflection coefficient depends significantly on the thickness of the barrier. The accuracy of the numerical results is checked by using energy identity and by obtaining results available in the literature as special cases. © 2020, Springer Nature B.V.

Journal of Engineering Mathematics

Oblique water waves scattering by a thick barrier with rectangular cross section in deep water

A mathematical model of the interaction of an oblique wave and rectangular submarine trench in an ice-covered ocean is given using linearized potential theory. The motion in the fluid is characterized by velocity potentials, which are expressed in terms of eigenfunctions. The continuity of the velocity potentials at the boundary of the trench produces a set of singular integral equations. These equations are solved using a multiterm Galerkin approach. A numerical study on the amplitude of reflection and transmission coefficients has been carried out to illustrate the influence of incidence angle, flexural rigidity of ice, and geometry of the trench. Known results in the absence of ice cover are covered as a special case. © 2019 American Society of Civil Engineers.

Journal of Waterway, Port, Coastal and Ocean Engineering

Oblique Wave Scattering by a Symmetric Trench Submerged Beneath an Ice Cover

Supply Chain Intelligence

Inventory Modeling and Inventory Control Application

The vibration of a functionally graded axisymmetric nonlocal thermoelastic hollow sphere with dual-phase-lag effect is addressed in this paper. Surfaces of the sphere are assumed to be thermally insulated or isothermal and stress free. According to a simple power law, the material is assumed to be graded in the radial direction. The linear theory of modified thermoelasticity with a dual phase lag based on Eringen’s nonlocal elasticity is employed to model this problem. The Matrix Frobenius method of continued power series is introduced to derive the analytical solutions. The phase velocity relations for the existence of various modes of vibrations in the designed hollow sphere are derived in compact forms. In order to explore the attributes of vibrations, the fixed-point numerical iteration technique is used to solve the secular equations. The numerical computations for the material crust in respect of the natural frequencies, thermoelastic damping and the frequency shifting are presented graphically using MATLAB software tools. © 2020, Springer-Verlag GmbH Austria, part of Springer Nature.