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Context. Less than one percent of the discovered small Solar System objects have highly inclined orbits (i > 60°), and revolve around the Sun on near-polar or retrograde orbits. The origin and evolutionary history of these objects are not yet clear. Aims. In this work we study the surface properties and orbital dynamics of selected high-inclination objects. Methods. BVRI photometric observations were performed in 2019–2020 using the 2.0 m telescope at the Terskol Observatory and the 2.6 m telescope at the Crimean Astrophysical Observatory. Additionally, we searched for high-inclination objects in the Sloan Digital Sky Survey and Pan-STARRS. The dynamics of the selected objects was studied using numerical simulations. Results. We obtained new photometric observations of six high-inclination objects (468861) 2013 LU28, (517717) 2015 KZ120, 2020 EP, A/2019 U5 (A/PanSTARRS), C/2018 DO4 (Lemmon), and C/2019 O3 (Palomar). All of the objects have similar B−V, V −R, R−I colours, which are close to those of moderately red TNOs and grey Centaurs. The photometric data that were extracted from the all-sky surveys also correspond to moderately red surfaces of high-inclination objects. No signs of ultra-red material on the surface of high-inclination asteroids were found, which supports the results of previous works. The comet C/2018 DO4 (Lemmon) revealed some complex morphology with structures that could be associated with particles that were ejected from the cometary nucleus. Its value of the parameter Afρ is around 100 cm for the aperture size of 6000 km. The value of Afρ for the hyperbolic comet C/2019 O3 (Palomar) is much larger, and is in the range from 2000 to 3700 cm for the aperture sizes from 25 000 to 60 000 km. For objects 2013 LU28, 2015 KZ120, and 2020 EP we estimated future and past lifetimes on their orbits. It appears that the orbits of considered objects are strongly chaotic, and with the available accuracy of the orbital elements no reliable predictions can be made about their distant past or future. The lifetimes of high-inclination objects turned out to be highly non-sensitive to the precision of the orbital elements, and to the Yarkovsky orbital drift.

We present new photometric observations for twelve asteroids ((122) Gerda, (152) Atala, (260) Huberta, (665) Sabine, (692) Hippodamia, (723) Hammonia, (745) Mauritia, (768) Struveana, (863) Benkoela, (1113) Katja, (1175) Margo, (2057) Rosemary) from the outer part of the main belt aimed to obtain the magnitude-phase curves and to verify geometric albedo and taxonomic class based on their magnitude-phase behaviors. The measured magnitude-phase relations confirm previously determined composition types of (260) Huberta (C-type), (692) Hippodamia (S-type) and (1175) Margo (S-type). Asteroids (665) Sabine and (768) Struveana previously classified as X-type show phase-curve behavior typical for moderate-albedo asteroids and may belong to the M-type. The phase-curve of (723) Hammonia is typical for the S-type which contradicts the previously determined C-type. We confirmed the moderate-albedo of asteroids (122) Gerda and (152) Atala, but their phase-curves are different from typical for the S-type and may indicate more rare compositional types. Based on magnitude-phase behaviors and V-R colors, (2057) Rosemary most probably belongs to M-type, while asteroids (745) Mauritia and (1113) Katja belong to S-complex. The phase curve of the A-type asteroid (863) Benkoela does not cover the opposition effect range and further observations are needed to understand typical features of the phase-curves of A-type asteroids in comparison with other types. We have also determined lightcurve amplitudes of the observed asteroids and obtained new or improved values of the rotation periods for most of them., Comment: 16 pages

