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Diversity of forms and kinds of speech communication and variability of national and regional accents in contemporary English define the necessity of phonetic variation study of oral speech and clearing up its sources. The speaker's accent indicates his social status (social class, education, religious, ethnic, professional affiliation). The present article is dedicated to the study of the speaker's social status prosodic markers. Complex prosodic investigation of speech behavior of the Australian native speech representatives of different professions has been conducted in the paper. The comparison of the revealed data allowed to state that the highest prosodic index is registered in the actress's speech and the lowest in the speech of the politician. Frequency range is correspondingly the widest in actress's speech, which can witness the high tonetic explication of female voice. The received by acoustic method intonograms allowed to speak about maximum frequency localization on the terminal tone in the speech of all the investigated informants. Corresponding to the aim and tasks of the paper prosodic markers of various professions of Australians have been defined. Prosodic markers of Australian politician are the following moderate pausation, which is revealed in speech delimitation average frequency range, and low tonetic variation. Main prosodic marker of the architect's speech is very insignificant syntagmatic division, prevalence of non-pausation means of utterance delimitation, monotonous character of speech due to low tonetic variation. Real estate agent and actress's speech can be defined as emotional on account of high tonetic level, wide frequency range, low recurrence of non-pausation delimitation and heightened level of tonetic utterance completion.

This paper is an attempt to reanalyze the established order within the category of parts of speech, in particular prepositions and adverbs, as the units from these categories are characterized by the highest level of functional transposition in the language. We argue that overlapping of the categories was caused by the inclination of the Old English grammarians to take over main grammatical rules and exceptions, class division, definitions etc. from the Latin language. At the same time, grammatical phenomena existing in Old English were ignored or fitted to the already adopted Latin definitions and rules. That led to confusions, misunderstandings and overlapping in the grammatical system of Old English. The paper addresses the processes of lexicalization and grammaticalization which, according to our hypothesis, are observed within the category of prepositions in Old English and predetermined subsequent functional transposition. The analysis explains the phenomenon of functional transposition of the units which are simultaneously ascribed to several categories, e.g. prepositions, adverbs, particles etc. The class of space and time prepositions has undergone lexical and grammatical transformations which were consequently institutionalized in the language and the units became subjects to functional-semantic and functional-grammatical transposition the results of which are observed in present-day English. The former process resulted in transposition of the meaning, sometimes metaphorical, and further functioning of these units as adverbs, particles etc.; whereas the latter led to purely grammatical usage of the units, for instance substitution of the category of cases in English, uprise of new grammatical prefixes, loss of rigidness in word order.

The present paper is devoted to the problem of study of the language means of realization of rhetorical strategies of business communication in their correlation with zones of influence of a human being. The business strategies – informative, regulative-directive, argumentative-persuasive, manipulative, of positive self-representation – and their correlation with zones of influence of a human being: rational-logical, volitional, psycho-emotional, moral-axiological, and aesthetic-imagery have been researched. The purpose of the paper is to find out correlations of rhetorical strategies and tactics of business communication and zones of influence of a human being. The object of study is rhetorical strategies and tactics of business communication and their correlations with zones of influence of a human being. The subject of the study is language means of realization of rhetorical strategies and tactics of business communication in their correlations with zones of influence of a human being. The methods applied include rhetorical, contextual, and discourse-analysis, methods of classification and systematization. Business communication is organized on the principles of co-operation and politeness. Its intentional nature molds business genre forms and influences the choice of rhetorical strategies and tactics. Rhetorical strategies and tactics, which are realized in certain language means, correlate with rational-volitional-emotional sphere of a human being. The perspectives of the research are to conduct a rhetorical analysis of the academic communication and to approve the results of the research at practical teaching of academic and business talk to Master students.

The URAN-4 decameter radio telescope, which is located in thevillageofMayakiof theOdessaregion, is an element of system of the URAN radio telescopes (Ukrainian Radiointerferometer of theAcademyofSciences). The radio telescope is used according to the following scientific programs: measurements in the composition of the Interferometer with the Super Large Base (VLBI), to study the angular structure of discrete radio sources; the study of the nonstationarity of the flux of cosmic radio sources and the study of the influence of the space environment on the characteristics of the received signals. RT URAN-4 operates at frequencies of 10-30 MHz and consists of an antenna and an equipment complex. A telescope antenna is an electrically controlled phased array of 128 turnstile vibrators. It identifies two linear signal components and is endowed with the possibility of changing the position of the antenna pattern in space (2048 discrete positions of the beam). The geometric dimensions of the array238 meters(West-East direction) and28 meters(North-South direction). The size of the antenna pattern in the modulation mode of signal reception at a frequency of 25 MHz is 2.7 x 22 degrees. In the VLBI interferometer mode, a resolution of about 2 seconds of arc is realized. The instrumental complex of the RT URAN-4 is represented by two types of modulation radiometers, which make it possible to measure the flux densities of radio sources and apparatus intended for VLBB measurements. The working frequency range in which RT URAN-4 operates has a high level of radio interference. The work gives definitions of interference acting in the decameter range. Considered methods of dealing with them. One of the methods to combat interference is the work of the radio telescope on the frequencies permitted and legally protected from interference, the list of which is given in the article. The paper deals with issues related to the organization of the security zone around the radio telescope. On its territory, the maximum allowable power for existing nearby transmitting radio facilities and interfering industrial facilities should be legitimized, in the designated working lanes. At the same time, a monitoring service for the radio spectrum should be organized. The paper deals with the developed and manufactured portable direction finder. Its characteristics are given, recommendations on its use are given.

The paper presents the first results of processing of photographic observations of SS bodies based on materials from the collection of plates of the Ulug Bek Astronomical Institute of theAcademyofSciencesof theRepublicofUzbekistan(AI ASRUz). The glass archive of the AI AI ASRUz has about 15 thousand photographic plates with images of various space objects. In this paper, we discuss the first results of processing of major planets’ photographic observations inUzbekistanusing the new technique. The observations were carried out on two astrographs –Tashkentnormal astrograph (TNA, D/F=330/3438) and Kitab Double Zeiss astrograph (DAZ, D/F=400/3000) in 1895-2004. Currently, in AI the work runs to streamline the archive and create a database of observations in a single xls-format. The number of photographic plates with images of major planets obtained on two telescopes is more than 300 negatives. In 2017, together with MAO NAS ofUkraine, the processing of these photographic observations using the new methodology was started. The plate digitization is performed on the flat-bed 10000XL in 1200dpi mode. Positions and photometric estimations in B-color of all registered on the plate objects are obtained using the software proposed and developed in MAO NAS of Ukrainerunning in LINUX/MIDAS/ROMAFOT environment. The search for major planets and their satellites among the whole set of plate objects and the comparison of their observed and predicted positions is carried out online with the help of internet-service (http://lnfm1.sai.msu.ru/neb/nss/nssephmr.htm). Up to date, the small part of the plate collection is treated, namely 23 negatives with images of Uranus, Neptune, Pluto and Saturn’s satellites, obtained on the Kitab DAZ astrograph. 16 negatives with 19 exposures gave the best results with (О-С) in the range ±1.5″. In total, we obtained 47 astrometric positions of the objects of interest in the wide interval of brightness’s (8m ±16m). The internal positional accuracy of the catalog in the Tycho-2 reference system is σαδ= 0.08″–0.13″, the photometric error of B-magnitudes is estimated as σB = 0.2m.

