An Anticommutation of Locally Measurable Operators Affiliated with a von Neumann Algebra / Ahramovich M.V., Muratov M.A. // Naukovi visti. - 2012. – N 4. – P. 7–13. Refs.: 11 titles.
The purpose of this paper is to complete the investigation of a q-commutation of two self-adjoint locally measurable operators affiliated with an arbitrary von Neumann algebra. Since possible values of the q parameter are 1 і -1, the problem reduces to consideration of conditions of commutation (q = 1) and anticommutation (q = −1) of locally measurable operators. The first case has been researched earlier. In this paper, we consider the case q = −1. An intersection of any two domains of locally measurable operators is a locally measurable subspace. By using this fact, we proved that for any self-adjoint locally measurable operators T,S ∈ LS(M) a dense invariant locally measurable subspace of joint bounded vectors of these operators exists. By using the criterion of anticommutation of unbounded operators, we proved that the operators T,S ∈ LS(M) anticommute if and only if they anticommute as elements of *-algebra LS(M).
The Modification of the Method of Resolving Functions for the Difference-Differential Pursuit’s Games/ Baranovskaya L.V.// Naukovi visti. - 2012. – N 4. – P. 14–19. Refs.: 6 titles.
The subject of investigation is game problems for the object control under the conditions of counteractions. The paper suggests that the object dynamics is described by the system of difference-differential equations. We consider the approach problem with fixed time. In the course of the game the information on the initial function and the prehistory of the evader’s control is used. We suggest the way to solution of problems with fixed time. The game is completed when an integral of some numeral function describing the game course turns into a unit. An approach to solution of this game is based on the method of Resolving Functions. The research technique is based on using Minkovskii inverse functional of multi-valued maps, closely related to the given conflict-controlled process, and on constructing the resolving functions. At the heart of the method’s scheme is the L.S. Pontryagin condition making it possible to choose a pursuers’ control in the form of Borel measurable selections of special multi-valued map. We show that for objects with different inertial Pontryagin’s Condition fails on some time interval. Moreover, the modification of the Pontryagin’s Condition is proposed. Specifically, we solve the similar problem to the one in “The Boy and the Crocodile” with lag.
r-Confluent Hypergeometric Functions and Their Applications/ Virchenko N.O., Didychenko Ie.V.// Naukovi visti. - 2012. – N 4. – P. 20–25. Refs.: 6 titles.
The new properties of the r-generalized confluent hypergeometric functions are investigated. The integral representations, the representation by series are constructed. Applications of these functions to the calculation of integrals absent in cash scientific and reference mathematical literature are given. Applications of the r-confluent hypergeometric functions in the theory of the special functions are considered, in partial, the r-generalized gamma-functions, incomplete gamma-functions, the r-generalized beta-functions, the r-generalized ς-functions, Volterra functions and contiguous to them are introduced, their basic properties are investigated. The theorems of addition, multiplication for r-generalized hypergeometric function are proved. The interesting generalization of Ramanujan formula involving r-generalized confluent hypergeometric function and r-generalized beta-function. This formula gives the possibility to calculate the new complicated improper integrals.
Asymptotic Properties of Estimator of Linear Regression Parameter in Case of Long-Range Dependent Regressors /Golubovska L.P., Ivanov A.V., Orlovsky I.V. // Naukovi visti. - 2012. – N 4. – P. 26–33. Refs.: 8 titles.
The paper considers linear regression model with long-range/weak dependent random noise and time dependent regressors which are observed with long-range dependent errors. Parameter estimation of these models is an important problem of statistics of random processes. We choose widely used least squares estimator for the estimation. The aim of this work is to prove consistency and asymptotic normality of least squares estimator of the regression model. Theory of stationary Gaussian random processes with long-range and weak dependence, properties of slowly varying functions and Hölder-Young-Brascamp-Lieb inequality are used to derive the results. In this paper, we obtain sufficient conditions for consistency and asymptotic normality of least squares estimator of regression parameters.
Convergence of Generalized Spitzer Series/Gregul Yu.O., Klesov O.I. // Naukovi visti. - 2012. – N 4. – P. 34–38. Refs.: 9 назв.
