Анотація. Актуальність. Розповсюдженість карієсу зубів та запальних захворювань ясену дитячого населення країни коливається, залежно від віку та регіону, при цьому можливим виглядає одночасний перебіг хвороб. Мета. Аналіз індексів інтенсивності ураження зубів карієсом, гігієни порожнини рота та запалення ясен у дітей шкільного віку. Методи. Обстежено 503 дитини віком від 7 до 15 років, які проживали у Вінниці, Чернігові та Києві. Вивчали індекс інтенсивності каріозного ураження зубів,папілярно-маргінально-альвеолярний індекс PMA та спрощений індекс гігієни порожнини рота OHI-S. Результати. У Вінниці у дітей 7-8 років індекс інтенсивності ураження зубів карієсом складав 2,87±0,22, у Чернігові – 6,03±0,39, у Києві – 5,07±0,39. Серед дітей 12–13 років найвищий індекс був у киян – 4,18±0,23, у Вінниці та Чернігові він складав 2,65±0,24 та 2,92±0,25. У 15-річних дітей у Чернігові та Києві значення становили 4,83±0,25 та 4,08±0,32.Серед дітей 7–8 років найнижчий індексPMA був у мешканців Вінниці – 13,2±1,7%, у дітей у Чернігові – 15,1±2,8%, у Києві – 14,8±0,9%. Індекси у дітей 12–13 років у Вінниці, Чернігові та Києві дорівнювали, відповідно, 15,8±1,1%, 17,8±2,1% і21,4±1,6%. Серед 15-річних дітей індекс був найвищим у Києві – 22,3±1,9%, у дітей з Чернігова – 14,1±0,7%. Стан гігієни порожнини рота виявився найкращим у дітей 7-8 років з Вінниці–0,93±0,05 бала, у дітей з Чернігова і Києва – 1,29±0,13 та 1,28±0,07 бала. У дітей 12-13 років найкраща гігієна зафіксована у Вінниці – 1,05±0,05 бала, у Чернігові та Києві – 1,22±0,11 та 1,55±0,04 бала. Найгірший гігієнічний стан був у 15-річних киян – 1,57±0,06 бала, у дітей з Чернігова –1,27±0,07 бала. Висновки. Найгірші показники інтенсивності ураження зубів карієсом, запалення ясен та гігієнічного стану порожнини рота виявлені у дітей, які мешкали у Чернігові та Києві, тобто у містах північного регіону країни. Кореляційний аналіз показав наявність достовірних зв’язків між показниками, що підтверджує високу імовірність одночасного перебігу карієсу зубів і запальних захворювань ясен та вимагає розробки лікувально-профілактичних заходів з урахуванням регіональних особливостей.

Until the end of twentieth century, deep currents of the Black Sea were rather poor studied. Even the question of whether the deep-water circulation is cyclonic, like the Rim Current in the surface layer of the sea, or anticyclonic was controversial. In this article, the latest data on the features of the Black Sea deep currents are summarized. Difficulties in studying the Black Sea currents, important results of recent years, and prospects for deep-water circulation research are discussed. It is shown that a comprehensive analysis of numerical simulations using advanced models of ocean dynamics and field observation data makes it possible to evaluate the main features of the deep-water circulation structure, such us anticyclonic undercurrents and mesoscale eddies. Possible directions for refining the existing results and further investigations of the Black Sea deep-water circulation are proposed.

The reasons for the origin of narrow time-dependent currents formed in the Black Sea in the lower region of the constant pycnocline and deeper are analyzed on the basis of the results of numerical modeling. The prepositions for the generation of deep-water countercurrents in the hydrophysical fields of the Black Sea are studied with reference to the example of its north-east region, where they manifest themselves most frequently. In September 2016 and February 2017 the countercurrents in the region of the North-Caucasian coast were fixed according to the observation data of the ARGO profiling float ID6901833. On the basis of the numerical model of the Marine Hydrophysical Institute (MHI) with a 1 km-resolution and the assimilated data of the hydrological observations of the temperature and salinity the hydrophysical fields of the Black Sea are numerically simulated for the period of 2016–2017. The results of the calculations are used to reproduce the variations in the deep-water flow directions in the above-noted region and to analyze the fields of the main geophysical parameters, together with their derivative parameters. The effect of the mesoscale anticyclonic eddies and the density gradients on the velocity field structure and variability is illustrated. It is established that countercurrents propagated during several days in the anticyclonic direction, along the continental slope on the horizons from 50–100 to 500 m, and their formation took place in the conditions of the attenuation of the cyclonic Black Sea Rim Current in the upper sea layer and the intensification of the Kerch anticyclone.

