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Studying the process of the modern human formation at the Eurasian ecumene has always been relevant during all periods of the Stone Age history research. The article contains results of recent studies of a Mid Palaeolithic complex of Darvagchai-Zaliv-1 site, materials of which are crucial for understanding the development of this vast cultural-chronological range for the northeast Caucasus. In 2012-2014, Darvagchai-Zaliv-1 site excavations were carried out in the upper terraced ledge slope, where the monument is situated. Lithological paleosol studies including archaeological materials allowed us to include this complex in the general regional paleogeographic picture. The chronological period of the ancient man living in the region is determined by the Riss-Wurm interglacial oxygen-isotope stage 5e. The stone industry is characterized with Levalloi technology of knapping and tools typical of Mid Palaeolith. The presence of focal spots accompanied with the archaeological material dispersion over wide area indicate multiple visits by ancient man to the third Caspian terrace. Based on the available data, the authors conclude that, despite a significant number of well-known mid-Palaeolithic sites in the Caucasus and a large technical and typological diversity within their groups, direct analogies among them with the Middle Palaeolithic materials of the Gedzhukh reservoir valley are currently not possible to trace. This may be due to incomplete representation of Dagestan industries, as well as to cultural diversity that existed at that time in the region, which does not exclude the possibility of the original Mid Palaeolithic culture’s presence in this territory.

Cave sites provide the most comprehensive insights into Paleolithic culture and environmental contexts of early human occupation. Archaeological caves are often recognized as stratified sites. A section structure in cave sediments as well as distribution of associated archaeological evidence depend on many different factors. The results of research carried out at stratified Paleolithic sites in the Altai Mountains, a key region for studying prehistory of North Eurasia, can be considered a prominent example of an integrated approach to investigate culture-bearing cave deposits. The most important findings have been obtained from examination of Paleolithic sites located in the Northwest Altai. Amongst them Denisova Cave is the most intensively studied archaeological locality. The investigation of loose sediments at the site involved a wide range of modern research techniques developed for archaeology, stratigraphy, lithology, paleontology, geochronology and other related disciplines. Thanks to such complex approach, a long sequence of sediments from Denisova Cave, containing cultural evidence spanning from the Middle Paleolithic to the Late Middle Ages, has now become a key section to study prehistory of the region. The cave deposits discussed in this paper represent a complex multi-component geological body, which contains evidence for human occupation. Each studied site in the cave reveals its own characteristic lithologic and stratigraphic sequence formed depending on the morphology of isolated cavities and their location in the karst system. Many sedimentation features change considerably starting from the cave entrance up to its far reaches. The chronological sequence of deposits in the cave sections has been made based on a dataset resulted from lithological and biostratigraphic studies, as well as absolute dating and paleomagnetic analysis of the Pleistocene deposits. The integrated research of stone tool industries, supported by geochronological evidence, has made it possible to correlate archaeological data recorded in different parts of the cave and to develop a cultural and chronological pattern showing changes that occurred in the Paleolithic assemblages of Denisova Cave.

About 40 major volcanic eruptions have occurred on the Kamchatka Peninsula over the last 10,000 14C years, which led to ecological changes throughout the peninsula. In turn, restructuring the environment has changed lives of human beings who lived through these events. A tephrochronological technique restores the history of volcanic deposits, which makes it possible to use it to specify the stratigraphy and chronology of archaeological sites; assume the reaction of inhabitants to volcanic activity in the region involving archaeological, ethnographic data. Based on the research of the multilayer Ushki V site , it was established that the territory of the modern Big Ushki Lake and surrounding areas were in the center of ash falls of the biggest catastrophic volcanic eruptions situated 30 to 630 km away from the place. For example, the population of a culture layer V (Initial Neolithic, 14C 7,705±38 BP (KIA-35,662) has been affected by a catastrophic eruption of the volcano Hangar (6,900 BP). The key episodes of volcanic activity were earthquakes, fires, devastating tsunamis, spreading eruptive clouds (ash falls) products, changes of relief, destruction and redistribution of biota, forming uninhabitable soil, etc. The population reacted to these phenomena by reducing sites and settlements, moving them to river banks, lake and sea coasts; this led to desolation of inhabited places during the period of 1,000 to 2,000 years. According to ethnographic data, volcanic eruptions and their consequences were reflected in omens, prognostications, faiths, and in granting anthropomorphic qualities to volcanoes. The fear and doom in the face of the forces of nature were in the basis of them all. In the future, interpretation of the data obtained based on the tephrochronological method allows reconstructing the environment in time, to identify patterns of changes of human living conditions in certain periods. The author does not exclude, that the stages of settling Kamchatka, changes in technologies, and, possibly, in population were related to catastrophic eruptions.