Тhе sequence of random variables {Yn, n≥1} completely converges to a constant c, if the series 
converges for all ε > 0 . In this paper, we consider generalized Spitzer series 
for sequence of independent identically distributed random variables with values t = 0 and r = 1. For t = 1 and L(x) = 1 and , the convergence of last series means complete convergence to zero of sequence 
. The main difference between the Spitzer generalized series and ordinary Spitzer series is the presence of slowly varying function in the series. The main purpose of this paper is to find sufficient conditions of convergence of the series for not necessarily monotonic and continuous slowly varying function. If function L is not monotonically increasing than the condition E [| X |L(| X |)] < ∞ does not yield finiteness of the expectation. In turn, it means that in general case we should study the series 
instead of 
. Generalized Spitzer series includes medians of sums of random variables in case of nonmonotonic functions. Our results generalize the theorem of Heyde and Rohatgi in case of non-monotonic slowly varying function. The proposed method for proving the convergence of Spitzer series can be applied for other classes of functions are studied in the theory of pseudo-regularly varying (PRV) functions.
Strong Law of Large Numbers for Random Variables with Superadditive Moment Function/Grozian T.M. // Naukovi visti. - 2012. – N 4. – P. 39–42. Refs.: 4 titles.
In this paper, we study random variables with moment function of superadditive structure. We do not impose any assumptions on the structure of dependence of these random variables. We prove the strong law of large numbers for such random variables under regularly varying normalization by the method developed by Fazekas and Klesov. In this proof we use different properties of superadditive and ragularly varying functions. The key role in the proof is played by the possibility of approximating the nondifferentiable slowly varying function by differentiable slowly varying function. This result can be applied for obtaining strong law of large numbers for independent, orthogonal and stationary dependent random variables, submartingales. It can be used for obtaining an analogical result in the case of random fields.
Asymptotic Properties of Solutions for Systems of Differential-Functional Equations with Linearly Transformed Argument/ Denysenko N.L.// Naukovi visti. - 2012. – N 4. – P. 43–47. Refs.: 6 titles.
The differential-functional equations with linear deviations of the argument have been the main object of the research by many mathematicians. Currently many directions are quite well studied. However, in the modern theory of such equations there are a number of vague issues. Specifically, among them are issues on asymptotic properties of continuously differentiable solutions for systems of linear differential-functional equations with linear transformed argument. Here we focus on equations in cases when deviation of the argument Δi(t) = (1 − λi ) t, i = 1,2,..., can be either positive or negative. We utilize basic methods of the theory of ordinary differential and differential-functional equations in the study, in particular, the method of successive approximations. We obtain new sufficient conditions of the existence of continuously differentiable, bounded on R solutions for systems of linear differential-functional equations with linear transformed argument and study the structure of a set of such solutions. Because such equations play an important role in the theory of differential equations and are widely used in the study of many problems of science and engineering, it is reasonable to hope that these results will be applied in the study of important practical problems..
A Method of Linear Summation of Trigonometric Fourier Series/ Denysiuk V.P.// Naukovi visti. - 2012. – N 4. – P. 48–54. Fig. 10. Refs.: 3 titles.
The paper considers the method of linear summation of trigonometric Fourier series of functions f (t) with limited variation due to introducing into this series the factors, depending on the number of series coefficient and the parameter α. The resulting function f (t,α) , obtained as a result of this summation, in some cases differs from the given function f (t) only at certain intervals, whose length can be arbitrarily small. The corresponding Fourier series for the function f (t,α) converges uniformly. A specific feature of the proposed summation method is the fact that the smoothing effect of the factor σ(k,α), affects the most in the vicinity of the points, where the function f (t) or its derivatives have jump type of discontinuity. When the parameter α has a countable set of discrete values, the proposed method of linear summation can be considered as a linear matrix method of summation of Fourier series. We provide quite a numbers of samples to back up theoretical data. It is feasible to study in future the properties of the proposed method of linear summation of Fourier series, specifically, the estimation of function approximations of various classes by partial sums Sn(α,t) .