This paper describes the Ukrainian database of long-term photometric observations of resident space objects (RSO). For the purpose of using this database for the outer space monitoring and space situational awareness (SSA) the open internet resource has been developed. The paper shows examples of using the Atlas of light curves of RSO's for analyzing the state of rotation around the center of mass of several active and non-functioning satellites in orbit.

This paper describes the developed model of dark matter cored density profiles. This model was recently proposed by Dmytro Iakubovskyi (Iakubovskyi & Rudakovskyi, in preparation). It has only one extra parameter – the maximal value fmax of phase-space distribution function – that turn a cusped Navarro-Frenk-White density profile into a cored one. This paper focuses on the estimation of the influence of velocity anisotropy on the cored density profile by using the Osipkov-Merritt model. The density profiles of the typical dwarf-spheroidal galaxy for different masses of fermionic dark matter particle and different anisotropy parameters ra was calculated. It was obtained that the influence of velocity anisotropy on the cored density profile is small.

In addition to the formulas (1) and (2) from work of the author (Bezdenezhnyi, 1999, hereafter Paper I) alternative formulas (3)--(6) are derived for description of two sequences of magic numbers. Their properties are described. Dependences of some physical parameters as a function of the number of chemical element (Z), number of neutrons (N) and the mass number (A) are analyzed. It is shown that magic numbers of protons (Z) and neutrons (N) are displayed in them. The concept of magic mass numbers (A) is proposed, and it is shown that they are also present in some dependences. The list of magic and twice magic (on Z and N) elements is extended, as well as the list of twice magic ones on A and Z or N. We propose to refer a nucleus that contains magic numbers of protons and neutrons to thrice magic nucleus if their sum is a magic number too. It is suggested that during the decay of "double-uranium" super-nucleus one of three twice magic elements ( X(112,168), Y(126,184) and Z(168,258) or Z'(168,240) ) predicted (in Paper I) will be formed fragment accompanying in areas of twice magic nuclei: Yb(70,112), Sn(50,70) and S(16,16) respectively.

The English language in Canada occupies the dominant position. Both British and American English influenced the formation of Canadian English, which has undergone a long historical process. According to the latest census survey the population of contemporary Canada is devided into 3 linguistic groups: anglophones – those whose native language is English; frankophones – whose native language is French and allophones – Canadians whose native is some other language. The aim of the given paper is to analyse which peculiarities of the British pronouncing system influence and are reflected on prosodic characteristics of anglophones’ speech. The tasks of the paper included the distribution of terminal tones and scales and the character of syntagmatic devision in the speech of the analysed groups of informants. The conducted investigation revealed definite specific character of the speech of Anglophones, where the peculiarities of British prosody – the frequency of low falling nuclear tone and Descending Stepping Head influenced the formation of Canadian intonational system.This statement is based on the earlier received data about the frequency of intonational Scalеs and terminal tones in the works of native and foreign linguists.

From the perspective of cultural linguistics, this paper a) investigates and compares the conceptualisations of beauty in the Chinese, English and Slavonic (Polish and Ukrainian), b) analyses the cultural contexts of in which beauty conceptualises and c) reveals the crucial peculiarities of the human’s perception and evaluation of beauty in the appointed languages. Based on the theory that language is an activity the character and structure of which express the culture and individuality of speakers (Humboldt 1907), attention is mainly focused on the interrelationship of language and culture pointing out ontological features of Chinese, Polish, English and Ukrainian worldview and perception of beauty. A suffient number of examples demonstrate the ontological features and the empirical generalizations embedded in conceptual images of beauty in the analysed languages. Furthermore, the findings of the paper may assist in learning the axiological value of beauty and its origin in the chosen languages and cultures.

Numerical simulations of the cold supersonic flows in different astrophysical problems meets with the loss of precision difficulty. For to overcome the difficulty it was suggested earlier to use conservation entropy equation instead of energy conservation law. In the paper we analyse quantitatively the error what appears in the shocked flow when isoentropic equations are used. The isentropic equations of gas dynamics can be used only when there are no shocks in the solution or when they are weak and do not significantly affect the flow. The results described here were represented as a talk at the 16-th Gamow Summer School: ”Astronomy and beyond: Astrophysics, Cosmology, Cosmomicrophysics, Astroparticle Physics, Radioastronomy and Astrobiology” 14-20 August, 2016,Odessa,Ukraine. The complete paper is published in Bisnovatyi-Kogan & Moiseenko, 2016.

In this paper astronomical two-matrix photometer is described. It differs from common one CCD camera photometers by using the second CCD camera. It enables simultaneously to carry out the studied star and standard star light inputs measurements. The second camera application enables significantly to increase measurements accuracy and at least twice time decrease of one star observation. The significant increase of measurements accuracy is reached by carrying out simultaneous observations, and errors caused by the Earth atmosphere fluctuation are the same as for studied star so for standard star. Time decrease is reached by carrying out both stars simultaneous observations. In the paper photometer’s optical mechanics scheme is given. The motion mechanism of receiving and recording block with micrometer screw rotated by stepping motor is described. It is demonstrated that exact coordinates of matrix position attached to clutch on micrometer screw are shoot by absolute magnetic encoder. The applied two-matrix photometer control system electronic equipment is described. The photometer operation control algorithm installed on Tien-Shan astronomical observatory 1-meter telescope is presented.

The paper discusses zeugma as a device characterized by a violation in the meaning of words functioning within the limits of the same grammatical structure. The semantic shift from what is semantically expected to unexpected meanings results in an illogical combination of words. The paper is intended as a practical aid while teaching the linguistic peculiarity of a stylistic device.

