In this paper we consider Giseker-Maruyama moduli scheme M := MP3(2;¡1; 2; 0) of stable coherent torsion free sheaves of rank 2 with Chern classes c1 = -1, c2 = 2, c3 = 0 on 3-dimensional projective space P3. We will de¯ne two sets of sheaves M1 and M2 in M and we will prove that closures of M1 and M2 in M are irreducible components of dimensions 15 and 19, accordingly.

In this paper we consider the scheme MQ( 2;¡1; 2; 0 ) of stable torsion free sheaves of rank 2 with Chern classes c1 = -1, c2 = 2, c3 = 0 on a smooth 3-dimensional projective quadric Q. The manifold MQ(-1; 2) of moduli bundles of rank 2 with Chern classes c1 = -1, c2 = 2 on Q was studied by Ottaviani and Szurek in 1994. In 2007 the author described the closure MQ (-1; 2) in the scheme MQ(2;¡1; 2; 0). In this paper we prove that in MQ(2;¡1; 2; 0) there exists a unique irreducible component diferent from MQ (¡1; 2) which is a rational variety of dimension 10.

The problem of finding the maximum flow in nets of a special form is considered. In such nets the arcs are related in such a way that the total flow passing through the related arcs does not exceed the minimum throughput of these arcs. It is shown that the theorem by Ford and Fulkerson, according to which the maximum flux value is equal to the throughput of a minimum cut, is not performed for such networks. The estimations of the maximum flow in a generalized net with bound arcs are proposed. And the algorithm for finding the maximum flow in such nets is developed.

A generalized kinetic equation of a grinding process is obtained. The equation is valid for arbitrary distribution of particle destruction waiting time. In terms of the equation a grinding process model with the power law of waiting time distribution is proposed. The particle size dependence of the power index is taken into account and its in°uence on grinding process kinetics is investigated.

We construct the duality for special probability spaces using the Gale duality.

The problem of a limiting degree of linear system stability is investigated. The conditions are received, where roots nearest to an imaginary axis are valid. When fulflling these conditions the limiting degree of stability for a typical industrial object with delay and "serial" laws of regulation is found.

The article is devoted to a type dynamics for a new object DBMS DIM [1, 2] and the schemes evolution of its databases.

We introduce a new metric on a space of right-sided infinite sequences drawn from a finite alphabet. Emerging from a problem of entropy estimation of a discrete stationary ergodic process, the metric is important on its own part and exhibits some interesting properties. For example, the measure of a ball is discontinuous at every binary rational value of log r, where r is the radius.

In this article a polynomial algorithm is described of verification of dynamic properties of Markov chains described by formulas of a subset of temporal logic PLTL (propositional temporal logic of linear time). The algorithm allows to find probability of the validity of the formula on the Markov chain, and also set of trajectories on which the verified formula is true.

We discuss some questions connected with the construction of a technology of analysing correctness of Programmable Logic Controller programs. We consider an example of modeling and automated verification of PLC-programs written in the Ladder Diagram language (including timed function blocks) of the IEC 61131-3 standard. We use the Cadence SMV for symbolic model checking. Program properties are written in the linear-time temporal logic LTL.

Modern methods and libraries for high quality pseudorandom number generation and for generation of parallel random number streams for Monte Carlo simulations are considered. The probability equidistribution property and the parameters when the property holds at dimensions up to logarithm of mesh size are considered for Multiple Recursive Generators.