Machine Cryptanalysis of Basic Cryptosystems by James Pate Williams, Jr. BA, BS, MSwE, PhD

In Winter and Spring 2018 I wrote a simple C# computer program to perform machine cryptanalysis of the following basic (elementary and easily breakable) cryptosystems:

  1. Affine Cipher Operating on Monographs and Digraphs
  2. Matrix Cipher
  3. Mono-alphabetic Cipher
  4. n-Rotor with Shifting Polyalphabetic Cipher

The key ingredient in this program is a relatively extensive English language dictionary.

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Exercises for the Feynman Lectures on Physics by Richard Feynman, Et Al. Chapter 38 Differential Calculus of Vector Fields – Detailed Work by James Pate Williams, Jr. BA, BS, MSwE, PhD

Feynman Exercises Chapter 38

Separation and Partial Solution of the Time Dependent Schrödinger Equation for the Non-Relativistic Hydrogen-Like Atom by James Pate Williams, Jr. BA, BS, MSwE, PhD

In the following terse document we start with the non-relativistic and time dependent Schrödinger equation for the hydrogen-like atom of atomic number Z. We then separate the equation into one ordinary differential equation eigenvalue problem involving the variable time and two partial differential equations eigenvalue problems, each with three variables. The resulting center of mass partial differential equation eigenvalue problem is separable in Cartesian coordinates. The other eigenvalue problem is not separable in Cartesian coordinates due to the nature of the potential energy function in the Hamiltonian operator. This treatment is an expansion on the excellent textbook section that is cited in the References section of the document.

The time dependent Schrödinger equation for the hydrogen

A Modern Reincarnation of Ordnance Pamphlet 770 October 1941 by James Pate Williams, Jr. BA, BS, MSwE, PhD

Ordnance Pamphlet 770 by the United States Navy is concerned with testing and calibrating the 16 inch/50 caliber guns of the Iowa class of fast battleships. I use modern digital computer methods to attempt to reproduce the analog computations of the ordnance pamphlet. Recall that digital computers did not exist in 1941, but analog computers using cams, differentials, gears, and levers did exist.

Pamphlet Paper

Exercises for the Feynman Lectures on Physics by Richard Feynman, Et Al. Chapter 36 Fourier Analysis of Waves– Detailed Computer Work by James Pate Williams, Jr. BA, BS, MSwE, PhD

Exercise 36.1 (a) Graph
f(x) = 1 for all x contained in the interval [0, 6.28]
Exercise 36.1 (a) Coefficients
Fourier coefficients for a constant function f(x) = 1

 

 

Exercise 36.1 (b) Graph
f(x) = sin x for all x in the interval [0, 6.28]
Exercise 36.1 (b) Coefficients
Fourier coefficients for f(x) = sin x for all x in [0, 6.28]
Exercise 36.2 Graph
Graph of the Fourier Series Approximation to the Square Wave with the Gibb’s Overshoot Phenomena Clearly Present

 

Exercise 36.2 Coefficients
Fourier Series Coefficients for the Square Wave

Exercise 36.2 (a)

Exercise 36.2 (b)

Exercise 36.2 (c)

 

 

Exercise 36.3 Graph
Graph of the Fourier Series Approximation to the Triangle Wave

 

Exercise 36.3 Coefficients
Fourier Coefficients for the Triangle Wave

Exercise 36.3 (b) (1)

Exercise 36.3 (b) (2)

 

Exercise 36.4

 

Exercise 36.6 Graph
Graph of the Fourier Series Approximation to a Saw-Tooth Wave

 

Exercise 36.6 Coefficients
Fourier Coefficients for the Saw-Tooth Wave

 

Exercise 36.8 Graph
Graph of the Fourier Approximation to the Rectified Sine Wave

 

Exercise 36.8 Coefficients
Fourier Series Coefficients for the Rectified Sine Wave