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The use of clustering algorithms to determine the types of malicious software files based on the analysis of the WinAPI function call sequences is investigated. The use of clustering algorithms such as k-means, EM-algorithm, hierarchical algorithm, and the affinity propagation method is considered. The quality of clustering is evaluated using the silhouette metrics, the Calinski–Harabasz index, and the Davies–Bouldin index.

We study how the statements on estimates of solutions to linear functional-differential equations, analogous to the Chaplygin differential inequality theorem, are connected with the positivity of the Cauchy function and the fundamental solution. We prove a comparison theorem for the Cauchy functions and the fundamental solutions to two functional-differential equations. In the theorem, it is assumed that the difference of the operators corresponding to the equations (and acting from the space of absolutely continuous functions to the space of summable ones) is a monotone totally continuous Volterra operator. We also obtain the positivity conditions for the Cauchy function and the fundamental solution to some equations with delay as long as those of neutral type.

In this paper we propose an iterative method for solving the equation Υ(x, x) = y, where the mapping Υ acts in metric spaces and is covering in the first argument and Lipschitzian in the second one. Each subsequent element xi+1 of the sequence of iterations is defined by the previous one as a solution to the equation Υ(x, xi) = yi, where yi can be an arbitrary point sufficiently close to y. Conditions for convergence and error estimates are obtained. The method proposed is an iterative development of the Arutyunov method for finding coincidence points of mappings. In order to determine xi+1 in practical implementation of the method in linear normed spaces, it is proposed to perform one step by using the Newton–Kantorovich method. The thus-obtained method of solving the equation of the form Υ(x, u) = ψ(x) − φ(u) coincides with the iterative method proposed by A.I. Zinchenko,M.A. Krasnosel’skii, and I.A. Kusakin.

We consider nonlinear nonlocal integral equation generalizing equations typically used in mathematical neuroscience. We investigate solutions tending to zero at any fixed moment with unbounded growth of the spatial variable (these solutions correspond to normal brain functioning). We consider an impulsive control problem, which models electrical stimulation used in the presence of various diseases of central nervous system. We define suitable complete metric space, where we obtain conditions for existence, uniqueness and extendability of solution to the problem as well as continuous dependence of this solution on the impulsive control.

We prove a new result on Lipshitz disturbances of vector covering maps in metric spaces. With methods of covering maps theory, we study controllable systems defined by differential equations that are not resolved with respect to the derivative of the unknown function.

The paper is concerned with the extension of tests for superpositional measurability, Filippov's implicit function lemma and the Scorza Dragoni property to set-valued (and, as a corollary, to single-valued) mappings that fail to satisfy the Caratheodory conditions (the upper Caratheodory conditions) and are not continuous (upper semicontinuous) in the phase variable. The corresponding results depend on the introduction of the space of all closed subsets (including the empty set) of an arbitrary metric space ; a metric on is proposed; the space is shown to be complete whenever the original space is; a criterion for convergence of a sequence is put forward; mappings with values in are studied. Some results on set-valued mappings satisfying the Caratheodory conditions and having compact values in are shown to hold for mappings with values in , measurable in the first argument, and continuous in the proposed metric in the second argument. Bibliography: 22 titles.

We prove some assertions about solvability, solution estimates, and well-posed solvability of equations with covering mappings in a product of metric spaces. The results are applied to the analysis of boundary value problems for differential equations unsolved for the derivative.

A thorough geostatistical analysis was performed of the spatial variability of the soil properties, the sowing parameters, and the wheat yield in a field experiment under precision agriculture conditions. It was found that most of the soil parameters are significantly correlated and can be successfully mapped using kriging procedures, which ensure the optimum development of agrochemical cartograms for agricultural fields. It was also shown that the sowing parameters had a significantly lower spatial correlation; their cartograms could be drawn, although with worse accuracy. The quality parameters of the wheat grain showed no spatial correlation.

We prove some results concerning solvability, estimates for solutions, and well-posed solvability of equations with conditionally covering mappings. These results are applied to the analysis of differential equations unsolved for the derivative.

For a Volterra equation in a function space we obtain conditions for the unique existence of a global or maximally extended solution and its continuous dependence on equation parameters. Based on these results, we state conditions for the solvability of the Cauchy problem for a differential equation with delay and the continuous dependence of solutions on the right-hand side of the equation, on the delay, on the initial condition, and the history.

We continue to study the properties of covering mappings of metric spaces and present their applications to differential equations. To extend the applications of covering mappings, we introduce the notion of conditionally covering mapping. We prove that the solvability and the estimates for solutions of equations with conditionally covering mappings are preserved under small Lipschitz perturbations. These assertions are used in the solvability analysis of differential equations unsolved for the derivative.

We propose a new general definition of Volterra operators. Several types of evolutionary operators, including Volterra ones in the sense of A.N. Tikhonov, satisfy this definition. For equations with generalized Volterra operators we introduce the notions of local, global, and maximally extended solutions. For solutions to nonlinear equations we formulate the existence, uniqueness, and extendability conditions. The theorems proved in this paper imply both known and new results on the solvability of concrete equations. We adduce an example of the application of obtained results to the study of the Cauchy problem for functional differential equations.

The definition of a Volterra operator on a system of equivalence relations is presented. For an appropriately selected system of relations this yields the well-known definitions treating the evolution property, the causality of operators, including Tychonoff's classical definition. The existence, the uniqueness, the extendability of local solutions to non-linear equations with Volterra operators are considered, estimates of the domains of definition of solutions are obtained, and theorems on the continuous dependence of solutions on the parameters are proved. The results so obtained are applied to the analysis of the well-posedness and to the approximate solution of the Cauchy problem for functional differential equations.

We present results on local solubility, extendability of solutions, and the existence of upper and lower solutions of equations with monotonic generalized Volterra operators in Banach function spaces. These results are analogous to the well-known theorems on the integral and differential inequality and can be used for estimating solutions of various functional-differential equations.

An Anderson model with N-fold degeneracy in the Kondo regime is considered. It is presumed that the electron-electron correlations in the system of f electrons have their maximum strength. A criterion for instability against the formation of a weakly antiferromagnetic phase superposed on the Kondo state is obtained by the auxiliary-boson method using the 1/N expansion. An effective interaction leading to the formation of magnetic ordering appears because of the spin fluctuations in the system of localized electrons. The phase diagram of the system is constructed.

Contraceptive preparations containing estrogens have a number of side effects caused primarily by the effect of the estrogen component. A search is underway in Russia for modified estrogens with sufficiently high contraceptive activity with a reduced hormonal (uterotropic) effect. In 1981 peculiarities of combining 8-isoanalogue estrogen steroids with cytoplasmic receptors of a rat uterus were detected making it possible to predict precisely what kind of micromodifications in the structure of 8-isoestradiol would result in a marked reduction in uterotropic activity. Experiments were conducted on female rats rabbits and mice. A physiological solution was injected in animals in the control group. Compound II was studied in rats in doses of 0.001 and 0.005 mg/kg; the contraceptive effect in a dose of 0.001 mg/kg was 6 (P

1. Dilution curves with an exponential drop with a time constant adjustable within 2.5–20 sec and error of its determination of not more than ±5% were obtained on the created device with a pulsating flow of the working fluid for reproducing the indicator-dilution process in the circulatory system.