The work objective is to determine the similarity of the Gumsanni burial mound findings in the southern Korean Peninsula with Kofun materials from the mounds of Japan. The cultural contacts between the population of the Japanese islands and mainland, including the Korean Peninsula, is an actual topic in the modern science. The authors discuss the directions of contact, the time of their occurrence, nature of borrowing elements of socio-economic, political and cultural life, a degree of population mutual influence in these territories. The presence of clay sculpture fragments in the Geumsan-ni mound in the southwestern Korean Peninsula aroused interest from both Korean and Russian archaeologists due to its uniqueness. Producing clay sculpture was not typical of Korea in the V-VI centuries. Attempts to interpret the findings led to the Kofun materials in Japan. A comparative analysis of the burial mound’s upper part (the inner part excavation has not started yet), the funeral goods found in the mound, allows authors to find features similar to the characteristics of the Kofun period in Japan. Typologically the Geumsan-ni mound has similarities with Japan mounds in the embankment form and structure. The fragments of the sculpture have analogies among Haniwa clay sculpture in Japan. Korean findings are head fragments of two anthropomorphic figures, fragments of the horse head and legs, part of a bird head and body, presumably a chicken. Japanese Haniwa represent images of people, animals, houses, boats, household items, which were installed in a certain order around the mound perimeter, along tiers and on its top. The discovery of similar clay figures in the Korean mound leads to conclusions about the existence of cultural contacts between the two territories, borrowing of traditions, and even kinship ties between influential clans.

The article studies a finding of the Kyrgyz iron battle-axe “ai-balta” from the archaeological collection of the traditional Kyrgyz culture in Tian Shan kept in the private museum “Rarity”, that belongs to V. V. Kadyrov - a famous businessman and philanthropist in Kyrgyzstan. The museum is situated in Bishkek in the Republic of Kyrgyzstan. The paper considers main events related to the history of studying battle-axes used to arm warriors of ancient and medieval nomadic peoples and states of Central Asian historical and cultural region. The author suggests the definition of typological, chronological and cultural identity of the Kyrgyz battle-axe finding; substantiates belonging of the analyzed finding to battle-axe tools for close combat of Kyrgyz warriors in Tian Shan, that relate to historical periods of the late Middle Ages and Modern era. The battle-axes “ai-balta” had a prominent element as a part of close combat armament complex available to Kyrgyz warriors in the territory of Tian Shan and adjacent regions during the mentioned period. Such battle-axes had wide rounded blades with curved tips after which they were named. They were fixed on the long wooden handles. Kyrgyz warriors attacked their adversaries using battle-axes in a close combat. Applying battle-axes by the Kyrgyz warriors to deliver striking blows to their opponents is reflected in the Kyrgyz epos. Similar combat clashes using battle axes of Kyrgyz are described in the Kyrgyz heroic epic “Manas”. The studied battle-axe from the museum «Rarity» is an important source of weapons history of the Kyrgyz warriors of the late Middle Ages and Modern era. The Kyrgyz warriors used such weapon while attacking their opponents on horseback. The battle axes “ai-balta” were used by the Kyrgyz warriors in the Tien Shan and Semirechie up to the chronological period of ethnographic modernity.

