An Algorithmic and Mathematical Investigation of Reactions
Lectures in Malta, 2019. february 19-21.
István Szalkai, dr.
U. Pannonia, Veszprém, Hungary
http://math.uni-pannon.hu/~szalkai/
email: Szalkai@almos.uni-pannon.hu
Content:
~~~~~~~
I. Linear algebraic simplexes /examples and definition/
II. Systems of linear homoeneous equations /structure/
III. An algorithm
IV. Examples
V. Number of simplexes
VI. Matroids
VII. Codes, Families
VIII.Hypergraphs
IX. General Hierarchy
X. Valuation Operator
XI. Graphs
The presentation: Download (pdf)
The architect Ybl Miklos Ybl-Miklos.pdf
Selected list of publications
(pdf)
[1967] Pethő,Á.:
On a Class of Solutions of Algebraic Homogeneous Linear Equations,
Acta Math. Acad. Sci. Hungaricae vol. 18 (1967), 19-23.
(pdf)
[1991c] Szalkai,I.:
Generating Minimal Reactions in Stoichiometry Using Linear Algebra,
Hung. J. Ind. Chem. vol. 19 (1991), 289-292. HU ISSN 0133-0276,
(pdf)
[1995a] Laflamme,C., Szalkai,I.:
Counting Simplexes in Rn, Hung. J. Ind. Chem. vol. 23 (1995), pp. 237-240,
(pdf)
[1996] Dósa,Gy., Laflamme,C., Szalkai,I.:
On the Maximal and Minimal Number of Bases and Simple Circuits in Matroids
and the Extremal Constructions, Preprint 046, Dept. Math. Univ. Veszprém, 1996.
(cover)
» » appeared in » » [2006]
[1997d] Szalkai,I.: Lineáris algebra, sztöchiometria és kombinatorika,
(Linear algebra, stoichiometry and combinatorics, in Hungarian),
Polygon VII. (1997), 35-51.
(pdf)
[1997p] Szalkai,I.: On the Number of Bases and Circuits in Matroids,
Colloquia Math. Soc. J.Bolyai, Conference on Extremal Graph Theory,
Balatonlelle, 1997, Problem No.14.
[1998ab] Laflamme,C., Szalkai,I.: Counting Simplexes in R3,
Electr. J. of Combinatorics vol. 5 (1998) No.1, Res.Paper No. 40, 11 pp.
(pdf)
J. Combin. 5 (1998), 597-607.
[1999b] Szalkai,I.: Handling Multicomponent Systems in Rn, I.:
Theoretical Results, J. Math. Chemistry vol. 25 (1999), 31-46.
(pdf)
[2000a] Szalkai,I.:
A New General Algorithmic Method in Reaction Syntheses Using Linear Algebra,
J. Math. Chemistry vol. 28 (2000), 1-34.
(pdf) ,
(doi)
[2000b] Szalkai,I.:
On Valuation Operators in Stoichiometry and in Reaction Syntheses,
J. Math. Chemistry vol. 27 (2000), 377-386.
(pdf)
» »
[2002] Szalkai,I.: Mathematical Models of Reaction Mechanisms,
PhD-Dissertation /old version, in English/,
(pdf)
[2006] Dósa,Gy., Szalkai,I., Laflamme,C.:
The Maximum and Minimum Number of Circuits and Bases of Matroids,
Pure Math. Appl. (PUMA) vol. 15 (2006), 383-392.
(pdf)
[2011o] Szalkai,B., Szalkai,I.:
Counting minimal reactions with specific conditions in R4 ,
J. Math. Chemistry vol. 49 (2011), 1071-1085.
(Springer) ,
(pdf)
[2012a] Szalkai,I., Dósa,Gy., Tuza,Zs., Szalkai,B.:
On Minimal Solutions of Systems of Linear Equations with Applications,
Miskolc Math. Notes, vol. 13 (2012), 529-541.
(MMN) ,
(pdf)
[2013a] Szalkai,B., Szalkai,I.:
Simplexes and their Applications - a Short Survey,
Miskolc Math. Notes, vol. 14 (2013), 279-290.
(MMN) ,
(pdf)
[2013d] Szalkai,I.:
Reakciómechanizmusok algoritmikus és kombinatorikai vizsgálata
(An Algorithmic and Mathematical Investigation of Reactions, in Hungarian)
PhD-Dissertation /new version/,
(Univ)
, (pdf) ,
(Summary, in English)
[2013e] Szalkai,I.:
Pontok, lapított tetraéderek, molekulák és kémiai reakciók
(Points, simplexes, molecules and chemical reactions - in Hungarian),
Haladvány Kiadvány,
http://math.bme.hu/~hujter/131030.pdf
[2014a] Tuza,Zs., Szalkai,I.:
Minimum Number of Affine Simplexes of Given Dimension,
Discr. Appl. Math. 180 (2014) 141–149, DOI: 10.1016/j.dam.2014.07.025.
(arxiv) ,
(pdf)
[20xx]Sellers,P., Pethő,Á., Szalkai,I.:
On the Mathematical Foundation of Reaction Mechanisms ,
in preparation, (pdf)
Last modified: 2019.02.18.
Selected list of publications
(pdf)