Introduction At present, the main database of asteroid absolute magnitudes is the Minor Planet Center (MPC). The MPC receives asteroid magnitudes from many observatories in different spectral bands of different photometric systems, but calculates absolute magnitudes ​​for V band of the Johnson photometric system using the HG-function [1]. A comparison of the MPC absolute magnitudes (HMPC) with the dataset of high-quality absolute magnitudes obtained by Pravec et al. [2] revealed systematical differences between these datasets. The new HG1G2 function was recommended by Muinonen et al. [3] to be used for more precise calculating the asteroid absolute magnitudes. This function was calibrated according to good measured magnitude-phase dependences, and the average parameters ​​for major taxonomic classes of asteroids were obtained [4, 5]. Using these average values, it is possible to calculate the absolute magnitudes of asteroids from individual observations at different phase angles. For sparse photometric data, it was suggested to use the two-parameter HG12 system [3, 4, 6]. Recently, large-scale survey programs such as Pan-STARRS and Palomar Transient Factory (PTF) [7, 8] performed new observations, within which absolute magnitudes of asteroids have also been derived. Both datasets are homogeneous, but they were obtained mostly in the Sloan system and then transformed to the Johnson system. Comparison of these datasets of absolute magnitudes ​​with the MPC data showed systematical deviations [7, 8]. It should be noted that the absolute magnitudes of asteroids in the Pan-STARRS and PTF surveys [7, 8] were obtained in the new HG12 system. In addition, the work is continued to obtain the asteroid absolute magnitudes in the new system for PTF and Pan-STARRS datasets [9]. To check the reliability of these datasets and identify systematic deviations, an independent set of high-quality data on absolute magnitudes is required. Thus, we initiated an observational program to determine the absolute magnitudes of several hundred asteroids. Here we present preliminary results of our program. Results For our dataset, we used first the data of the asteroid magnitude-phase dependences collected at the Institute of Astronomy of V. N. Karazin Kharkiv National University [5, 10–12]. We also used observational data of asteroids from our other programs and performed new observations of some asteroids [13–14]. We calculated our absolute magnitude dataset in the Johnson V band with a correction for lightcurve variations using the HG1G2 system according to its extension to low-accuracy data [4]. In such manner, we obtained a homogenous dataset of absolute magnitudes of about 300 asteroids in the range from 6.5 to 16 mag. Fig. 1 shows the correlations of the absolute magnitudes from the MPC, Pan-STARRS (HPS), and PTF (HPTF) datasets with those of the Kharkiv dataset (HKH). Figure 1: Absolute magnitudes of MPC (HMPC), Pan-STARRS (HPS), and PTF (HPTF) vs. those of the Kharkiv dataset (HKH). We observe a high correlation between our dataset and the other three datasets. There are small differences in the constant terms and slopes that point out some systematical deviations especially for the MPC and the PTF datasets. Figure 2: Histogram of the absolute magnitude deviations between the Kharkiv and Pan-STARRS datasets. Figure 3: Histogram of the absolute magnitude deviations between the Kharkiv and MPC datasets. For the MPC dataset, we found a systematical deviation of about 0.1 mag (Fig. 3). It is less than that obtained in [2] and close to that obtained in [7]. The smallest deviations were found for the Pan-STARRS dataset. This is confirmed by the histogram of absolute magnitude deviations between the Kharkiv and Pan-STARRS datasets presented in Fig. 2. The solid line is a fit to the data using the Gaussian function. Conclusions We prepared a preliminary comparative analysis of the asteroid absolute magnitudes between the Kharkiv dataset and the MPC, Pan-STARRS, and PTF datasets. The analysis has shown that the absolute magnitude dataset obtained from the Pan-STARRS survey project is closest to our dataset and can be the most suitable for the determination of diameters or albedos of asteroids. Acknowledgments This research has made use of data and/or services provided by the International Astronomical Union's Minor Planet Center. References [1] Bowell, E., Hapke, B., Domingue, D., et al. In Asteroids II. Tucson. Univ. Arizona Press. P. 524−556, 1989. [2] Pravec, P., Harris, A.W., Kušnirák, P., et al. Icarus, 221, 365-387, 2012. [3] Muinonen, K., Belskaya, I.N., Cellino, A., et al. Icarus, 209, 542–555, 2010. [4] Penttilä, A. Shevchenko, V.G., Wilkman, O., Muinonen, K. PSS, 123, 117–125, 2016. [5] Shevchenko, V.G., Belskaya, I.N., Muinonen, K., et al. PSS, 123, 101−116, 2016. [6] Oszkiewicz, D.A., Muinonen, K., Bowell, E., et al. JQSRT, 112, 1919-1929, 2011. [7] Veres, P., Jedicke, R., Firzsimmons, A., et al. Icarus, 261, 34-47, 2015. [8] Waszczak, A., Chang, C.-K., Ofeck, E.O., et al. Astron. J., 150, A75, 2015. [9] Penttilä, A., Cellino A., Lu X., et al. DPS, 48, No 7, 228, 2016. [10] Shevchenko, V.G., Belskaya I.N., Lupishko D.F., et al. EAR-A-COMPIL-3-MAGPHASE-V1.0. NASA PDS, 2010. [11] Shevchenko, V.G., Belskaya, I.N., Slyusarev, I.G., et al. Icarus, 217, 202–208, 2012. [12] Slyusarev, I.G., Shevchenko, V.G., Belskaya, I.N., et al. LPSC 43, 1885, 2012. [13] Chiorny, V.G., Shevchenko V.G., Krugly Yu.N., et al. PSS, 55, 986−997, 2007. [14] Shevchenko, V.G., Mikhalchenko O.I., Belskaya I.N., et al. LPSC 50, Abstract #1771, 2019.

