Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
Not a member yet
409 research outputs found
Sort by
Determination of the covalent bond dipole moments with CLPO analysis
Get PDFBasing on the orbitals localization method which provides the most accurate (in a Frobenius norm sense) approximation for the reduced one-particle density matrix of the molecule, the model is proposed for partitioning the dipole moment of the molecule into additive contributions, defined in CLPO basis. By augmenting the proposed model with the Ruedenberg scheme for partitioning the nuclear contribution to the dipole moment, the contributions to the dipole moment associated with particular covalent bonds and lone pairs of the atoms were determined. Using the datasets composed of 11410 12-atomic molecules with zero total charge and the set of 613 conformations of electroneutral 2\u27-deoxycytidine-5\u27-monophosphate molecule, it has been found that the error in approximating the total dipole moment of the molecule by the sum of localized contributions, determined in the framework of the proposed model, is close to 10%, and is noticeably below the similar error when only the NPA charges are used to compute the approximate dipole moment. The typical angle between the true dipole moment vector and the dipole moment vector approximated with the proposed model is 5.5 deg.Key words: localized orbitals, CLPO-analysis, dipole moment, conformation.Pages of the article in the issue: 105 - 108Language of the article: Ukrainia
The peculiarity of intercalation of carbon nanomaterials containing nanotubes
Get PDFThe possibility of intercalation of carbon nanomaterials containing carbon nanotubes is considered. Carbon nanomaterials containing multiwall carbon nanotubes of different structure and size were intercalated by iodine chloride with use standard one-temperature method. As it is shown by electron microscopic studies, after intercalation the size and morphology of carbon nanotubes are essentially changed. The diameter of carbon nanotubes increases two times more. This increase in diameter is due to the penetration of iodine chloride molecules between layers of a multiwall carbon nanotubes or into the inner cavity of nanotubes. According to X-ray diffraction, the position of the most intense band in the 00ldiffractogram of carbon nanomaterial moves to the region of smaller angles after intercalation. The exact angular position of the 00l-band corresponds to reflection from the intercalate layers for the third stage compound. The hysteresis in the temperature dependence of resistivity for compacted intercalated carbon nanomaterial is observed. This hysteresis is explained by the change of the charge carriers effective relaxation time at the scattering on the phonons of the graphite layer and the intercalate layer. Such change occurs at the phase transitions in the intercalate layers from an ordered "quasicrystalline state" to an unordered "quasiliquid" state.Key words: carbon nanomaterial, intercalation, hysteresis.Pages of the article in the issue: 109 - 112Language of the article: Ukrainia
Optimization of functionals under uncertainties for Ito-Skorokhod stochastic differential equations in Hilbert spaces
Get PDFIn the article for the stochastic differential equations of Ito-Skorokhod, problems of optimization of functionals under conditions of uncertainty in Hilbert spaces are investigated. Purpose of the article is to investigate some properties of stochastic differential equations in Hilbert spaces. These objects arise in diverse areas of applied mathematics as models for various natural phenomena, in particular, the evolution of complex systems with infinitely many degrees of freedom. For instance, one may think of the liquid fuel motion in the tank of a spacecraft. Spacecraft constructors should take into account this motion, for it influences heavily the path of a spacecraft. Also, optimization of the motion is an issue of principal importance. It is not trivial to carry over the results concerning stochastic differential equations in finite-dimensional spaces to the infinite dimensional case. We give some statements, in which the existence, uniqueness is proved and the explicit form ?-optimal controls for such equations is constructed, in particular, ?-optimal control is found as a linear inverse relationship.Key words: stochastic differential equation, space of guillotine, optimization of functionals under uncertainty.Pages of the article in the issue: 65 - 70Language of the article: Ukrainia
Features of changes in optical response within the surface oxide layer in Si and GaAs
Get PDFIn this paper, the angular ellipsometric studies of natural oxidized surface layer on silicon and gallium arsenide are carried out. The mean wavelength of probe radiation beam was ? = 625 nm, with FWHM = 10 nm. Angular dependencies of ellipsometric parameters ? and ? (azimuth of restored linear polarization and phase shift between p- and s- components of reflected radiation) were recorded. The combined approach for their analysis, which consists in sectioning the investigated medium near-surface area into 500 ultrathin layers interconnected by the dielectric permittivity function and determining the ellipsometric parameters of the medium by applying matrix methods for calculating the amplitudes and phases of the reflected waves from such a system in two polarizations, was used. The depth of the optical response profile was determined by the method of differential evolution by varying optical constants in accordance with the chosen theoretical model to achieve a minimum deviation (MSE, Mean Squared Error) between the calculated and measured ellipsometric parameters. Optical response profiles corresponding to the models of half-infinite medium, a homogeneous layer, as well as the linear and exponential profiles are analyzed.Key words: ellipsometry, multilayer model, oxide layer, silicon, gallium arsenide.Pages of the article in the issue: 99 - 104Language of the article: Ukrainia
Convergence rate for the estimation of impulse response function in the space of continuous functions
