Multiplicity free Jacquet modules

Let F be a non-Archimedean local field or a finite field. Let n be a natural number and k be 1 or 2. Consider G:=GL(n+k,F) and let M:=GL(n,F) x GL(k,F)<G be a maximal Levi subgroup. Let U< G be the corresponding unipotent subgroup and let P=MU be the corresponding parabolic subgroup. Let J denote the Jacquet functor from representations of G to representations of M (i.e. the functor of coinvariants w.r.t. U). In this paper we prove that J is a multiplicity free functor, i.e. dim Hom(J(\pi),\rho)<= 1, for any irreducible representations \pi of G and \rho of M. To do that we adapt the classical method of Gelfand and Kazhdan that proves "multiplicity free" property of certain representations to prove "multiplicity free" property of certain functors. At the end we discuss whether other Jacquet functors are multiplicity free.Comment: 12 pages; Canadian Mathematical Bulletin, Published electronically on June 29, 201

Structure and peculiarities of the (8 x n)-type Si(001) surface prepared in a molecular-beam epitaxy chamber: a scanning tunneling microscopy study

A clean Si(001) surface thermally purified in an ultrahigh vacuum molecular-beam epitaxy chamber has been investigated by means of scanning tunneling microscopy. The morphological peculiarities of the Si(001) surface have been explored in detail. The classification of the surface structure elements has been carried out, the dimensions of the elements have been measured, and the relative heights of the surface relief have been determined. A reconstruction of the Si(001) surface prepared in the molecular-beam epitaxy chamber has been found to be (8 x n). A model of the Si(001)-(8 x n) surface structure is proposed.Comment: 4 pages, 8 figures. Complete versio

Electromagnetic characteristics of biosilica from rice husk

Rice husk, being a widely available natural plant renewable agricultural resource, can be transformed into effective reinforcing fillers of special concrete and gypsum building materials. The samples of silica from rice husks were synthesized by thermal oxidative pyrolysis and their electromagnetic and microstructural characteristics were investigated. It was found that the rice husk itself is practically EM-wave transparent material in the frequency range of 0.1-7 GHz, while the products of its thermal oxidative pyrolysis have different microwave absorbing properties, depending on the amount of oxidizing agent used. The X-ray powder diffraction data showed the predominant presence of amorphous silica in the samples of rice husk ash with a small amount of α-quartz, α-cristobalite and α-tridymite. At a pyrolysis reaction temperature of rice husk of about 560 ± 20°C, the resulting product, in addition to amorphous silica and crystalline phases of silicon dioxide, contains traces of graphite particles, which leads to a sharp increase in dielectric characteristics and effective microwave absorption. When the temperature of the pyrolysis reaction of rice husk rises above 700°C the EM-wave absorption of such materials decreases. Thus, on the basis of the experiments carried out, the optimal ratios of rice husk and the used oxidizer of ammonium nitrate were revealed to obtain environmentally friendly ecological low-cost powder nanostructured biosilica additives for concrete and gypsum building compositions with increased effective radio absorption in the frequency range of the electromagnetic field above 1 GHz

Strategy of protection against hazardous channel and hydrological processes in rivers of developed territories and territories with focal development

In 2012-2015, the Makkaveev Research Laboratory of Soil Erosion and Fluvial Processes of MSU, Department of Geography, carried out a research, including analysis of hydrological and channel regimes of the Tom river in the Kuznetsk basin (Kuzbass) and the Katun river up to Uimonsky (the Altai), intra-mountain drainage basins, the survey of floodplains and eroded banks, and modelling of floods occurring in floodplains. As a result, a concept has been developed to improve protection measures against hazardous hydrological and channel processes. More than 200 engineering and organisational events were suggested as part of the concept. Given the dense network of river banks and the high potential damage caused by floods in Kuzbass, the continuous protection of cities, large residential and commercial areas, as well as sections of roads and railways subject to erosion is a priority in the flood control concept. In the case of the Katun river basin, characterized by local development, low population density, and relatively small damage caused by floods, the emphasis is put on organisational measures: prevention, evacuation of people and property, insurance and compensation. Selective engineering structures should, as a matter of priority, reduce the dangerous erosion of river banks and ensure a high level of protection of the territory against floods