Spectral Properties of Singularly Perturbed qs-Normal Operator/ Dudkin N.E.// Naukovi visti. - 2012. – N 4. – P. 55–58. Refs.: 14 titles.
Using described singularly perturbed rank one qs-normal operator, we study their spectral properties. We construct the singularly perturbed qs-normal operator with the prescribed set of eigenvectors and eigenvalues. When constructing this operator, we use the previously proven theorem on the structure of singularly perturbed self-adjoint operators with prescribed set of eigenvalues and corresponding eigenvectors. In such case the eigenvalues are located on the real axis. Its construction was a step-by-step process. Each next operator was a singular perturbation rank one of the previous operator. On each step, under some simple condition, we preserve possessed earlier eigenvalue and corresponding eigenvector. Corresponding proposition was proved by mathematical induction. Taking into account that singular perturbations of normal operator are possible only when its spectrum is located on the real axis, the self-adjoint case has generalization on a normal one. In case of infinite set under some additional conditions, we prove the existence of such operators. Using the latter, we prove the existence of singularly perturbed qs-normal operators with continuous spectrum that has a fractal structure.
Periodogram Estimator Properties of the Parameters of the Regression Model with Strongly Dependent Noise/ Zhurakovskiy B.M., Ivanov A.V. // Naukovi visti. - 2012. – N 4. – P. 59–65. Refs.: 17 titles.
The problem of detection of hidden periodicities is considered in the paper. In the capacity of useful signal model the harmonic oscillation observed on the background of random noise, that is a local functional of Gaussian strongly dependent stationary process is taken. For estimation of unknown angular frequency and amplitude of harmonic oscillation periodogram estimator is chosen, for which sufficient conditions of asymptotic normality are obtained and limit normal distribution is found. To obtain the main result there were used limit theorems of random processes, weak convergence of a family of measures to the spectral measure of a regression function, etc. The novelty, compared with the known results in the theory of periodogram estimator in observation models on weakly dependent noise, is assuming that the random noise is a local functional of Gaussian strongly dependent stationary process.
An Estimate for the Rate of Convergence in the Central Limit Theorem for Integrals of Shot Noise Processes / Ilienko A.B.// Naukovi visti. - 2012. – N 4. – P. 66–71. Refs.: 15 titles.
In this paper, we study the rate of convergence of the normalized integrals of stationary shot noise processes in the central limit theorem. More precisely, we establish an estimate for the distance between pre-limit distribution functions of the normalized integrals and limit Gaussian one. The key machinery of the proof is the study of convergence rates in terms of characteristic functions with a subsequent use of Berry–Esseen bound. We also give an analogous estimate of convergence rates in Lévy metric and an estimate for integrals with explicit normalization. The convergence rate in the bound obtained in Theorem 3 turns out to depend on the spectral characteristics of the input Lévy process and of the response function. The key role is played here by the behavior of the Fourier transform of the response function in the neighborhood of origin. The estimates obtained are of both theoretical and practical interest. They can be used in statistics of shot noise processes, specifically in testing hypotheses concerning unknown response function.
Conditions of Existense and Uniqueness of Solutions of Parabola-Hyperbolic Equation with Nonolocal Boundary Conditions / Kapustyan V.O., Pyshnograiev I.O.// Naukovi visti. - 2012. – N 4. – P. 72–76. Refs.: 5 titles.
Processes described with parabola-hyperbolic differential equations are crucial in the theory of mathematical physics. The article deals with the heterogeneous parabola-hyperbolic equation with nonlocal boundary conditions. To further investigate this class of problems, we need to find its classical solution. We show the system of eigenfunctions and associated functions of the boundary value problem. Using these biorthogonal systems forming the basis Riesz, we build the desired classical solution that presents an infinite number whose elements are defined as solutions of the corresponding Cauchy problem. We prove the lemma for evaluating the elements of the problem solution. Using calculations for homogeneous parabola-hyperbolic equations and statements required auxiliary lemmas on assessing the elements solution; we derive the conditions for existence and uniqueness of the problem solution, which is formulated as a theorem. The results can be used to study optimal control problems for parabola-hyperbolic equations.
