Методика синтеза трёхмерных фрактальных видео для видеоарта, телевидения и очкового стереокино
The article describes a method of producing three-dimensional video using fractal mathematics and information technologies. Various 3D visualization technologies of three-dimensional fractals, both in static and dynamic form are considered. Methods of three-dimensional fractal video synthesis used for various applications are described. One of the applications is a 3D cinema with glasses, where the background video series uses mathematical, not painted and not obtained by standard methods of filming various plurality of frames for animation, video and television.
The method of obtaining dynamic graphic art objects using mathematics and information technologies is presented. Various technologies of graphic dynamic and interactive art objects based on the generated fractal images and software are considered. Results of information and mathematical computer experiments of Trubochkinf N.K. are analyzed:
- Art- video based on recording dynamic transformation of a fractal-image;
- Multilayer programmable animations (motion, color, transparency) fractals animations with internal layers of varying length, can be generated over a long recurring time image;
- Video art on the basis of three-dimensional fractals (dynamic and interactive).
The three already traditional volumes of the WDS Proceedings you are holding in the hands are composed of the contributions which have been presented during the 21st Annual Conference of Doctoral Students that was held in Prague, at Charles University, Faculty of Mathematics and Physics from May 29 to June 1, 2012. In this year, 100 student manuscripts were submitted to publishing and 88 were accepted after the review process.
The paper discusses in detail the scale of translation of primary points scored by school graduates in the unified state exam in mathematics, used from 2013 to the present time. Based on the analysis of the dynamics of these scales, a conclusion is made about the annual increase in the "average" 100-point result, as well as the presence of a significant increase in the final grade compared with the linear scale. Additionally, the authors describe the effect of reducing the value of primary points as they approach the maximum.
This article presents the results of a pilot study assessing the level of formation of a stochastic competence among teachers of mathematics. Besides, the indicators that reflect the competence of formation of stochastic students are identified and ranked in order of importance. Different instruments (questionnaires, tests, assignments) have been used to solve the problem under study.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.