Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
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Encoding and classification of permutations b? special conversion with estimates of class power
No full textScientific articles investigating properties and estimates of the number of so-called complete permutations are surveyed and analyzed. The paper introduces a special S-transform on the set of permutations and determines the permutation properties according to this transform. Classification and coding of permutations by equivalence classes according to their properties with respect to S-transformation is proposed. This classification and permutation properties, in particular, generalize known results for complete permutations regarding determining certain cryptographic properties of substitutions that affect the cryptographic transformations security. The exact values of the number of permutations in equivalence classes for certain permutation sizes are calculated and the estimates of the cardinality of classes with various properties are constructed by statistical modeling. The complete list of permutation classes with the exact values of their sizes for permutations of order n = 11 is presented. The interval estimates for the size of classes with various characteristics for permutations of order n = 11, 26, 30, 31, 32, 33, 45, 55 are obtained. Monte Carlo estimates and bounds of confidence intervals used the approximation of the binomial distribution by the normal and Poisson distributions, as well as the Python programming language package Scipy. Statistical tables have been calculated that can be used for further conclusions and estimates. The classification of permutations by their properties with respect to the introduced transform can be used in constructing high-quality cryptographic transformations and transformations with special features. The classes of complete permutations with their properties are selected as the best for rotary cryptosystems applications. The obtained results can be used, in particular, to search for permutations with certain characteristics and properties, to find the probability that the characteristic of the generated permutation belongs to a collection of given characteristics, to estimate the complexity of finding permutations with certain properties. A statistical criterion of consent, which uses the characteristics of permutations by S-transformation to test the generators of random permutations and substitutions is proposed.Key words: permutations, substitutions, classification, statistical modeling.Pages of the article in the issue: 36 - 43Language of the article: Ukrainia
Representation of Words in Natural Language Processing: ? Survey
Get PDFThe article is devoted to research to the state-of-art vector representation of words in natural language processing. Three main types of vector representation of a word are described, namely: static word embeddings, use of deep neural networks for word representation and dynamic) word embeddings based on the context of the text. This is a very actual and much-demanded area in natural language processing, computational linguistics and artificial intelligence at all. Proposed to consider several different models for vector representation of the word (or word embeddings), from the simplest (as a representation of text that describes the occurrence of words within a document or learning the relationship between a pair of words) to the multilayered neural networks and deep bidirectional transformers for language understanding, are described chronologically in relation to the appearance of models. Improvements regarding previous models are described, both the advantages and disadvantages of the presented models and in which cases or tasks it is better to use one or another model.Key words: artificial intelligence, natural language processing, computational linguistics, word embeddings.Pages of the article in the issue: 82 - 87Language of the article: Englis
Analytical model of deformation of flange with concatenated shell under internal pressure
Get PDFThe rings torsion theory that is based on the assumption about flat rigid cross-section was suggested by the authors in the previous papers. The analytical expressions of torsional stiffness have been derived for different kind of loads: pure moment, shear force and surface pressure. In the present paper the analytical model of flange with attached cylindrical shell deforming under internal pressure is suggested. The mechanical system is split into two parts (flange and shell) with the help of imaginary section method. An unknown shear force and bending moments are applied to both parts according to this method. Therefore flange is loaded under internal pressure, shear force and bending moments. As mentioned above, for all these loads the angle of flange cross-section rotation can be presented in analytical form based on the rings torsion theory. Full rotation angle is presented as a sum of these angles. The radial displacement of imaginary section was determined on the basis of the assumption about flat rigid cross-section. On another hand, the rotation angle and radial displacement of imaginary section are determined on the base of the cylindrical shell bending theory too. Two linear equations in the unknown shear force and bending moment were derived by equating corresponding expressions. In such ? way the analytical model of flange with attached shell deforming was built. The comparison calculations by finite element methods confirmed the adequacy of proposed model.Key words: analytical model, flange, shell, internal pressure, rings torsion theory.Pages of the article in the issue: 98-101Language of the article: Ukrainia
