Notes on Several Special Transformations

Lecture notes on several complex variables

Notes on the Structure of Linear Transformations

The goal of these notes is to give an accessible introduction to the structure theory of linear transformations. We want to develop enough of the theory for use in differential equations, with only basic linear algebra as a prerequisite. In a following set of notes, we will show how these results can be applied to differential equations. In the rest of the section, we will cover some topics tha...

Notes on the use of data transformations

Data transformations are commonly used tools that can serve many functions in quantitative analysis of data. The goal of this paper is to focus on the use of three data transformations most commonly discussed in statistics texts (square root, log, and inverse) for improving the normality of variables. While these are important options for analysts, they do fundamentally transform the nature of ...

Lecture Notes on Orthogonal Polynomials of Several Variable

Several notes on the power of Gomory-Chvatal cuts

We prove that the Cutting Plane proof system based on Gomory–Chvátal cuts polynomially simulates the lift-and-project system with integer coefficients written in unary. The restriction on the coefficients can be omitted when using Krajı́ček’s cut-free Gentzenstyle extension of both systems. We also prove that Tseitin tautologies have short proofs in this extension (of any of these systems and wi...