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As data rates for multi-gigabit serial interfaces within multi-node compute systems approach and exceed 10 Gigabits per second (Gbps), board-to-board and chip-to-chip optical signaling solutions become more attractive, particularly for longer (e.g. 50-100 cm) links. The transition to optical signaling will potentially allow new high performance compute (HPC) system architectures that benefit from characteristics unique to optical links. To examine these characteristics, we built and tested several optical demonstration vehicles; one based on dense wavelength division multiplexing (DWDM), and others based on multiple point-to-point links carried across multimode fibers. All test vehicles were constructed to evaluate applicability to a multi-node compute system. Test results, combined with data from recent research efforts are summarized and compared to equivalent electrical links and the advantages and design characteristics unique to optical signaling are identified., Comment: 25 pages, 18 figures, DesignCon 2011

We find all non-abelian generalizations of $\text{P}_1 - \text{P}_6$ Painlevé systems such that the corresponding autonomous system obtained by freezing the independent variable is integrable. All these systems have isomonodromic Lax representations.

All Hamiltonian non-abelian Painlevé systems of $${{\,\mathrm{P_{1}}\,}}-{{\,\mathrm{P_{6}}\,}}$$ P 1 - P 6 type with constant coefficients are found. For $${{\,\mathrm{P_{1}}\,}}-{{\,\mathrm{P_{5}}\,}}$$ P 1 - P 5 systems, we replace an appropriate inessential constant parameter with a non-abelian constant. To prove the integrability of new $${{\,\mathrm{P_{3}^{\prime }}\,}}$$ P 3 ′ and $${{\,\mathrm{P_{5}}\,}}$$ P 5 systems thus obtained, we find isomonodromic Lax pairs for them.

We study non-abelian systems of Painlevé type. To derive them, we introduce an auxiliary autonomous system with the frozen independent variable and postulate its integrability in the sense of the existence of a non-abelian first integral that generalizes the Okamoto Hamiltonian. All non-abelian P6-P2-systems with such integrals are found. A coalescence limiting scheme is constructed for these non-abelian Painlevé systems. This allows us to construct an isomonodromic Lax pair for each of them.

All Hamiltonian non-abelian Painlevé systems of ${\rm{P}}_{1}-{\rm{P}}_{6}$ type with constant coefficients are found. For ${\rm{P}}_{1}-{\rm{P}}_{5}$ systems, we replace an appropriate inessential constant parameter with a non-abelian constant. To prove the integrability of new ${\rm{P}}_{3}^{\prime}$ and ${\rm{P}}_{5}$ systems thus obtained, we find isomonodromic Lax pairs for them.

For all non-equivalent matrix systems of Painlevé-4 type found by authors in arXiv:2107.11680, isomonodromic Lax pairs are presented. Limiting transitions from these systems to matrix Painlevé-2 equations are found.

Using the Painlevé--Kovalevskaya test, we find several new matrix generalizations of the Painlevé-4 equation. Some limiting transitions reduce them to known matrix Painlevé-2 equations.

The paper considers a method of laser correction of geometrical errors of multi-axis CNC-controlled systems, i.e. machine-tools and CMMs. Calman’s "Observation and control" concept is applied to the method. A laser interferometer is used to observe multi-axis system for digital industry and a program postprocessor is used for accuracy control, introduced between CAM- and CNC- systems.

The paper describes a new developed approach to CNC-controlled multi-axis systems geometric errors compensation based on optimal error correction strategy. Multi-axis CNC-controlled systems – machine-tools and CMM‘s are the basis of modern engineering industry. Similar design principles of both technological and measurement equipment allow usage of similar approaches to precision management. The approach based on geometric errors compensation are widely used at present time. The paper describes a system for compensation of geometric errors of multi-axis equipment based on the new approach. The hardware basis of the developed system is a multi-function laser interferometer. The principles of system‘s implementation, results of measurements and system's functioning simulation are described. The effectiveness of application of described principles to multi-axis equipment of different sizes and purposes for different machining directions and zones within workspace is presented. The concepts of optimal correction strategy is introduced and dynamic accuracy control is proposed.

We exploit variation in consumer price inflation across 71 Russian regions to examine the relationship between the perceived stability of the domestic currency and financial dollarization. Our results show that regions with higher inflation experience an increase in deposit dollarization and a decrease in the dollarization of loans to households and firms in non-tradable sectors. The negative impact of inflation on credit dollarization is weaker in regions with less integrated banking markets. This suggests that the asset-liability management of banks constrains the currency-portfolio choices of both households and firms without a natural currency hedge.

Large-scale features of Arctic Ocean temperature and salinity distributions observed during 2007-2009 are described and discussed in the context of historical observation in order to document long-term variations. Oceanographic observations carried out in the frame of the International Polar Year (IPY 2007/2008) demonstrated unique conditions in the Arctic Ocean and seas during that period. For example, analyses of upper ocean temperature and salinity patterns 2007-2009 revealed an apparent frontal zone separating the Eurasian and Canadian Basins. We found that after 2007 the temperature and salinity trends of the surface layer of the Arctic Ocean followed the same trajectory as in the past, however their regional distribution and intensity changed. The average salinity in the surface 5-50 m layer of the Eurasian Basin in winter of 2007-2009 was higher than in the 1950s and 1970s, but did not exceed the average salinity in the early 1990s. In the Canadian Basin, the upper ocean salinity in 2007-2009 was much lower than in the 1950s-1960s. Volumetric analysis of water masses demonstrated a general increase of volume of the intermediate (150-900 m depth range) Atlantic Water (AW) temperature, with substantial rise of the upper boundary of the AW. The thermal expansion of AW in the Arctic Basin is unique during the last 20 years. The most distinct variations of the hydrographic conditions were observed in the Canadian Basin. In general, the maximum of the AW temperature decreased in 2009 relative to 2007 and the upper boundary became shallower by 50 to 150 m the Eurasian Basin. The AW salinity in 2007-2009 was not exceptional during the IPY. Observations in the deeper layers indicated that the bottom waters have become slightly warmer and less saline.