Stochastic Integral and Stochastic Derivative Connected with a Lévy Progress /Kachanovsky N.A. // Naukovi visti. - 2012. – N 4. – P. 77–81. Refs.: 12 titles.
The extended stochastic integral with respect to a Lévy process and the corresponding Hida stochastic derivative have many applications in the stochastic analysis, in particular, in the theory of stochastic differential and integral equations. One of main lacks of these operators, if one considers them as linear operators on the space of square integrable random variables (L2), consists in their unboundedness. Moreover, the domain of the extended stochastic integral (and of the conjugated to this integral operator – the stochastic derivative) depends on an interval of integration. As a result, there are problems with some applications of the above-mentioned operators. Therefore an important problem is a modification of definitions of the extended stochastic integral and the Hida stochastic derivative that gives us the possibility to define these operators as linear bounded (i.e., continuous) ones. In this paper, using the theory of Hilbert equipments, we introduce and study the extended stochastic integral with respect to a Lévy process and the Hida stochastic derivative as linear continuous operators on a suitable rigging of (L2). This gives a possibility to extend an area of applications of these operators.
Structure of a Set of Orthogonal Projections Connected with Cycle and Antenna/ Kyrychenko A.A., Strelets A.V.// Naukovi visti. - 2012. – N 4. – P. 82–85. Refs.: 7 titles.
In this paper we study algebras of Temperley–Lieb type generated by orthogonal projections connected with unicyclic graph which is a cycle with the antenna. The goal of the paper is to study representations in a Hilbert space of such algebras in the simplest case and to comprehensively describe the set parameters when such representations exist. The simplest algebra corresponds to unicyclic connected graph which is a cycle connected by an edge by one separate vertex. Parameters of such algebras are a set of angles between pairs of subspaces which are images of orthogonal projections corresponding to points in the graph, connected by the edge. For every non-trivial irreducible representation, images of all orthogonal projections are one-dimensional. Depending on angles: a) the problem has a tame type (irreducible representations parametrized by the circle or closed circular arc); b) a single irreducible representation exists; c) nonzero representations does not exist. The results are obtained by using Gram matrices technique.
Integration of the System of Linear Partial Differential Equations of the First Order / Kopets M.M.// Naukovi visti. - 2012. – N 4. – P. 86–90. Refs.: 3 titles.
In this paper the method for determining the general solution of the system of first-order linear homogeneous partial differential equations is proposed. This method is the generalization of Euler method for defining general solution of linear homogeneous partial differential equation. The essence of Euler method implies that qui pro quo the solution of the equation 
can be found in the form z(t,x) = p(x + λt), where n times of continuously differentiable function p(x) and numerical parameter λ. The paper studies the analogue of Euler method for the next system of linear homogeneous partial differential equations 
The formulae for determining general solution of this system are proposed in two cases: a) the matrices A and B are diagonal; b) the matrices A and B are commutative. To illustrate the obtained results some specific examples are considered.
An Analysis of the Anticipatory Logistic Equation with the Strong Anticipation/ Lazarenko S.V., Makarenko A.S.// Naukovi visti. - 2012. – N 4. – P. 91–96.
Fig. 2. Refs.: 11 titles.
This article investigates the logistic equation with the first order strong anticipation, studies the stability scopes of its fixed points in parameter space and the sufficient condition for existing of the accumulating hyperincursion behaviors. We consider the anticipatory system constructed by the multivalue evolution operator with two selectors. We use the dynamic system iterating tools with the multivalue operators, Lamerey diagrams. On the basis of Lamerey diagrams we describe main types of hyperincursion. We employ basic concepts of the discrete anticipatory system theory of such type. We define hyperincursion behavior types by changing the cardinality of system state sets. Specifically, in separate cases of such hyperincyrsion behavior the fractal structure can emerge which is of great practical interest. We recommend using the stability scopes of the fixed points in the anticipatory system parameter space for investigation of various transition scenarios from the regular behavior to chaos of such systems. We formulate the sufficient condition for existance of the accumulating hyperincursion behaviors.
