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

Three Gelfand-Mazur type theorems are proved. One of these provides a C*-property analogue of Zalar's recent generalizations of the EroelichIngelstam-Smiley Theorems concerning unital multiplication in Hilbert spaces; the second illustrates that the assumption in Kaplansky's version of the Gelfand-Mazur Theorem can be weakened in the presence of a C*-norm; whereas the third provides a real analogue of a result due to Srinivasan. © 1998 American Mathematical Society.

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Proceedings of the American Mathematical Society

A note on the gelfand-mazur theorem

Let H1 and H2 be real Hilbert spaces. Suppose H2 is partially 2 ordered, a, b ε H2, c ε H1 and A :H1→H2is a continuous linear 21 12 map. We consider the following interval linear program: Maximize &lt;c, x&gt; subject to a ≤Ax ≤ b. Conditions under which explicit solutions to the above problem can be found are studied. The solutions are represented in terms of generalized inverses of A. Several examples are given to illustrate the main results. © 1995, Taylor &amp; Francis Group, LLC. All rights reserved.

Numerical Functional Analysis and Optimization

Applications of Generalized Inverses to Interval Linear Programs in Hilbert Spaces

Let A be a real B*-algebra containing a p*-subalgebra that is isomorphic to the real quaternion algebra H. Suppose the spectrum of every self-adjoint element in A is contained in the real line. Then it is proved that there exists a quaternionic Hubert space X and an isometric isomorphism n of A onto a closed *-subalgebra of BL(X), the algebra of all bounded linear operators on X. If, in addition to the above hypotheses, every element in A is normal, then A is also proved to be isometrically isomorphic to C(Y, E), the algebra of all continuous H-valued functions on a compact HausdorfF space Y. © 1994 American Mathematical Society.

Representation of a real B*-algebra on a quaternionic hilbert space

For a compact Hausdorff space X, let C(X, H) denote the set of all quaternion-valued functions on X. It is proved that if a real B* -algebra A satisfies the following conditions: (i) the spectrum of every selfadjoint element is contained in the real line and (ii) every element in A is normal, then A is isometrically *-isomorphic to a closed *-subalgebra of C(X, H) for some compact Hausdorff X. In particular, a real C*-algebra in which every element is normal is isometrically *-isomorphic to a closed *-subalgebra of C(X, H). © 1992 American Mathematical Society.

Representations of a class of real B*-algebras as algebras of quaternion-valued functions

Proceedings of the Indian Academy of Sciences - Mathematical Sciences

Analytic and harmonic maps into a topological space

Communications on Pure and Applied Analysis

Bifurcation, uniqueness and multiplicity results for classes of reaction-diffusion equations arising in ecology with nonlinear boundary conditions

We consider semi-linear elliptic equations of the following form:\begin{equation*}\left\{\begin{aligned}-\Delta u &amp;= \lambda[u-\dfrac{u^2}{K}-c \dfrac{u^2}{1+u^2}-h(x) u]=:\lambda f_h(u) &amp;&amp;\textcolor{black}{\rm{in}} ~ \Omega,\\frac{\partial u}{\partial \eta}&amp;+qu = 0 &amp;&amp;\textcolor{black}{\rm{on}} ~ \partial\Omega,\end{aligned}\right.\end{equation*}where, $h\in U=\{h\in L^2(\Omega): 0\leq h(x)\leq H\}.$ We prove the existence and uniqueness of the positive solution for large $\lambda.$ Further, we establish the existence of an optimal control $h\in U$ that maximizes the functional$J(h)=\int_{\Omega}h(x)u_h(x)~{\rm{d}}x-\int_{\Omega}(B_1+B_2 h(x))h(x)~{\rm{d}}x$over $U$, where $u_h$ is the unique positive solution of the above problem associated with $h$, $B_1&gt;0$ is the cost per unit effort when the level of effort is low and $B_2&gt;0$ represents the rate at which the cost rises as more labor is employed. Finally, we provide a unique optimality system.