Advanced Computational Methods for Knowledge Engineering - Proceedings of the 4th International Conference on Computer Science, Applied Mathematics and Applications, ICCSAMA 2016, 2-3 May, 2016, Vienna, Austria

This proceedings consists of 20 papers which have been selected and invited from the submissions to the 4th International Conference on Computer Science, Applied Mathematics and Applications (ICCSAMA 2016) held on 2-3 May, 2016 in Laxenburg, Austria. The conference is organized into 5 sessions: Advanced Optimization Methods and Their Applications, Models for ICT applications, Topics on discrete mathematics, Data Analytic Methods and Applications and Feature Extractio, respectively. All chapters in the book discuss theoretical and practical issues connected with computational methods and optimization methods for knowledge engineering. The editors hope that this volume can be useful for graduate and Ph.D. students and researchers in Applied Sciences, Computer Science and Applied Mathematics

Corrigendum on Wiener index, Zagreb Indices and Harary index of Eulerian graphs

In the original article ``Wiener index of Eulerian graphs'' [Discrete Applied Mathematics Volume 162, 10 January 2014, Pages 247-250], the authors state that the Wiener index (total distance) of an Eulerian graph is maximized by the cycle. We explain that the initial proof contains a flaw and note that it is a corollary of a result by Plesn\'ik, since an Eulerian graph is $2$-edge-connected. The same incorrect proof is used in two referencing papers, ``Zagreb Indices and Multiplicative Zagreb Indices of Eulerian Graphs'' [Bull. Malays. Math. Sci. Soc. (2019) 42:67-78] and ``Harary index of Eulerian graphs'' [J. Math. Chem., 59(5):1378-1394, 2021]. We give proofs of the main results of those papers and the $2$-edge-connected analogues.Comment: 5 Pages, 1 Figure Corrigendum of 3 papers, whose titles are combine

Elementary Introduction to Stochastic Finance in Discrete Time

This article gives an elementary introduction to stochastic finance (in discrete time). A formalization of random variables is given and some elements of Borel sets are considered. Furthermore, special functions (for buying a present portfolio and the value of a portfolio in the future) and some statements about the relation between these functions are introduced. For details see: [8] (p. 185), [7] (pp. 12, 20), [6] (pp. 3-6).Ludwig Maximilians University of Munich, GermanyGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495-500, 2001.Hans Föllmer and Alexander Schied. Stochastic Finance: An Introduction in Discrete Time, volume 27 of Studies in Mathematics. de Gruyter, Berlin, 2nd edition, 2004.Hans-Otto Georgii. Stochastik, Einführung in die Wahrscheinlichkeitstheorie und Statistik. deGruyter, Berlin, 2 edition, 2004.Achim Klenke. Wahrscheinlichkeitstheorie. Springer-Verlag, Berlin, Heidelberg, 2006.Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.Andrzej Nędzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.Konrad Raczkowski and Andrzej Nędzusiak. Series. Formalized Mathematics, 2(4):449-452, 1991.Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990