Working with two scholars on two themes.
Theme1: Constrained PDE optimization
Theme2 : Cortical surface reconstruction using level sets.
కొంచెం స్పీడ్ ఎక్కువే !
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."
Deterministic approach Vs Probabilistic approach
The time taken will be deterministic if you proceed by steps else it will be random variable.
Stone weight in your ornament formula - మీ నగల్లో ఉన్న రాయి బరువెంత ?
d1 and d2 are densities of gold and the stone, resp.
densities can be found by the standard density tables online for various stones and gold types.
M and V are the total mass and volume of the ornament.
Mass is easy.
Volume can be easily found by dipping in water in a graduated cylinder or volumetric glass of chemistry lab.
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