РОЛЬ РОДИНИ ЛЕВИЦЬКИХ У РОЗВИТКУ ОСВІТИ І КУЛЬТУРИ ПРИОРІЛЛЯ (КІНЕЦЬ ХVIII – ПОЧАТОК ХХ СТ.)

У історії України мало знайдеться родин, які б впродовж більше 300 років так плідно працювали на ниві культури і освіти, як це було з родиною Левиць-ких. Корені роду Левицьких знаходяться на Волині А на Приоріллі його предста-вники з’явилися у другій половині ХVII ст. в період «Руїни», коли правобережні українські землі були перетворені на пустку [12, c. 553]. Уряд гетьмана Самой-ловича охоче надав правобережні поорільські землі для розселення втікачам з Правобережної України, маючи на меті їх руками освоїти ці тоді ще малозаселені землі і водночас перетворити містечка Нехворощу, Маячку, Китайгород, Царичанку на оборонні пункти від набігів орд кримських татар та своєї експансії на лівобережні поорільські землі , які запорозькі козаки вважали своєю територією [3, c. 414-415]. Саме в цей час Кирило Степанович Левицький стає в містечку Маячці священиком місцевої Михайлівської церкви , поклавши цим самим поча- ток цьому славетному роду і місцевій священицькій діяльності [3, c. 416]

Binary black hole merger dynamics and waveforms

We study dynamics and radiation generation in the last few orbits and merger of a binary black hole system, applying recently developed techniques for simulations of moving black holes. Our analysis of the gravitational radiation waveforms and dynamical black hole trajectories produces a consistent picture for a set of simulations with black holes beginning on circular-orbit trajectories at a variety of initial separations. We find profound agreement at the level of one percent among the simulations for the last orbit, merger and ringdown. We are confident that this part of our waveform result accurately represents the predictions from Einstein's General Relativity for the final burst of gravitational radiation resulting from the merger of an astrophysical system of equal-mass non-spinning black holes. The simulations result in a final black hole with spin parameter a/m=0.69. We also find good agreement at a level of roughly 10 percent for the radiation generated in the preceding few orbits.Comment: 11 pages, 11 figures, submitted to PRD, update citations, minor change

Binary black hole late inspiral: Simulations for gravitational wave observations

Coalescing binary black hole mergers are expected to be the strongest gravitational wave sources for ground-based interferometers, such as the LIGO, VIRGO, and GEO600, as well as the space-based interferometer LISA. Until recently it has been impossible to reliably derive the predictions of General Relativity for the final merger stage, which takes place in the strong-field regime. Recent progress in numerical relativity simulations is, however, revolutionizing our understanding of these systems. We examine here the specific case of merging equal-mass Schwarzschild black holes in detail, presenting new simulations in which the black holes start in the late inspiral stage on orbits with very low eccentricity and evolve for ~1200M through ~7 orbits before merging. We study the accuracy and consistency of our simulations and the resulting gravitational waveforms, which encompass ~14 cycles before merger, and highlight the importance of using frequency (rather than time) to set the physical reference when comparing models. Matching our results to PN calculations for the earlier parts of the inspiral provides a combined waveform with less than half a cycle of accumulated phase error through the entire coalescence. Using this waveform, we calculate signal-to-noise ratios (SNRs) for iLIGO, adLIGO, and LISA, highlighting the contributions from the late-inspiral and merger-ringdown parts of the waveform which can now be simulated numerically. Contour plots of SNR as a function of z and M show that adLIGO can achieve SNR >~ 10 for some intermediate-mass binary black holes (IMBBHs) out to z ~ 1, and that LISA can see massive binary black holes (MBBHs) in the range 3x10^4 100 out to the earliest epochs of structure formation at z > 15.Comment: 17 pages, 20 figures. Final published versio

GRAVITATIONAL WAVE EXTRACTION FROM AN INSPIRALING CONFIGURATION OF MERGING BLACK HOLES

We present new techniques for evolving binary black hole systems which allow the accurate determination of gravitational waveforms directly from the wave zone region of the numerical simulations. Rather than excising the black hole interiors, our approach follows the "puncture" treatment of black holes, but utilizing a new gauge condition which allows the black holes to move successfully through the computational domain. We apply these techniques to an inspiraling binary, modeling the radiation generated during the final plunge and ringdown. We demonstrate convergence of the waveforms and and good conservation of mass-energy, with just over 3% of the system s mass converted to gravitational radiation

Gauge Conditions for Moving Black Holes Without Excision

Recent demonstrations of unexcised, puncture black holes traversing freely across computational grids represent a significant advance in numerical relativity. Stable an$ accurate simulations of multiple orbits, and their radiated waves, result. This capability is critically undergirded by a careful choice of gauge. Here we present analytic considerations which suggest certain gauge choices, and numerically demonstrate their efficacy in evolving a single moving puncture

