Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
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Rating change classication of insurance companies indicators
Get PDFIn this paper we investigate the relationship between financial indicators of insurance companies and news space. The news space is considered as a set of topics. The goal of the paper is to fit the model in order to forecast company\u27s rating change for given indicators — whether rating will go up or down regarding the current value. As the data set we use news articles of the relevant insurance topics for the specified time period. The approach we use includes search for the most influential topics for the given indicator. To retrieve topics, we used Latent Dirichlet Allocation (LDA) algorithm and Naive Bayes model. For the validation the Leave-One-Out approach was used with accuracy metric.Key words: LDA, news space analysis, topic modelling, Naive Bayes, financial indicators of insurance company.Pages of the article in the issue: 31 - 35Language of the article: Ukrainia
Some negative results for the interpolation monotone approximation of functions having a fractional derivative
Get PDFWe discuss whether on not it is possible to have interpolatory estimates in the approximation of a function by polynomials. The problem of positive approximation is to estimate the pointwise degree of approximation of a function where is the set of positive functions on [0,1].Estimates of the form (1) for positive approximation are known ([1],[2]). The problem of monotone approximation is that of estimating the degree of approximation of a monotone nondecreasing function by monotone nondecreasing polynomials. Estimates of the form (1) for monotone approximation were proved in [3],[4],[8]. In [3],[4] is consider r ? ?, r > 2. In [8] is consider r ? ?, r > 2. It was proved that for monotone approximation estimates of the form (1) are fails for r ? ?, r > 2. The problem of convex approximation is that of estimating the degree of approximation of a convex function by convex polynomials. The problem of convex approximation is that of estimating the degree of approximation of a convex function by convex polynomials. The problem of convex approximation is consider in ([5],[6]). In [5] is consider r ? ?, r > 2. In [6] is consider r ? ?, r > 2. It was proved that for convex approximation estimates of the form (1) are fails for r ? ?, r > 2. In this paper the question of approximation of function by algebraic polynomial is consider. The main result of the work generalize the result of work [8] for .Key words: approximation of function, Sobolev space, algebraic polynomial, monotone function, convex function.Pages of the article in the issue: 122 - 127Language of the article: Ukrainia
Analysis of pre-training and initialization methods of neural networks
Get PDFIn this paper we investigate main pre-training and initialization methods of parameter values of neural networks such as pre-training using restricted Boltzmann machines, deep autoencoders, Glorot and He initialization of parameters, transfer learning and domain adaptation. Given methods are useful for finding of appropriate parameter values and initial initialization of neural network, what is necessary condition for further efficient training of deep models, because it give a possibility during training to reduce negative effects such as vanishing or explosion of gradient, overfitting, stucking in one of local minimums of loss function, etc. These methods belong to group of unsupervised training algorithms and do not need any labeling for data which will be used later for model’s training after parameters initialization. Firstly, in this paper, we analyze all these methods and describe advantages and disadvantages of each of them. Secondly, we describe results of our experiments applying these methods for solving of classification task of MNIST dataset and introduce ideas for further development and improvement of these algorithms.Key words: neural network, pre-training, restricted Boltzmann machines, contrastive divergence algorithm, autoencoder, Glorot initialization, He initialization, domain adaptation, Jaccard index.Pages of the article in the issue: 84-91Language of the article: UkrainianIn this paper we investigate main pre-training and initialization methods of parameter values of neural networks such as pre-training using restricted Boltzmann machines, deep autoencoders, Glorot and He initialization of parameters, transfer learning and domain adaptation. Given methods are useful for finding of appropriate parameter values and initial initialization of neural network, what is necessary condition for further efficient training of deep models, because it give a possibility during training to reduce negative effects such as vanishing or explosion of gradient, overfitting, stucking in one of local minimums of loss function, etc. These methods belong to group of unsupervised training algorithms and do not need any labeling for data which will be used later for model’s training after parameters initialization. Firstly, in this paper, we analyze all these methods and describe advantages and disadvantages of each of them. Secondly, we describe results of our experiments applying these methods for solving of classification task of MNIST dataset and introduce ideas for further development and improvement of these algorithms.Key words: neural network, pre-training, restricted Boltzmann machines, contrastive divergence algorithm, autoencoder, Glorot initialization, He initialization, domain adaptation, Jaccard index.Pages of the article in the issue: 84 - 91Language of the article: Ukrainia
