Programming in Delphi

• 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 MathJax
  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

1. Contour Thinning, without theory but with executable
   This replaces the deprecated pixel thinning
2. Fuzzy Frenet Analysis, with theory and executable
3. Fuzzy Lissajous Analysis upgraded, with theory and executable
4. Last but not least: accompanying B&W bitmap files

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

• No fancy Windows
• No syntax checking on input
• Chemical formulas with parentheses, like Ca(PO₃)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

• Sources & Executables
• Theory in PDF (with 'ps2pdf')
• Additional material in PDF
  and accompanying sources

• L.S.FEM
• Heat Exchanger
• Corroding Concrete

• Sources & Executables
• Windows BitMaP files for input