__Online Presentations__

__Lambert's W Function, Infinite Exponentials, Powertowers, Iterated Exponentials and Tetration__- The Author's Strange Encounter With Johann Heinrich Lambert
- Infinite Exponentials (often called infinitely iterated exponentials or exponential towers)
- A Slightly Deeper Analysis of Infinite Exponentials
- A MacLaurin Expansion for Lambert's W function
- Approximating the Principal Branch of the Complex Lambert's W Function
- Approximating the Branches of the Complex Lambert's W Function Using Analytic Continuation
- An Infinite Family of Hyper-Lambert Functions And Their Use In Solving Exponential Tower Equations
- A Detailed Look at the Hyperroot Functions Using Lambert's W Function
- A Continuous Extension of the hyper4 Operator
- An Infinitely Differentiable Extension for the hyper4 Operator
- A Series Expansion for
^{m}(e^{x}) Using Lambert's W Function - A More Consistent Definition of Tetration for Rational Exponents
- The General Infinite Exponential and its Limit
- The Analytic Continuation of the Infinite Hyperpower Function F(x) =
^{+∞}x - The Birth of the Infinite Tetration Fractal
- A Strange Hyperexponential Series
- Solving the First Auxiliary Real Exponential Equation using Lambert's W function
- Solving the Second Auxiliary Real Exponential Equation using Lambert's W function
- Solving the n-th Auxiliary Real Exponential Equation
- A Family of Hyperpower/Hyperfactorial Series
- File Signatures and Tetration of 2
- A Collection of References for Infinite Exponentials and Tetration

__Various__- An Interesting Sequence of Cyclic Digits
- Suprema and Infima in Real Life
- The Cantor Function
- The 3n+1 problem
- Temperatures on The Surface of the Earth
- A Program to Solve Loyd's Wooden Tile Puzzle
- Is There a Limit on How Fast the Olympic 100 Meters Can Be Ran?
- Modelling Time Under Total Anesthesia
- The Author's View of the Universe
- The Author's Puzzles
- Distinct Resistances Possible With at Most n Distinct Resistors
- Can Mathematics Explain What Is Real?
- Estimating the Area and Perimeter of a Circle and π Using Archimedes' Method
- The Most Beautiful Construction in Mathematics
- Overall Function Behavior
- Does Arc Light Flickering Interfere With Video?
- Understanding Symbolic Levels
- Trends in Euler's Totient φ Function
- The Author's Webpage Statistics Projector
- Using Maple to Visualize the Complex w-Plane
- From Mathematics To Color Perception
- A Short Tutorial On Big Numbers
- Modelling Relative Mind Power Using the ELO Rating System
- Every Chess Configuration
- Should New Mathematics Ideas Be Announced?
- How Does tinyurl Work?
- The Main Principles of a Chess Engine
- The Dynamics of Computer Programming
- Is The Mind Infinite?

Function/data graphs were done with Maple and THINK Pascal and geometrical schematics with EucliDraw.

__Refereed Journal Papers (in order of publication)__

- "On An Application Of Lambert's W Function to Infinite Exponentials",
*Complex Variables*,**49**(11) (Sep. 2004), 759-780. - "On Solving the p-th Complex Auxiliary Equation f
^{(p)}(z)=z",*Complex Variables*,**50**(13) (Oct. 2005), 977-997. - "Lambert's W Function and Convergence of Infinite Exponentials in the Space of Quaternions",
*Complex Variables*,**51**(12) (Dec. 2006), 1129-1152. - "Corrigendum for 3",
*Complex Variables*,**52**(4), (Apr. 2007), 351. - "Explicit Solution of the Kepler Equation" (jointly with Alexandr Dubinov),
*Physics of Particles and Nuclei, Letters*,**4**(3) (May 2007), 213-216. - "On Some Applications of the Generalized Hyper-Lambert Functions",
*Complex Variables*,**52**(12) (Dec. 2007), 1101-1119.

- "On The Convergence of Series With Infinite Exponentials and Iterated Factorials".
- "On Extending hyper4 and Knuth's Up-arrow Notation to the Reals".
- "On a Conjecture Between the Asymptotic Densities of φ and the Timing of the GCD Algorithm and a Tetration Function".
- "An Almost Everywhere Analytic Extension of Tetration" (work in progress).

- The author's math pages and papers are devoted to his parents and his superb mathematics teacher: Kostas Sourlas.