About this blog

I feel this blog as a reflection of my thoughts to myself , and sometimes as a public diary, and the is my only friend to share my thoughts who says never a "oh no! ,you shouldn't....That is boring...."

A probability question on Sudoku Grid

 What is the probability that given n trials to fill the numbers in Sudoku grid how many(X) valid numbers will filled at the end ?

What is the probability distribution for the random variable X ?


Currently working on ...

 Working with two scholars on two themes.

Theme1: Constrained PDE optimization

Theme2 : Cortical surface reconstruction using level sets.

If cheese do not show up your video on linux

 Check if sudo cheese work ?

If works, then add user to the "video" group (if exists)

then login afresh or (temporary )instantiate the group video .


Theorems on Roots of Polynomials in Geometry, Topology, Complex Analysis and Functional Analysis

 Roots of Polynomials
Prof. V. Kannan
Dept. of Mathematics
SRM University-AP
23 February 2022

Abstract: "We discuss four classical theorems on roots of polynomials. They relate to four
different branches of Mathematics, namely, Geometry, Topology, Complex Analysis and
Functional Analysis. The theorems are stated below:
Theorem 1 (Lucas). Every root of the derivative of a polynomial lies within the convex
polygon formed by the roots of that polynomial.
Theorem 2: The roots of a polynomial vary continuously with its coefficients.
Theorem 3 (Cauchy): If all the coefficients of a polynomial lie in the unit disc D, then all
the roots lie in the disc 2D.
Theorem 4 (Bernstein): The norm of the linear operator D (namely the differentiation) on
(The space of polynomials of degree at most n on D) is exactly n."