Методика оптимального размещения компенсирующих устройств в сети электроэнергетической системы

The paper reveals an opportunity to apply a method of nonlinear mathematical programming in order to solve the formulated problem. A simplified evaluation problem statement is given in the paper and principles of its realization are determined in view of regime and technological limitations.Показана возможность использования метода нелинейного математического программирования для решения поставленной задачи. Дана упрощенная оценочная постановка задачи и определены принципы ее реализации с учетом режимных и технологических ограничений

Atomic composition, microstructure, and electromagnetic properties of schungite micropowder

The goal of the work was to study the microstructural, elemental, and electromagnetic properties of the samples of micropowder made from a natural mineral schungite. It was found that according to an X-ray spectral microanalysis, the carbon content in the studied samples of the mineral schungite was from 44 to 54 wt% while the iron content did not exceed 3.9 wt%. The iron content increased up to 6.1 wt% in the produced schungite micropowder. It can be presumed that in the schungite, micropowder iron exists in the form of ferrimagnetic nanoparticles of magnetite and pyrite, which is formed when grinding schungite particles in ball mills with a steel body and a milling bowl. The produced schungite micropowder also showed the presence of weak ferrimagnetic properties according to the measurements of magnetic permeability performed by vector analysis of the impedance of electrical circuits. In accordance with its electromagnetic characteristics, schungite micropowder made from shungite mineral is an effective radio-absorbing filler for building materials for cellular communication frequency band

STM and RHEED study of the Si(001)-c(8x8) surface

The Si(001) surface deoxidized by short annealing at T~925C in the ultrahigh vacuum molecular beam epitaxy chamber has been in situ investigated by high resolution scanning tunnelling microscopy (STM) and reflected high energy electron diffraction (RHEED). RHEED patterns corresponding to (2x1) and (4x4) structures were observed during sample treatment. The (4x4) reconstruction arose at T<600C after annealing. The reconstruction was observed to be reversible: the (4x4) structure turned into the (2x1) one at T>600C, the (4x4) structure appeared again at recurring cooling. The c(8x8) reconstruction was revealed by STM at room temperature on the same samples. A fraction of the surface area covered by the c(8x8) structure decreased as the sample cooling rate was reduced. The (2x1) structure was observed on the surface free of the c(8x8) one. The c(8x8) structure has been evidenced to manifest itself as the (4x4) one in the RHEED patterns. A model of the c(8x8) structure formation has been built on the basis of the STM data. Origin of the high-order structure on the Si(001) surface and its connection with the epinucleation phenomenon are discussed.Comment: 26 pages, 12 figure

Investigations of perspective materials for aggressively scaled gate stacks and contact structures of MOS devices

The thesis discusses a fundamental question of reconstruction on the Si(100) surface as well as three material combinations, which are important for perspective microelectronics technologies: Si/Pr2O3/Si(100), W/WNx/poly-Si/SiO2/Si(100), and CoSix/Si(100). A refined mixed ad-dimer model is developed for the Si(100)-c(4´4) reconstruction on the basis of scanning tunnelling microscopy investigations. A thermal stability of Pr2O3/Si(100) and Si/Pr2O3/Si(100) structures is studied with ion sputtering assisted Auger electron spectroscopy. The latter technique is also applied for precise determination of O and N content in the new W/WNx/poly-Si/SiO2/Si(100) structure, and to study the preferential sputtering of Si in CoSi2, CoSi, and Co2Si phases on Si(100) surface. The WSix/poly-Si/SiO2/Si(100) system, which was previously used in microelectronics, is studied for comparison. The preferential sputtering of Si in WSix is shown to be qualitatively similar as in the CoSix case.Die Arbeit beschäftigt sich mit einer grundlegenden Frage der Rekonstruktion auf der Si(100) Oberfläche sowie mit drei Materialkombinationen deren Bedeutung für perspektivische Mikroelektronik-Technologien sind: Si/Pr2O3/Si(100), W/WNx/poly-Si/SiO2/Si(100), und CoSix/Si(100). Ein verbessertes gemischtes "ad-dimer" Modell war für die Si(100)-c(4´4) Rekonstruktion auf dem Grund der neuesten Raster Tunnel Mikroskopie Untersuchungen entworfen worden. Die thermische Stabilität der Pr2O3/Si(100) und Si/Pr2O3/Si(100) Systeme war mit der Hilfe von Auger Elektronen Spektroskopie und Ionen Bestrahlung untersucht worden. Diese Methode ist auch für die genaue Messung von O und N Inhalt in W/WNx/poly-Si/SiO2/Si(100) Strukturen verwendet, sowie um das selektive Sputtern von Si in CoSi2/Si(100), CoSi/Si(100), Co2Si/Si(100), und WSix/poly-Si/SiO2/Si(100) Systemen festzustellen. Es wurde gezeigt, daß das selektive Sputtern von Si in den obengenannten Systemen qualitativ ähnlich läuft

