25 resultados para special functions
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, - u(x, y, t), D = [0, a] [0, b] [0, ). , 2x 2y. u v C(D). . , , (C(D), ).
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. , . , - . . . , . . , , . , - , . , .
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. , . - . . xx yy . . . . .
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MSC 2010: 33-00, 33C45, 33C52, 30C15, 30D20, 32A17, 32H02, 44A05
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Experiences from a German-Ukrainian project for the joint development of dynamic learning environments are reported. General methodological and technological aspects are discussed as well as special items arising from the cross-cultural collaboration.
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Special generalizing for the artificial neural nets: so called RFT FN is under discussion in the report. Such refinement touch upon the constituent elements for the conception of artificial neural network, namely, the choice of main primary functional elements in the net, the way to connect them(topology) and the structure of the net as a whole. As to the last, the structure of the functional net proposed is determined dynamically just in the constructing the net by itself by the special recurrent procedure. The number of newly joining primary functional elements, the topology of its connecting and tuning of the primary elements is the content of the each recurrent step. The procedure is terminated under fulfilling natural criteria relating residuals for example. The functional proposed can be used in solving the approximation problem for the functions, represented by its observations, for classifying and clustering, pattern recognition, etc. Recurrent procedure provide for the versatile optimizing possibilities: as on the each step of the procedure and wholly: by the choice of the newly joining elements, topology, by the affine transformations if input and intermediate coordinate as well as by its nonlinear coordinate wise transformations. All considerations are essentially based, constructively and evidently represented by the means of the Generalized Inverse.
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Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20
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Mathematics Subject Classification: 33D15, 44A10, 44A20
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Stability of nonlinear impulsive differential equations with "supremum" is studied. A special type of stability, combining two different measures and a dot product on a cone, is defined. Perturbing cone-valued piecewise continuous Lyapunov functions have been applied. Method of Razumikhin as well as comparison method for scalar impulsive ordinary differential equations have been employed.
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Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09
