Harmonic analysis on the infinite symmetric group

Let S be the group of finite permutations of the naturals 1,2,... The subject of the paper is harmonic analysis for the Gelfand pair (G,K), where G stands for the product of two copies of S while K is the diagonal subgroup in G. The spherical dual to (G,K) (that is, the set of irreducible spherical unitary representations) is an infinite-dimensional space. For such Gelfand pairs, the conventional scheme of harmonic analysis is not applicable and it has to be suitably modified. We construct a compactification of S called the space of virtual permutations. It is no longer a group but it is still a G-space. On this space, there exists a unique G-invariant probability measure which should be viewed as a true substitute of Haar measure. More generally, we define a 1-parameter family of probability measures on virtual permutations, which are quasi-invariant under the action of G. Using these measures we construct a family {T_z} of unitary representations of G depending on a complex parameter z. We prove that any T_z admits a unique decomposition into a multiplicity free integral of irreducible spherical representations of (G,K). Moreover, the spectral types of different representations (which are defined by measures on the spherical dual) are pairwise disjoint. Our main result concerns the case of integral values of parameter z: then we obtain an explicit decomposition of T_z into irreducibles. The case of nonintegral z is quite different. It was studied by Borodin and Olshanski, see e.g. the survey math.RT/0311369.Comment: AMS Tex, 80 pages, no figure

32-Channel Single Photon Counting Module For Ultra-sensitive Detection of DNA Sequences

ABSTRACT We continue our work on the design and implementation of multi-channel single photon detection systems for highly sensitive detection of ultra-weak fluorescence signals, for high-performance, multi-lane DNA sequencing instruments. A fiberized, 32-channel single photon detection (SPD) module based on single photon avalanche diode (SPAD), model C30902S-DTC, from Perkin Elmer Optoelectronics (PKI) has been designed and implemented. Unavailability of high performance, large area SPAD arrays and our desire to design high performance photon counting systems drives us to use individual diodes. Slight modifications in our quenching circuit has doubled the linear range of our system from 1MHz to 2MHz, which is the upper limit for these devices and the maximum saturation count rate has increased to 14 MHz. The detector module comprises of a single board computer PC-104 that enables data visualization, recording, processing, and transfer. Very low dark count (300-1000 counts/s), robust, efficient, simple data collection and processing, ease of connectivity to any other application demanding similar requirements and similar performance results to the best commercially available single photon counting module (SPCM from PKI) are some of the features of this system

System of technical vision based on active laser triangulation method

The number of failures, the percentage of faulty electric locomotives, and the number of unplanned repairs remain high at the enterprises for repair of traction rolling stock of the network of the main-line Russian railways. It was found that the main reasons for this situation are the unsatisfactory quality of current repairs and maintenance, the insufficient level of mechanization and automation of labor-intensive repair processes. The paper considers an existing positive example of the use of robotic equipment in assembly production for the repair of traction rolling stock. The analysis and classification of sensor control devices for industrial robots is performed. A method for controlling the driving devices of the repair equipment is proposed by obtaining a spatial-geometric image of the object’s surface before the beginning of technological processing by the method of active laser triangulation scanning. The principle of the action of three-dimensional scanning is described; a number of equipment with its technical characteristics and software used during the research in the laboratory of the university is listed. The result of the experiment of the proposed method on the model of the truck frame of the electric locomotive is presented. The metrological characteristics of the measurement results are calculated, allowing comparing and assessing the accuracy of the model obtained and the mock-up of the rolling stock truck. Based on the results of these calculations, it can be said with certainty that all errors and deviations of the results from true values lie within the limits of the norm and this technology can be used to design a vision system for robotic equipment

Integrated development of carrying capacities of the Baikal-Amur Mainline and Trans-Siberian Railway

The paper considers actual technical and technological problems in the development of the Eastern polygon of the Russian railway network. The purpose of the study is to develop a methodology and software tools that ensure the search for effective solutions for given resource and logistical constraints. Methods of simulation modeling, distribution of flows on networks and graphs are used. The result of the study is a hybrid set of model calculations