Getting a kick out of numerical relativity

Recent developments in numerical relativity have made it possible to follow reliably the coalescence of two black holes from near the innermost stable circular orbit to final ringdown. This opens up a wide variety of exciting astrophysical applications of these simulations. Chief among these is the net kick received when two unequal mass or spinning black holes merge. The magnitude of this kick has bearing on the production and growth of supermassive black holes during the epoch of structure formation, and on the retention of black holes in stellar clusters. Here we report the first accurate numerical calculation of this kick, for two nonspinning black holes in a 1.5:1 mass ratio, which is expected based on analytic considerations to give a significant fraction of the maximum possible recoil. We have performed multiple runs with different initial separations, orbital angular momenta, resolutions, extraction radii, and gauges. The full range of our kick speeds is 86--116 km s$^{-1}$, and the most reliable runs give kicks between 86 and 97 km s$^{-1}$. This is intermediate between the estimates from two recent post-Newtonian analyses and suggests that at redshifts $z\gtrsim 10$, halos with masses $\lesssim 10^9 M_\odot$ will have difficulty retaining coalesced black holes after major mergers.Comment: Updated. Accepted by ApJ Letter

Recoil velocities from equal-mass binary black-hole mergers: a systematic investigation of spin-orbit aligned configurations

Binary black-hole systems with spins aligned with the orbital angular momentum are of special interest, as studies indicate that this configuration is preferred in nature. If the spins of the two bodies differ, there can be a prominent beaming of the gravitational radiation during the late plunge, causing a recoil of the final merged black hole. We perform an accurate and systematic study of recoil velocities from a sequence of equal-mass black holes whose spins are aligned with the orbital angular momentum, and whose individual spins range from a = +0.584 to -0.584. In this way we extend and refine the results of a previous study and arrive at a consistent maximum recoil of 448 +- 5 km/s for anti-aligned models as well as to a phenomenological expression for the recoil velocity as a function of spin ratio. This relation highlights a nonlinear behavior, not predicted by the PN estimates, and can be readily employed in astrophysical studies on the evolution of binary black holes in massive galaxies. An essential result of our analysis is the identification of different stages in the waveform, including a transient due to lack of an initial linear momentum in the initial data. Furthermore we are able to identify a pair of terms which are largely responsible for the kick, indicating that an accurate computation can be obtained from modes up to l=3. Finally, we provide accurate measures of the radiated energy and angular momentum, finding these to increase linearly with the spin ratio, and derive simple expressions for the final spin and the radiated angular momentum which can be easily implemented in N-body simulations of compact stellar systems. Our code is calibrated with strict convergence tests and we verify the correctness of our measurements by using multiple independent methods whenever possible.Comment: 24 pages, 15 figures, 5 table

Die Strandaster-Seidenbiene Colletes halophilus Verhoeff, 1944 (Hymenoptera: Colletidae) ist weit verbreitet an der Ostseeküste von Dänemark und Deutschland

The Sea Aster mining bee Colletes halophilus Verhoeff, 1944 is known as an endemic of the western European coasts of the Atlantic and the North Sea. The species has specific habitat requirements and is restricted to coastal habitats with populations of the Sea Aster (Tripolium pannonicum), its preferred host plant. Due to the late summer activity of adults and habitat specialisation, this solitary bee species is easily overlooked. In 2019, C. halophilus was first found at the Baltic Sea coast of the island of Fyn (Denmark), 2020 on the island of Rügen (Mecklenburg-Vorpommern, Germany) and in 2021 in Sehlendorf (Schleswig-Holstein, Germany), demonstrating that the species is far more widespread and also occurring along the more continental Western Baltic Sea coast and Kattegat. Targeted sampling in 2022 revealed that C. halophilus is now present in most of the potentially suitable coastal habitats in Schleswig-Holstein and at least in some parts of Mecklenburg-Vorpommern. We here present data on the currently known distribution of C. halophilus along the Baltic Sea coast of Denmark and Germany and discuss hypotheses of a potential recent range extension.Die Strandaster-Seidenbiene Colletes halophilus Verhoeff, 1944 ist ein Endemit der Atlantik- und Nordseeküste Westeuropas und aufgrund ihrer spezifischen Habitatansprüche an Küstenbiotope mit Vorkommen der Strandaster (Tripolium pannonicum) als bevorzugter Futterpflanze gebunden. Aufgrund der späten Flugzeit und ihrer Habitatspezifität kann die Art leicht übersehen werden. Durch Funde der Art auf der Insel Fünen (DK) 2019, Rügen (MV) 2020 und Sehlendorf (SH) 2021 wurde deutlich, dass die Art deutlich weiter verbreitet ist und auch im Bereich der kontinentaleren Ostseeküste vorkommt. Durch gezielte Nachsuche im Jahr 2022 konnte die Art in den meisten potentiell geeignet erscheinenden Küstenhabitaten in Schleswig-Holstein und einigen Gebieten in Mecklenburg-Vorpommern festgestellt werden. Der aktuelle Kenntnisstand zur Verbreitung von C. halophilus an der Ostseeküste wird vorgestellt und Hypothesen einer möglichen rezenten Aus- breitung der Art werden diskutiert

Gauge conditions for long-term numerical black hole evolutions without excision

Numerical relativity has faced the problem that standard 3+1 simulations of black hole spacetimes without singularity excision and with singularity avoiding lapse and vanishing shift fail after an evolution time of around 30-40M due to the so-called slice stretching. We discuss lapse and shift conditions for the non-excision case that effectively cure slice stretching and allow run times of 1000M and more.Comment: 19 pages, 14 figures, REVTeX, Added a missing Acknowledgmen