Convergence of Series Whose Terms are Elements of Weakly Dependent and Strongly Dependent Gaussian Markov Sequences/ Runovska М.К.// Naukovi visti. - 2012. – N 4. – P. 97–103. Refs.: 12 titles.
This paper is devoted to the finding of necessary and sufficient conditions for the almost sure convergence of the random series whose terms are elements of one-dimensional zero-mean Gaussian Markov sequences. Mainly in the paper the series whose terms are elements of weakly dependent and strongly dependent Gaussian Markov sequences are considered. Criterions which provide almost sure convergence of the series whose terms are elements of weakly dependent and strongly dependent Gaussian Markov sequences respectively are the main results of this work. These criterions are formulated in terms of correlation characteristics of Gaussian Marlov sequences and are of a simple kind. Obtained results also enable to find criterions for the almost sure convergence of the series whose terms are elements of weakly dependent and strongly dependent Gaussian Markov sequences with weighted coefficients. Moreover, obtained results automatically provide sufficient conditions for the almost sure convergence of a series whose terms are elements of some regressive sequences generated by independent sub-Gaussian random variables with uniformly bounded standards.
Fractal Recursive Function Posses-sing Hyperexponential Growth/ Skuratovskii R.V.// Naukovi visti. - 2012. – N 4. – P. 104–110. Refs.: 6 titles.
This article considers the research methods of deterministic fractal sets. Specifically, it develops constructive methods for studying recursive functions. The obtained results allow consider deterministic fractal functions from the novel theoretical standpoint. Studied primitive recursive function, which is similar to the functions of the form Dn = D2n−1 + c, depending on the specific parameter с. We elaborate the theoretical background for determining the area limitations of this feature. Of some theoretical and practical interest is the first ever approach to defining generating function allowing use previously found generators functions. Moreover, despite the fact that the direct calculation by iteration, this function has hyperexponential increase of the required minimum amount of memory, due to the proposed calculation method it can be successfully applied for addressing many practical issues
On the Approximate Solution of One Infinite-Dimensional Problem of Optimal Stabilization with Nonautonomous Perturbations in the Coefficients/ Yasinsky V.V., Kapustian O.A.// Naukovi visti. - 2012. – N 4. – P. 111–115. Refs.: 12 titles.
This paper considers the optimal stabilization problem for solutions of parabolic inclusion in which nonautonomous perturbations act on the differential operator coefficients and multivalue interaction function. Such objects naturally occur in applied problems where medium characteristics change over time, and the interaction functions are discontinuous on a phase variable. Under general conditions on nonautonomous coefficients the solvability of the initial problem was proved. Given the G-convergence of perturbed operators to elliptic differential operator and convergence of multivalue perturbations to zero in the Hausdorff metric it was proved that any solution of the initial optimal stabilization problem converges to regulator of unperturbed linear-quadratic problem, whose explicit form is determined by the Fourier method. The main result of this paper is justification of the fact that the formula of the unperturbed problem regulator implements the approximate synthesis of the initial problem. These results make it possible to develop approximate stabilization methods for a class of infinite-dimensional evolution problems with nonautonomous multivalue perturbations.
Calculation of Energy Chemical Communication Phases Containing Boron in Alloy Fе–B–C/ Beryoza Ye.Yu., Philonenko N.Yu., Baskevich A.S.// Naukovi visti. - 2012. – N 4. – P. 116–120. Fig. 3. Refs.: 8 titles.
This paper deals with establishing the type of a solid solution (penetration or substitution) for Fe–B–C system alloys. We investigate the alloys of boron content of 0,0001-0,1% (w.) and of carbon content of 0,005-0,5% (w.).To study the properties of obtained alloys, we use X-ray and durametric analyses. Under boron content of 0,0003-0,003 % (w.) in alloy the parameter of ferrite crystal lattice and microhardness decreases. Under alloy boron content increase > 0,003% (w.) the above parameters are increasing. The calculation of communication energy between the components of hard solution of a-Fe show that there is the most communication energy between the components of hard solution of a-Fe and coniferous forest in position of substitution. Besides, taking into account that binding energy between iron and boron atoms in penetrating position is more than binding energy between iron and carbon atoms is less than by 10%, and then there is possible competition between boron and carbon atoms in ferrite. So, we establish that boron can constitute both solution of the only type entirely (substitution or penetration) in a-iron and solution, in which some atoms are located in the sites of crystal lattice and some atoms penetrate into the intersite.