The aim — to evaluate the submuscular augmentation mammoplasty long‑term results in women with relative breast volume asymmetry with identical and different size implants.Materials and methods. The study included 102 women with breast volume asymmetry, in whom the submuscular augmentation mammoplasty was performed in the period from 2012 to 2017 in the Clinic of Plastic Cosmetic Surgery. In the comparison group (n = 49), breast implants of different volume were installed, in the main group (n = 53) — the same volume calculated with developed nomogram and formula. In all cases, anatomical implants were installed. Women in both groups were representative by age, pregnancy rate, breastfeeding, absolute volumetric asymmetry of the breast (in the comparison group — 133.8 ± 3.9 ml (from 78 to 244 ml), in the main group — 134.8 ± 4.2 ml (from 79 to 206 ml), p = 0.907) and relative volumetric asymmetry of the breast (relative breast volume asymmetry) (32.2 ± 0.6 % (from 21.0 to 47.7 %) and (31.9 ± 0.7 % (from 21.4 % to 44.1 %), respectively, p = 0.925). Evaluation of the relative breast volume asymmetry was carried out in 12 — 15 months. According to previously obtained data, the value of relative breast volume asymmetry from 1.1 to 25.4 % can be considered the population norm, from 19.3 to 25.4 % — the upper limit of the norm. In the same period, the presence of such complications as caudal prosthesis migration, breast fluid ptosis, in particular asymmetric ptosis, contouring of the prosthesis were determined. The analysis of the obtained data was performed using descriptive statistics, the comparison of the mean values of the variables was carried out with the Mann — Whitney U‑test, the comparison of the shares of the variables was performed with the χ2‑Pearson test.Results and discussion. The average values of absolute breast volume asymmetry and relative breast volume asymmetry in the comparison group decreased significantly compared with the preoperative values and amounted to 76.7 ± 2.5 ml and 10.9 ± 0.3 %, all p, Цель работы — оценить отдаленные результаты субмускулярной аугментационной маммопластики у женщин с относительной объемной асимметрией молочных желез с использованием одинаковых и разных по объему имплантатов.Материалы и методы. В исследование были включены 102 женщины с относительной объемной асимметрией молочных желез, которым выполнили субмускулярную аугментационную маммопластику в период с 2012 до 2017 г. на базе ООО «Клиника пластической косметической хирургии» (Полтава). В группе сравнения (n = 49) устанавливали имплантаты молочных желез разного объема, в основной группе (n = 53) — одинакового объема, рассчитанного с использованием разработанной номограммы и формулы. Во всех случаях устанавливали анатомические имплантаты. Женщины обеих групп были репрезентативны по возрасту, частоте беременности, кормления грудью, величине абсолютной объемной асимметрии молочных желез (в группе сравнения — (133,8 ± 3,9) мл (от 78 до 244 мл), в основной группе — (134,8 ± 4,2) мл (от 79 до 206 мл), р = 0,907) и относительной объемной асимметрией молочных желез (соответственно (32,2 ± 0,6) % (от 21,0 до 47,7 %) и (31,9 ± 0,7) % (от 21,4 до 44,1 %), р = 0,925). Оценку величины относительной объемной асимметрии молочных желез проводили через 12 — 15 мес. Согласно полученным ранее данным, значение относительной объемной асимметрии молочных желез от 1,1 до 25,4 % можно считать популяционной нормой, от 19,3 до 25,4 % — верхней границей нормы. В этот же ­период определяли наличие таких осложнений, как каудальная миграция протеза, птоз молочных желез, в частности асимметричный птоз, контурирование протеза. Анализ полученных данных выполняли с использованием дискриптивной статистики, сравнение средних значений переменных — с помощью U‑критерия Манна — Уитни, сравнение долей переменных — с помощью χ2‑критерия Пирсона.Результаты и обсуждение. После выполнения субмускулярной аугментационной маммопластики средние значения абсолютной и относительной объемной асимметрии молочных желез в группе сравнения статистически значимо уменьшились по сравнению с дооперационными значениями и составили (76,7 ± 2,5) мл и (10,9 ± 0,3) %, все р, Мета роботи — оцінити віддалені результати субмускулярної аугментаційної мамопластики у жінок з відносною об’ємною асиметрією молочних залоз з використанням однакових та різних за об’ємом імплантатів.Матеріали і методи. В дослідження було залучено 102 жінки з відносною об’ємною асиметрією молочних залоз, яким виконано субмускулярну аугментаційну мамопластику в період з 2012 до 2017 р. на базі ТОВ «Клініка пластичної косметичної хірургії» (Полтава). У групі порівняння (n = 49) встановлювали імплантати молочних залоз різного об’єму, в основній групі (n = 53) — однакового об’єму, розрахованого з використанням розробленої номограми та формули. В усіх випадках встановлювали анатомічні імплантати. Жінки обох груп були репрезентативні за віком, частотою вагітності, годування грудьми, величиною абсолютної об’ємної асиметрії молочних залоз (у групі порівняння — (133,8 ± 3,9) мл (від 78 до 244 мл), в основній групі — (134,8 ± 4,2) мл (від 79 до 206 мл), р = 0,907) і відносною об’ємною асиметрією молочних залоз (відповідно (32,2 ± 0,6) % (від 21,0 до 47,7 %) та (31,9 ± 0,7) % (від 21,4 до 44,1 %), р = 0,925). Оцінку величини відносної об’ємної асимет­рії молочних залоз проводили через 12 — 15 міс. Згідно з отриманими раніше даними, значення відносної об’ємної асимет­рії молочних залоз від 1,1 до 25,4 % можна вважати популяційною нормою, від 19,3 до 25,4 % — верхньою межею норми. У цей же період визначали наявність таких ускладнень, як каудальна міграція протеза, птоз молочних залоз, зокрема асиметричний птоз, контурування протеза. Аналіз отриманих даних виконували з використанням дискриптивної статистики, порівняння середніх значень змінних — за допомогою U‑критерія Манна — Уїтні, порівняння часток змінних — за допомогою χ2‑критерію Пірсона.Результати та обговорення. Після виконання субмускулярної аугментаційної мамопластики середні значення абсолютної та відносної об’ємної асимет­рії молочних залоз у групі порівняння статистично значущо зменшилися порівняно з доопераційними значеннями і становили (76,7 ± 2,5) мл та (10,9 ± 0,3) %, всі р 0,05), тоді як значення відносної об’ємної асимет­рії молочних залоз значно зменшилося ((15,5 ± 0,3) %, р