Get PDFThe problem of estimation of a stochastic linear system has been a matter of active research for the last years. One of the simplest models considers a ‘black box’ with some input and a certain output. The input may be single or multiple and there is the same choice for the output. This generates a great amount of models that can be considered. The sphere of applications of these models is very extensive, ranging from signal processing and automatic control to econometrics (errors-in-variables models). In this paper a time-invariant continuous linear system is considered with a real-valued impulse response function. We assume that impulse function is square-integrable. Input signal is supposed to be Gaussian stationary stochastic process with known spectral density. A sample input–output cross-correlogram is taken as an estimator of the response function. An upper bound for the tail of the distribution of the supremum of the estimation error is found that gives a convergence rate of estimator to impulse response function.Key words: impulse response function, linear time-invariant system (LTI), Gaussian process, crosscorrelogram.Pages of the article in the issue: 30 - 36Language of the article: Ukrainia
About asymptotic behavior of the mathematical expectation of the total energy of the harmonic oscillator with random perturbation
Get PDFIn this article, the asymptotic behavior of the mathematical expectation of the total energy of a harmonic oscillator without friction under the influence of an energy pump with a controlling element of the form of a stochastic harmonic oscillator without friction with a white noise perturbation in resonant and non-resonant cases is found. During the analytical solving the problem of finding the mathematical expectation of the total energy of a harmonic oscillator with random perturbation, the properties of the Wiener process, the stochastic Ito integral, and the mathematical expectation of the product of stochastic integrals are used.Key words: harmonic oscillator, total energy, white noise.Pages of the article in the issue: 47 - 52Language of the article: Ukrainia
The features of the contact angle evaluation at the nanoscale
Get PDFThe information regarding the wetting characteristic is important in various aspects of surface science. One of the markers that more frequently uses for describing of wetting characteristics is the wetting angle. Even an estimation of the wetting at the macroscale is a tricky issue, because of the hysteresis between receding and advancing values presence. In the same time, the situation is more complicated for a nanoscopic droplet due to the tangible thickness of the interphase region, what causes an uncertainty of the dividing surface determination, as a consequence it causes an uncertainty of the contact angle determination. In this work using methods molecular dynamics we performed simulations of the cylindrical nanodprolet and the layer of the argon fluid. The density maps and the maps of tension tensor were also measured. Basing on the analysis of the maps within the framework of the Gibbs approach, the equimolar surfaces and the surfaces of tension on the liquid-gas interface and the liquid-solid interface was determined. For the cylindrical nanodroplet, the equilibrium contact wetting angles formed by the corresponding dividing surfaces were estimated. The measured angles differ by more than 10%.Key words: wetting, nanodroplet, surface tension, surfaces of tension, hydrophobic forces.Pages of the article in the issue: 83 - 88Language of the article: Ukrainia
Tying of embeddings for improving regularization in neural networks for named entity recognition task
Get PDFWe analyze neural network architectures that yield state of the art results on named entity recognition task and propose a new architecture for improving results even further. We have analyzed a number of ideas and approaches that researchers have used to achieve state of the art results in a variety of NLP tasks. In this work, we present a few of them which we consider to be most likely to improve existing state of the art solutions for named entity recognition task. The architecture is inspired by recent developments in language modeling task. The suggested solution is based on a multi-task learning approach. We incorporate part of speech tags as input for the network. Part of speech tags to be yielded by some state of the art tagger and also ask the network to produce those tags in addition to the main named entity recognition tags. This way knowledge distillation from a strong part of speech tagger to our smaller network is happening. We hypothesize that designing neural network architecture in this way improves the generalizability of the system and provide arguments to support this statement.Key words: neural networks, named entity recognition, regularization, generalizability, multi-task learning.Pages of the article in the issue: 59 - 64Language of the article: Ukrainia
Numerical-analytic solution of the problem about the damping isothermal vibrations of viscoelastic rectangular plates
Get PDFThe damping of vibrations of rectangular plates by means of both viscoelastic layers and using piezoelectric inclusions is considered. For modeling viscoelastic properties of passive and piezoelectric materials, linear models of integral type viscoelasticity are used, which are most effective for simulating the dissipative properties of materials in the linear region. In the case of taking into account the influence of the piezoelectric inclusions on the rigid characteristics of the passive plate and in other types of boundary conditions (for example, with rigid fixing of the ends), the finite element method was used to solve the problem of damping. The solutions of concrete problems of damping of stationary and non-stationary vibrations of plates using analytical and finite element methods are given. On the basis of the aforementioned approach, algorithms for solving dynamical problems with both fully and partially electrodes are implemented.Key words: active damping, actuators.Pages of the article in the issue: 77 - 80Language of the article: Ukrainia