Quasi-Equilibrium Heterogeneous States of Electrolyte at Steel Ball Etching in a Magnetic Field/ Gorobets O.Yu., Gorobets Yu.I., Bondar I.A., Legenkiy Yu.A.// Naukovi visti. - 2012. – N 4. – P. 121–129. Fig. 7. Refs.: 28 titles.
In this paper, research into the formation of interface separating phases (regions) with different magnetic susceptibilities of paramagnetic etching products is carried out in an inhomogeneous magnetic field of a magnetized steel ball at its corrosion. The theoretical model is proposed describing shape, size of this area and distribution of paramagnetic etching product concentration within the region. The characteristic times of formation, existence and destruction of this interface boundary was experimentally identified. The interface form between phases with different magnetic susceptibilities and concentrations of electrolyte was calculated at corrosion of ferromagnetic samples in the magnetic field taking into account surface tension. The model proposed in this work quantitatively explains the experimental effects of quasi-stationary heterogeneous states of electrolyte at electrodeposition and etching process in a gradient magnetic field of a magnetized ferromagnetic ball.
Signal Stabilization for Combined Gaussian-Vortex Beam Propagating Through Atmospheric Optical Link/ Gorshkov V.N., Torous S.V.// Naukovi visti. - 2012. – N 4. – P. 130–137. Fig. 5. Refs.: 14 titles.
The paper numerically investigates the spatial evolution of the structure of coherent and partially coherent laser beams, including the optical vortices, propagating in turbulent atmospheres. The influence of beam fragmentation and wandering relative to the axis of propagation (z-axis) on the value of the scintillation index of the signal at the detector is analyzed. These studies were performed for different strengths of the atmospheric turbulence C2n. A method for significantly reducing the SI is described. This novel method is to combine two laser beams – Gaussian and vortex beams, with different frequencies (the difference between these two frequencies being significantly smaller than the frequencies themselves). The result is important for achieving gigabit data rates in long-distance laser communication through turbulent atmospheres without any high-frequency modulators.
Stationary Magnetic Interactional Magnetization Waves in Ferromagnetic with Easy-Axis Anisotropy/ Dzhezherya Yu.I., Kuz O.P., Derecha D.O., Demichev K.O.// Naukovi visti. - 2012. – N 4. – P. 138–142. Refs.: 11 titles.
Results of research have shown that in regular ferrite-garnet films with perpendicular lightweight anisotropy in parallel to the film plane magnetic field long-wave inhomogeneous magnetic configuration of harmonic type can be created and observed. Field removes devolution in the direction of magnetization and promotes the formation of inhomogeneous magnetic configuration. During the work it was thought that the magnetic field is close to the critical value at which film homogeneously magnetization happens. This made it possible to develop a linear theory and reduce the Landau-Lifshitz and Maxwell equations systems, that describe the magnetic state of the system to a general equation for the magnetostatic potential. Unlike Walker equation that describes the dynamics of magnetostatic waves. Resulting equation describes the steady periodic distribution of magnetization in the film with easy-axis anisotropy. Magnetic fields range and parameters of their material in which the probable formation of inhomogeneous periodic configuration defined. Period dependence of the magnetic field amplitude calculated.
Compact spherical vortex model/ Lukianov P.V.// Naukovi visti. - 2012. – N 4. – P. 143–148. Fig. 1. Refs.: 11 titles.