We studied a sample of 93 asteroid pairs, i.e., pairs of genetically related asteroids that are on highly similar heliocentric orbits. We estimated times elapsed since separation of pair members (i.e., pair age) that are between 7 × 10 yr and a few 10 yr. With photometric observations, we derived the rotation periods P for all the primaries (i.e., the larger members of asteroid pairs) and a sample of secondaries (the smaller pair members). We derived the absolute magnitude differences of the studied asteroid pairs that provide their mass ratios q. For a part of the studied pairs, we refined their WISE geometric albedos and collected or estimated their taxonomic classifications. For 17 asteroid pairs, we also determined their pole positions. In two pairs where we obtained the spin poles for both pair components, we saw the same sense of rotation for both components and constrained the angles between their original spin vectors at the time of their separation. We found that the primaries of 13 asteroid pairs in our sample are actually binary or triple systems, i.e., they have one or two bound, orbiting secondaries (satellites). As a by-product, we found also 3 new young asteroid clusters (each of them consisting of three known asteroids on highly similar heliocentric orbits). We compared the obtained asteroid pair data with theoretical predictions and discussed their implications. We found that 86 of the 93 studied asteroid pairs follow the trend of primary rotation period vs mass ratio that was found by Pravec et al. (2010). Of the 7 outliers, 3 appear insignificant (may be due to our uncertain or incomplete knowledge of the three pairs), but 4 are high mass ratio pairs that were unpredicted by the theory of asteroid pair formation by rotational fission. We discuss a (remotely) possible way that they could be created by rotational fission of flattened parent bodies followed by re-shaping of the formed components. The 13 asteroid pairs with binary primaries are particularly interesting systems that place important constraints on formation and evolution of asteroid pairs. We present two hypotheses for their formation: The asteroid pairs having both bound and unbound secondaries could be “failed asteroid clusters”, or they could be formed by a cascade primary spin fission process. Further studies are needed to reveal which of these two hypotheses for formation of the paired binary systems is real., The work at Ondfejov Observatory and Charles University Prague and observations with the Danish 1.54-m telescope on the ESO La Silla station were supported by the Grant Agency of the Czech Republic, Grant 17-00774S. Petr Fatka was supported by the Charles University, project GA UK No. 842218. Access to computing and storage facilities owned by parties and projects contributing to the National Grid Infrastructure MetaCentrum provided under the program >Projects of Large Research, Development, and Innovations Infrastructures> (CESNET LM2015042), and the CERIT Scientific Cloud LM2015085, is greatly appreciated. Operations at Sugarloaf Mountain Observatory and Blue Mountains Observatory were supported by a Gene Shoemaker NEO grant from the Planetary Society. We thank to A. Golubaev for his contribution to processing of the observations from Kharkiv Observatory. The observations at Maidanak Observatory were supported by grants F2 -FA -F026 and VA -FA -F-2-010 of the Ministry of Innovative Development of Uzbekistan. Jose Luis Ortiz acknowledges a support by the Spanish project AYA2017-89637-R and Andalusian project P12-FQM1776.The work at Tatranska Lomnica was supported by the Slovak Grant Agency for Science VEGA, Grant No. 2/0023/18, and project ITMS No. 26220120029, based on the supporting operational Research and Development program financed from the European Regional Development Fund. David Polishook is grateful to the AXA research fund for their generous postdoctoral fellowship. Josef Hanug> work was also supported by the Charles University Research program No. UNCE/SCl/023. The work at Abastumani was supported by the Shota Rustaveli National Science Foundation, Grant FR/379/6300/14. The work at Modra was supported by the Slovak Grant Agency for Science VEGA, Grant 1/0911/17. We thank the AGORA association which administrates the 60 -cm telescope at Reunion Les Makes observatory, under a financial agreement with Paris Observatory.

