Old (Fortran/Basic/Turbo Pascal) programs have been ported to Borland Delphi 3/5/6:

**Labrujère's Problem**

with executable and how it was done

Including PDF documentation and source

Even more PDF documentation and source

Appendix, the PDF and its source**Corroding Reinforced Concrete**

with executable and how it was done

Associated (and more elaborated) Theory in PDF with

software & source**Intermediate Heat eXchanger**

with executable and how it was done

Including some PDF documentation and its source

More PDF documentation and its source- The direct Solution of Linear Equations Systems,

with a sample (console) Resistor Network Demo

and accompanying Source Code - Experiments with the Fast Fourier Transform in 1-D and 2-D,

implemented as a console program

The **Trilogy**, reported in this section, consists (indeed) of three
mutually related Projects:

**Contour Thinning**, without theory but with executable

This replaces the*deprecated*pixel thinning- Fuzzy
**Frenet Analysis**, with theory and executable - Fuzzy
**Lissajous Analysis***upgraded*, with theory and executable - Last but not least: accompanying B&W bitmap files

All Source code has been made available too, for the serious researcher.

Is it possible to entirely **automate** the art of **Balancing**
a **Chemical Equation** ? The answer has found to be affirmative.

And somewhat suprising too !
Because the method used in my program is an integer version of the Least
Squares Method. (The latter has also been employed for solving the problem
of Ideal Flow around a circular cylinder, as has been formulated in 1976 by
Th.E. Labrujère)

The gist of the method is as follows. In the chemical equation, let M be the number of Elements and N be the number of unknown coefficients. Then, mathematically speaking, we have to solve a system of M linear equations with N unknowns. Applying the Least Sqares Method results in a more convenient system: of N equations with N unknowns. The load vector of this system is zero. We know, in addition, that the outcome is an array of integers. And any multiple of the outcome must be considered as another mathematical solution. Because the equations are mutually dependent, the last equation can be cancelled. Furthermore, the last coefficient is set to unity, for the moment being, and the accompanying matrix coefficients are moved to the right hand side. Then the equations are solved by a direct method. The integer nature of the problem must preferrably be left intact. Therefore multiply everything with the determinant, instead of performing a division with it. At last, the coefficients are to be simplified, by dividing all of them with their GCD (Greatest Common Divisor).

Anyway, here comes:

- The
**Balancing**of**Chemical Equations**(console version),

with executable, source code & data all zipped together - Here is a sample input and accompanying output

Known Limitations:

- No fancy Windows
- No syntax checking on input
- Chemical formulas with parentheses, like
Ca(PO
_{3})_{2}, cannot be processed - No equations with ions in it,
like H
^{+}, (OH)^{-}and the like. Balancing of charges is not done.

P. Ramasami, A Concise Description of an Old Problem: Application of Matrices to Obtain the Balancing Coefficients of Chemical Equations, Journal of Mathematical Chemistry, Volume 34, Issue 1-2, July 2003, Pages 123 - 129

Kind of an update of "Sensible Densities", is (no longer) under development. It is placed here for a reference:

**Sources & Executables****Theory in PDF**(with 'ps2pdf')**Additional material in PDF**

and accompanying sources

Contouring routines for functions defined at a triangular mesh are found in my source code archives for numerical work.

You must have the 'GRAFISCH.PAS' module in: For the (still far-fetched) purpose of character recognition and the like:

**Sources & Executables****Windows BitMaP files**for input