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Nikolay Kuznetsov

Publications and source records attributed to Nikolay Kuznetsov.

At least 19 recordsLinked to original sources

On sloshing in containers with porous baffles

Sloshing eigenvalues are studied for containers with porous baffles extending throughout the constant (possibly infinite) depth. The fluid transmission across the baffles is described by Darcy's law, and so the spectral problem is nonself-adjoint. In particular, much attention is paid to vertical cylinders with circular walls and radial baffles. Explicit solutions are obtained, whose crucial feature is that the corresponding pressure difference vanishes across the baffle. These real solutions coincide with those that describe sloshing in the presence of rigid baffles, thus demonstrating that at certain frequencies the damping efficiency of porous baffles is the same as that of the rigid ones having the same configuration.

physics.flu-dyn

Sloshing in containers with vertical walls: isoperimetric inequalities for the fundamental eigenvalue

One isoperimetric inequality for the fundamental sloshing eigenvalue is derived under the assumption that containers have vertical side walls and either finite or infinite depth. It asserts that among all such containers, whose free surfaces are convex, have two axes of symmetry and a given perimeter length, this eigenvalue is maximized by infinitely deep ones provided the free surface is either the square or the equilateral triangle. The proof is based on the recent isoperimetric result obtained by A. Henrot, A. Lemenant and I.~Lucardesi for the first nonzero eigenvalue of the two-dimensional Neumann Laplacian under the perimeter constraint. Another isoperimetric inequality for the fundamental eigenvalue, which describes sloshing in containers with vertical walls, is a consequence of the classical result due to G. Szeg\H o concerning the first nonzero eigenvalue of the free membrane problem.

math.AP

The fundamental eigenfrequency is simple in the two-dimensional sloshing problem

The two-dimensional sloshing problem is considered; it describes the transversal free oscillations of water in an open, infinitely long canal of uniform cross-section. It is proved that the fundamental eigenfrequency is simple, whereas the corresponding velocity potential has only one nodal line connecting the free surface and the bottom; its harmonic conjugate (stream function) does not change sign under the proper choice of the additive constant.

math.AP

A characterisation of harmonic functions by quadrature identities of annular domains and related results

A new characterization of harmonic functions is obtained. It is based on quadrature identities involving mean values over annular domains and over concentric spheres lying within these domains or on their boundaries. The analogous result with a logarithmic weight in the volume means is conjectured. The similar characterization is derived for real-valued solutions of the modified Helmholtz equation (panharmonic functions), whereas for solutions of the Helmholtz equation (metaharmonic functions) the analogous result is just outlined. Weighted mean value identities are also obtained for solutions of these equations in two-dimensions. The dependence of coefficients in these identities on a logarithmic weight is analysed and characterizations of these functions are conjectured.

math.AP

Forecasting and stabilizing chaotic regimes in two macroeconomic models via artificial intelligence technologies and control methods

One of the key tasks in the economy is forecasting the economic agents' expectations of the future values of economic variables using mathematical models. The behavior of mathematical models can be irregular, including chaotic, which reduces their predictive power. In this paper, we study the regimes of behavior of two economic models and identify irregular dynamics in them. Using these models as an example, we demonstrate the effectiveness of evolutionary algorithms and the continuous deep Q-learning method in combination with Pyragas control method for deriving a control action that stabilizes unstable periodic trajectories and suppresses chaotic dynamics. We compare qualitative and quantitative characteristics of the model's dynamics before and after applying control and verify the obtained results by numerical simulation. Proposed approach can improve the reliability of forecasting and tuning of the economic mechanism to achieve maximum decision-making efficiency.

math.OC

Two-dimensional sloshing: domains with interior `high spots'

Considering the two-dimensional sloshing problem, our main focus is to construct domains with interior high spots; that is, points, where the free surface elevation for the fundamental eigenmode attains its critical values. The so-called semi-inverse procedure is applied for this purpose. The existence of high spots is proved rigorously for some domains. Many of the constructed domains have multiple interior high spots and all of them are bulbous at least on one side.

math.AP

From Malware Samples to Fractal Images: A New Paradigm for Classification. (Version 2.0, Previous version paper name: Have you ever seen malware?)

To date, a large number of research papers have been written on the classification of malware, its identification, classification into different families and the distinction between malware and goodware. These works have been based on captured malware samples and have attempted to analyse malware and goodware using various techniques, including techniques from the field of artificial intelligence. For example, neural networks have played a significant role in these classification methods. Some of this work also deals with analysing malware using its visualisation. These works usually convert malware samples capturing the structure of malware into image structures, which are then the object of image processing. In this paper, we propose a very unconventional and novel approach to malware visualisation based on dynamic behaviour analysis, with the idea that the images, which are visually very interesting, are then used to classify malware concerning goodware. Our approach opens an extensive topic for future discussion and provides many new directions for research in malware analysis and classification, as discussed in conclusion. The results of the presented experiments are based on a database of 6 589 997 goodware, 827 853 potentially unwanted applications and 4 174 203 malware samples provided by ESET and selected experimental data (images, generating polynomial formulas and software generating images) are available on GitHub for interested readers. Thus, this paper is not a comprehensive compact study that reports the results obtained from comparative experiments but rather attempts to show a new direction in the field of visualisation with possible applications in malware analysis.

cs.CR

Weighted means of harmonic functions and characterization of balls

Weighted mean value identities over balls are considered for harmonic functions and their derivatives. Logarithmic and other weights are involved in these identities for functions. Some applications of weighted identities are presented. Also, new analytic characterizations of balls are proved; each of them requires the volume mean of a single weight function over the domain under consideration to be equal to a prescribed number depending on the weight.

math.AP

Characterizations of discs via weighted means

New theorems characterizing analytically discs in the Euclidean plane $\RR^2$ are proved. Weighted mean value properties of solutions to the modified Helmholtz equation and harmonic functions are used for this purpose. The presence of a logarithmic weight diminish coefficients in the mean value identities. A weighted mean is also valid for solutions of the Helmholtz equation.

math.AP

On characterization of balls via solutions to the Helmholtz equation

A new analytical characterization of balls in the Euclidean space $\RR^m$ is obtained. Unlike previous results of this kind, using either harmonic functions or solutions to the modified Helmholtz equation, the present one is based on solutions to the Helmholtz equation. This is achieved at the expense of a restriction imposed on the size of a domain -- a feature absent in the inverse mean value properties known before.

math.AP

Inverse mean value properties (a survey)

Several mean value identities for harmonic and panharmonic functions are reviewed along with the corresponding inverse properties. The latter characterize balls, annuli and strips analytically via these functions.

math.AP

Harmonicity of a function via harmonicity of its spherical means

It is proved that harmonic functions are characterized by harmonicity of their spherical means, for which purpose the iterated spherical means are used. The similar characterization of solutions to the modified Helmholtz equation (panharmonic functions) is given. Another description of harmonic functions is the pointwise equality of a function and its iterated mean over an admissible pair of spheres.

math.AP

Asymptotic mean value properties of meta- and panharmonic functions

Asymptotic mean value properties, their converse and some other related results are considered for solutions to the $m$-dimensional Helmholtz equation (metaharmonic functions) and solutions to its modified counterpart (panharmonic functions). Some of these properties have no analogues for harmonic functions.

math.AP