The aim — to define mechanisms of formation of secondary relative volumetric breast asymmetry after reductional mammoplasty and to develop a method of its prevention.Materials and methods. In a prospective study, 118 women aged 24 years to 57 years (on average 37.5 ± 0.7 years) were treated by WISE method in the period from 2012 to 2017 in LLC Clinic of Plastic Cosmetic Surgery in Poltava. The comparison group (group C) consisted of the patient, who performed reductional mastopexy (RMP) with the same volume of tissue reduction in both breasts; the main group (group M) — with different volume of tissue reduction in both breasts, which was calculated depending on the base‑line absolute volumetric breast asymmetry (AVBA). The volume of breast in pre‑and postoperative periods was determined by the author’s method. AOAMZ and VOAMZ were evaluated. The analysis of the data obtained was performed using discrete statistics, the comparison of mean values of variables using the Man‑Whitney U‑criterion and the comparison of the particle variables using the Pearson Hi‑squared. The calculations were made using the IBM SPSS Statistics 22 software.Results and discussion. In the patients of group P after RMP, the average value of AVBA remained stable, while an increasement in the value of relative volumetric breast asymmetry (RVBA) was noted in average values from 14.9 ± 0.8 % to 17.5 ± 1.1 %, and in the group of patients with RVBA indicators, which exceed the norm: 21.8 % vs. 5.5 %, p = 0.012. The increasement in the value of RVBA was associated with a decreasement in the volume of breast. Removal of bigger portion of larger breast in comparison with smaller breast, based on preoperative AVBA in patients in group M allowed to reduce the RVBA index from 13.6 ± 0.7 % to 2.9 ± 0.3 % (from 0 % to 8, 3 %).Conclusions. After RMP with the removal of equal volumes of tissue in both breasts, the AVBA remains constant, and RVBA increases and in 21.8 % of patients exceeds the population norm. Removal of larger portion of breast in comparison with smaller breast, based on preoperative RVBA, allows to reduce the pre‑surgery RVBA and to avoid its values higher than the popular norm., Цель работы — определить механизмы формирования вторичной относительной объемной асимметрии (ООА) молочных желез (МЖ) после редукционной маммопластики и разработать методику ее профилактики.Материалы и методы. В проспективное исследование было включено 118 женщин в возрасте от 24 до 57 лет (средний возраст — (37,5 ± 0,7) года), которым выполнили редукционную мастопексию в период с 2012 до 2017 г. в клинике пластической косметической хирургии (Полтава). Женщин распределили на две группы: сравнения (n = 55) — пациентки, которым в период с 2012 до 2014 г. выполнили редукционную мастопексию по классической методике RJ Wise с одинаковым объемом редукции ткани обеих МЖ, и основную (n = 63) — пациентки, которым в период с 2015 до 2017 г. выполнили редукционную мастопексию с разным объемом редукции ткани обеих МЖ, рассчитанным в зависимости от исходной абсолютной объемной асимметрии МЖ (АОАМЖ). Объем МЗ в дооперационный и послеоперационный (через 2 — 3 мес после редукционной мастопексии) период определяли авторским методом. Оценивали АОАМЖ и ООАМЖ.Результаты и обсуждение. У пациенток группы сравнения после редукционной маммопластики средняя величина АОАМЖ не изменилась, тогда как средняя величина ООАМЖ увеличилась с (14,9 ± 0,8) до (17,5 ± 1,1) %, а количество больных со значениями ООАМЖ, превышающими норму, — с 5,5 до 21,8 % (р = 0,012). Возрастание величины ООАМЖ было связано с уменьшением объема МЖ. Удаление у пациенток основной группы в большей МЖ лоскута большего объема, чем в меньшей МЖ, на величину дооперационной АОАМЖ позволило уменьшить величину ООАМЖ с (13,6 ± 0,7) до (2,9 ± 0,3) %.Выводы. После редукционной мастопексии с удалением одинаковых объемов ткани обеих МЖ величина АОА не изменилась, а значение ООА увеличилось и у 21,8 % пациенток превысило популяционную норму. Удаление в большей МЖ лоскута большего объема, чем в меньшей МЖ, на величину дооперационной АОА позволяет уменьшить ООА и избежать ее значений, превышающих популяционную норму., Мета роботи — визначити механізми формування вторинної відносної об’ємної асиметрії (ВОА) молочних залоз (МЗ) після редукційної мамопластики та розробити методику її профілактики.Матеріали і методи. До проспективного дослідження залучили 118 жінок віком від 24 до 57 років (середній вік — (37,5 ± 0,7) року), яким виконали редукційну мастопексію в період з 2012 до 2017 р. у клініці пластичної косметичної хірургії (Полтава). Жінок розподілили на дві групи: порівняння (n = 55) — пацієнтки, яким у період з 2012 до 2014 р. виконано редукційну мастопексію за класичною методикою RJ Wise з однаковим обсягом редукції тканини обох МЗ, та основну (n = 63) — пацієнтки, яким у період з 2015 до 2017 р. виконано редукційну мастопексію з різним об’ємом редукції тканини обох МЗ, розрахованим залежно від вихідної абсолютної об’ємної асиметрії МЗ (АОАМЗ). Об’єм МЗ у доопераційний і післяопераційний (через 2 — 3 міс після редукційної мастопексії) період визначали авторським методом. Оцінювали АОАМЗ та ВОАМЗ.Результати та обговорення. У пацієнток групи порівняння після редукційної мамопластики середня величина АОАМЗ не змінилася, тоді як середня величина ВОАМЗ збільшилася від (14,9 ± 0,8) до (17,5 ± 1,1) %, а кількість хворих зі значеннями ВОАМЗ, котрі перевищують норму, — з 5,5 до 21,8 % (р = 0,012). Зростання величини ВОАМЗ було пов’язано зі зменшенням об’єму МЗ. Видалення у пацієнток основної групи в більшій МЗ клаптя більшого об’єму, ніж у меншій МЗ, на величину доопераційної АОАМЗ дало змогу зменшити величину ВОАМЗ з (13,6 ± 0,7) до (2,9 ± 0,3) %.Висновки. Після редукційної мастопексії з видаленням однакових об’ємів тканини обох МЗ величина АОА не змінилася, а значення ВОА збільшилося та у 21,8 % пацієнток перевищило популяційну норму. Видалення в більшій МЗ клаптя більшого об’єму, ніж у меншій МЗ, на величину доопераційної АОА дає змогу зменшити ВОА та уникнути її значень, вищих за популяційну норму.