The study of meteoroids and the phenomena arising from their entry into the Earth's atmosphere is of considerable scientific and practical interest to obtain data on the origin and evolution of the solar system, to study the physics of planetary atmospheres, and to solve the problem of problem of asteroid-cometary-meteoroid hazard. Today the most effective and informative are photometric and spectral studies of meteor phenomena, which provide information on the chemical composition and physical properties (density, combustion temperature, etc.) of meteoroids that allow us to classify these bodies by parental origin and mineralogical structure. This paper presents the results of a study of the photometric system of eight meteor telescopes of the same type with a lens having a wide field of view (f = 50 mm, f / 1.2) and WAT-902H2 cameras. Telescopes equipped with broadband Cokin filters P050 (cyan) and P003 in the blue and red bands are installed in Mykolaiv and Odesa. An original method is used to observe meteors - the method of accumulation of shifted frames for TV cameras, which provide an accumulated image of reference stars in the form of points on a motionless telescope. In this work, simultaneous observations of reference stars in two filters obtained on 2 different observation nights were used. Cross-identification of the observational data with the Gaia DR2 catalog showed that the standard error of the residual coordinate differences (Obs – Gaia DR2) is about 7 "for both coordinates in both filters. The bandwidths of our filters are closest to the photometric system Gaia BP / RP, which was selected as a standard system to which the obtained instrumental stellar magnitudes were transformed. Transformation coefficients for converting instrumental stellar magnitudes into Gaia BP/RP photometric system were obtained by linear regression. Average standard photometric solution errors were 0.2 mag and 0.3 mag for red i and blue band, respectively. The possibility of determining the color index based on the array of common stars from observations in two bands is shown

The all-sky survey conducted by the InfraRed Astronomical Satellite (IRAS) in the 1980’s discovered many objects with infrared excesses whose nature has not been explored until recently. IRAS07080+0605 is one of those identified in the visual spectral range with an early-type star, which shows the B[e] phenomenon. The object is puzzling, because it exhibits one of the strongest infrared excesses associated with a star of one of the lowest surface temperatures (∼8500 K) among objects with the B[e] phenomenon, an apparent combination of spectral features of dwarfs and supergiants, and the absence of a surrounding optical nebula. Our photometric and spectroscopic study shows that the object’s properties are similar to those of the famous Red Rectangle proto-planetary nebula. In this paper we describe our findings and hypotheses about the nature and evolutionary status of IRAS07080+0605

This paper presents the results of the analysis of possible existence of nine near-Earth meteorite-producing groups in asteroidal orbits, consisting of sporadic fireballs from the IAU MDC 2007 database, sporadic meteors from the SonotaCo database, meteorites – namely, L5, L6 and H4-H6 ordinary chondrites and an ureilite, for which atmospheric and orbital parameters are known from instrumental observations – and their plausible parent bodies, that is, near-Earth asteroids (NEAs). Orbits of the selected members of meteorite- producing groups were classified as asteroidal according to the Tisserand parameter T J > 3.1. In order to test the link between meteorite-producing groups in asteroidal orbits and their plausible parent bodies, we carried out an investigation into the possible existence of some known NEAs that move in similar orbits. Based on the orbital similarity, determined using the Drummond (D D ) and Southworth & Hawkins (D SH ) orbital similarity criteria, some associations between the identified NEAs, known meteorites in asteroidal orbits and small, as well as meteorite-dropping, meteoroids have been suggested. As a result, several meteorite-dropping sporadic fireballs and small meteors, whose orbits are currently similar to the orbits of known meteorites, have been detected and reckoned as possible members of the groups in asteroidal orbits; their plausible source regions have also been considered.

The article reports on the study of the interferential influence of Welch intonation on the speech of Australians. Special focus is given to historical factors which influence the phonetic realization of Australians’ speech. The article contains overview of the results of lingual and historical analysis proving that the first emigrants of Australia were representatives of the lowest social classes, native Cockney, Venaculas speaker from different parts of Britain. Investigators consider that Australian English is more likely to be close to Cockney dialect with a touch of Welsh, Irish and a definite share of Scottish dialects. In the frame of the conducted complex investigation on the basis of auditory and computer analysis melodic and frequency characteristic of Australian speech were studied and the influence of English speech of the first emigrants from Britain was traced. In the result of the auditory analysis the prevalence of the Falling terminal tone was fixed, which is the peculiarity of the British intonation, and also high frequency of Rising and Rising-Falling nuclear tones. Such tendency is the result of the Welsh intonation influence on the speech of Australians. Computer analysis showed the frequency characteristics in the speech of the investigated informants vary which depend on gender and territorial belonging of the speaker. Uniqueness of Australian English has been revealed in the paper, which was formed in the run of historical development of the country under the influence of emigrants’ speech as well as from different areas of Britain and other countries. The analysis of segmental characteristics which were formed under the influence of regional factors inside and outside Australia are to be the subject of the future investigation.

In the paper, the author has outlined the metamodern specificity, explicated through the system of ideas, as well as the manifestations of intertextuality (including paratextuality) in the novel “The Cleft” by Doris Lessing. The views expressed and substantiated by L. Miroshnychenko in her work in 2012, analyzing the novel of the British writer in the paradigm of the philosophy of skepticism, have been developed. It is emphasized that both the epigraph and the plot complex of “The Cleft” represent a system of ideas that cannot be considered through the prism of stereotypes, in particular in the feminist studies. It is proved that the British author seeks to bring the conversation about anthropological and ontological (defined by the “divine” nature) differences between men and women to a new level of understanding, which is typologically related to the post-postmodern world, including metamodernism as one of its trends. Metamodernism makes it possible to construct a world, in which subjects with fundamentally different positions converge, but each of them has the right to exist. In this case, it is argued that “The Cleft” is an example of an intellectual British post-postmodern novel. D. Lessing from the first epigraph sets a special intellectual dynamics in the novel, where neither the position of a man nor the position of a woman, in the end, rises above each other, but exists, asserting its own anthropological status, determined by various external and internal factors. The role of women and the role of men are marked by differences that have biological, psychological, anthropological, etc. nature, and, hence, the differentiation of the world into one in which feminine and masculine models function is natural in the novel. The masculine world is associated with travel, movement, the discovery of new territories, while the feminine discourse is marked by the motive of preserving space. Such positions, according to the narrator, have ingrained in the masculine and feminine differences. It is emphasized that the “The Cleft” deconstructs feminist approaches, which for the British author are simplified, schematic and stereotypical in terms of understanding the nature of women.

This paper reports on the optical imaging polarimetry of geostationary satellite Express-AM5. Precise optical polarimetry was carried out using the Nayuta 2-m telescope at Nishi-Harima Astronomical Observatory and a polarimeter. V-band images were continuously taken in 312 minutes. The degree of polarization decreased with time until the minimum phase angle was reached at midnight, and then, it increased until morning. This change in the degree of polarization is well explained by the reflection of sunlight from monocrystalline solar panels of the satellite and possibly from other satellite components such as the antenna dishes and/or bus.

