Riesz potentials are convolution operators with fractional powers of some distance (Euclidean, Lorentz or other) to a point. From application point of view, such potentials are tools for solving differential equations of mathematical physics and inverse problems. For example, Marsel Riesz used these operators for writing the solution to the Cauchy problem for the wave equation and theory of the Radon transform is based on Riesz potentials. In this article, we use the Riesz potentials constructed with the help of generalized convolution for solution to the wave equations with Bessel operators. First, we describe general method of Riesz potentials, give basic definitions, introduce solvable equations and write suitable potentials (Riesz hyperbolic B-potentials). Then, we show that these potentials are absolutely convergent integrals for some functions and for some values of the parameter representing fractional powers of the Lorentz distance. Next we show the connection of the Riesz hyperbolic B-potentials with d’Alembert operators in which the Bessel operators are used in place of the second derivatives. Next we continue analytically considered potentials to the required parameter values that includes zero and show that when value of the parameter is zero these operators are identity operators. Finally, we solve singular initial value hyperbolic problems and give examples.

In this article the technique of classification of the Early Holocene microblade industries on sites with mixed cultural layers of Central Yakutia (Tuymaada valley) is discussed. This technique is based on classification in the complexes on stone artifacts of microliths, as a characteristic for the Sumnagin culture. Materials from sites are associated with the Mesolithic on the basis of the technical-typological and statistical analysis of materials from precisely stratified sites of the Sumnagin Culture of the Aldan and Olekma river basins. The stone inventory of the Sumnagin culture is based on the maximal use of blades from which practically all stone tool industrial products were produced, except for large cutting instruments. The presence of microblade tools in the common statistics of tool types is supported by a big amount of blades and the tools made of them. Prevailing amount of blades in relation to the flake tools, absence of ceramics or its small amount, in some cases, also testifies in favour of early dating. On the basis of analysis, the Sumnagin cultural complex on 11 sites of Tuymaada Valley is established: Kapitonovka, Kil'dyamtsy III, Severo-Zapadnaya II, Fermennoe Ozero, Syrdakh VI, Zernovaya II, Us'-Khatyng I, V, Vladimirovka IV, and Horo I, III. On about 25 sites where the microblades industries are excavated, at expansion of works the assumption of presence the Mesolithic stone assemblage in cultural layers can prove to be true.
Работа посвящена проблеме изучения мезолита в Центральной Якутии. Здесь было известно небольшое количество стоянок сумнагинской культуры, характеризующихся смешанными культурными комплексами, и датированных этим временем лишь по аналогиям инвентаря. В работе предложена методика определения раннеголоценовых комплексов в смешанных культурных слоях, основанная на выделении в общих комплексах каменного инвентаря микролитов, в большей степени характерных для сумнагинской культуры. Проведённый анализ позволил выделить сумнагинский культурный комплекс на 11 памятниках Туймаады. На ещё около 25 памятниках, где обнаружены микропластинчатые индустрии, при расширении работ, может подтвердиться предположение о наличии в культурных слоях мезолитического каменного инвентаря

The Dst-index obtained by hourly average values of the magnetic field at four stations located in various longitudinal sectors at latitudes Φ′≈20-30° is the index of magnetic field depression at low latitudes during the magnetic storm periods. Recently for the characteristics of magnetic field depression the SYM-H index has been used. It is obtained from 1 min data of the magnetic field at ~10 stations, located mainly at latitudes Φ′≈40-50° [1]. It is considered in [2-4] that the SYM-H index is an analog of Dst but with a better temporal resolution. As shown in [5], during super magnetic storms with Dst variation ≥ 400 nT, the SYM-H variations can considerably differ from Dst behavior and thus the SYM-H index is not always an analog of Dst. In this paper the relation between the Dst and SYM-H variations for magnetic storms of different intensity, with Dst varying from ~ -50 nT to -450 nT is investigated.

В статье обосновывается необходимость комплексного подхода к изучению литературного и научного творчества П.А. Ойунского как определенной творческой целостности. Отношение к устной традиции, по-разному и в различных контекстах акцентируемое в творчестве П.А. Ойунского, между тем как нельзя лучше выявляет его цельность как личности в этом вопросе. По текстам II.A. Ойунского. как литературным, так и научным, предпринята попытка последовательной реконструкции того, как формировалось творческое преломление им устной культуры народа. Скрытая логика повествовательных возможностей в его текстах позволяет сделать предположение о том. что в этом вопросе П.А. Ойунский пошел дальше своего предшественника - поэта А.Е. Кулаковского. Новизна творческого переосмысления П.А. Ойунским устной традиции народа нашла выражение в прецеденте создания инвариантного текста олонхо о Нюргун Боотуре, в воссоздании в стихотворной (ҺКрасный Шаманһ) и прозаической (ҺВеликий Кудангсаһ) формах мифологической основы этой традиции. Общая тенденция освоения фольклорного материала обусловлена включенностью этого процесса в творческую биографию П.А. Ойунского на всех этапах ее формирования, эволюцией автора в последовательном движении от стилистической организации поэтического языка фольклора к мифу, к воссозданию в литературном тексте его нарративной структуры и мифологической семантики.
The article substantiates the need for an integrated approach to the study of the literary and scientific creativity of P. Oyunsky as a certain creative integrity. The attitude of the oral traditions, in different ways and in different contexts focused in the work of P.A. Oyunsky, meanwhile, could not be better reveals his integrity as individuals in this matter. According to the texts of Oyunsky, both literary and scientific, an attempt was made to consistently reconstruct how the creative refraction of the oral culture of the people was formed. Hidden logic of narrative possibilities in texts Oyunsky allows us to make an assumption that in this matter he went further than his predecessor, the poet A.E. Kulakovsky. Novelty creative interpretation of P.A. Oyunsky oral traditions of the people found expression in the precedent of creating invariato text Olonkho about Nurgun Bootur. recreating in verse (“Red Shaman") and prose (“the Great Kudangsa”) forms the mythological basis of this tradition. The General trend of development of folklore material is due to the inclusion of this process in the creative biography of P. Oyunsky at all stages of its formation, the evolution of the author in a consistent movement from the stylistic organization of the poetic language of folklore to the myth, to the reconstruction in the literary text of its narrative structure and mythological semantics.