Oscillation of Fourier Integrals with a spectral gap

Suppose that Fourier transform of a function f is zero on the interval [-a,a]. We prove that the lower density of sign changes of f is at least a/pi, provided that f is a locally integrable temperate distribution in the sense of Beurling, with non-quasianalytic weight. We construct an example showing that the last condition cannot be omitted.Comment: 1 Figur

Quasi-exactly solvable quartic: elementary integrals and asymptotics

We study elementary eigenfunctions y=p exp(h) of operators L(y)=y"+Py, where p, h and P are polynomials in one variable. For the case when h is an odd cubic polynomial, we found an interesting identity which is used to describe the spectral locus. We also establish some asymptotic properties of the QES spectral locus.Comment: 20 pages, 1 figure. Added Introduction and several references, corrected misprint

Bifurcations in the Space of Exponential Maps

This article investigates the parameter space of the exponential family $z\mapsto \exp(z)+\kappa$. We prove that the boundary (in \C) of every hyperbolic component is a Jordan arc, as conjectured by Eremenko and Lyubich as well as Baker and Rippon. In fact, we prove the stronger statement that the exponential bifurcation locus is connected in \C, which is an analog of Douady and Hubbard's celebrated theorem that the Mandelbrot set is connected. We show furthermore that $\infty$ is not accessible through any nonhyperbolic ("queer") stable component. The main part of the argument consists of demonstrating a general "Squeezing Lemma", which controls the structure of parameter space near infinity. We also prove a second conjecture of Eremenko and Lyubich concerning bifurcation trees of hyperbolic components.Comment: 29 pages, 3 figures. The main change in the new version is the introduction of Theorem 1.1 on the connectivity of the bifurcation locus, which follows from the results of the original version but was not explicitly stated. Also, some small revisions have been made and references update

Two-parametric PT-symmetric quartic family

We describe a parametrization of the real spectral locus of the two-parametric family of PT-symmetric quartic oscillators. For this family, we find a parameter region where all eigenvalues are real, extending the results of Dorey, Dunning, Tateo and Shin.Comment: 23 pages, 15 figure

Development of neural network model of the multiparametric technological object

At present, there are a large number of methods for identifying the technological objects on the basis of data of their industrial operation [1-3]. The most promising direction is the construction of a model, which will allow to take into account the multifactorial nature of the object, and the nonlinearity of interrelation between variables. This will make it possible to control the object, taking into account the change in its states, and based on the current data,to predict the change in the output value with different input characteristics[4-6]. All this will provide the opportunity to create an operating system, based on the currently measured technological indicators. In order to implement this approach, a comparative study of the regression analysis models, using polynomials of various types and neural network algorithms, for the synthesis of a complex technological unit model, was carried out in the work. In the regression analysis, the following models were investigated: polynomials, linear, fractional and exponential functions, Kolmogorov-Gabor polynomial. In the process of the research of neural networks to solve this problem, their structure was varied, with subsequent learning according to the Levenberg-Marcardt algorithm. In the process of simulation of the object models in the Matlab package, the degree of similarity of the outputs for each of the obtained models and the actual output of the object were estimated. Quadratic criterion and the coefficient of correlation were calculated, that made it possible to judge the accuracy of the constructed models. The best structure of the model was established for identifying a complex multiparameter object, using the example of statistics for the operation of a ball mill.It was a network with three hidden layers and 50, 35 and 25 neurons in them, with activation functions, respectively by layers - hyperbolic tangent, sigmoid function in 2 layers, and a linear activation function in the output layer. The vector, including 15 parameters, was supplied to the network input: the volume of ore supply to the mill, the volume of water supply to the mill and the mill’strommel, the signals with the first-, the second-, and the thirdorder lags, and the signal of current with the first-, the second-, and the third-order lags. This approach to identification has increased the accuracy of the object model, that ultimately will affect the quality of the developed control system of the unit as a whole, allowing to improve the quality of the ball millcontrol

Influence of low energy scattering on loosely bound states

Compact algebraic equations are derived, which connect the binding energy and the asymptotic normalization constant (ANC) of a subthreshold bound state with the effective-range expansion of the corresponding partial wave. These relations are established for positively-charged and neutral particles, using the analytic continuation of the scattering (S) matrix in the complex wave-number plane. Their accuracy is checked on simple local potential models for the 16O+n, 16O+p and 12C+alpha nuclear systems, with exotic nuclei and nuclear astrophysics applications in mind

Characteristics of anomalously high multiplicity cosmic ray interactions

Six events with the number of secondaries ranging from 250 to several thousands were registered by an installation consisting of a thin graphite target, above and under which are placed photolayers followed by the usual lead X-ray film and emulsion chambers. Data concerning the number of secondaries and their angular distribution are given. The variance of the angular distribution is compared with data obtained at accelerator energies

Maximally and non-maximally fast escaping points of transcendental entire functions

We partition the fast escaping set of a transcendental entire function into two subsets, the maximally fast escaping set and the non-maximally fast escaping set. These sets are shown to have strong dynamical properties. We show that the ntersection of the Julia set with the non-maximally fast escaping set is never empty. The proof uses a new covering result for annuli, which is of wider interest. It was shown by Rippon and Stallard that the fast escaping set has no bounded components. In contrast, by studying a function considered by Hardy, we give an example of a transcendental entire function for which the maximally and non-maximally fast escaping sets each have uncountably many singleton components

Ответ на комментарий В.А. Мазурка к статье Р.Д. Комнова и А.А. Еременко «Интеллектуальные режимы респираторной поддержки в Российской Федерации: результаты анкетного исследования»

Ответ на комментарий В.А. Мазурка к статье Р.Д. Комнова и А.А. Еременко «Интеллектуальные режимы респираторной поддержки в Российской Федерации: результаты анкетного исследования

THEORETICAL BASES OF MANAGEMENT OF ADAPTATION OF INNOVATIVE PROCESSES AT THE ENTERPRISE OF MECHANICAL ENGINEERING

Conceptual bases of management of adaptation of innovative processes at the enterprises of mechanical engineering which feature is consideration of management of adaptation of innovative processes in as counter process of adaptation of innovative solutions and processes to conditions of activity of the enterprise, on the one hand, and the adaptation of the enterprise to various changes with use of innovations, with another are defined. This approach allows to improve methods of management of innovative processes by continuous fine tuning under changes of external influences and change of the internal environment