Summary .A mathematical model of the process of mixing cream- and vegetable spread was developed. In modeling the diffusion understanding of the nature of the process were used, allowing escape from the apparatus geometry. After turning on the mixer the mixing process begins. Its duration can be determined by the behavior of the tracer particles introduced into the agitated medium in a predetermined quantity through the free liquid surface within a short period of time. If tracer particles have the same density with the surrounding bulk liquid phase, then the path of movement of the particles and the fluid are identical. The degree of homogeneity of the composition can be stirred calculated by the coefficient of variation, which is identified by the local concentrations of tracer particles in the volume of stirred medium. The task of a one-dimensional particle transport in the plane layer of the mixed liquid is solved for their calculation. The calculated ratios obtained allow us to calculate the particle concentration at any point in the volume being mixed at random times. Based on the experiment effective mixing coefficients are identified and relations for their assessment, depending on the Reynolds number of the mixer in the range studied variations of process are offered. Using the time dependence of the variation coefficient characterizing the homogenity of the system being mixed, it is possible to determine the duration of mixing to obtain the product with the desired uniformity and homogeneity of the product under the definition of a predetermined duration of the mixing process. The variation coefficient %, indicating a sufficiently good uniformity of the spread composition was found for the spread №1, being mixed with a stirrer rotating at a speed of n=150 rev / min, and the dimensionless length of the process Fo =0,0935 for obtaining estimated relations. Using the proposed calculation algorithm one can estimate the homogeneity of the product at any time.

The current concepts on the physical properties of the Jovian Trojans are reviewed in the paper. The distributions of rotation periods and light-curve amplitudes, the features of the phase dependencies of brightness, and the available data on the surface composition, density, diameters, and albedo of the Trojans are analyzed. The history of the discovery of Trojans, their dynamical properties, and the hypotheses on their origin are also briefly considered. A framework of the unsolved problems in the study of this population of small bodies is outlined.

We search for possible differences in rotational frequencies, diameters, albedos, and orbital parameters between Trojans belonging to the L4 and L5 swarms using our own observations and literature data. With increasing number of observational data it becomes evident that the L4 and L5 populations have very similar distributions of most parameters with an exception of orbital inclination distribution.

CCD-photometry was performed for two Jupiter Trojan asteroids (911) Agamemnon and (4709) Ennomos for which the diameters were obtained from occultation events. New data on rotation periods, lightcurve amplitudes, color indices, magnitude–phase slopes, and absolute magnitudes were obtained for these asteroids. We have used the diameters from occultations (166 and 99 km) and new data on absolute magnitudes at the instant occultation (7.95 and 8.85 mag) to revise their albedos to 0.042 (911 Agamemnon) and 0.052 (4709 Ennomos).

Based on diffusion concepts, the problem of deposition of monodisperse large Stokesian particles in a stirred plane layer with a vertically moving free boundary has been formulated and solved.