Apart from the main versions of the origin of the Chuvash people, there are quite curious ones. The article deals with two versions: Syanbi and Yuhuani. As is well known, those tribes lived and migrated in South Siberia. Syanbi which were ancient Mongolian nomads originally lived in the north-eastern part of Internal Mongolia. They separated from the Donghu tribal confederation as early as before Christ. It is common knowledge that originally Syan-bi is not an ethnographic name, but a geographic one. Peoples of the Syanbi race named themselves by the names of those mountains and valleys where they lived. In this particular case, the mountain Syan-bi-shan is meant, now it is called Great Khingan Mountain. It is believed that Syanbi, Uhuani and Donghu were ancient Mongolian tribes. The relation of the ethnonym syanbi with sebir is just one of a number of working hypotheses of the Chuvash origin which is far from being irreproachable. Anyway, in the 4th century, the Syanbi were still the northern neighbours of China, and by the 6th century they dispersed among the tribes of the southern part of West Siberia and China. The historical ancestors of the Chuvash (Savars/Savirs) were fixed in the Caucasus no later than the 2nd century A.D. Even if we leave aside all other aspects of ethnogenesis, identification of Savirs/Suvars with Syanbi in the spatiotemporal terms is untenable. This assumption only relies upon the remote and doubtful consonance of the ethnonyms. Uhuani belong to the Montolian anthropological family and trace their origin to the Donghu tribes. They are known in history by their relations with Syanbi and North Chinese tribes. The attempt to identify the Uhuani with East European Ogur tribes is untenable. Orientalist scholars tend to believe that Uhuani are ancestors of Avars. Such being the case, the attempt to speak of Uhuani as historical ancestors of the Chuvash is absolutely hopeless. Using an integrated historical and anthropological analysis the author comes to conclusion that none of the two versions (Syanbi and Uhuani ones) have any relevance to the history of the Chuvash people’s origin.

The choice of a place for religious buildings is a multifaceted problem, the solution of which takes a symbolic aspect. It is established that there were regularities in placing iconic religious buildings as Orthodox churches in the Tobolsk diocese based on materials of the late XIX - early XX centuries using a case-study techniques and architectural analysis. A chapel was built in small villages, a church, or a church and a chapel- in big villages. Their place was chosen in the settlement center or its outskirts facing the natural landscape. When located at the crossroads, the churches did not close the perspective, but were slightly out of the way allowing to view the natural environment. In some cases, there was a cemetery near the church. A church and a clergy’s houses near it often formed a building complex, administrative and educational buildings occupied places away from it, but on the same street, central one as a rule. It is impossible to determine the ratio of the height of churches and other buildings, because horizontals were not indicated on plans, however, the location of the church is noted mainly on high river banks. All temple buildings were within walking distance from any part of the settlement (up to 1.5 km or 20 min walk), which was important for the possibilities of worship. Every plan preserved churches’ location, although the existing structure of residential buildings could be broken in favor of a two-way street type. Moreover, the importance of the temple was enhanced by architectural means: newly planned streets led to it, church buildings rose above the one-story buildings fixing a planning structure of a settlement by placing them at the end or crossroads of streets, solid stone buildings stood out among the predominantly wooden buildings.

An adaptive analog of the Nesterov method for variational inequalities with a strongly monotone operator is proposed. The main idea of the method proposed is the adaptive choice of constants in maximized concave functional at each iteration. In this case there is no need in specifying an exact value of this constant, because the method proposed makes possible to find a suitable constant at each iteration. Some estimates for the parameters determining the quality of the solution of the variational inequality depending on the number of iterations have been obtained.

In this article, a weighted finite difference scheme is proposed for solving a class of parameterized singularly perturbed problems (SPPs). Depending upon the choice of the weight parameter, the scheme is automatically transformed from the backward Euler scheme to a monotone hybrid scheme. Three kinds of nonuniform grids are considered: a standard Shishkin mesh, a Bakhavalov-Shishkin mesh, and an adaptive grid. The methods are shown to be uniformly convergent with respect to the perturbation parameter for all three types of meshes. The rate of convergence is of first order for the backward Euler scheme and of second order for the monotone hybrid scheme. Furthermore, the proposed method is extended to a parameterized problem with mixed type boundary conditions and is shown to be uniformly convergent. Numerical experiments are carried out to show the efficiency of the proposed schemes, which indicate that the estimates are optimal.

For the mathematical model of the sea thermodynamics, developed in the Institute of Numerical Mathematics of the Russian Academy of Sciences, the problem of variational assimilation of the sea surface temperature data is considered, with allowance for the observation data error covariance matrices. Based on the variational assimilation of satellite observation data, the inverse problem of restoring a heat flux on the sea surface is solved. The sensitivity of functionals with respect to observation data in a problem of variational assimilation is studied, and the results of numerical experiments for the model of the Baltic Sea dynamics are presented.