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

Irreducible Artin groups of finite type can be parametrized via their associated Coxeter diagrams into six sporadic examples and four infinite families, each of which is further parametrized by the natural numbers. Within each of these four infinite families, we investigate the relationship between elementary equivalence and isomorphism. For three out of the four families, we show that two groups in the same family are equivalent if and only if they are isomorphic; a positive, but weaker, result is also attained for the fourth family. In particular, we show that two braid groups are elementarily equivalent if and only if they are isomorphic. The 1 fragment suffices to distinguish the elementary theories of the groups in question. As a consequence of our work, we prove that there are infinitely many elementary equivalence classes of irreducible Artin groups of finite type. We also show that mapping class groups of closed surfaces - a geometric analogue of braid groups - are elementarily equivalent if and only if they are isomorphic. © 2018 World Scientific Publishing Company.

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International Journal of Algebra and Computation

Elementary equivalence in Artin groups of finite type

Information geometry describes a framework where probability densities can be viewed as differential geometry structures. This approach has shown that the geometry in the space of probability distributions that are parameterized by their covariance matrices is linked to the fundamental concepts of estimation theory. In particular, prior work proposes a Riemannian metric - the distance between the parameterized probability distributions - that is equivalent to the Fisher Information Matrix and helpful in obtaining the deterministic Cram{\'{e}}r-Rao lower bound (CRLB). Recent work in this framework has led to establishing links with several practical applications. However, classical CRLB is useful only for unbiased estimators and inaccurately predicts the mean square error in low signal-to-noise (SNR) scenarios. In this paper, we propose a general Riemannian metric that, at once, is used to obtain both Bayesian CRLB and deterministic CRLB along with their vector parameter extensions. We also extend our results to the Barankin bound, thereby enhancing their applicability to low SNR situations.

IEEE International Symposium on Information Theory - Proceedings

Information Geometric Approach to Bayesian Lower Error Bounds

arXiv preprint arXiv:1807.

A 1-point Quadrature domain of order 1 not biholomorphic to a balanced domain

We show that the structure of proper holomorphic maps between the n-fold symmetric products, n ≥ 2, of a pair of noncompact Riemann surfaces X and Y, provided these are reasonably nice, is very rigid. Specifically, any such map is determined by a proper holomorphic map of X onto Y . This extends existing results concerning bounded planar domains, and is a non-compact analogue of a phenomenon observed in symmetric products of compact Riemann surfaces. Along the way, we also provide a condition for the complete hyperbolicity of all n-fold symmetric products of a noncompact Riemann surface. © 2018 Deutsche Mathematiker Vereinigung.

Documenta Mathematica

Proper holomorphic mappings onto symmetric products of a Riemann surface

Let B1 be a ball in ℝN centred at the origin and let B0 be a smaller ball compactly contained in B1. For p ∈ (1, ∞), using the shape derivative method, we show that the first eigenvalue of the p-Laplacian in annulus B1 \B0 strictly decreases as the inner ball moves towards the boundary of the outer ball. The analogous results for the limit cases as p → 1 and p →∞ are also discussed. Using our main result, further we prove the nonradiality of the eigenfunctions associated with the points on the first nontrivial curve of the Fučik spectrum of the p-Laplacian on bounded radial domains. ©2018 American Mathematical Society.

Transactions of the American Mathematical Society

On the strict monotonicity of the first eigenvalue of the p-Laplacian on annuli

Let A be a Banach algebra with identity 1 and p ∈ A be a nontrivial idempotent. Then q = 1-p is also an idempotent. The subalgebras pAp and qAq are Banach algebras, called reduced Banach algebras, with identities p and q respectively. For a ∈ A and ε &gt; 0, we examine the relationship between the ε-pseudospectrum Λε(A, a) of a ∈ A, and ε-pseudospectra of pap ∈ pAp and qaq 2 qAq. We also extend this study by considering a finite number of idempotents p1, · · ·, pn, as well as an arbitrary family of idempotents satisfying certain conditions. © 2016 by the Tusi Mathematical Research Group.

Advances in Operator Theory

Pseudospectra of elements of reduced banach algebras

We prove that the space of dominant/non-constant holomorphic mappings from a product of hyperbolic Riemann surfaces of finite type into certain hyperbolic manifolds that can be covered by a bounded domain is a finite set. © 2017 World Scientific Publishing Company.

International Journal of Mathematics

Finiteness theorems for holomorphic mapping from products of hyperbolic Riemann surfaces

We relate the set of complete reduction vectors of a Zs-graded admissible filtration of ideals F with the set of multigraded regularities of G(F). We prove reg(G(F))=reg(R(F)). We establish a relation between the sets of complete reduction vectors of F and postulation vectors of F under some cohomological conditions. © 2017 Elsevier Inc.

Journal of Algebra

Multigraded regularity, reduction vectors and postulation vectors

We find conditions on the local cohomology modules of multi-Rees algebras of admissible filtrations which enable us to predict joint reduction numbers. As a consequence, we are able to prove a generalization of a result of Reid, Roberts and Vitulli in the setting of analytically unramified local rings for completeness of power products of complete ideals. © 2016 by The Editorial Board of the Nagoya Mathematical Journal Â.

Nagoya Mathematical Journal

Local cohomology of multi-rees algebras, joint reduction numbers and product of complete ideals

A new finite difference scheme is applied to solve partial differential equations in domains with discontinuities due to the presence of time dependent moving or deforming interfaces. This scheme is an extension of the finite difference idea developed for solving incompressible, steady stokes equations in discontinuous domains with fixed interfaces [1]. This new idea is applied at the irregular points at each time step in conjunction with the Crank-Nicolson (CN) implicit scheme and a recently developed Higher Order Compact (HOC) scheme at regular points. For validation, Stefan's problem is considered with a moving interface in one dimension. In two dimensions, heat equation is considered on a square domain with a circular interface whose radius is continuously changing with time. HOC scheme is found to produce better results and the order of accuracy is slightly better than that of the CN scheme. However, both the schemes show around second order accuracy and good agreement with the analytical solution.