The paper examines data on the effects of the lunar tidal wave in the Earth 's upper atmosphere on the observed flux of radio sources. Monitoring of the fluxes of powerful galactic and extragalactic radio sources is carried out at the URAN-4 radio telescope of the Odessa Observa- tory of the Institute of Radio Astronomy of the NAS of Ukraine since 1987 till now. The monitoring program in- cludes radio galaxies 3C274, 3C405 and supernova rem- nants 3C144, 3C461. Changes of fluxes of radiation sources at decameter waves are determined by the condi- tion of an ionosphere resulted due to space weather varia- tion and tidal events. When radio sources are observed through a tidal wave, a "plasma lens" effect is realized in the ionosphere. Depending on the position of the radio source relative to the tidal wave, the radiation wave front is sought. As a result, various effects are realized: strong fo- cusing, intense flickering or "blurred" recording of the ra- dio source. According to the data of radiation monitoring of powerful radio sources, the dimensions and structure of the tidal wave zone in the upper atmosphere producing the effect of "plasma lensing" have been determined. The total size of this zone according to observations on frequent 20 and 25 MHz is on the order of 30-60 angular degrees in right ascension and declination.

This paper presents the results of the study of evolution of Jupiter-family comet-like orbits of six meteorite-producing groups, including sporadic fireballs from the IAU MDC database 2007 [1], sporadic meteors from the SonataCo database [2], instrumentally observed H5 and L3.5 ordinary chondrites, as well as near-Earth asteroids which are potential parents of the examined groups. In order to verify the relationship between meteorite-producing groups and their potential parents, we performed backward numerical integration of the orbital motion of these groups’ members over several millennia. The numerical integration was carried out using the Halley software [3]. The equations of motion factored in gravitational perturbations due to the major planets, radiation pressure effects and the Poynting-Robertson drag. The equations of motion were numerically integrated using the 11 th -order Everhart method applicable to studying the motion of Jupiter-approaching short-period comets. The numerical integration of the mean orbital elements of a group, as well as those of the relevant meteorite and potential parent asteroid, over 5,000 years has shown that the respective perihelia, eccentricities and arguments of perihelion evolved in a similar manner over the specified period. The D SH -criterion of Southworth and Hawkins [4], which is a quantitative measure of orbital similarity, has remained below 0.3 [5] for about 5,000 years in the groups of Neuschwanstein and Mason Gully meteorites and for about 3,500 to 4,500 years in the groups of Benešov and Park Forest meteorites. In the groups of the Košice and Pribram meteorites, the mean orbits and those of their potential parents remained similar as defined in terms of the D SH -criterion over a relatively short period of about 2,000 to 3,000 years. We can infer from our findings that meteorite-producing sporadic fireballs and sporadic meteors are related to the H5 and L3.5 ordinary chondrites and their potential parents, i.e. near-Earth asteroids, in the investigated groups. The estimated time intervals, over which the evolving orbits of the groups’ members have shown good similarity, are indicative of relatively recent formation of meteorite-producing groups as a result of fragmentation of their parent bodies.

Population studies of the extragalac- tic objects are a major part of the universe large-scale structure study. Apart from radio, infrared, and visible wavelength bands, observations and further identification of extragalactic objects such as galaxies, quasars, blazers, liners, and active star burst regions are also conducted in the X-ray and gamma bands. In this paper we make identification and cross-correlate of the infrared and X-ray observational data, build a distribution of a selected sample sources by types and attempted to analyze types of the extragalactic objects at distances up to z = 0.1 using observational data of relevant space observatories. Data from a leading X-ray space observatory XMM-Newton were used to compile the largest catalog of X-ray sources. Current version of XMM SSC (Serendipitous Source Catalog) contains more than half a million sources. In our previous works we selected and analyzed a sample of 5021 X-ray galaxies observed by XMM-Newton. Identification and classification of these sources is essential next step of the study. In this study we used infrared apparent magnitudes from WISE catalog of AGN candidates. In 2010 space telescope WISE performed full sky survey in four infrared bands and detected 747 million sources. WISE catalog of AGN candidates amounts 4 million of possible extragalactic sources. We built infrared color-color diagram for our sample of X-ray galaxies and assessed their types using WISE telescope data. In this study we also analyzed large scale structure of the universe (distances up to z=0.1). This analysis revealed Coma galaxy cluster and SDSS Sloan Great Wall. In the further studies we are planning to investigate the distribution of different types of X-ray galaxies within the large-scale structures of the Universe.

In this paper, we study the distribu- tion of images from a point source in N - point gravi- tational lenses. It is well known that in a Schwarzschild lens (N = 1) from a point source, there are always two images. Moreover, one of them is always inside the Einstein ring, and the second outside it. It follows that: a) the image plane is divided into two areas; b) in each area there is always only one image; c) the source plane, with the exception of the caustic point (origin), is uniquely mapped onto each of the two areas of the image plane. In our study, we describe an algorithm that allows us to determine the single-valued regions in a 2-point gravitational lens and demonstrate it using an exam- ple of a binary symmetric lens in which the distance between the point masses is 1. We have shown that in this case the full prototype of the caustic divides the image plane into eight simply connected areas that have the following properties: a) if the point source is inside the caustic, then it has five images in five (internal) areas; b) if the point source is outside the caustic, then it has three images in three (external) areas; c) in each area there can be no more than one image; d) if the image of a point source is located in one of the five internal areas, then the remaining four also have images, while none of the three external areas have images of the source; e) if the image of the source is located in one of the three external areas, then its images also exist in the remaining two, while none of the five internal areas contains a prototype of this source; f) a caustic is a continuous, piecewise smooth, closed Jordan curve that has a finite number of singular points; each smooth, open part of the caustic, the ends of which are singular points (the caustic arc) has four inverse images, of which only one belongs to the critical set, the caustic arcs are positively oriented (when going around, the interior of the caustic remains to the left; g) the boundaries of the regions consist of arcs (closure of the image of arcs) with a hereditary orien- tation; all eight regions are divided into the following two classes: four regions in which the orientation of the boundary coincides with the orientation on the caustic and four regions in which the orientation of the bound- ary is opposite to the orientation on the caustic.

This article considers life stories told by beneficiaries of children's charities; the stories are published on the Internet sites of these organizations. Framing our research in terms of narrative, we aim to bring to light formal and meaningful aspects of the stories under consideration, differentiating several layers of their meaning. Besides, we target to establish the specificity of the narratively constructed identities of those involved in the processes of narration and interpretation. Since the definition of narrative itself is in dispute, the article starts with introducing the key elements of traditional (structural) and newly emergent (social-constructivist) approaches to linguistic analysis of narratives. It is shown that the stories under consideration are not about events, but significant changes in the life of individuals, which are brought about by a charity. The narrative structure of the stories under consideration is explored by drawing on the principles of the traditional narratological approach, while the study of their sematic and pragmatic characteristics is underpinned with social-constructivist assumptions. Since sites of charity organizations are specially designed to project a favourable image, stories of the beneficiaries of charity are actively influenced on, or, in Plummer's parlance, "coached", but not independently "produced". This can be seen both in the standardized structure of the stories published on the site of a particular organization and in specific linguistic choices prompted by the pragmatic intention (in the broad sense) of all charities to stimulate people to donate, thus bringing to life a beneficiary in the giver. The paper ends with outlining prospects for further research.