This paper presents the first results of CCD photometry of selected Hilda group asteroids. These observations are part of a program carried out in the Institute of Astronomy of the Kharkiv National University, that is aimed to receive the parameters of the rotation and the optical properties of asteroids from the resonant groups. The observations were carried out at the standard spectral bands V and R. We have observed 12 Hilda asteroids: 334 Chicago, 1038 Tuckia, 1162 Larissa, 1180 Rita, 1269 Rollandia, 1578 Kirkwood, 1746 Brouwer, 1748 Mauderli, 1754 Cunningham, 3134 Kostinsky, 3990 Heimdal, 9829 Murillo. 80 light curves of these asteroids were obtained. The obtained data allowed us also to defined, substantially improved or made estimates the rotation periods of 9 asteroids. New detailed magnitude – phase dependences were obtained for three asteroids: 334 Chicago, 1162 Larissa, 1748 Mauderli.

We present new observational data for selected main-belt asteroids of different compositional types. The detailed magnitude–phase dependences including small phase angles (

Based on diffusion concepts of transfer of slightly concentrated polydisperse suspensions in the gravity field, we propose a mathematical model of the kinetics of deposition of such suspensions in a plane layer of a homogeneously mixed medium through the free surface of which Stokesian particles penetrate according to the rectangular pulse law.

Seasonal investigations of the reflecting properties of pine forests were conducted using an air-borne multifrequency radar polarimetric system. The multifrequency radar images (RIs) obtained during the September–February period were analyzed. Anomalous behavior of seasonal backscattering in the L, P, and VHF bands was observed. The moisture content of the tree elements were measured. The specific features of the water-regime state observed during the September–June period were noted. A seasonal relation between the reflecting properties of pine trees and the water regime of the elements of the trees is used as a basis for explaining the RI specific features.

A method of calculating a free-convection flow of a viscous incompressible medium in a rectangular cavity is proposed. The lateral boundaries of the cavity have the same constant temperature, the top and bottomboundaries are thermally insulated, and the half-width to height ratio is much smaller than unity. A decomposition of the flow domain into zones with ascending and descending flows made it possible to formulate and solve analytically a coupled parabolic system of linear equations based on the classic Oberbeck-Boussinesq assumptions.

Context. We present observations of the GRB 080319B afterglow at optical, mm, and radio frequencies between a few hours and 67 days after the burst.Aims. We attempt to understand the nature of this extraordinarily bright explosion based on the observed properties and its comparison with afterglow models.Methods. Our observations and other published multiwavelength data were used to reconstruct the light curves and spectral energy distributions of the burst afterglow.Results. Our results indicate that the observed features of the afterglow agrees equally well with the inter stellar matter and the stellar wind density profiles of the circumburst medium. In the case of both density profiles, the maximum synchrotron frequency nu(m) is below optical value and the cooling break frequency nu(c) is below X-rays, similar to 10(4) s after the burst. The derived value of the Lorentz factor at the time of naked-eye brightness is also similar to 300 for a corresponding blast-wave size of similar to 10(18) cm.Conclusions. The numerical fit to the multiwavelength afterglow data constraints the values of physical parameters and the emission mechanism of the burst.

An analytical solution to a 2D nonstationary heat conduction equation at second-kind boundary conditions modeling the conductive regime of free convection has been obtained by using a method of successive use of integral Hankel and Laplace transforms.

Using our photometric observations taken between 1996 and 2013 and other published data, we derived properties of the binary near-Earth asteroid (175706) 1996 FG3 including new measurements constraining evolution of the mutual orbit with potential consequences for the entire binary asteroid population. We also refined previously determined values of parameters of both components, making 1996 FG3 one of the most well understood binary asteroid systems. We determined the orbital vector with a substantially greater accuracy than before and we also placed constraints on a stability of the orbit. Specifically, the ecliptic longitude and latitude of the orbital pole are 266{\deg} and -83{\deg}, respectively, with the mean radius of the uncertainty area of 4{\deg}, and the orbital period is 16.1508 +/- 0.0002 h (all quoted uncertainties correspond to 3sigma). We looked for a quadratic drift of the mean anomaly of the satellite and obtained a value of 0.04 +/- 0.20 deg/yr^2, i.e., consistent with zero. The drift is substantially lower than predicted by the pure binary YORP (BYORP) theory of McMahon and Scheeres (McMahon, J., Scheeres, D. [2010]. Icarus 209, 494-509) and it is consistent with the theory of an equilibrium between BYORP and tidal torques for synchronous binary asteroids as proposed by Jacobson and Scheeres (Jacobson, S.A., Scheeres, D. [2011]. ApJ Letters, 736, L19). Based on the assumption of equilibrium, we derived a ratio of the quality factor and tidal Love number of Q/k = 2.4 x 10^5 uncertain by a factor of five. We also derived a product of the rigidity and quality factor of mu Q = 1.3 x 10^7 Pa using the theory that assumes an elastic response of the asteroid material to the tidal forces. This very low value indicates that the primary of 1996 FG3 is a 'rubble pile', and it also calls for a re-thinking of the tidal energy dissipation in close asteroid binary systems., Comment: Many changes based on referees comments