This paper examines the impacts of the 2005 shift in Russian exchange rate policies from single-currency to bi-currency basket targeting on domestic interest rates and sovereign risk premium dynamics. The policy shift disconnected domestic interest rates from US dollar-denominated interest rates, replacing them with a growing positive relationship with the dual-currency basket (USD-EUR) adopted by the Central Bank of Russia, as well as a synthetic interest rate composed of the US dollar LIBOR and the euro LIBOR. The paper also considers the insulating properties of Russian basket targeting policies during the recent global liquidity crisis. I present evidence that the Russian MosIBOR rate was negatively related to the US dollar LIBOR rate and positively related to the synthetic USD-EUR rate during the "decoupling" stage of the crisis. Even with the steep quantitative easing of the US Fed during this period, the finding suggests the Russian money market was more in sync with the monetary policies of the euro area. The central conclusion here is that, in conditions of managed floating exchange rate policies and liberalized capital accounts, the relationship between a country's domestic interest rates and their foreign counterparts depends on the de facto operating target of the central bank of this country, whether it is a single currency or a basket.

Given an associative multiplication in matrix algebra compatible with the usual one or, in other words, linear deformation of matrix algebra, we construct a solution to the classical Yang-Baxter equation. We also develop a theory of such deformations and construct numerous examples. It turns out that these deformations are in one-to-one correspondence with representations of certain algebraic structures, which we call M-structures. We also describe an important class of M-structures related to the affine Dynkin diagrams of A, D, E-type. These M-structures and their representations are described in terms of quiver representations., Comment: 26 pages, latex

We investigate a special class of quadratic Hamiltonians on so(4) and so(3,1) and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree., Comment: 16 pages

A polynomial deformation of the Kowalewski top is considered. This deformation includes as a degeneration a new integrable case for the Kirchhoff equations found recently by one of the authors. A $5\times 5$ matrix Lax pair for the deformed Kowalewski top is proposed. Also deformations of the two-field Kowalewski gyrostat and the $so(p,q)$ Kowalewski top are found. All our Lax pairs are deformations of the corresponding Lax representations found by Reyman and Semenov-Tian {S}hansky. In addition, a similar deformation of the Goryachev-Chaplygin top and its $3\times 3$ matrix Lax representation is constructed., Comment: 9 pages, LaTeX, with corrections

Year-round observations of the physical snow and ice properties and processes that govern the ice pack evolution and its interaction with the atmosphere and the ocean were conducted during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition of the research vessel Polarstern in the Arctic Ocean from October 2019 to September 2020. This work was embedded into the interdisciplinary design of the 5 MOSAiC teams, studying the atmosphere, the sea ice, the ocean, the ecosystem, and biogeochemical processes. The overall aim of the snow and sea ice observations during MOSAiC was to characterize the physical properties of the snow and ice cover comprehensively in the central Arctic over an entire annual cycle. This objective was achieved by detailed observations of physical properties and of energy and mass balance of snow and ice. By studying snow and sea ice dynamics over nested spatial scales from centimeters to tens of kilometers, the variability across scales can be considered. On-ice observations of in situ and remote sensing properties of the different surface types over all seasons will help to improve numerical process and climate models and to establish and validate novel satellite remote sensing methods; the linkages to accompanying airborne measurements, satellite observations, and results of numerical models are discussed. We found large spatial variabilities of snow metamorphism and thermal regimes impacting sea ice growth. We conclude that the highly variable snow cover needs to be considered in more detail (in observations, remote sensing, and models) to better understand snow-related feedback processes. The ice pack revealed rapid transformations and motions along the drift in all seasons. The number of coupled ice-ocean interface processes observed in detail are expected to guide upcoming research with respect to the changing Arctic sea ice.

A method of quantitative analysis of substances based on nuclear magnetic resonance comprises the steps of weighing a sample of substance to be analyzed, obtaining therefrom and accumulating nuclear magnetic resonance signals during n measuring cycles, computing a mean value of the nuclear magnetic resonance signals, and determining percentage of components in the sample being analyzed with regard to its mass and the mean value of the nuclear magnetic resonance signals. The mean value of the accumulated signals and its standard deviation are computed as the accumulation occurs during each of the n measuring cycles, the subsequent step being subtraction of the standard deviation from the permissible limiting standard deviation value whereupon the accumulation is stopped during the n i th cycle in which a difference between said magnitudes is a positive value. A nuclear-resonant quantitative analyzer for accomplishing the aforesaid method comprises a magnetic system, a nuclear magnetic resonance signal pick-up arranged in its gap, an amplifier, a selector and an analog-to-digital converter, which are connected to the output of said pick-up, a video-pulse generator connected to the input thereof, and a radio-pulse generator. The analyzer also comprises an automatic sample weighing unit composed of such series-connected components as a weight-to-frequency converter, a load-receiving platform thereof being inserted in the nuclear magnetic resonance pick-up, and a frequency-to-code converter, a data swapping unit, a processor, a control unit, a programming unit and a data output unit.