Contemporary “stormy” changes in global and national political economic, social, societies are causing changes in traditional, archaic ideologies, outlooks, mentalities which are definitely reflected in languages, particularly in phraseology. The aim of the paper is to focus the readers’ attention on the potentialities of enhancing the efficiency of teaching future philologists by using project-work as the mechanism of integrating a variety of theoretical linguistics (theoretical grammar, lexicology, semantics, syntax, text linguistics; communicative linguistics, discourse linguistics, stylistics, cognitive linguistics, contrastive linguocultural studies) and applied linguistics (corpus linguistics, sociolinguistics, psycholinguistics etc.). It is of special importance because the most competitive specialists in 2030 are envisaged to be critical thinking, creative, collaborative and communication competent. The project consists of 3 main stages. Stage 1. Information collection of deformed proverbs: potential integration of sociolinguistics corpus linguistic and mathematical statistic methods. Stage 2. Linguistic analysis. Stage 3. Analysis of changes in the systems of conceptual values and priorities as proverbs and aphorisms are specific regulators of human behaviour and outlook, they reflect folk morale protecting the traditional family welfare and spiritual morale challenging murders. Comparative and contrastive analysis of English, Ukrainian and Russian deformed proverbs show that, in general, the processes of proverb decomposition are identical. But Ukrainian and Russian proverbs express national and cultural component more explicitly more proper names, stronger emotive, evaluative connotation and more specific national elements.

The paper is an attempt of a cognitive pragmatic analysis of communicative situations in which the personages of English literary artistic discourse use utterances of approval, praise, compliment and flattery as the means of manipulative impact upon the listener. Approval is defined as a positive evaluative expressive syncretic speech act, its evaluation object being things, ideas, and phenomena that do not refer to the addressee's sphere of interests. The latter fact makes approval different from the other evaluative speech acts. Approval evaluation theme is that feature of the evaluated objects, which attracts the addresser's attention. Praise is defined as a positive evaluative expressive syncretic speech act, its evaluation theme being the moral and intellectual traits, skills and actions of the interlocutor or a person who is not present during a speech exchange but is praised by the speaker. Compliment is defined as a positive evaluative expressive syncretic speech act, characterized by the overlapping of the addressee and the evaluation object. The main fact about compliment is that it is always exaggerated. The subject of evaluation in a compliment speech act is the hearer's appearance, possessions, and accomplishments. Flattery is defined as a pseudosincere positive evaluative manipulative expressive syncretic speech act, characterized by forethought, by a certain strategy, and also, by its addressee and evaluation object being the same person. Flattery evaluation themes are the addressee's appearance, their moral and intellectual traits, skills, accomplishments, and actions. The speaker flatters the addressee not being motivated by some feelings but wishing to gain some benefit. It has been established that conclusions about the manipulative / non-manipulative character of a certain tactics in each particular case should be arrived at not judging by the analysis of this tactics structure but proceeding from the analysis of the speaker’s communicative intention. A communicative tactics is interpreted as a manipulative one if its speech actions contradict the ethical or communicative standards. It has been found out that manipulative strategy is the major one for flattery speech acts but it can also be used by the addressers of other positive evaluative speech acts.

In this paper, we determine the causes of correlations between the observed logarithmic lu- minosity logL of galaxies with active nuclei (AGN) with particular attention to BL Lac type objects. The properties of flux variations of these galaxies in γ-rays (logL γ ) and in optics (logL O ) are associated with the combined action of cosmic rays (CR), and also with hard radiation around the entire perimeter of AGN. The necessity of using positron spectroscopy in such objects is found. The importance of high-precision measurements of 1.022 MeV line arising from the anni- hilation of positrons with K-electrons of multielectron atoms in the interstellar medium of disk component of the studied galaxies is emphasized. The relation- ship between the single-photon positron annihilation and the Doppler line broadening of the same atoms in optics is investigated in AGN. We found that indi- rect evidence of the presence of a sufficient number of positrons and their annihilation are the cascade chan- nels observed in the form of ∆-resonance. According to the available data from the AGN’s catalogs the cal- ibration of their luminosity in other spectral regions is proposed.

The paper discusses the construction of characteristic curves for various astronegatives with a single exposure. Particular attention is paid to the question of extrapolation of the characteristic curve for the region of the weakest stars in the absence of standards. A new method for constructing an individual characteristic curve for digitized films and plates in the UBVR system has been proposed and implemented. The processing of frames of digitized plates and films with sky areas is car- ried out using LINUX/MIDAS/ROMAFOT software tools. ROMAFOT application allows us to extract astro- metric rectangular coordinates X,Y and photometric char- acteristics such as instrumental photometric magnitudes m, FWHM, and the intensity in the center of the star im- age I c for all fixed objects on each astronegative. For all frames, the connection between instrumental photometric values m with stellar magnitudes in any system (Johnson UBVR, Tycho-2 or GAIA catalogs, etc.) is not linear and multipurpose. It is presented as the characteristic curve for each astronegative. Currently, the determination of U, B, V, R magnitudes of stars and other space objects is in pro- gress for astronegatives with the single exposure obtained in the frameworks of selected observational projects.

A spacecraft in near-Earth orbit is exposed to extreme environmental factors, such as high vacuum, zero gravity, collisions with meteors and orbital debris, corpuscular and electromagnetic radiations, etc. These factors result in changing properties of spacecraft surfaces which leads to changes in mechanical, optical, electrical and physical properties of materials and elements of spacecrafts. This paper presents experimental data obtained from ground-based photometric observations of several geostationary satellites (GSS) built on different types of buses, starting from the beginning of their operational lives and during several years after their launches. It has been experimentally proved that spectral reflectance properties of the satellite surface materials undergo gradual degradation with time of the satellite’s stay in space. Noticeable changes in spectral reflectance properties of GSS make it possible to detect damages to the satellite external payload. Comparison of changes in the reflective characteristics of different platforms over time can show the level of technical and scientific progress of spacecraft designers