Usage of generalized functions formalism in modeling of defects by point singularity
Get PDFThe paper proposes a new approach to the construction of point defect models, based on the solution of boundary value problems with non smooth coefficients. Heterogeneity is included in the determining equation of the boundary problem. This approach allows us to formalize defects at the stage of use of state equations, and thus automatically reconciles the defect with the hypotheses of diminution of dimension and does not break the energy closed. The solution is sought in the form of weakly convergent series of generalized functions. The proposed approach simplifies the mechanical interpretation of defect parameters and is demonstrated in several examples. In the first example, the Green function for harmonic oscillations of an elastic beam with a point defect is constructed. The defect model is a limiting state of elastic inclusion with weakening or strengthening. The second example considers the inclusion of an elliptical shape in the problem of harmonic oscillations of the elastic plate. The first approximation of the equivalent volumetric force is constructed and the path to the following approximations is indicated. In the third example, a model of a brittle crack with a known displacement jump is constructed for a static two-dimensional problem of elasticity theory.Key words: generalized functions, inhomogeneity modeling, continuous environment.Pages of the article in the issue: 58-61Language of the article: Ukrainia
Bending by concentrated force of thin plate located on elastic foundation and weakened by contact crack
Get PDFThe paper considers the two-dimensional formulation of the problem of the contact interaction of the crack edges in a plate bent by the concentrated force on the elastic Winkler foundation. The crack closure is described using the model of contact along a line in one of the plate surfaces. Within the framework of this model, the boundary value problem is formulated for the equations of the classical theories of plate bending on the elastic foundation and a plane stress state with interrelated tension and bending conditions on the crack line. The obtained boundary value problem has been solved using singular integral equations method.Based on numerical solutions of the integral equation the dependences of forces and moments intensity factors in the vicinity of the defect tips and distribution of contact forces along the crack line on the parameters of elastic foundation stiffness and the coordinate of the application point of the load have been investigated. The effect of crack closure and influence of the elastic foundation stiffness on the limit equilibrium of the plate, depending on the coordinate of the point of application of the concentrated force, has been evaluated. The area of the correctness of the problem statement when the crack closure occurs throughout its length has been established. It was found that the crack closure leads to the appearance of nonzero forces intensity factor, reduction of the moments intensity factor and increase of the limit load. The dependences of the forces and moments intensity factors and the limit load on the dimensionless coordinate of the point of application of the concentrated force are nonmonotonic. Numerical analysis showed that increasing the elastic foundation stiffness, as well as the displacement of the point of application of the force from the center of the cut, increase the limit load and weaken the contact reaction.Key words: plate, elastic foundation, crack closure, concentrated force, bending, strength.Pages of the article in the issue: 118-121Language of the article: Ukrainia
Unsteady processes in stiffened by thin shell viscoelastic cylinder under pulse loading
Get PDFSolid propellant rocket motor is considered as hollow viscoelastic cylinder inserted in multilayered elastic shell-like case. The material of propellant is considered to be compressible. An estimation of maximum unsteady stresses on cylinder-shell boundary and shell under growing pressure on interior or external cylindrical surface were calculated by FEM. Four corner isoparametric finite element is utilized. Numark method to integrate by time the dynamic equations is used. The problem of linear viscoelasticity have been employing of the Schapery method. `In the case of internal pressure, the possibility of tensile radial stresses on the contact surface of the propellant-shell during the transition process has been established. The dependence of the maximum contact stresses as well as circumferential stresses in the shell on the shell thickness is established. In the case of external pressure pulse, the presence of significant tensile radial stresses on the propellant-shell interface is shown. Insignificant tensile circumferential stresses in the transient wave process are possible in the shell.Key words: viscoelastic cylinder, pulse loading, maximum dynamical stresses.Pages of the article in the issue: 202-205Language of the article: Russia
Manifestations of triplet electronic excitations migration in ?-electron containing polymers
