Let H be the orthogonal projection onto polynomials of n variables of degree < 1 and \\ \\ be the norm of an operator from C ([0,1]ⁿ) to C ([0,1]ⁿ). In this paper we show that C₁O_n <= \\H\\ <= C₂O_n, n G N. Here O_n denotes the minimal norm of a projection dealing with the linear interpolation on the cube [0,1]ⁿ. The proofs make use of certain properties of the Eulerian numbers and the central B-splines and also some previous results of the author.

The dynamics of a generalized Hutchinson's equation with two delays is investigated. A local analysis of a loss of a stability for the nonzero equilibrium state for the problem has been made. Phase reorganizations have been analyzed with numerical methods with the help of the obtained asymptotic formulas. The bifurcation curves that correspond to the principal bifurcations, which take place in the system, have been built on the parameters' plane.

A new model of the neuron cell - the generalized automatic neuron (GAN) is considered. This model has an universal character. It combines properties of neuron-oscillator and neuron-detector. The problem of berst influence on the generalized automatic neuron is raised and solved.

Let £o,..., £n be strings drawn from some finite alphabet. In this paper we describe an algorithm for finding mean minimum distances between strings io,..., £s for all s ^ n. The complexity of the algorithm is O(nm), where m is the length of strings.

The paper describes NumGRID metacomputing system which allows to integrate several high performance computational resources into a united Grid. Using this Grid it is possible to solve a lot of large-scale numerical problems. Here one can find key ideas and objectives of NumGRID middleware, analysis of large-scale numerical tasks class, descriptions and results of different tests that were done using NumGRID. There are also some conclusions about Grid applicability to a range of scientific problems solution.

The paper is devoted to passports of scientific specialities which define problems, borders and the depth of future research. The resonant interaction of the passport of a scientific speciality and a dissertation defines an algorithmic basis in the practical realization of the cognitive decision-making technology.