In this paper, we studied the incompre- hensible fading of a continuum of noise storms and type IV continual bursts in the decameter range, coinciding in time with coronal mass ejections (CMEs) for solar proton events (SPE). A comparative analysis showed that about 60% of the CMEs are accompanied by the fading of the continuum of noise storms and type IV continual bursts in the range of 25-30 MHz. It is shown that the fading of the continuum of a noise storm associated with a CME is distinguished by the intensity and duration of fading, as well as the width of the fading band and the frequency at which the maximum fading depth is observed. Moreover, detailed studies have shown that, against the background of a general decline in the radiation flux, a fine temporal structure at adjacent fre- quencies remains. This may indicate that the radiation is shielded by an external region in the path of radiation prop- agation. It can be a cold and dense cloud of the CME itself or absorption in the ionosphere. Absorption at low frequen- cies in the Earth's ionosphere is quite possible, since the x- ray and ultraviolet radiation of the flare can cause addi- tional short-term ionization. In this regard, studies have been conducted on the relationship of the fading of the con- tinuum of noise storms with x-ray flares. A comparative analysis showed that there is a fairly strong relationship be- tween the integral flux and the effective duration of x-ray flares with the integral flux and the effective duration of the decrease in the continuum of noise storms, respectively. Moreover, the relationship between the effective durations is slightly higher, where the correlation coefficient between the studied values is ≈ 0.71. It was also shown that short- term impulse fading is associated with impulse x-ray flares, and long-term with gradual long-term x-ray flares. It was noted above that absorption can also occur in the body of the CME itself, therefore, the relationship between the pa- rameters for lowering the continuum of noise storms at a given frequency and the speed of the CME was investi- gated. A comparative analysis showed that there is a fairly strong relationship between the maximum fading depth and the CME speed, where the correlation coefficient between the studied values is ≈ 0.65.

This work is a continuation of the work (Isaeva E., 2018) in which a new approximation of the in- tegral energy spectrum of solar cosmic ray (SCR) protons was presented in the range > 1-100 MeV. In this work, the comments and wishes of colleagues working in this field were taken into account. First, the comments were taken into account on the form of the functional for approximat- ing the energy spectrum of protons, which must correspond in form to the functionals predicted by particle acceleration theories. Secondly, the previously obtained functional should be checked for high-energy protons with energies >1000 MeV. For the analysis, we used original records of the intensity of the flux of SCR protons according to the data from GOES. The studied sample contains 349 solar proton events (SPE) for the period from 03-02-1986 to 12-02-2018 years, accompanied by protons with energies in the range > 1-850 MeV. Of 349 SPE, 53 were accompanied by high- energy protons with energies > 850 MeV. In this paper, we present the results of approximation of the integral energy spectrum of SCR protons with energies > 1-850 MeV using a functional containing power and ex- ponential functions. A comparative analysis showed that this functional gives a very good approximation for SCR protons with energies in the range > 1-850 MeV.

In the paper, the author has provided the hermeneutical analysis of the play “The Dresser” (1980) by English playwright Ronald Harwood. It has been investigated that in this literary work, the writing of which was finalized in postmodernism, there are philosophical features of postpostmodernism. The role of Shakespearean intertext in the play has been outlined. A number of provisions on the features of post-postmodernism in English literature of 1980s has been clarified, as well as features of connection between postmodernism and neo-fabulism as one of the directions of post-postmodern literature. In the aspect of the development of B. Shalahinov’s literary approaches regarding the specificity of the interaction of two metaforms of world culture – carnival and mystery – in the play “The Dresser” has been spotlighted. The representation of existentialistic features in the outlook of the main actor (Sir) in the play, as well as King Lear, played by Sir, has been revealed. It is emphasized the explication of Shakespearean masks system as intertextual manifestations in order to counter the absurd reality and lift above it. The features of the humanistic worldview in the outlook of the main actors of the play have been described.

The article deals with the investigation of dynamic peculiarities of oral prayer texts used in modern English film discourse. Prayer personages’ appeal to God manifests intertextuality of the film discourse, that is the use of the elements of the existing text in the process of the creation of a new one. Two ways of personages’ appeal to God – with a canonical prayer registered in the Book of Common Prayers and with a “spontaneous” prayer address – have been investigated in the present paper. Four compositional parts having different pragmatic aims typical of the prayer texts of both types have been singled out. To determine the degree of the dynamic component participation in the organization of the prayer oral text, a complex phonetic analysis was conducted, the purpose of which was to identify the general trend of the dynamic organization of the prayer texts within a film discourse under study. As a result of perceptive and electroacoustic analysis, the main dynamic characteristics of the investigated texts were revealed. Distinctive intonation characteristics of the canonical prayer and the “spontaneous” prayer within a film component of intonation as a leading parameter. Instrumentally, it is found out that the differences in maximum intensity of the investigated prayer texts are essential. The “spontaneous” prayer demonstrates much higher maximum intensity than the canonical prayer. Howeverthe canonical prayer texts as well are characterized by the increased maximum intensity in introductory and concluding parts. The average syllabic intensity of the phrases constituting supraphrasal unities shows both the differences in their rate and the mutual tendency in their variability in different parts of the prayer. Thus the experimental research proved the hypothesis about the leading role of the dynamic component of intonation in prayer texts within a film discourse differentiation.

The article deals with the history of Ukrainian translations of French women’s prose. The role of the journal of Foreign Literature “Vsesvit” is described. It has been established that the Soviet period had its particularities of translation of French female literature through the interaction of different contexts – historical, cultural and political, literary, which influenced the choice of translation methods and the degree of faithfulness to the author’s plan. The role of ideological factors, including censorship, attitude to feminism, literary canons and translation were also under consideration. Special emphasis is given to the publications in the journal “Vsesvit”. The paper also contains the discussion of major difficulties translators (Viktor Koptilov and Hryhoriy Filipchuk) experience in rendering Françoise Sagan (Un profil perdu) and Régine Deforges’s (Sous le Ciel de Novgorod) novels in the target language. The Ukrainian translation by V. Koptilov of the novel «Un Profil Perdu» by Francoise Sagan was analyzed. Certain shifts in translation towards minimization or hyperbolization of feminine and masculine characters’ features can be interpreted as a translator’s effort to increase the expression of the translated text. The results of the study showed that the publication in 1991 of the novel by R. Deforges “Sous le Ciel de Novgorod” translated by H. Filipchuk became the desire of Ukraine to go out of the colonial translation discourse of the USSR and dependence on the ideology and publishing policy of Moscow. This novel contains erotic scenes, which for the first time in the history of French-Ukrainian translation were reproduced into Ukrainian. R. Deforges’ “Sous le Ciel de Novgorod” was published in Ukrainian translation under the title “Anna Kyivska”. The analysis demonstrates that translators used lexical and stylistic resources of the Ukrainian language, thus applying the strategy of domestication.

