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

The following result is proved: Let A be a commutative real Banach algebra with unit 1. Let G denote the group of invertible elements of A and let G1 be the connected component of G containing 1. If the quotient group G/G1 contains an element of finite order other than G1, then the order of such an element must be 2. If the group G/G1 is of finite order, then its order must be 2n for some nonnegative integer n. © 2014 University of Houston.

Houston Journal of Mathematics

The group of invertible elements of a real Banach algebra

For 0 &lt; ε &lt; 1, the ε-condition spectrum of an element a in a complex unital Banach algebra A is defined as, (Formula Presented). This is a generalization of the idea of spectrum introduced in [5]. This is expected to be useful in dealing with operator equations. In this paper we prove a mapping theorem for condition spectrum, extending an earlier result in [5]. Let f be an analytic function in an open set Ω containing σε(a). We study the relations between the sets σε(f(a)) and f(σε (a)). In general these two sets are different. We define functions φ(ε), ψ (ε) (that take small values for small values of ε) and prove that f(σε(a)) ⊆ σφ(ε)(f(a)) and σε(f(a)) ⊆ f(σ ψ(ε)(a)). The classical Spectral Mapping Theorem is shown as a special case of this result. We give estimates for these functions in some special cases and finally illustrate the results by numerical computations. © 2014 Springer Basel.

World University root node

Operator Theory: Advances and Applications

An analogue of the spectral mapping theorem for condition spectrum

It is shown that every hyperbolic rigid polynomial domain in ℂ3 of finite-type, with abelian automorphism group is equivalent to a domain that is balanced with respect to some weight. © 2014 Copyright Taylor &amp; Francis Group, LLC.

Complex Variables and Elliptic Equations

Model domains in ℂ3 with abelian automorphism group

For a closed subspace Y of a Banach space X, we define a separably determined property for Y in X. We prove that if the strong 11/ 2-ball property is separably determined for Y in X, then L 1(μ, Y) has the strong 11/2ball property in L 1(μ, X). For an M-embedded space X, we give a class of elements in L 1(μ, X having best approximations from L 1(μ, X). We also prove that some of the proximinality properties are stable under polyhedral direct sums of Banach spaces. © 2014 Copyright Taylor &amp; Francis Group, LLC.

Numerical Functional Analysis and Optimization

Proximinality properties in Lp(μ, X) and polyhedral direct sums of banach spaces

We prove a result on the structure of finite proper holomorphic mappings between complex manifolds that are products of hyperbolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert and Stein, the proof of the full result relies on the interplay of the latter ideas and a finiteness theorem for Riemann surfaces. © 2014 World Scientific Publishing Company.

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International Journal of Mathematics

Proper holomorphic mappings between hyperbolic product manifolds

We prove that a proper holomorphic map between two nonplanar bounded symmetric domains of the same dimension, one of them being irreducible, is a biholomorphism. Our methods allow us to give a single, all-encompassing argument that unifies the various special cases in which this result is known. We discuss an application of these methods to domains having noncompact automorphism groups that are not assumed to act transitively. © 2014 Mathematical Sciences Publishers.

Pacific Journal of Mathematics

Proper holomorphic maps between bounded symmetric domains revisited

Mississippi State University Scholars Junction

Classes of Singular Nonlinear Eigenvalue Problems with Semipositone Structure

We introduce a weaker notion of central subspace called almost central subspace, and we study Banach spaces that belong to the class (GC), introduced by Veselý (1997). In particular, we prove that if Y is an almost central subspace of a Banach space X such that Y is in the class (GC), then Y is a central subspace of X . We also prove that if Y is a semi M -ideal in a Banach space X such that Y is an almost central subspace of X, then Y is an M -ideal in X. Certain stability results for quotient spaces, injective tensor product spaces, and polyhedral direct sums of Banach spaces are also derived. © 2013 C. R. Jayanarayanan.

Journal of Function Spaces and Applications

Intersection properties of balls in Banach spaces

Two-dimensional incompressible, viscous fluid flow around a rotationally oscillating circular cylinder is studied numerically by using a recently developed higher order compact finite difference scheme (HOC) at Reynolds number Re = 500. The stream function vorticity formulation of Navier Stokes equations in cylindrical polar coordinates are considered as the governing equations. Different values of peak rotation rate $\alpha$m and forced oscillation frequency fe are considered. The simulated results are in a good agreement both qualitatively and quantitatively with the previously published results. {\textcopyright} (2013) Trans Tech Publications, Switzerland.

Applied Mechanics and Materials

A transform free higher order compact finite difference scheme for simulating the flow behind a rotationally oscillating circular cylinder at reynolds number 500

We derive estimates for approximation numbers of bounded linear operators between normed linear spaces. As special cases of our general results, approximation numbers of some weighted shift operators on p and those of isometries andprojections of norm 1 are found. In the case of finite-rank operators, we obtain estimatesfor the smallest nonzero approximation number in terms of their generalizedinverses. Also, we prove some results regarding the relation between approximationnumbers and the closedness of the range of an operator.We recall that the closednessof the range is a necessary condition for the boundedness of a generalized inverse.We give examples illustrating the results and also show that certain inequalities neednot hold. © Springer India 2013.