Traction capabilities of a dual-voltage electric locomotive 2EV120 on the West Siberian Railway

The paper discusses the traction parameters of an electric locomotive of a new generation. The existing schemes of sections served by electric locomotives and locomotive crews at the studied railway operating domain are presented. A comparison of the main parameters of DC and single-phase AC electric locomotives, the operation of which is currently organized at sections with trains of estimated weight in the long-term traction mode on the ground slopes with different steepness, is made. The scheme of the proposed organization of operation of dual-voltage electric locomotive and locomotive crews is presented. Traction parameters of a dual-mode electric locomotive are calculated, taking into account the plan and profile of the track at the proposed sections of operation, the specific basic resistance to the movement of the locomotive and the train at the estimated speed, the specific accelerating and decelerating forces of the train. When dual-mode electric locomotives are put into operation, it will be possible to reduce the fleet of locomotives in operation, the number of locomotive runs due to their lengthening, and the number of locomotive crew relief points, reduce the transit time of freight trains, increase technical and service speed, average daily mileage and average daily performance of the locomotive, reduce power consumption for traction. The operation of such electric locomotives contributes to the development of technologies for rail traffic management and the improvement of quantitative and qualitative indicators of various railway facilities

Traction capabilities of a dual-voltage electric locomotive 2EV120 on the West Siberian Railway

The paper discusses the traction parameters of an electric locomotive of a new generation. The existing schemes of sections served by electric locomotives and locomotive crews at the studied railway operating domain are presented. A comparison of the main parameters of DC and single-phase AC electric locomotives, the operation of which is currently organized at sections with trains of estimated weight in the long-term traction mode on the ground slopes with different steepness, is made. The scheme of the proposed organization of operation of dual-voltage electric locomotive and locomotive crews is presented. Traction parameters of a dual-mode electric locomotive are calculated, taking into account the plan and profile of the track at the proposed sections of operation, the specific basic resistance to the movement of the locomotive and the train at the estimated speed, the specific accelerating and decelerating forces of the train. When dual-mode electric locomotives are put into operation, it will be possible to reduce the fleet of locomotives in operation, the number of locomotive runs due to their lengthening, and the number of locomotive crew relief points, reduce the transit time of freight trains, increase technical and service speed, average daily mileage and average daily performance of the locomotive, reduce power consumption for traction. The operation of such electric locomotives contributes to the development of technologies for rail traffic management and the improvement of quantitative and qualitative indicators of various railway facilities

Contact interaction “brush – collector” and working efficiency of locomotive traction electric motor

The working efficiency of locomotive traction electric motors of direct current is largely determined by the reliability of the collector-brush assembly. The paper presents the results of simulation of the contact interaction “brush-collector” in the traction electric motor of an electric locomotive. The influence of the structural features of the brush holder, the conditions and operating modes on the contact area “brush-collector”, and the quality of switching is considered. Technical solutions for improving the current collection quality in the contact “brush-collector” and ensuring the working efficiency of traction electric motors of locomotives are proposed

МЕТОДЫ МОНИТОРИНГА РЕЗЬБОВЫХ СОЕДИНЕНИЙ (ОБЗОРНАЯ СТАТЬЯ)