Assessments of the state of sea waters and complex studies of the marine environment in various ocean basins are often based on hydrophysical fields (currents, temperature, salinity, etc.) obtained through the use of numerical modeling. The regular fields of currents are of particular importance for assessing the transport of impurities in sea waters at different depths, including pollutants of various origins. The results of hydrophysical field modeling, in turn, depend on the conditions set at the boundaries of the basin. Therefore, the correct setting of rapidly changing atmospheric conditions is extremely important for the reconstruction of marine dynamics. This paper presents model estimates of the Black Sea circulation obtained using two different datasets, SKIRON and ERA5, as atmospheric forcing. Numerical experiments for 2016 are carried out based on the eddy-resolving MHI-model. ARGO floats and R/V Cruises data are used to validate the simulation results. It was discovered that temperature and salinity RMSE between the model and measurement data are decreased under ERA5 forcing. Near the northeastern continental slope, a change in the direction of the alongshore subpycnocline current, which is detected in the ARGO float trajectory, is modeled using ERA5 rather than SKIRON. Therefore, for a more accurate reconstruction of the Black Sea circulation, ERA5 atmospheric forcing is recommended.

Purpose. The study is purposed at analyzing the physical mechanisms of formation of the Black and Marmara seas circulation structures based on the numerical experiments with climatic boundary conditions. Methods and Results. To investigate the reasons for the formation of circulation features, the energetic approach was applied that permitted to calculate the work of the forces affecting the marine environment. Location in the same geographical region determines similarity of atmospheric conditions for the Black and Marmara seas, and a clearly pronounced two -layer water stratification in both basins is related to a significant difference in salinity of the Black Sea and Mediterranean waters. To analyze the mechanisms of circulation variability, the mean and eddy fields formed under the impact of climatic atmospheric forcing and calculated using a numerical model of sea dynamics were considered. Wind influence, thermohaline fluxes on the sea surface, buoyancy work, friction, and diffusion were quantitatively assessed based on calculation of the Lorenz energy cycle components. The common features were found in the mechanisms of mesoscale variability, and the differences - in the mechanisms of large-scale circulation variability. Conclusions. It is shown that the main source of energy for the Black Sea mean circulation is wind stress work, and as for the Marmara Sea, the dominant factor is buoyancy work. For both basins, variability of the eddy kinetic energy characterizing the mesoscale dynamics is conditioned by baroclinic instability. At that, about a quarter of the available potential energy in the Black Sea, and about a half of it in the Marmara Sea is transformed into the eddy kinetic energy.

The purpose of this work is to study the behavior of the Black Sea deep-water currents below the permanent pycnocline under regular (climatic) and anomalous atmospheric forcing. The annual variability of Black Sea current fields at horizons deeper than 300 m and the response of deep-water currents to the atmospheric anomalous quasitropical cyclone in September 2005 in the southwestern Black Sea are analyzed. Thus, the variability of deep-water currents is assessed both when the climatic fluxes of heat, moisture and wind at the sea surface change quite smoothly throughout the year and when the circulation is forced by an extreme atmospheric cyclone during its 5-day passage over the sea surface and one month after the cyclone leaves the sea basin. It is shown that the velocities of Black Sea currents during anomalous cyclone forcing can increase several times compared to their typical values, and the relaxation of the current field after the quasitropical cyclone crosses the sea edge can take up to 4–5 weeks in the deep sea layer.