The article focuses on rendering non-equivalent lexis in English language fiction and nonfiction texts. Research has been done on the basis of the following texts: Odessa Tales by Isaac Babel, Moonlight in Odessa by Janet Skeslien Charles, journals – The Odessa Review and The Awesome Odesa and Internet resources. The final objective of the work is to describe local Odesa realia and systematize the ways of their rendering. The objective determined the tasks of the research: to analyse different scholar definitions of the term “realia” and formulate own definition; to outline relevant for linguistics and translation studies classifications of realia and the ways of their rendering, to single out 400 examples (obtained by random selection) from the texts given; to determine the place of each realia in semantic classifications and the classification of rendering realia. Our study relies substantially on the application of linguistic descriptive methodology and devices. The research gives recommendations to the enhancement of the S. Vlahov and S. Florin’s classification as it ignores some reality phenomena. The paper singles out the most frequent kinds of Odesa realia-localisms and the ways of their rendering. The work discovers that realia concerned society and politics and loan translation, half-calque and mix translation as ways of rendering realia are the most frequently used in fiction as well as non-fiction texts. The research highlights the ways of rendering realia which occurred to be omitted in the S. Vlahov and S. Florin’s classification. The prospects of the research lie in elaborating a bilingual glossary of the Odesa realia to fulfil professional needs of translators, interpreters, guides, culture and history researchers.

This article deals with the development of the English language in South Africa which can be regarded as a historically extraterritorial language. The aim of the investigation is to consider the influence of the specific ethnic environment on the lexical system of South African English in the eco-linguistic perspective. A special focus is laid on indigenous onyms which are considered as a means of maintaining the nation’s identity in the modern globalized society. The analysis was carried out on the basis of the autobiography of Nelson Mandela “Long Walk to Freedom” (1995). The article begins with a brief outline of a historic background for the formation of the South African variant of the English language. Then the researcher singles out the indigenous onyms employed in the text of N. Mandela’s autobiography and classifies them into anthroponyms, nationality names, names of clans, royal houses, and toponyms, including a wide variety of geographical names. After that the chosen onyms are subjected to the analysis in the eco-linguistic perspective, exemplifying the thesis that SAA is not only an extraterritorial, but also a contact-induced variety of English. Methodologically, this paper is grounded on the theory of language ecology as a framework for the study of language as an open synergetic system actively interacting with its environment. The study shows that the English language is in tough competition with the rest of official and national languages of the Republic, which form the unique linguistic environment of English in South Africa.

This article examines the conditions for the implementation of the mixing strategy in Spanish and Italian business writing communications. An attempt is being made to determine whether mitigation is a strategy or tactic in business communication. In this regard, these two concepts borrowed from many sciences, including linguistic, from military terminology are considered. In this paper, the mitigation is considered as a communicative strategy involving the use of a number of tactical techniques for the implementation of which language means are involved. Communicative category of mitigation considered as an element of communicative consciousness, which regulates the communicative behavior of communication participants. The linguistic pragmatics category of categorical utterance and linguistic means of its softening that realize communicative mitigation are investigated. The communicative category of mitigation (from the Latin verb 'mitigare' - to mitigate) is associated with a decrease in the illocutionary force of influence on the addressee in special communicative situations, namely, in potentially conflicting situations that often arise in business communication. Strategy mitigation, as well as tactical techniques of its implementation, is also the subject of research in the sciences related to management. They are of considerable interest to politicians, journalists, etc. On the one hand, the mixing strategies are considered in connection with the categories of cooperation, courtesy, trust, tolerance, non-domination and equality, on the other, conflict and rivalry, domination and inequality. The article states that, being associated with courtesy and mitigation of categoricality, tying however not their synonym is. Mitigation is a strategy, a means of expressing courtesy and softening categorical manner of statement - just some of the number of tools, techniques and moves tactically used in this communicative strategy. The linguistic characteristics and pragmatic tools of communicative language interaction in the process of updating their communicative intentions are studied. The linguistic behavior of participants in business correspondence is structured through the implementation of a communicative strategy, which is defined as a complex of pragmatically oriented speech actions aimed at achieving a communicative goal with the use of language tactics that contribute to the implementation of this strategy. In the course of the study, we draw conclusions about the role of pragmalinguistic tools for realizing the communicative strategy of mitigation in achieving success in business communication and the perlocutive effect.

In this paper, we study fixed points of N-point gravitational lenses. We use complex form of lens mapping to study fixed points. Complex form has an advantage over coordinate one because we can describe N-point gravitational lens by system of two equation in coordinate form and we can describe it by one equation in complex form. We can easily transform the equation, which describe N-point gravitational lens, into polynomial equation that is convenient to use for our research. In our work, we present lens mapping as a linear combination of two mapping: complex analytical and identity mapping. Analytical mapping is specified by analytical function (deflection function). We studied necessary and sufficient conditions for the existence of deflection function and proved some theorems. Deflection function is analytical, rational, its zeroes are fixed points of lens mapping and their number is from 1 to N-1, poles of deflection function are coordinates of point masses, all poles are simple, the residues at the poles are equal to the value of point masses. We used Gauss-Lucas theorem and proved that all fixed points of lens mapping are in the convex polygon. Vertices of the polygon consist of point masses. We proved theorem that can be used to find all fixed point of lens mapping. On the basis of the above, we conclude that one-point gravitational lens has no fixed points, 2-point lens has only 1 fixed point, 3-point lens has 1 or 2 fixed points. Also we present expres- sions to calculate fixed points in 2-point and 3-point gravitational lenses. We present some examples of parametrization of point masses and distribution of fixed points for this parametrization.

The comparison results of three catalogues (FON-KIEV, FON-KITAB and FON-DUSHANBE) were received as result of work of the FON project and presented in the paper. The data of zero zone (from -2 to 2 degrees of declination) from the mentioned catalogues was used during the research. The number of common objects after cross-match of catalogues with a circular search window equals to 1.5 arc seconds was more than 500 thousands. The estimation of random accuracy of stars positions from the mentioned catalogues was performed by the Wielen method. Final dispersions were calculated for every sub-range of magnitudes. The stars with individual differences of position and magnitude that exceed three standard deviations were rejected. The data from catalogues РМА was used for estimation of the systematic errors. It is obvious that the internal estimates of position accuracy of stars in the compared catalogues are low in one or all catalogues, and additional research is required. Analysis of the behavior of the systematic differences and standard deviations of the stellar positions of these catalogues have shown that there are a big values reaching 1 arcsec only in small sky regions. However, the internal accuracy that presented in catalogues is well matched with the systematic differences and standard deviations in the other sky regions. Astrometry, astrometry-catalogue, data analysis.