Spherical vortex with only radial distribution and also to derive self-similar equation for the vortex’s difusion and it’s solution. The investigations are theoretical ones. The obtained results are the following ones. Any of the vortical flows that has zero radial velocity is always helical one. Meridianal and azimuthal velocity components have the same distributions (are invariant). The vorticity field compensation condition for spherical coordinates does not result into vortex compactness as it is for cylindrical vortexes. The general vortical flow velicity field compactness condition has been formulated. The self-similar solution for spherical vortex diffusion equation has been obtained. Conclusions. It has been derived compact spherical vortex model. The difference between compact spherical vortex and it’s cylindrical counterpart was pointed out. The kinetik energy of obtained flow is finit and agrees with energy conservation low.
Blade Shape and Cross Section’s Curvature Influence Parameters of the Rotor’s Rotational Noise/ Lukianov Petro V.// Naukovi visti. - 2012. – N 4. – P. 149–153. Fig. 4. Refs.: 11 titles.
The aim of this work is to study the influence of the blade shape and curvature changing of characteristics of the helicopter’s rotational noise. To this end, we consider 4-digits NASA profiles whose rotational noise is compared with one of the parabolic blade. Calculations results show that 4-digits blade generated rotational noise of higher level and its distribution on the blade’s shape are smooth in comparison with noise distribution of parabolic blade. However, the parabolic blade has more expressive maximum of noise level than the 4-digits blade. It can be explained by the difference of low-frequency spectrum generated by parabolic blade. We determine that the maximum of the rotational noise L (with respect to 2•10−5Pа ) was at the distance of 0,7–0,75 blade radius. This agrees with Gutin’s model assumptions. As the distance from the blade increases, the sound wave for both parabolic and 4-digital blades turns into the plane wave. Nevertheless, the pressure level of the 4-digits blade is higher 6 Db than the one for parabolic blade. The calculation data can be used for modeling of the cross-section of the helicopter’s blade shape to reduce the rotational noise.
Reflection of Surface Spin Waves from the Interface of Uniaxial and Biaxial Ferromagnets in a Planar Magnetic Field / Reshetnyak S.O., Nastenko M.Yu.// Naukovi visti. - 2012. – N 4. – P. 154–158. Fig. 4. Refs.: 8 titles.
The article investigates the reflection of surface spin waves passing through an interface of uniaxial and biaxial ferromagnets in a planar external magnetic field directed along the hard axis of ferromagnet. The problem is solved in the formalism of spin density based on equations of Landau-Lifshitz in the absence of dissipation in the system. The paper uses geometrical optics formalism to describe the processes of refraction of surface spin waves propagating in the ferromagnetic medium with nonuniform distribution of magnetic parameters as well as quantum mechanical method of calculating the amplitudes of reflection and transmission. We show that spin wave double-refraction effect appears in the interface of uniform ferromagnetic components. Frequency and field dependencies of reflection coefficients obtained for different branches of spin waves showed the ability to manage their relative values by changing frequency and magnitude of external homogeneous magnetic field.
Reconstruction of Hardronic Jets with Clustering Algorithms and Modern Statistical Methods of Data Analysis in High Energy Physics/ Iudin A.S., Bogorosh A.T., Voronov S.O.// Naukovi visti. - 2012. – N 4. – P. 159–163. Fig. 1. Refs.: 15 titles.
In a wide range of statistical data processing in high energy physics jet clustering algorithms and applications for function minimization are used. The aim of the study is to validate the acceptability of the programs and FastJet and MINUIT, that provide a powerful tool for finding jets from data and Monte Carlo models after the selection of events and for the subsequent approximation method of least squares. The study is performed using as an example a recent measurements of ZEUS experiment at the collider HERA, which conducted the collision of a proton with an energy of 920 GeV and an electron with an energy of 27.5 GeV. The extraction of the two-pion invariant mass distribution and the electromagnetic pion form factor y(2S) in the two-pion electroproduction with a mass in the range 0.4 < Mpp < 2.5 GeV is shown. Iintegrated luminosity of 82 pb-1 in the kinematic range of virtuality 2 < Q2 < 80 GeV2, the energy of the photon-proton center of mass of 32 < W < 180 GeV and squared momentum transfer | T | £ 0,6 GeV2 was used. Good agreement within errors between measured data and theoretical calculations after jet selection and minimization indicate the reliability and acceptability of these programs titles.