Thermomechanical problem on vibration of a viscoelastic rubberlike rod under dynamic loading
No full textThe problem on vibration of a viscoelastic rod under dynamic load at one of its ends is considered. The external loading has a signfficant influence on the dynamic characteristics of the material. By using the complex moduli, the problem on vibration of the viscoelastic rod was solved. The complex shear and Young\u27s moduli of a rubberlike material should exhibit the same dependence on frequency. The properties of a rubberlike material was applied. The temperature influence is associated both with the Newton boundary conditions and dissipative heating. The dissipative function is expressed in terms of deformations. The frequencies of high-damping materials occur at or near frequencies that are normally of interest in vibration problems at room temperature. For solving the problem a finite element model was applied. Using this model, qualitative analysis of the influence of dynamic load and dissipative heating on the resonant vibrations of viscoelastic rod is performed. According to the theory of viscoelasticity an analysis of the results was done. The reliability of the values of frequencies for the first resonances was checked. The numerical results qf the problem on vibration of a viscoelastic cylindrical rod under dynamic load at one of its end by the general thermomechanical laws on vibration in damped mechanical systems were obtained and investigated. Distribution of the temperature of dissipative heating along the rod axis is analyzed.Key words: Neo-Hookean material, dynamic load, dissipative function, thermomechanics.Pages of the article in the issue: 146-149Language of the article: Ukrainia
Investigation of the semi-strip’s stress state in the case of steady-state oscillations
Get PDFThe elastic semi-strip under the dynamic load concentrated at the centre of the semi-strip’s short edge is considered. The lateral sides of the semi-strip are fixed. The case of steady-state oscillations is considered. The initial problem is reduced to the one-dimensional problem with the help of the semi-infinite sin-, cos-Fourier’s transform. The one-dimensional problem is formulated in the vector form. Its solution is constructed as a superposition of the general solution for the homogeneous equation and the partial solution for the inhomogeneous equation. The general solution for the homogeneous vector equation is found with the help of the matrix differential calculations. The partial solution is expressed through Green’s matrixfunction, which is constructed as the bilinear expansion. The inverse Fourier’s transform is applied to the derived expressions for the displacements. The solving of the initial problem is reduced to the solving of the singular integral equation. Its solution is searched as the series of the orthogonal Chebyshev polynomials of the second kind. The orthogonalization method is used for the solving of the singular integral equation. The stress-deformable state of the semi-strip is investigated regarding both the frequency of the applied load, and the load segment’s length.Key words: semi-strip, steady-state oscillations, Fourier’s transform, Green’s matrix-function, singular integral equation.Pages of the article in the issue: 54-57Language of the article: Ukrainia
Formulation and study of the problem of optimal excitation of plate oscillations
Get PDFA model problem of harmonic oscillations of a hinged plate, that is is under the influence of a certain number of point concentrated forces, is considered. The plate model is considered to satisfy Kirchhoff\u27s conditions. The main task of the consideration is to determine the optimal characteristics of excitation - the number of forces, coordinates of their application, amplitudes and phases. The optimality criterion is constructed as the standard deviation of the complex deflections from a given profile function. With the given excitation characteristics, the problem of determining the vibrations is solved in the form of a superposition of the Green functions with singularities at the points of application of forces. The Green function is constructed as a Fourier series by a circular coordinate. By using Parseval equality in L2, the objective function of the optimization problem is represented as a combination of linear and Hermitian forms with respect to complex amplitudes of forces whose matrices are nonlinear (and not convex) dependent on the coordinates of singular points. A complete study of the objective function is performed. Sufficient conditions are determined for reducing the dimension of the control space by analytical determination of the amplitudes of forces. Expressions were obtained to calculate the gradients of the objective function by angular and radial coordinates. A partial case of grouping of excitation forces on concentric circles is considered, that leads to the degeneration of the problem.Key words: harmonic plate oscillations, optimal excitation.Pages of the article in the issue: 62-65Language of the article: Ukrainia
On some ways to achieve the absence of thermal stresses in an inhomogeneous through thickness infinite layer under stationary thermal loading
