Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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IIT Palakkad

Department of Mathematics

World University root node

arXiv e-prints, arXiv: 2104.

Hybrid and Generalized Bayesian Cramér-Rao Inequalities via Information Geometry

We extend projection theorems concerning Hellinger and Jones et al. divergences to the continuous case. These projection theorems reduce certain estimation problems on generalized exponential models to linear problems. We introduce the notion of regularity for generalized exponential models and show that the projection theorems in this case are similar to the ones in discrete and canonical case. We also apply these ideas to solve certain estimation problems concerning Student and Cauchy distributions.

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Journal of Multivariate Analysis

Projection theorems and estimating equations for power-law models

arXiv preprint arXiv:2103.

Structure theorems for Power Series in Several Complex Variables

We consider the problem (Formula presented.) where (Formula presented.), n>2, λ is a positive parameter, (Formula presented.) belongs to a class of continuous functions which satisfy certain decay assumptions, and (Formula presented.) belongs to a class of continuous functions which are superlinear at ∞ with (Formula presented.). Recently, several authors have studied positive radial solutions to this problem assuming that the weight function is radial. We allow non-radial weights and study the existence and non-existence of positive solutions. We prove the existence of a positive solution for small values of λ using variational methods. A non-existence result is established for large values of λ. © 2021 Informa UK Limited, trading as Taylor & Francis Group.

Complex Variables and Elliptic Equations

Positive solutions to superlinear semipositone problems on the exterior of a ball

In this article, we prove the proximinality of closed unit ball of M-ideals of compact operators on Banach spaces. We show that every positive (self-adjoint) operator on a Hilbert space has a positive (self-adjoint) compact approximant from the closed unit ball of space of compact operators. We also show that K(L1), the space of compact operators on L1, is ball proximinal in B(L1), the space of bounded operators on L1, even though K(L1) is not an M-ideal in B(L1). Moreover, we prove the ball proximinality of M-embedded spaces in their biduals. © 2021 American Mathematical Society. All rights reserved.

Proceedings of the American Mathematical Society

Ball proximinality of m-ideals of compact operators

Transactions of the American Mathematical Society

The Lie bracket of undirected curves on a surface

In order to understand the behaviour of a square matrix or a bounded linear operator on a Banach space or more generally an element of a Banach algebra, some subsets of the complex plane are associated with such an object. Most popular among these sets is the spectrum σ(a) of an element a in a complex unital Banach algebra A with unit 1 defined as follows: σ(a):={λ∈C:λ-aisnotinvertibleinA}.Here and also in what follows, we identify λ. 1 with λ. Also quite popular is Numerical range V(a) of a. This is defined as follows: V(a):={ϕ(a):ϕisacontinuouslinearfunctionalonAsatisfying‖ϕ‖=1=ϕ(1)}.Then there are many generalizations, modifications, approximations etc. of the spectrum. Let ϵ&gt; 0 and n a nonnegative integer. These include ϵ- condition spectrum σϵ(a) , ϵ- pseudospectrum Λ ϵ(a) and (n, ϵ) - pseudospectrum Λ n,ϵ(a). These are defined as follows: σϵ(a):={λ∈C:‖λ-a‖‖(λ-a)-1‖≥1ϵ}In this and the following definitions we follow the convention : ‖ (λ- a) - 1‖ = ∞ if λ- a is not invertible. Λϵ(a):={λ∈C:‖(λ-a)-1‖≥1ϵ}Λn,ϵ(a):={λ∈C:‖(λ-a)-2n‖1/2n≥1ϵ}. In this survey article, we shall review some basic properties of these sets, relations among these sets and also discuss the effects of perturbations on these sets and the question of determining the properties of the element a from the knowledge of these sets. © 2019, Forum D'Analystes, Chennai.

Journal of Analysis

Spectrum and related sets: a survey

The effective applications of Casson fluid in drilling processes, biological treatments, food processing and bio-engineering activities have caught the interest of a wide range of researchers. The suitable knowledge of heat transfer via non-Newtonian fluid is essential for the achievement of best quality products in industry. Thus, the three-dimensional Casson nanofluid flow over a stretching sheet with Arrhenius activation energy and exponential heat source effects is investigated in this paper using a computational process based on iterative power series (IPS) method. To provide useful insights into the physical and dynamic examinations of this topic, convective heat and convective mass boundary conditions are used. The developed model of nonlinear partial differential equations (PDEs) has been transformed into ordinary differential equations (ODEs) using similarity transformations. The numerical solution of the transformed ODEs is obtained by employing the IPS technique combined with shooting iteration approach. The results of this study are validated with the previous studies and excellent agreements have been obtained. The behavior of various capable physical parameters is analyzed. It is observed that the thermal and concentration fields show an enhancement with respect to the exponential heat source parameter and thermal and concentration Biot numbers. Further, the Arrhenius activation energy parameter has shown a significant effect on the concentration field.

Complexity

Computational Study on Three-Dimensional Convective Casson Nanofluid Flow past a Stretching Sheet with Arrhenius Activation Energy and Exponential Heat Source Effects

This work presents a methodology to address the problems of bubbles and drops evolving in incompressible, viscous flows due to the effect of surface tension. It is based on the combination of a recently developed immersed interface method to resolve discontinuities, with the level set (LS) method to reproduce the evolving interfaces. The paramount feature of this immersed interface method is the use of Lagrange interpolation enclosing grid points positioned in the vicinity of the interface and few exceptional grid points positioned on the interface. Different problems are considered to assert the accurateness of the proposed methodology, involving both simple and complex interface geometries. Precisely, the following problems are addressed: circular flow with a fixed interface, the dispersion of capillary waves, initially circular, ellipse, star shaped bubbles oscillating to an equilibrium state and circular drops deforming in shear flows. The transient evolution of bubbles/drops in terms of their shapes, pressure profiles, velocity vectors, deformation ratios of major and minor axis is analyzed to observe the effect of surface tension. The proposed methodology is seen to recover the exact numerical equilibrium between the surface tension and pressure gradient in the vicinity of complex interface geometries as well, while recreating the flow physics with an adequate level of accuracy with well representation of overall trends. Moreover, the numerical results yield a good level of agreement with the reference data. Keywords immersed interface level set (LS) surface tension multiphase Navier-Stokes equations shear flows HOC

Experimental and Computational Multiphase Flow

A coupled immersed interface and level set method for simulation of interfacial flows steered by surface tension

We examine the role of information geometry in the context of classical Cram{\'{e}}r–Rao (CR) type inequalities. In particular, we focus on Eguchi's theory of obtaining dualistic geometric structures from a divergence function and then applying Amari–Nagoaka's theory to obtain a CR type inequality. The classical deterministic CR inequality is derived from Kullback–Leibler (KL) divergence. We show that this framework could be generalized to other CR type inequalities through four examples: $\alpha$-version of CR inequality, generalized CR inequality, Bayesian CR inequality and Bayesian $\alpha$-CR inequality. These are obtained from, respectively, I$\alpha$-divergence (or relative $\alpha$-entropy), generalized Csisz{\'{a}}r divergence, Bayesian KL divergence and Bayesian I$\alpha$-divergence.