Everyday Science By Akram Kashmiri.pdf [Extra Quality]



 
 
 
 
 
 
 

Everyday Science By Akram Kashmiri.pdf

It does not contain many programming questions but is a good resource for intermediate students.. I have tried to read the books written by Akram Kashmiri, he is very good at explaining .—
abstract: ‘We present a new procedure for building a probability distribution $\pi_n$ on $S_{n}$ that satisfies the Wigner-Racah (WR) symmetry, $d_{i\to j}(\pi_n)=d_{i\to j}(\pi_n)$. $\pi_n$ can be built from an $A$-noncrossing, $B$-noncrossing, or $C$-noncrossing collection of orthogonal polynomials by defining the generating functions, $f(z)=\sum_{n=0}^{\infty}\pi_{n} z^{n}$, $g(z)=\sum_{n=0}^{\infty} e^{i\alpha_n}\pi_{n} z^{n}$, and $h(z)=\sum_{n=0}^{\infty} e^{i\beta_n}\pi_{n} z^{n}$, of the three collections (called “sets”). Using the parameters $A$, $B$, and $C$, defined by the location of the zeros of the generating functions, we are able to determine the value of $\pi_{n}$ for any $n$. We demonstrate the power of this new method by obtaining probability distributions on $S_{4}$ using generating functions on $S_{3}$, $S_{2}$, $S_{1}$ and $S_{0}$, which was not possible in the past.’

[**$A, B, C$ [^1]**]{}

Introduction
============

Wigner-Racah Symmetry and Interlacing
======================================

[^1]: D.E. was supported in part by NSF grant DMS-0653738.
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