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

In this paper, we study two optimization problems where solutions on a dense set yield global solution. We study these problems for spaces of Bochner integrable functions and for spaces of continuous functions. The first one deals with expressing the length of a vector as a sum of the distance to a best approximation and minimal best approximation and the second one relates to approximating a subsequence of a minimizing sequence with a sequence of proximinal vectors. © 2016 Belgian Mathematical Society. All rights reserved.

World University root node

Bulletin of the Belgian Mathematical Society - Simon Stevin

Optimization through dense sets

In this expository paper, we present proofs of Grothendieck-Serre formula for multi-graded algebras and Rees algebras for admissible multi-graded filtrations. As applications, we derive formulas of Sally for postulation number of admissible filtrations and Hilbert coefficients. We also discuss a partial solution of Itoh’s conjecture by Kummini and Masuti. We present an alternate proof of Huneke-Ooishi Theorem and a generalisation for multi-graded filtrations. © Springer Science+Business Media Singapore 2016.

Springer Proceedings in Mathematics and Statistics

Variations on the Grothendieck-Serre formula for Hilbert functions and their applications

The purpose of this article is to provide an exposition of domains of convergence of power series of several complex variables without recourse to relatively advanced notions of convexity.

arXiv preprint arXiv:1601.

Power Series in Several Complex Variables

In this paper, we prove that the second eigenfunctions of the p- Laplacian, p &gt; 1, are not radial on the unit ball in RN, for any N ≥ 2. Our proof relies on the variational characterization of the second eigenvalue and a variant of the deformation lemma. We also construct an infinite sequence of eigenpairs {τn,Ψn} such that Ψn is nonradial and has exactly 2n nodal domains. A few related open problems are also stated. © 2015 American Mathematical Society.

Fulltext

Proceedings of the American Mathematical Society

On the structure of the second eigenfunctions of the p-laplacian on a ball

arXiv preprint arXiv:1607.

Global nilpotent cone is isotropic : parahoric torsors on curves

arXiv preprint arXiv:1609.

A NON-CANCELLATION LEMMA FOR GOLDMAN BRACKET

In this paper, we propose a new methodology for numerically solving elliptic and parabolic equations with discontinuous coefficients and singular source terms. This new scheme is obtained by clubbing a recently developed higher-order compact methodology with special interface treatment for the points just next to the points of discontinuity. The overall order of accuracy of the scheme is at least second. We first formulate the scheme for one-dimensional (1D) problems and then extend it directly to two-dimensional (2D) problems in polar coordinates. In the process, we also perform convergence and related analysis for both the cases. Finally, we show a new direction of implementing the methodology to 2D problems in cartesian coordinates. We then conduct numerous numerical studies on a number of problems, both for 1D and 2D cases, including the flow past circular cylinder governed by the incompressible Navier–Stokes equations. We compare our results with existing numerical and experimental results. In all the cases, our formulation is found to produce better results on coarser grids. For the circular cylinder problem, the scheme used is seen to capture all the flow characteristics including the famous von K{\'{a}}rm{\'{a}}n vortex street. Copyright {\textcopyright} 2016 John Wiley & Sons, Ltd.

International Journal for Numerical Methods in Fluids

A class of finite difference schemes for interface problems with an HOC approach

Indian Institute of Technology Mandi, Himachal Pradesh, India

A Class of Higher Order Accurate Schemes for Fluid Interface Problems

In this paper, we present a new finite difference scheme for solving incompressible, steady stokes equations in discontinuous domains. While solving two phase Stokes equations, across some interfaces, there are discontinuities in the pressure, viscosity and velocity. Since, these jump conditions are coupled together, it is difficult to discretise and solve the system of equations accurately. We apply the augmented approach introduced by Li et al. (Int J Numer Meth. Fluids 44:33–53, 2004) to decouple these jump conditions. A new finite difference method is then developed and presented to solve the resulting augmented system of Stokes equations. Points of intersection of grid lines and the interface are used as a node in the finite difference stencil and jump conditions are then used to determine the values at these intersection points. Numerical solutions are compared with the corresponding analytical solutions and those of the augmented immersed interface method. The method is found to be second order accurate for almost all the variables in the infinity norm.

Advances in Intelligent Systems and Computing

A Cartesian grid method for solving stokes equations with discontinuous viscosity and singular sources

This paper studies forward and reverse projections for the Renyi divergence of order $\alpha$ ∈ (0, ∞) on $\alpha$-convex sets. The forward projection on such a set is motivated by some works of Tsallis et al. in statistical physics and the reverse projection is motivated by robust statistics. In a recent work, van Erven and Harremoes proved a Pythagorean inequality for Renyi divergences on $\alpha$-convex sets under the assumption that the forward projection exists. Continuing this study, a sufficient condition for the existence of a forward projection is proved for probability measures on a general alphabet. For $\alpha$ ∈ (1, ∞), the proof relies on a new Apollonius theorem for the Hellinger divergence and for $\alpha$ ∈ (0,1), the proof relies on the Banach-Alaoglu theorem from the functional analysis. Further projection results are then obtained in the finite alphabet setting. These include a projection theorem on a specific $\alpha$-convex set, which is termed an $\alpha$-linear family, generalizing a result by Csiszar to $\alpha$ ≠ 1. The solution to this problem yields a parametric family of probability measures, which turns out to be an extension of the exponential family and it is termed an $\alpha$-exponential family. An orthogonality relationship between the $\alpha$-exponential and $\alpha$-linear families is established and it is used to turn the reverse projection on an $\alpha$-exponential family into a forward projection on an $\alpha$-linear family. This paper also proves a convergence result of an iterative procedure used to calculate the forward projection on an intersection of a finite number of $\alpha$-linear families.