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

Projection theorems of divergences enable us to find reverse projection of a divergence on a specific statistical model as a forward projection of the divergence on a different but rather "simpler" statistical model, which, in turn, results in solving a system of linear equations. Reverse projection of divergences are closely related to various estimation methods such as the maximum likelihood estimation or its variants in robust statistics. We consider projection theorems of three parametric families of divergences that are widely used in robust statistics, namely the R\'enyi divergences (or the Cressie-Reed power divergences), density power divergences and the relative $\alpha$-entropy (or the logarithmic density power divergences). We explore these projection theorems from the usual likelihood maximization approach and from the principle of sufficiency. In particular, we show the equivalence of solving the estimation problems by the projection theorems of the respective divergences and by directly solving the corresponding estimating equations. We also derive the projection theorem for the density power divergences.

World University root node

arXiv

Projection theorems of divergences and likelihood maximization methods

We study the Wu metric on convex egg domains of the form where m &gt; 1/2, m ≠ 1. The Wu metric is shown to be real analytic everywhere except on a lower dimensional subvariety where it fails to be C2-smooth. Overall however, the Wu metric is shown to be continuous when m = 1/2 and even c1-smooth for each m &gt; 1/2, and in all cases, a non-Kähler Hermitian metric with its holomorphic curvature strongly negative in the sense of currents. This gives a natural answer to a conjecture of S. Kobayashi and H. Wu for such E2m.

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

Analysing the Wu metric on a class of eggs in Cn -1

Goldman Bracket: Center, Geometric Intersection Number &amp; Length Equivalent Curves

In this article, we discuss the strong proximinality of the closed unit ball of closed linear subspaces of L1-predual spaces. We prove that M-ideals in L1-predual spaces are strongly ball proximinal. We characterize finite co-dimensional strongly ball proximinal closed linear subspaces of C(K) spaces and prove that they are precisely the finite co-dimensional strongly proximinal closed linear subspaces of C(K). For a Choquet simplex K, we give a sufficient condition for the strong ball proximinality of finite co-dimensional closed linear subspaces of A(K) spaces. We prove that metric projection onto a finite co-dimensional strongly proximinal closed linear subspace of an L1-predual space is Hausdorff metric continuous. Moreover, we prove that the metric projection onto the closed unit ball of an M-ideal in an L1-predual space is Hausdorff metric continuous. © 2016 Elsevier Inc.

Journal of Approximation Theory

Strong ball proximinality and continuity of metric projection in L1-predual spaces

The ε-pseudospectrum Λε (a) of an element a of an arbitrary Banach algebra A is studied. Its relationships with the spectrum and numerical range of a are given. Characterizations of scalar, Hermitian and Hermitian idempotent elements by means of their pseudospectra are given. The stability of the pseudospectrum is discussed. It is shown that the pseudospectrum has no isolated points, and has a finite number of components, each containing an element of the spectrum of a. Suppose for some ε &gt; 0 and a,b ∈ A, Λε (ax) = Λε (bx) ∀x ∈ A. It is shown that a = b if: (i) a is invertible. (ii) a is Hermitian idempotent. (iii) a is the product of a Hermitian idempotent and an invertible element. (iv) A is semisimple and a is the product of an idempotent and an invertible element. (v) A = B(X) for a Banach space X. (vi) A is a C∗ -algebra. (vii) A is a commutative semisimple Banach algebra. © ELEMENT, Zagreb.

Operators and Matrices

Pseudospectrum of an element of a Banach algebra

We study the relationship between postulation and reduction vectors of admissible multigraded filtrations F = [[[[F(n)]]]]n∈Zs of ideals in Cohen-Macaulay local rings of dimension at most two. This is enabled by a suitable generalization of the Kirby-Mehran complex. An analysis of its homology leads to an analogue of Huneke's fundamental lemma which plays a crucial role in our investigations. We also clarify the relationship between the Cohen-Macaulay property of the multigraded Rees algebra of F and reduction vectors with respect to complete reductions of F. © 2017 Rocky Mountain Mathematics Consortium.

Journal of Commutative Algebra

Postulation and reduction vectors of multigraded filtrations of ideals

We study the Wu metric for the non-convex domains of the form E2m = (z ∈ ℂn: |z1|2m + |z2|2 + · · · + |zn-1|2 + |zn|2 &lt; 1), where 0 &lt; m &lt; 1/2. We give explicit expressions for the Kobayashi metric and the Wu metric on such pseudoeggs E2m. We verify that the Wu metric is a continuous Hermitian metric on E2m, real analytic everywhere except along the complex hypersurface Z = ((0, z2, . . . , zn) ∈ E2m). We also show that the holomorphic curvature of the Wu metric for this noncompact family of pseudoconvex domains is bounded above in the sense of currents by a negative constant independent of m. This verifies a conjecture of S. Kobayashi and H. Wu for such E2m. © Indian Academy of Sciences.

Analysing the Wu metric on a class of eggs in ℂn - II

Numerical simulations of unsteady two-dimensional flow around a rotationally oscillating circular cylinder, placed in a uniform cross flow of a constant property Newtonian fluid, are performed at a fixed Reynolds number of 200. The investigation is based on the solutions of stream function-vorticity formulation of Navier-Stokes equations on non-uniform polar grids using a higher order compact (HOC) formulation. The flow field is mainly influenced by Reynolds number, Re, maximum angular velocity of the cylinder, $\alpha$m and the frequency ratio, f/f0, which represents the ratio between the frequency of oscillation, f and the natural vortex shedding frequency, f0. The ranges considered for these parameters are 0.5⩽$\alpha$m⩽6.0 and 0.5⩽f/f0⩽3.0. The resulting vortex formation modes and lock-on phenomena behind the cylinder as well as the fluid forces acting on the cylinder are analyzed. Occurrence of new multiple lock-on regions is demonstrated in detail by the variation of f and $\alpha$m. The instances of high drag reduction at high values of $\alpha$m are confirmed. Comparisons with previous numerical and experimental results verify the accuracy and validity of the present study.

Ocean Engineering

Locked-on vortex shedding modes from a rotationally oscillating circular cylinder

The initial development of the two dimensional viscous, incompressible flow induced by an impulsively started circular cylinder which performs time dependent sinusoidal rotational oscillations about its axis is investigated numerically. The investigation is based on the solutions of stream functionvorticity formulation of Navier-Stokes equations on non-uniform polar grids using higher order compact formulation. The numerical method is validated by comparing the computed results with existing experimental and numerical results for Reynolds numbers Re = 150 and 500. The effects of forced oscillation frequency f and peak rotation rate $\alpha$m on the early development of the flow structure in the near wake region are discussed. Results are given for the initial development with time of the flow structure at the rear of the cylinder at Re = 200. The details of the formation, movement, closure points and strengths of the vortices behind the cylinder are presented. The velocity profiles at different locations and vorticity profiles at the surface of the cylinder are also shown. The effect of increase in $\alpha$m on the timing of the formation of the vortices, the closed wake length and the thickness of the boundary layer is investigated.

Physics of Fluids

A numerical study of initial flow past an impulsively started rotationally oscillating circular cylinder using a transformation-free HOC scheme

We show that the center of the Goldman Lie algebra associated to a closed orientable surface is generated by the class of the trivial loop. For an orientable nonclosed surface of finite type, the center is generated by closed curves which are either homotopically trivial or homotopic to boundary components or punctures. © 2016, Mathematical Sciences Publishers. All rights reserved.