Methodology for Optimimum Location of Compensating Devices in Network of Electrical Power Engineering System

The paper reveals an opportunity to apply a method of nonlinear mathematical programming in order to solve the formulated problem. A simplified evaluation problem statement is given in the paper and principles of its realization are determined in view of regime and technological limitations

The trends in the non-resource development of the Russian regions during the last 20 years

There is a lack of complex regional analysis studies in the economic research landscape. The relevance of this study has to do with the Russian government&rsquo;s high interest in identifying the main trends and factors of non-commodity-based development in the 21st century. Obviously, a significant part of Russia&rsquo;s national wealth is associated with the extractive sector, which limits the scope for economic diversification and can negatively affect Russia&#39;s long-term development. The novelty of this research is that it provides complex regional analysis over the past 20 years. The practical significance of the work lies in the possibility of using its findings to prepare policy recommendations, and to assess the impact of the decisions implemented. The aim of the research was to identify long-term trends and patterns of socioeconomic development in the Russian regions. The objectives were to observe the dynamics of a set of socioeconomic development indicators in various regions and identify spatial patterns of non-commodity growth. The work uses such scientific research methods as statistical analysis and graph-analytical methods, comparative-historical and cartographic methods. During the work, the following results were obtained: the overall growth dynamics of non-resource sectors of the Russian economy in the past 20 years has been determined by changes in the macroeconomic, geopolitical and institutional conditions; the global economic crisis of 2008, the introduction of anti-Russia sanctions and the import substitution policy in 2014-2015 have had the greatest impact on structural changes in the economy; gross regional product and GRP excluding extractive industries doubled or more in the period between 1998-2008 in most regions; after 2008, however, growth rates were close to zero in many regions, which caused a growing lag behind developed economies; in recent years, the share of investment in GRP and R&amp;D spending have dropped to low values as in the early 2000s in most regions; internet access, and average years of schooling have been growing almost continuously in most regions; the air emissions to GRP ratio has been decreasing with the growing share of the service sector and the development of technologies, but has slightly increased in recent years due to motorization. Conclusions. Over the past 20 years, the regions with the largest conurbations that have lost many industrial features but have formed a service consumer economy have undergone the most significant transformation. The oil-producing regions in northern Russia, while showing significant per capita GRP, have not been able to fully diversify their economies and are dependent on fluctuations in energy prices. Many agricultural regions have benefited from the implementation of counter-sanctions, as the government supported large agricultural holdings. Certain regions have vigorously attracted investment through proactive policies: the Kaluga, Belgorod, Leningrad, and Tomsk regions. Most of the Far Eastern regions have been losing population and economic potential. As part of a long-term study, further research may include the identification of factors of non-resource development, its complex estimation with the use of indexes, estimation of the impact of the extractive industries on regional economic growth, as well as assessing the regions&rsquo; potential to improve the quality of education for technological development. This paper is based on research findings delivered in accordance with the State Assignment for RANEPA in 202