Conference, 26 June 2018

• 09:00
  Wolfram Language and CDF—Interactive Presentations of the Results of Scientific Works

  The lecture focuses on the possibilities of interactive presentation of scientific results, discussing both programming procedures and techniques in the Wolfram Language environment as well as the possibilities of interactive visualization outside the Mathematica environment.

  Zbigniew Galon

  Gambit Centrum Oprogramowania i Szkoleń Sp. z o.o.

• 09:30
  Applied Mathematics and Computer Simulations in Higher Education

  Presentation of the textbook Introduction to Mathematical Modeling and Computer Simulations by V. Mityushev, W. Nawalaniec and N. Rylko, 2018.

  Vladimir Mityushev

  Professor, Institute of Computer Sciences, Cracow

• 10:00
  Advanced Symbolic Computations in Scientific Applications

  Symbolic computation lies at the core of the Mathematica computing system. The main part of the talk concerns different techniques of implementation of symbolic manipulations and their application to selected scientific problems.

  Wojciech Nawalaniec

  Associate Professor, Institute of Computer Sciences, Cracow

• 10:30

  Coffee break

• 10:45
  Artificial Intelligence in the Wolfram Language Environment

  This presentation is about procedures of the Wolfram Language environment in the field of artificial intelligence, enabling the implementation of supervised and unsupervised learning. Issues of object classification, regression, prediction of features, clustering and reduction of dimensions will also be presented.

  Zbigniew Galon

  Gambit Centrum Oprogramowania i Szkoleń Sp. z o.o.

• 11:15
  Image Processing and Treatment in Biology

  Pattern recognition and image processing are fundamental fields of modern science. It should not surprise anyone that the Mathematica package offers fundamental support in the fields of image processing and analysis. This talk concerns the use of the Mathematica package in image analysis. Chosen tools that allow recognition of certain patterns in biomedical images and images of biological structures will be presented. Selected dynamic visualisations of algorithms related to modeling bio structures in Mathematica will also be demonstrated.

  Roman Czapla

  Assistant, Institute of Computer Sciences, Cracow

• 11:45
  Symbolic Computations of Effective Properties of Composites

  This presentation is on the symbolic computation and recursive algorithms to compute the effective properties of composites by means of the advanced Mathematica operators.

  Piotr Drygaś

  Senior Lecturer, University of Rzeszów

• 12:15

  Lunch

• 13:15
  Homotopy Analysis Method and the Examples of Its Applications

  In recent times, the methods enabling one to find the solutions of various physical and technical problems have found a number of applications. The set of methods under discussion includes, among others, the Adomian decomposition method, the variational iteration method, the Taylor transformation method, the homotopy analysis method and a special case of the last one—the homotopy perturbation method. In their general mathematical formulations, the discussed methods give the possibility of solving the linear and nonlinear operator equations. In these methods there is constructed the functional sequence or series, the limit (sum) of which is the function giving the solution of the investigated problem (under appropriate conditions). In general, the respective sequences or series converge quite rapidly, thanks to which the computation of only the few first terms (components) ensures a very good approximation of the sought solution. In this presentation, the homotopy analysis method and the examples of its application will be presented.

  Damian Słota

  Professor, Silesian University of Technology

• 13:45
  Complex Roots of the Bernoulli Polynomials and Selected Identities for the Central Binomial Coefficients

  With the numerical assistance of the Mathematica software, we have described some regularities and irregularities of the real and complex nonreal roots of the Bernoulli polynomials. This subject matter appeared in connection with the decompositions of the hyperbolic and semihyperbolic polynomials into the iterated integrals. Moreover, by applying the Mathematica program, we have managed to give the alternative final description to some identities connected with the inverses of the central binomial coefficients. We have also generated the triangular tables of the new double-indexed number sequences.

  Roman Wituła

  Professor, Silesian University of Technology

• 14:15
  Application of the Biologically Inspired Optimisation Algorithms in the Solution of Technical Problems

  The optimisation algorithms inspired by the behaviour of natural creatures have found a number of practical applications in recent years. In this talk, the ant colony optimisation and the artificial bee colony algorithms will be discussed and their usage in reconstruction of the cooling conditions in the continuous casting process will be presented. The presentation will contain the description of the algorithms and theoretical findings of investigated problems, as well as the results of numerical examples obtained with the use of the Mathematica software.

  Edyta Hetmaniok

  Assistant Professor, Silesian University of Technology

• 14:45

  Coffee break

• 15:00
  On the Orbits of Kaprekar's Transformations

  Even though some theoretical results about the description of the Kaprekar's orbit are already known (their existence, amount, cardinality), the numerical assistance of Mathematica software was and still is necessary in the research executed by us. The name "Kaprekar's transformations" concerns the whole family of transformations on the finite sets. In some cases of these transformations, the full descriptions of orbits are known, but for many Kaprekar's transformations, only Mathematica enabled us to notice some relations and to indicate the sequences of orbits compatible in the description for infinitely many Kaprekar's transformations. Finally, thanks to Mathematica, we could make some observations leading to the formulation of the new, original problems!

  Mariusz Pleszczyński

  Assistant Professor, Silesian University of Technology

• 15:30
  Student talks devoted to their projects during their study at the Pedagogical University of Cracow
• 15:50
  Student talks devoted to their projects during their study at the Pedagogical University of Cracow
• 16:10
  Closing remarks