On a Conditional Cauchy-type Functional Equation Involving Powers

We solve the functional equation f(x^m + y) = f(x)^m + f(y) in the realm of polynomials with integer coefficients.

Generalizing of Neural Nets: Functional Nets of Special Type

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.

Dubrovin Type Equations for Completely Integrable Systems Associated with a Polynomial Pencil

Dubrovin type equations for the N -gap solution of a completely integrable system associated with a polynomial pencil is constructed and then integrated to a system of functional equations. The approach used to derive those results is a generalization of the familiar process of finding the 1-soliton (1-gap) solution by integrating the ODE obtained from the soliton equation via the substitution u = u(x + λt).

A Gradient-Type Optimization Technique for the Optimal Control for Schrodinger Equations

In this paper, we are considered with the optimal control of a schrodinger equation. Based on the formulation for the variation of the cost functional, a gradient-type optimization technique utilizing the finite difference method is then developed to solve the constrained optimization problem. Finally, a numerical example is given and the results show that the method of solution is robust.

Analysis of Dermatoglyphic Signs for Definition Psychic Functional State of Human's Organism

Relation between dermatoglyphic signs and temperaments types is considered. An algorithm for papillary patterns classification and Izenk’s two factors model are used for establishment relationship asymmetry signs with psychic functional state of human’s organism.

Some Mean-Value Theorems of the Cauchy Type

2000 Mathematics Subject Classification: Primary 26A24, 26D15; Secondary 41A05

Direct and Converse Theorems for Generalized Bernstein-Type Operators

2000 Mathematics Subject Classification: 41A25, 41A27, 41A36.

Oscillation Properties of Some Functional Fourth Order Ordinary Differential Equations

2010 Mathematics Subject Classification: 34A30, 34A40, 34C10.

Weighted Approximation by a Class of Bernstein-Type Operators

AMS classification: 41A36, 41A10, 41A25, 41Al7.