The aim of the presented study is to investigate one remarkable feature of the Black Sea deep-water circulation. These are unsteady narrow anticyclonic currents that propagate under the main pycnocline in the direction opposite to the surface circulation and are called undercurrents. According to observation data, undercurrents were discovered in several field expeditions, and were also revealed in some results of the Black Sea dynamic modeling. However, due to the lack of regular observations, it was not entirely clear whether they were a real feature of the Black Sea current field or an artifact of the experiments carried out. In this work, to assess the spatial variability of the Black Sea current field and identify undercurrents, the results of modeling the Black Sea circulation for several periods were analyzed. Simulations were carried out using the MHI model, and the results were validated based on deep-water field observation data on temperature and salinity. As well, in the northeastern part of the sea the simulated currents were compared with the data of ADCP deep-water velocity measurements (with Aqualog profiler). It is shown that undercurrents are more often formed in the spring–summer period and their lifetime is from one to several weeks. And although the length of undercurrents along the continental slope can reach several hundred kilometers, their width is only 8–12 km. Such characteristics of undercurrents explain the difficulty of their detection and identification in previous works.

Based on the numerical MHI model of 1.6 km horizontal resolution, a prognostic experiment was carried out to reconstruct the circulation of the Black Sea in 2011. The temperature and salinity profiling data of ARGO floats obtained for this year are used to validate the calculations results. As well, the simulation results are agreed with the data of deep-water measurements of the current velocity in June 2011 in the region of the North Caucasian coast (northeastern part of the Black Sea). The qualitative and quantitative characteristics of the deep-water currents in the northeastern part of the Black Sea are obtained.

Numerical simulation results of the Black Sea circulation obtained by four ocean dynamics models are compared to each other and to in situ data in order to determine the features of the Black Sea deep-water circulation such as deep-water undercurrents. The year 2011 is chosen as the test period due to the availability of deep-sea observations, including ARGO profiles and ADCP current velocities. Validation of the simulation results is based on comparison with the temperature and salinity measured by the ARGO floats. Anticyclonic currents (undercurrents) under the cyclonic Rim Current are detected by the results of all numerical models near the North Caucasian coast. The main characteristics of undercurrents are consistent with in situ data on current velocity up to a depth of 1000 m obtained by the Aqualog probe at the IO RAS test site near Gelendzhik in June 2011. The analysis of the spatio-temporal variability of the modeled salinity and velocity fields reveals that the most probable origin of the undercurrents is the horizontal density gradient of seawater in the region.

Purpose. The purpose of the study is to assess the coefficient of vertical turbulent exchange for different layers of the Black Sea basin based on the experimental data on microstructure of the physical fields obtained for the period 2004–2019 in the Black Sea and using the semi-empirical models. Methods and Results. New array of the temperature and salinity climatic fields was assessed by the results of numerical experiments. In the experiment, annual variation of the Black Sea hydrophysical parameters was reconstructed by the numerical model. Modeling included the scheme of assimilating the data of the climatic temperature and salinity array assessed. In contrast to the averaged data of the field observations, the modeled fields are compliant with equations of motion. Besides the temperature and salinity three-dimensional fields, the three-dimensional climatic fields of the Black Sea currents were also reconstructed for each day of a climatic year that is quite impossible using the observational data only. Spatial-temporal variability of the modeled three-dimensional fields was analyzed. The integral characteristics of the Black Sea water dynamics for the recent 30-year climatic period were studied and compared with the analogous ones for the previous century. Simulation was carried out by three-dimensional non-linear model of the Black Sea dynamics developed in Marine Hydrophysical Institute. The horizontal resolution of the model was 5 km, and the EMODNet bathymetry was used. The performed calculations showed that the increased spatial resolution of the temperature and salinity climatic array for the recent period made it possible to reconstruct the dynamics of the Black Sea in all layers in more detail. At the same time, significant small-scale variability of salinity fields was revealed. It was most pronounced at the deep-water horizons. Conclusions. Modeling using a new array of thermohaline fields revealed an increase in the integral temperature of the upper mixed layer in comparison with the experiment with assimilation of the previous version of the climatic array. At that, thinning and «break» of the cold intermediate layer found in the central part of the sea, indicates warming of the sea upper layer during the last 30 years. The highest noise detected at the deep-water horizons in the modeled salinity fields is related to quantity and quality of the salinity data resulted from the field observations. Taking into account insufficient calibration facilities for measuring seawater electrical conductivity, the next version of climatic TS-array requires a more strict procedure for verifying and processing the observation data obtained in the deep-sea layers.

