Estimation of Overspread Scattering Functions

In many radar scenarios, the radar target or the medium is assumed to possess randomly varying parts. The properties of a target are described by a random process known as the spreading function. Its second order statistics under the WSSUS assumption are given by the scattering function. Recent developments in operator sampling theory suggest novel channel sounding procedures that allow for the determination of the spreading function given complete statistical knowledge of the operator echo from a single sounding by a weighted pulse train. We construct and analyze a novel estimator for the scattering function based on these findings. Our results apply whenever the scattering function is supported on a compact subset of the time-frequency plane. We do not make any restrictions either on the geometry of this support set, or on its area. Our estimator can be seen as a generalization of an averaged periodogram estimator for the case of a non-rectangular geometry of the support set of the scattering function

Identification of stochastic operators

Based on the here developed functional analytic machinery we extend the theory of operator sampling and identification to apply to operators with stochastic spreading functions. We prove that identification with a delta train signal is possible for a large class of stochastic operators that have the property that the autocorrelation of the spreading function is supported on a set of 4D volume less than one and this support set does not have a defective structure. In fact, unlike in the case of deterministic operator identification, the geometry of the support set has a significant impact on the identifiability of the considered operator class. Also, we prove that, analogous to the deterministic case, the restriction of the 4D volume of a support set to be less or equal to one is necessary for identifiability of a stochastic operator class

Sampling of stochastic operators

We develop sampling methodology aimed at determining stochastic operators that satisfy a support size restriction on the autocorrelation of the operators stochastic spreading function. The data that we use to reconstruct the operator (or, in some cases only the autocorrelation of the spreading function) is based on the response of the unknown operator to a known, deterministic test signal

Effect of the focusing magnetostatic field profile on the diffraction radiation oscillator excitation

Effect of the focusing magnetostatic field (FMF) profile on the output characteristics of diffraction radiation oscillator (DRO) is studied experimentally. The laboratory prototype of the mm range DRO produced in IRE NAS of Ukraine was used in the research. Peculiarities of the output power, oscillation frequency, starting current and other DRO characteristics for the cases of the decreasing, sagging and increasing magnetostatic field along the direction of the electron flow motion were determined. Prospects for the use of the increasing FMF in DRO are shown. При цитуванні документа, використовуйте посилання http://essuir.sumdu.edu.ua/handle/123456789/9323Експериментально досліджується вплив профілю фокусуючого магнітостатичного поля (ФМП) на вихідні характеристики генератора дифракційного випромінювання (ГДВ). Для дослідження використову-ється лабораторний зразок приладу – ГДВ мм діапазону, створеного в ІРЕ НАН України. Встановлені особливості зміни вихідної потужності, частоти генерації, стартового струму та інших характеристик генератора у випадку спадаючого, провисаючого або зростаючого магнітостатичного поля у напрямку руху електронного потоку. Відмічається перспектива застосування у ГДВ зростаючого ФМП. При цитировании документа, используйте ссылку http://essuir.sumdu.edu.ua/handle/123456789/9323Экспериментально исследуется влияние профиля фокусирующего магнито-статического поля (ФМП) на выходные характеристики генератора дифракционного излучения (ГДИ). При исследованиях используется лабораторный образец прибора – ГДИ мм диапазона, созданного в ИРЭ НАН Украины. Установлены особенности изменения выходной мощности, частоты генерации, пускового тока и других характеристик генератора в случаях спадающего, провисающего или нарастающего магнитостатического поля в направлении движения электронного потока. Показана перспектива использования в ГДИ нарастающего ФМП. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/932

Existence of solutions for a higher order non-local equation appearing in crack dynamics

In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann operator, corresponding to the square root of the Laplace operator on a bounded domain with Neumann boundary conditions (which can also be defined using the periodic Hilbert transform). In our study, we have to deal with the usual difficulty associated to higher order equations (e.g. lack of maximum principle). However, there are important differences with, for instance, the thin film equation: First, our equation is nonlocal; Also the natural energy estimate is not as good as in the case of the thin film equation, and does not yields, for instance, boundedness and continuity of the solutions (our case is critical in dimension $1$ in that respect)

An empirical analysis of the impact of mergers and acquisitions involving institutional cross-owners on post-merger bankruptcy risk of acquirers in the United States between 1984 and 2020

I study 1858 mergers and acquisitions by US public acquirers between 1984 and 2020 to assess the impact of cross-ownership on post-M&A acquirer bankruptcy risk. Addressing a gap in existing literature, my statistically significant findings indicate that presence of cross ownership and a higher number of cross-owners decrease bankruptcy risk. Notably, risk is elevated with greater cross-ownership levels and larger cross-owner stakes in acquirers, explained by higher asymmetric information. Conversely, bigger cross-owner stakes in targets reduce bankruptcy risk. In conjunction with cross-ownership, greater executive motivation lowers risk, whereas interaction between higher number of cross-owners and monitoring increases post-M&A bankruptcy risk