Get PDFThe results of spectral studies of polymers with aromatic side groups are considered and analyzed. In particular, the phosphorescence spectra of polyvinylcarbazole (PVCa) polyvinyl-7-benzocarbazole (PV7BK) polypropylcarbazole (PEPC) are presented and analyzed. The phosphorescence of these polymers has been shown to be related to the migration of triplet excitons in macromolecules. The phosphorescence of PVC is determined at 77by deep traps (oxides), at 4.2 -shallow traps (monomer units of PVCa). The spreading length of triplet excitons in PVCa macromolecules is 600 A – that corresponds to the average distances between adjacent traps in the macromolecule. There are no such traps in PV7BK macromolecules. The boundary conditions for triplet excitons in macromolecules of PV7BCa were used for evaluation the excitons spreading length. With this aim the dependence of phosphorescence spectra on molecular weihgt were studied The effect of changing of spectral positions of phosphorescence bands when exciton rich the end macromolecular cell was used. The average trip length of triplet excitons is approximately 1000 A. This distance is in fact limited by the probability of the meeting of triplet excitons in the macromolecule and their annihilation at a given excitation intensity.Key words: polymers, phosphorescence, triplet excitons, deep and shallow traps.Pages of the article in the issue: 242-245Language of the article: Ukrainia
Optimization of sprint interplanetary trajectories with nuclear bimodal thermal propulsion
Get PDFInterplanetary missions require fast and fuel-efficient transfers. Combining small times transfers of high-thrust and efficiency of low-thrust propulsion can provide a good compromise. Saving an amount of fuel from the initial high-thrust burn and using it to correct the trajectory could lead to an economy of fuel. We investigated the optimal way to take advantages of both high and low-thrust propulsion benefits in order to maximize the payload mass of the mission. Using a simple model of ideal engine of limited power and the transporting trajectory method, we determined the analytical expression of final payload mass. The solution of the optimization problem gave us the optimal repartition of fuel between high and low-thrust maneuvers for a given thrust of thermal propulsion and electrical power of low-thrust propulsion system. As the mass of the low-thrust propulsion system depends on the electrical power, we took it into account to determine the optimal electrical power for a sprint trajectory in a given time. As a result, we could obtain the interval of transfer time for which the combination of high and low thrust becomes optimal.Key words: sprint trajectory, bimodal nuclear propulsion, transporting trajectory method.Pages of the article in the issue: 74-77Language of the article: Englis
Direct integration method in three-dimensional elasticity and thermoelasticity problems for inhomogeneous transversely isotropic solids: governing equations in terms of stresses
Get PDFAn efficient technique for thermoelastic analysis of inhomogeneous anisotropic solids is suggested within the framework of three-dimensional formulation. By making use of the direct integration method, a system of governing equations is derived in order to solve three-dimensional problems of elasticity and thermoelasticity for transversely isotropic inhomogeneous solids with elastic and thermo-physical properties represented by differentiable functions of the variable in the direction that is transversal to the plane of isotropy. By implementing the relevant separation of variables, the obtained equations can be uncoupled and reduced to second-kind integral equations for individual stress-tensor components and the total stress, which represents the trace of the stress tensor. The latter equations can be attempted by any of the numerical, analyticalnumerical, or analytical means available for the solution of the second-kind integral equations. In order to construct the solutions in an explicit form, an advanced solution technique can be developed on the basis of the resolvent-kernel method implying the series representation by the recurring kernels, computed iteratively by the original kernel of an integral equation.Key words: transversally isotropic inhomogeneous solids, direct integration method, three-dimensional problem, governing equations.Pages of the article in the issue: 102-105Language of the article: Ukrainia
Modeling and numerical research of the self-excitation phenomenon of the drill bit whirlings vibrations
Get PDFIn the paper an initial stage of a rotating drill string bit whirl motion proceeding on a well bottom surface is studied on the basis of nonholonomic kinematic models of mechanic interaction between the contacting uneven bodies. It is assumed that the drill bit is an absolutely rigid spherical body, the well bottom surface is spherical too. It is supposed that the system coaxiality is disturbed through small initial curvature of the drill string, defects of the bit and bore-well geometry or the debalance of the system mass. Linearized equations of the drill bit movement are derived, the frequencies of periodic motions are calculated, and their types are constructed for different geometric parameters of the spherical bits. It is shown that, depending on the system properties, the drill bit motion can to transit to the state of stationary spinning relative to an immovable center of velocities or acquire the regimes of forward and backward whirlings.Key words: Deep drilling, drill bits, nonholonomic dynamics, forward and backward whirls n.Pages of the article in the issue: 28-33Language of the article: Ukrainia