Using the analogy with the properties of plane electromagnetic waves in Minkowski space, a definition of an affine-metric space of the plane wave type is given, which is characterized by the null action of the Lie derivative on the 40 components of the nonmetricity 1-form in the 4-dimensional affine-metric space. This leads to the conclusion that the nonmetricity of a plane wave type is determined by five arbitrary functions of delayed time. A theorem on the structure of the nonmetricity of the plane wave type is proved, which states that parts of the nonmetricity 1-form irreducible with respect to the Lorentz transformations of the tangent space, such as the Weyl 1-form, the trace 1-form, and the symmetric 1-form, are defined by one arbitrary function each, and the antisymmetric 1-form is defined by two arbitrary functions. Presence of arbitrary functions in the description of nonmetricity plane waves allows transmitting information with the help of nonmetricity waves.

In the framework of the Stueckelberg-Wheeler-Feynman concept of a “one-electron Universe” we consider a world line implicitly defined by a system of algebraic (precisely, polynomial) equations. A collection of pointlike “particles” of two kinds on the world line (or its complex extension) is defined by the real (complex conjugate) roots of the polynomial system and is detected then by an external inertial observer through light cone connections. Then the observed collective dynamics of the particle ensemble is, generally, subject to a number of Lorentz-invariant conservation laws. Remarkably, this property follows from the Vieta formulas for roots of the generating polynomial system. At some discrete instants of the observer’s proper time, mergers and subsequent transmutations of a pair of particles-roots take place, thus simulating the processes of annihilation/creation of a particle/antiparticle pair.

У Д К 5 5 1 .4 6 5 О.А.Дымова, Н.А.Миклашевская , Н.В.Маркова Морской гидрофизический институт РАН, г.Севастополь ОСОБЕННОСТИ ГЛУБОКОВОДНОЙ ЦИРКУЛЯЦИИ ЧЕРНОГО МОРЯ ЛЕТОМ 2013 Г

В рамках исследования структуры циркуляции Черного моря на глубинах ниже главного пикноклина представлены данные о преобладающих направлениях, изменчивости и скорости течений. Данные о вертикальных профилях течений были получены контактными методами в ходе экспедиционных работ Морского гидрофизического института. Для исследования глубинных течений были выбраны 25 станций, которые содержали измерения на горизонте 500 м и более. Приводятся характеристики приборов и географическое расположение станций. Периоды зондирований на станциях варьировали в пределах от нескольких часов до двух месяцев. Обеспеченность данными как по времени, так и по пространству существенно неравномерна, однако в работе впервые описан и проанализирован полный массив измерений глубоководных течений начиная с 1960 года. После оценки качества данных и приведения к горизонтам 500, 750 и 1000 м сформирована таблица, демонстрирующая обеспеченность, повторяемость направления и средние оценки скоростей течений. Анализ вертикальных профилей показал, что векторы скорости течений на некоторых станциях в приповерхностном и глубинных слоях имеют близкие направления. Однако на большинстве из рассмотренных профилей направления скорости на разных горизонтах существенно отличаются. Для каждой станции и каждого горизонта были построены и проанализированы диаграммы направлений и модуля скорости течений, они использованы для иллюстрации случаев разворота течений на разных горизонтах. Абсолютная величина вектора скорости на горизонтах глубже 500 м может превышать значение в вышележащих слоях.

Modeling of hydrophysical fields of the Black Sea for the one year period (2011) is carried out using the MHI z-coordinate nonlinear model with a spatial resolution of 1.6 km. Comparison of the simulation results with ARGO floats data shows a quite satisfactory agreement between the model and the measured parameters below the main pycnocline up to the maximum profiling depth of the floats equal to 1500 m in 2011. The greatest differences for temperature and salinity are in the seasonal thermocline, which is reproduced by the model a few meters deeper in comparison with the data of measurements. In most cases the shift of the thermocline reconstructed is the main reason of the discrepancy between the model and in-situ data in the upper layer. It is shown, that in the layer below 300 m, the circulation features are simulated in a quite sufficient agreement with ARGO data and allow us to describe the field of the deep Black Sea currents.