The original publication is available at www.aanda.org. Copyright ESO.; International audience; The spin state of small asteroids can change on a long timescale by the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect, the net torque that arises from anisotropically scattered sunlight and proper thermal radiation from an irregularly-shaped asteroid. The secular change in the rotation period caused by the YORP effect can be detected by analysis of asteroid photometric lightcurves. We analyzed photometric lightcurves of near-Earth asteroids (1865) Cerberus, (2100) Ra-Shalom, and (3103) Eger with the aim to detect possible deviations from the constant rotation caused by the YORP effect. We carried out new photometric observations of the three asteroids, combined the new lightcurves with archived data, and used the lightcurve inversion method to model the asteroid shape, pole direction, and rotation rate. The YORP effect was modeled as a linear change in the rotation rate in time d\omega /dt. Values of d\omega/ dt derived from observations were compared with the values predicted by theory. We derived physical models for all three asteroids. We had to model Eger as a nonconvex body because the convex model failed to fit the lightcurves observed at high phase angles. We probably detected the acceleration of the rotation rate of Eger d\omega / dt = (1.4 +/- 0.6) x 10^{-8} rad/d (3\sigma error), which corresponds to a decrease in the rotation period by 4.2 ms/yr. The photometry of Cerberus and Ra-Shalom was consistent with a constant-period model, and no secular change in the spin rate was detected. We could only constrain maximum values of |d\omega / dt| < 8 x 10^{-9} rad/d for Cerberus, and |d\omega / dt| < 3 x 10^{-8} rad/d for Ra-Shalom.

International audience; CCD-photometry of three Jupiter Trojan asteroids were carried out to study their opposition effect. We obtained well-sampled magnitude-phase curves for (588) Achilles, (884) Priamus, and (1143) Odysseus in the maximal attainable phase angle range down to 0.1-0.2°. The magnitude-phase relations have a linear behavior in all observed range of phase angles and do not show any non-linear opposition brightening. We have not found any confident differences between phase slopes measured in B, V and R bands. The values of the measured phase slopes of Trojans are different from available data for Centaurs. They are within the range of phase slopes measured for some low-albedo main belt asteroids, also exhibit a linear behavior down to small phase angles. An absence of non-linear opposition brightening puts constraints on the surface properties of the studied objects, assuming very dark surfaces where single scattering plays dominating role. We also determined the rotation periods, amplitudes, the values of color indexes B-V and V-R, and the absolute magnitudes of these asteroids.

International audience; Context: Research of asteroid families has been recently refreshed by the discovery of very young ones. These families are of great interest because they represent the product of their parent body fragmentation before orbital and physical evolutionary processes can change them. A cluster of seven objects around the largest body (1270) Datura is of particular interest because it has enough known members and resides in the inner part of the main asteroid belt, facilitating observations. Aims: We carried out photometric observations of the two largest members of the Datura family - asteroids (1270) Datura and (90265) 2003 CL5 - with the goal of inferring their physical parameters. We also used numerous astrometric observations of Datura-family members in the past few years to revisit the age of this cluster. Methods: We performed numerous photometric observations of (1270) Datura over several oppositions. We then used the lightcurve inversion method to determine the spin state and shape of this asteroid. In the case of (90265) 2003 CL5, for which only limited lightcurve data have been acquired so far, we used Fourier analysis to determine the synodic rotation period during the 2008 apparition. We also used backward numerical integration of the improved orbits of Datura family members to reduce uncertainty in its age. Results: We determined the rotation state of (1270) Datura, the largest member of its own family. Its major properties are a short rotation period of ~3.36 h and small obliquity, which, however, exhibits ~±15° excursions because of a forced Cassini state of the proper nodal frequency. Any possible initial non-principal rotation state has probably been damped and the asteroid rotates about the shortest axis of the inertia tensor. Its global shape, although convex in our representation, may reflect regions related to the excavation of the family members from the parent body surface. Interestingly, the second largest member of the Datura family - (90265) 2003 CL5 - appears to be very slow rotator with the rotation period ~24 h. The large amplitude of its rotation curve suggests that its shape is extremely elongated, possibly bi-lobed. Improved orbits of the family members allow us to re-determine the possible age of this family. We find an age that is slightly older than previously reported. Using a conservative approach, we obtain an age in the 450 to 600 kyr range. With strengthened, but plausible, conditions, we find that the current data may support an age of 530±20 kyr. Further astrometric and photometric observations of the Datura cluster members are needed to determine its age more accurately.