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Information × Registration Number 0213U005893, 0110U005872 , R & D reports Title Differential-geometric and Lie-algebraic methods of research. System of artificial intelligence, based on inductive methods popup.stage_title Head Prytula Mykola, Registration Date 25-09-2013 Organization Ivan Franko National University of Lviv popup.description2 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 obtained results provided indication as to when is it best to utilize each approach when it comes to computationally intensive tasks. Product Description popup.authors Притула Микола Миколайович Щербина Юрій Миколайович popup.nrat_date 2020-04-02 Close