Арифметика на эллиптических кривых с использованием графических вычислителей
We consider different parallel algortihms for operations in prime fields and their applications for operations on points of elliptic curves. The work provides results for implementations of these algorithms on NVIDIA graphical processors.
This paper describes aspects of development of decision support system based on neural networks and a genetic algorithm. We justify the use of general-purpose computing on graphics processing units (GPGPU) for our decision support system. Example of CUDA successful application to increase computing performance of the system in question is presented.
In this article we ground some advantages of the evolutionary approach to the solution of problems of decision support system development. The most popular methods of forecasting and detection of dependences are considered. Advantages of use of neural networks to forecast and to determine of dependences between parameters of systems are given. Advantages of interval neural networks are considered. Methods of finding of optimal input parameters for neural networks are appreciated. Realization of decision-making support systems with use of genetic algorithm and neural networks is described. The main advantages of parallelization of the general purpose calculations with use of the graphics processing units are listed. The realized system shell based on communication of neural networks and genetic algorithm, and optimized at the expense of use of general-purpose graphics processing units is described.
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.
For a class of optimal control problems and Hamiltonian systems generated by these problems in the space l 2, we prove the existence of extremals with a countable number of switchings on a finite time interval. The optimal synthesis that we construct in the space l 2 forms a fiber bundle with piecewise smooth two-dimensional fibers consisting of extremals with a countable number of switchings over an infinite-dimensional basis of singular extremals.
The problem of minimizing the root mean square deviation of a uniform string with clamped ends from an equilibrium position is investigated. It is assumed that the initial conditions are specified and the ends of the string are clamped. The Fourier method is used, which enables the control problem with a partial differential equation to be reduced to a control problem with a denumerable system of ordinary differential equations. For the optimal control problem in the l2 space obtained, it is proved that the optimal synthesis contains singular trajectories and chattering trajectories. For the initial problem of the optimal control of the vibrations of a string it is also proved that there is a unique solution for which the optimal control has a denumerable number of switchings in a finite time interval.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.
In this paper, we construct a new distribution corresponding to a real noble gas as well as the equation of state for it.