Registration Number
0212U004221,
0110U001373
, R & D reports
Title
Mathematical methods of research of the nonlinear dynamic systems, objective methods of design of information and optimization tasks.
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Head
Prytula M.,Bartish M.,
Registration Date
31-01-2012
Organization
Ivan Franko National University of Lviv
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Purpose of work: there is finding of endless hierarchy of laws of maintainance, construction on their basis of implectic operators, and L- of the operator Lax. Being of partial decisions of the set nonlinear dynamic systems.. Development of algorithms is on the basis of artificial neuron networks for the design of information. A construction of the combined algorithms of untiing of tasks of minimization is in the case of singular matrix of Gesse in the point of decision, and also at untiing of the redefined system of nonlinear equations. A Hamiltonian analysis of nonlinear dynamical Korteweg-de Vries type systems was conducted utilizing the differential-algebraic algorithm and method of small parameter. Two precise solutions have been found for the Korteweg-de Vries equation and their plots have been obtained using the method of Hyperbolic Tangent functions. An infinite hierarchy of conservation laws have been found for the nonlinear hydrodynamic evolution model of the slim liquid layered streams. Proved that for specific values of coefficients the nonlinear dynamic system is Bi-Hamiltonian. Researched nonlinear hydrodynamic system of Korteweg-de Vries type. Proved the existence of an infinite hierarchy of functionally independent and involutional conservation laws for such systems. Found a pair of compatible implectic operators, which provide a way to formulate the system as Bi-Hamiltonian. An explicit representation of the Lax mapping has been found utilizing the gradient-holonomic algorithm. Researched approaches for organizing effective computations of the processes associated with training and using Self-Organizing Maps (SOM) as the software running in multi-core and multi-processor computational environments. Developed multi-threaded algorithms for SOM training and clustering based on the idea of decomposed lattice of SOM elements. Undertaken a comparative analysis of two principal contemporary paradigms for implementing multi-threaded algorithms - Actor Model and MapReduced using a functional-OOP programming language Scala. The new approach for building algorithms for solving of unconstrained minimization problem is proposed. The rate of convergence of suggested algorithms are established and proved. A numerical investigation of modification and the basis methods is conducted. The nonstationary nonlinear heat conduction problem is considered given that heat capacity and coefficient of heat conductivity are set analytically and tabularly. According to the method of finite differences, the nonlinear boundary problem is reduced to a system of nonlinear equations. This system is numerically solved by two parametric secant type methods. The numerical results of the considered problem are presented.
Product Description
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Бартіш М.Я.
Гнатишин О.П.
Николайчук Л.В.
Притула М.М.
Шахно С.М.
Щербина Ю.М.
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2020-04-02