Get PDFA method for determining the characteristics of functional gradient materials (FGM) for providing zero thermal stresses in an infinite layer with given constant thermal loads is proposed. We assume that the classical convective conditions of heat transfer are given on the surfaces of the layer, the temperature field is stationary, the characteristics of the FGM are described by the model of a simple mixture, the characteristics of the thermo-stressed state and the material depend only on the transverse variable. Precise analytical expressions were obtained for the distribution of the concentration of one of the materials on the thickness of the layer in the absence of mass forces and heat sources, which provides zero longitudinal stresses.Key words: functional-gradient materials, thermomechanical characteristics, layer, model of a simple mixture, absence of stresses, stationary temperature field, composites.Pages of the article in the issue: 66-69Language of the article: Ukrainia
Circular thermoactive interphase inclusion in a piecewise homogeneous transversal-isotropic space
Get PDFAn exact solution of the stationary thermoelasticity problem about interfacial circular absolutely rigid inclusion, which is under conditions of complete adhesion and under conditions of smooth contact with transversely homogeneous spaces, is constructed. The task with the help of the constructed discontinuous solution, by the method of singular integral relations, is reduced to a system of singular integral equations (SIE). An exact solution has been built for the specified systems of two-dimensional singular integral equations. As a result, dependences jumps of stresses and displacement on temperature, equivalent load, main moments and thermomechanical characteristics of transversally isotropic materials. The influence of the type of contact interaction on the behavior of the solutions is established. In particular, it has been shown that the stresses in the neighborhood of the inclusion with a smooth contact have a root singularity, and with complete coupling, the root singularity, which is amplified by oscillation. The behavior of the generalized intensity coefficient (GCIN) was studied for the combination of various transversely isotropic materials at different power and temperature loads.Key words: thermal conductivity, inhomogeneous orthotropic space, interphase defect, two-dimensional singular integral equations.Pages of the article in the issue: 90-93Language of the article: Ukrainia
Methods of calculating the deflection of an orthotropic inhomogeneous plate on an elastic basis
Get PDFThe problem of elastic equilibrium of an orthotropic nonhomogeneous rectangular plate on an elastic basis (one-parameter Winkler model) is considered, hingedly fixed from all sides. We use the Navier method for finding the deflection function at each step of the iterative process and perturbation methods and successive approximations as iterative methods for solving the problem. The suitability of the method of successive approximations and the method of perturbations for the numerical solution of the problem of determining the stress-strain state of such a plate, the limits of the applicability of these methods, their accuracy and convergence of the iterative process in solving the deformation problems of heterogeneous orthotropic plates have been analyzed.The dependence of the deflection on the mechanical and geometric parameters of the plate and the base is established. It was found that the Poisson ratio practically does not affect the stress state of the plate (when the Poisson ratio is changed two times, the difference between the intensities of the shear stresses does not exceed 10%), it is possible to consider it as a constant using the methods of successive approximations and disturbances. It is also established that the method of successive approximations and the method of perturbations has a limit on the nature of inhomogeneity, the convergence essentially depends on the nature of the heterogeneity.Key words: method of successive approximations, perturbation method, orthotropic inhomogeneous plate.Pages of the article in the issue: 106-109Language of the article: Ukrainia
Application of a quasi-linear visco-elastic model for the creep of a non-heterogeneous geological media prediction
Get PDFThe problem of computer modeling of physical and mechanical processes in geological environments whose properties change in time is considered. The theoretical substantiation of approaches to the method of constructing micromechanical geophysical models of a porous medium with a liquid is proposed. The analysis of the current state of the problem of construction of calculated nonlinear models of multiphase geological environments is carried out and the necessity of using nonlinear rheology approaches is indicated. The results obtained earlier within the elastic linear and nonlinear domains of the behavior of the medium are generalized to the case of visco-elastic quasilinear behavior. The method of identification of creep parameters and permeability of multiphase porous medium and forecasting algorithms is proposed on the basis of developed numerical-analytical modeling of effective physical and mechanical properties of fluid-saturated rocks. Considered variants of random or periodic microstructure. The model is based on the use of the fundamental relations of the mechanics of the viscoelastic continuous medium, integral Fourier transforms and Laplace-Carson using the corresponding numerical algorithms.Key words: nonlinear visco-elasticity, multiphase medium.Pages of the article in the issue: 122-125Language of the article: Ukrainia