Since the launch of Sputnik 1, the number of objects in near-earth orbit has been constantly increasing. The growth of number of these objects increases the risk of their collisions with existing satellites and ones which will be launched, that can be accompanied by their failure or even destruction. Most space agencies and many countries have their own space surveillance networks. These networks continually measure the positions of known objects, find new ones and predict their future positions. It is necessary to know the position of the objects with an accuracy of up to the characteristic size of the operating satellites (about 10 cm or more) to prevent collisions. Today, this task can be solved only for a small number of reference satellites and only for the past. The calculation of the objects positions in near-Earth space requires the implementation of complex models of the Earth motion and a space object using many factors affecting the final result. Some of these factors, for example, the atmospheric density and the attitude of the satellite in the space, are not well predicted by modern models and require constant refinement from observations. Ukrainian Optical Facilities for Near-Earth Space Surveillance Network (UMOS) is used to surveillance and study near-Earth space in Ukraine. There are many practical tasks that require knowledge of the positions of the space objects. The different software solutions are being applied to solve them. All of them must implement motion models of near-Earth space objects, the Earth and the main bodies of the Solar System for their needs. Space dynamics libraries are developed to implement these models. Orekit is one of these libraries. The Kotlin Orbit Estimation Library (KOrbEstLib) is built on the features of Orekit and extends them. KOrbEstLib expands the set of input and output data types, implementing the support of a number of Ukrainian and international data formats, in particular, the formats used in the UMOS network. In addition, KOrbEstLib offers an alternative implementation for estimating the parameters of the motion model of space objects in comparison with Orekit. This paper discusses a number of implementation features of the KOrbEstLib.

The CoLiTec software is a large complex of processing modules that implements computational methods for the different purposes: brightness equalization of CCD-frames; automated calibration of the frames by bias-frame, dark-frame, and flat-field for reducing the dynamic range of brightness of the image background; frames track & stack; automated rejection of the anomaly pixels; automated excluding of the objects with anomaly errors; determining the equatorial coordinates of the Solar System small bodies; accurate parameter’s estimation of objects in frames; star’s identification in the frames; astronegative plate’s processing; ensemble differential photometry using comparison stars; determining the instrumental brightness of stars in CCD-frames; automated light curve creation; detection of very slow and very fast objects in series of CCD-frames; detection of objects with a near-zero apparent motion in series of CCD-frames. The described methods work with the different forms of object images (point, long) and during the different observational conditions (with daily telescope guidance and without it). These methods lead to the increasing of astrometry and photometry accuracy indicators as well as the quality indicators for detection of the Solar System small bodies in series of CCD-frames. The CoLiTec software is installed at several observatories of the world. In total, it was used for about 700 000 observations and discovery of more than 1560 asteroids, including five NEO, four comets (C/2011 X1 (Elenin), P/2011 NO1 (Elenin), C/2012 S1 (ISON), and P/2013 V3 (Nevski)), 21 Trojan asteroids of Jupiter, and one Centaur. The paper deals with the CoLiTec software 1) to process the different types of astroinformation, which can be fed on-line in different forms, for example, files stream and video stream, astroplates; 2) to decide the data saving problem at various servers and virtual observatories sites; 3) to improve computational methods and algorithms for automated detection of Solar System small objects; 4) to improve the accuracy of astrometry/photometry reduction.

This paper discusses the existence of groups of meteorite-producing fireballs and ordinary chondrites in the Earth-crossing Jupiter-family comet-like (JFC) orbits. The similarity of the orbits of meteorite-producing fireballs and those of meteorites in the groups was established by applying three criteria of orbital similarity – namely, the DSH criterion introduced by Southworth and Hawkins, the DDR criterion suggested by Drummond, and DN criterion reported by Jopek. We have detected six groups of meteorite-producing meteoroids and ordinary chondrites of L3.5-H5 types observed over the determined periods of increased fireball activity. Carrying out systematic and well-targeted observations, especially during the determined periods of increased fireball activity, enables to obtain reliable statistics from the collected observational data on the meteorite-producing meteoroids in order to determine their orbits, as well as their physical characteristics. The six target groups in this study, which contain 89 meteorite-producing meteoroids and six ordinary chondrites, may be groups of dynamically connected bodies. The genetic relationship between the investigated bodies within groups needs to be considered on the basis of the analysis of orbital evolution of the members of each group over the past several thousand years. The data on the mean heliocentric orbit of the group of meteorite-producing meteoroids enable us to link the group with its likely source, which may be either an asteroid, a family of asteroids or a comet, thereby making it possible to obtain information about the source itself. The search for potential parent bodies of the investigated groups of meteorite-producing fireballs and meteorites was carried out among new near-Earth asteroids. Consequently, several asteroids were selected in each group with the following criteria of the similarity between the asteroid orbit and mean orbit of the respective group: DD ≤ 0.06, DSH and DN ≤ 0.12.

Currently, in the field of computer processing, there are difficulties. When processing astrophysical experimental data, the difficulties are connected, on the one hand, with a large amount of information that requires processing, and, on the other hand, with the technical capabilities of computers. The use of analytical methods can significantly reduce information processing time. The information that is entered is recorded in an analytical form, more convenient for processing. Information is processed analytically (Kotvytskiy & Bronza, 2016), and not by methods of the Ray Tracing type. Some results were obtained strictly analytically, and they do not need further computer processing (Kotvytskiy et al., 2016). The goal of this paper is to analyze images in N-point gravitational lenses by: - reduction of research of an arbitrary source to the study of a circular source; - reduction of research of a circular source in an N-point gravitational line to its study in the Schwarzschild lens and other few-point lenses; - analytical study of a circular source in the Schwarzschild lens and other few-point gravity lenses; - research of the place of the Schwarzschild lens, in the set of N - point gravitational lenses. Using the methods of algebraic geometry, algebraic topology and the theory of functions, we have prepared a problem for computer modeling: finding images of arbitrary sources in an N-point gravitational lens. We researched the images of a circular source in the Schwarzschild lens and proved that the study of images of any other sources is combinatorial reduced to this case.

In this paper, we consider a new approximation of the integrated energy spectrum of protons of solar cosmic rays (SCR) in the range Ep> 1-100 MeV. The sample studied contains 342 proton events for the period from 03-02-1986 to 23-07-2016. This sample is complete, since it contains very weak and superimposed proton events. The superimposed events were separated and identified according to the criteria of protonity. Out of 342 proton events, 164 events were identified and processed by the author independently. For the analysis, original records of the intensity of the proton flux with energy Ep> 1-100 MeV from the spacecraft GOES series were used. As the parameter characterizing the intensity of the proton flux, the maximum intensity of the proton flux Ip in each energy channel during the proton event was chosen. The intensity of the proton flux Ip was calculated from the preflare level. In the case of superposition of proton events, the intensity of the proton flux Ip was calculated from the level of the preceding event. Also, when processing original records of proton events, emissions associated with technical interference and with the of interplanetary shock waves were eliminated. Comparative analysis showed that all events can be conditionally divided into 5 types according to the form of the energy spectrum of protons. It is known that for most proton events, the energy spectrum of SCR protons is described quite accurately by two power-law models. However, there remains a large number of events for which the energy spectrum of protons can not be approximated accurately by two power-law models. In connection with this, another dependence was used in this work, which allows us to approximate the energy spectrum of the protons for all events quite accurately.