Threaded connections, including connected parts and threaded fasteners (bolts, screws, studs, nuts, washers), are widely used in industry, construction, and everyday life due to the numerous advantages they have over other types of connections. However, under conditions of variable loads, a weakening of tightening of threaded connections is observed up to the opening of their joint and destruction of fasteners. A sign of a loosening of the tightening of threaded connections is a decrease in the axial force (stress) in the rod of a bolt (stud, screw), and a sign of incipient destruction of the connection is a crack in the fasteners. Continuous monitoring of the measured parameters and comparison of their values with threshold values is carried out by monitoring, respectively, the magnitudes of stresses and cracks in bolts (studs, screws). This article discusses the basic principles, gives comparative characteristics, analyzes the advantages and disadvantages of the most well-known methods for monitoring threaded connections with large fasteners (d = 30 ...200 mm), and also discusses the possibility of using some of them for monitoring threaded connections of turbine equipment of power plants.Резьбовые соединения, включающие соединяемые детали и резьбовой крепёж (болты, винты, шпильки, гайки, шайбы), широко используются в промышленности, строительстве, быту благодаря многочисленным преимуществам, которыми они обладают по сравнению с другими видами соединений. Однако в условиях переменных нагрузок наблюдается ослабление затяжки резьбовых соединений вплоть до раскрытия их стыка и разрушения крепежа. Признаком ослабления затяжки резьбовых соединений является уменьшение осевой силы (напряжения) в стержне болта (шпильки, винта), а признак начинающегося разрушения соединения ˗ трещины в деталях крепежа. Непрерывный контроль измеряемых параметров и сравнение их величин с пороговыми значениями осуществляется мониторингом соответственно величин напряжений и трещин в болтах (шпильках, винтах). В настоящей статье рассмотрены основные принципы, даны сравнительные характеристики, проанализированы достоинства и недостатки наиболее известных методов мониторинга резьбовых соединений с крупным крепежом (d = 30…200 мм), а также обсуждается возможность применения некоторых из них для мониторинга резьбовых соединений турбинного оборудования электростанций.Резьбовые соединения, включающие соединяемые детали и резьбовой крепёж (болты, винты, шпильки, гайки, шайбы), широко используются в промышленности,строительстве, быту благодаря многочисленным преимуществам, которыми они обладают по сравнению с другими видами соединений. Однако в условиях переменных нагрузок наблюдается ослабление затяжки резьбовых соединений вплоть до раскрытия их стыка и разрушения крепежа.  Признаком ослабления затяжки  резьбовых соединенийявляется уменьшение осевой силы (напряжения) в стержне болта (шпильки, винта),а признак начинающегося разрушения соединения ˗ трещины в деталях крепежа.Непрерывный контроль измеряемых параметров и сравнение ихвеличин с пороговыми значениями осуществляется мониторингомсоответственно величиннапряжений и трещин вболтах (шпильках, винтах). В настоящей статье рассмотрены основные принципы, даны сравнительные характеристики, проанализированы достоинства и недостатки наиболее известных методов мониторингарезьбовых соединений с крупным крепежом (d= 30…200 мм), а также обсуждается возможность применения некоторых из них длямониторинга резьбовыхсоединенийтурбинного оборудования электростанци

Magnetism and EPR Spectroscopy of Nanocrystalline and Amorphous TiO₂: Fe upon Al Doping

This work is devoted to the study of the magnetic properties and Electron Paramagnetic Resonance (EPR) spectroscopy of TiO2:Fe nanoparticles doped with Al in different structural states. The sol-gel methods have been used to obtain the particles in both crystalline (average size from 3 to 20 nm) and X-ray amorphous states. The electron paramagnetic resonance spectra of crystalline samples TiO2:Fe doped with aluminum besides a resonance line with g-factor ~2 exhibit a small signal with a g-factor of 4.3 from Fe3+ ions with rhombohedral distortions. The fraction of Fe3+ with rhombohedral distortions increases with increasing aluminum content. For the amorphous state at Al doping, the resonance with a g-factor of 4.3 is completely dominant in the electron paramagnetic resonance spectrum. The density functional theory calculation shows that aluminum prefers to be localized near iron ions, distorting the nearest Fe3+ environment. The complex integral electron paramagnetic resonance spectrum of all samples was fitted with sufficient accuracy by three separate resonance lines with different widths and intensities. The temperature behavior of the electron paramagnetic resonance spectrum can be described by the coexistence of paramagnetic centers (isolated Fe3+ ions including dipole-dipole interactions) and iron clusters with negative exchange interactions