The results of a prognostic numerical experiment on simulation of the Black Sea circulation are given for warm period of 2013. The MHI hydrophysical ocean model and ERA-Interim atmospheric forcing are used for the modeling. Comparison of observed and simulated temperature and salinity is carried out. A satisfactory agreement between measured and simulated data is obtained. The greatest attention is paid to the deep Black Sea circulation structure. Hydrophysical fields at the depths below the main pycnocline are studied in detail. It is confirmed that the field of deep currents contains vortex formations and flows that qualitatively and quantitatively differ from the surface ones. There are a number of vortexes that form not at the sea surface but near the low boundary of the main pycnocline (at depths of 150–300 m) and propagate down to the bottom without weakening. As well, in summer 2013, quasi-periodic narrow deep currents propagating anticyclonically are generated in some regions along the Black Sea continental slope.

Results of the Black Sea hydrophysical field reanalysis for the period of 1992-2012 are considered. The simulation was carried out using z-coordinate non-linear ocean model of the Marine Hydrophysical Institute. The hydrophysical fields were calculated with resolution of 4.8 km horizontally and by 38 vertical levels along the depth from the sea surface to the bottom. In contrast to a number of previous works, the focus now is on studying the variability of the Black Sea circulation below the main pycnocline (horizon of 300 m and deeper). Analysis of instantaneous and mean velocity fields is carried out, and main structural features are found in deep layers of the sea. It is shown that the most intensive dynamic structures are mainly the cyclonic mesoscale eddies moving from 33-38°E westward and passing through the abyssal central part of the sea. The problem of the existence of reverse (anticyclonic) deep currents opposite to the surface ones is also considered. It is shown that along the narrow north-eastern continental slope such currents exist occasionally. They are formed on the background of topography regional features mainly in summer and could be associated with the weakening of the overlying cyclonic Rim Current.

The Black Sea deepwater currents below the main pycnocline at the depths more than 350 m are considered. Current velocities derived from different datasets are compared. Results of two numerical experiments with MHI non-linear z-coordinate ocean model, estimates of deep Argo float velocities, and in-situ data accumulated in MHI Database are analyzed. It is shown that sub-pycnocline velocities obtained by simulation with MHI model and SKIRON atmospheric forcing generally correlate with Lagrangian deep Argo velocity estimations and MHI Database mean velocities. Existence of deepwater cyclonic and anticyclonic vortexes is drawn from the datasets under consideration. The qualitative difference between modeling results and measurements is the narrow quasi-periodic currents along the northeast continental slope which are not succeeded to verify by available data of Argo and MHI Database collected so far.

Modeling results of the Black Sea deep-water current reconstruction are considered.Computations are provided by applying the nonlinear z-coordinate model developed in Marine Hydrophysical Institute (MHI).Climatic atmospheric forcing and the atmospheric reanalysis data (ALADIN, Era-Interim) obtained for 2006, 2010 and 2013 are taken into account in different numerical experiments.The Black Sea climatology experiment is performed with a spatial grid step equal to 5 km, and in other experiments the 1.6 km grid step is used.Three-dimensional structure of the Black Sea currents on 45 levels within the surface horizon (2.5 m) and the bottom one (2100 m) is reconstructed.The anticyclonic current (countercurrent) extending along the Black Sea continental slope in direction opposite to the Rim Current is detected at about 1000 m and deeper.In the climatic fields the countercurrent exists in spring and summer in the northern part of the basin.In the experiments that included the reanalysis forcing, the countercurrent is revealed as separate streams in various continental slope areas and in different seasons.Its mean velocity is about 5 cm/s, the highest one is equal to 10 cm/s.In the overlying layer in the northeastern part of the Black Sea, the countercurrent is also detected by modeling as well as it is revealed by CTD and ADCP measurements.

We consider the light cone (‘retardation’) equation (LCE) of an inertially moving observer and a single world line parameterized by arbitrary rational functions. Then a set of apparent copies, R- or C-particles, defined by (real or complex conjugate) roots of the LCE will be detected by the observer. For any rational world line the collective R-C dynamics is manifestly Lorentz-invariant and conservative; the latter property follows directly from the structure of Vieta formulas for the LCE roots. In particular, two Lorentz invariants, the square of total 4-momentum and total rest mass, are distinct and both integer-valued. Asymptotically, at large values of the observer’s proper time, one distinguishes three types of LCE roots and associated R-C particles, with specific locations and evolutions; each of three kinds of particles can assemble into compact large groups—clusters. Throughout the paper, we make no use of differential equations of motion, field equations, etc.: the collective R-C dynamics is purely algebraic.