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In the previous paper, we showed that the wave functions of the quantum Ruijsenaars hyperbolic system diagonalize Baxter Q-operators. Using this property and duality relation, we prove orthogonality and completeness relations for the wave functions or, equivalently, unitarity of the corresponding integral transform. [ABSTRACT FROM AUTHOR]

In the previous paper, we introduced a commuting family of Baxter Q-operators for the quantum Ruijsenaars hyperbolic system. In the present work, we show that the wave functions of the quantum system found by M. Hallnäs and S. Ruijsenaars also diagonalize Baxter operators. Using this property, we prove the conjectured duality relation for the wave function. As a corollary, we show that the wave function solves bispectral problems for pairs of dual Macdonald and Baxter operators. Besides, we prove the conjectured symmetry of the wave function with respect to spectral variables and obtain new integral representation for it. [ABSTRACT FROM AUTHOR]

We introduce Baxter Q-operators for the quantum Ruijsenaars hyperbolic system. We prove that they represent a commuting family of integral operators and also commute with Macdonald difference operators, which are gauge equivalent to the Ruijsenaars Hamiltonians of the quantum system. The proof of commutativity of the Baxter operators uses a hypergeometric identity on rational functions that generalize Ruijsenaars kernel identities. [ABSTRACT FROM AUTHOR]

We present a proof of hypergeometric identities which play a crucial role in the theory of Baxter operators in the Ruijsenaars model. [ABSTRACT FROM AUTHOR]

The note is devoted to the factorization formula for the matrix with the generators of the group GL(N, ℝ) in the regular representation. The factorization formula helps to evaluate these generators and Casimir operators in the case of arbitrary N and clarifies the connection between GL(N, ℝ) and the quantum Toda chain. [ABSTRACT FROM AUTHOR]

In this note we present a new derivation of Bäcklund transformations for the nonlinear Schroedinger equation. We discuss the conserved quantities related with this transformation and its connection with the inverse scattering method. Besides, we construct a quantum analog of the Bäcklund transformation defined by Baxter's Q-operator. [ABSTRACT FROM AUTHOR]

The basic formulas for the unitary principal series representations of the group SL(2, ℂ) are given, and the decomposition of a tensor product of two representations into irreducible representations is considered. A simple proof of the completeness of the 3j-symbols is given. [ABSTRACT FROM AUTHOR]

We have analyzed the possibility of improving deformation–force properties of ring-shaped drives made of titanium nickelide and operating in the regime of two-way shape memory effect (TWSME). For this purpose, thermocycling of an oval sample was used with the transformation of the material from the low-temperature martensite phase to the high-temperature austenite phase in free state and cooling via the temperature interval of the transformation under a load. The possibility of generation of force in ring-shaped structures changing shape during heating as well as during cooling due to the TWSME process is demonstrated. The reported results indicate asymmetry of these properties relative to the direction of temperature variation. It is shown that the cooling rate substantially affects the deformation and force properties of ring-shaped drives. [ABSTRACT FROM AUTHOR]

In this paper, we show that an operator introduced by A. A. Tsvetkov enjoys all the necessary properties of a Q-operator. It is shown that the Q-operator of the XXX spin chain with spin ℓ turns into Tsvetkov's operator in the continuous limit as ℓ→∞. Bibliography: 18 titles. [ABSTRACT FROM AUTHOR]

The deformation-thermal stability of a clusterized amorphous-crystalline structure prepared from a CuFe powder mixture at a logarithmic strain e = 4.6 and subjected to isochronous (40 min) annealings at T = 200-800°C has been investigated. Periodic changes (Δ T = 300°C) in the order and disorder with a maximum ordering at T = 300 and 600°C and a maximum disordering at T = 400 and 700°C have been observed. The periodicity of the dominant crystallographic order with a period Δ T = 400°C in the annealing temperature has been revealed for face-centered cubic copper phase planes separated by a singular point at T = 500°C characterized by the dominant body-centered cubic iron phase ordering. It has been shown that the sawtooth shape of the size distribution of strain clusters formed within the crystal structure of deformed samples slowly changes with increasing annealing temperature from exponential ( T = 200-700°C) to linear ( T = 800°C). This indicates a high density of internal local distortions in structural units. [ABSTRACT FROM AUTHOR]

Quasar-KVO RT-32 radio telescopes of the radio interferometric complex of the Russian Academy of Sciences are equipped with unique 32-m-diameter antennas. The telescopes provide radio astronomy observations in the centimeter wavelength range within a network of radio telescopes, as well as in the single dish mode. The antenna system structure has a significant size and weight, thus determining the engineering difficulties in controlling the movement of the RT-32. The electrical drive of the antenna system must provide two different operating modes: on the one hand, a rapid change in the antenna angular position, and on the other, precise tracking of a cosmic signal source. The high operational load and requirements for the service of radio telescopes as parts of radio interferometry networks impose stringent reliability requirements on the electrical drive and control system. The pointing system consists of subsystems that include dc drives, power equipment for controlling these drives, position sensors based on rotary transformers, and other items. All subsystems are integrated using switching devices of control signals and coordinate-transforming devices. The system is operated by a working monitoring and control station, which is based on an industrial computer and specially developed software. [ABSTRACT FROM AUTHOR]

The structure of compacted Cu60Fe40 powder in various stages of thermomechanical processing (with a logarithmic strain varied within e = 0−7.4) has been studied by X-ray diffraction. It is established that the atomic order evolution in this system is characterized by a certain critical strain ( e = 4.6), at which a specific deformation-induced nanostructure is formed. In this structure, clusters of a bcc α-Fe phase with dimensions on the order of 200 Å are coherently conjugated with a polycrystalline fcc structure of copper, thus representing a new class of materials. [ABSTRACT FROM AUTHOR]

Using repeated bundle extrusion of a Cu/NbTi composite, we have obtained a high-strength heterophase alloy having superconducting properties. X-ray diffraction characterization has shown that the material we obtained has an unstressed, relaxed structure in the form of self-consistent, locally diffusion-alloyed atomic groups ranging widely in size, which can be divided into three groups: (1) microcrystalline long-range-ordered particles about 450 Å in size, showing up as Debye peaks with sharp tops; (2) mesoscopic clusters with a nanoscale atomic order, responsible for broad diffuse lines; and (3) small low-dimensional atomic groups with short-range order (10–50 Å), responsible for incoherent diffuse X-ray scattering (very broad diffuse halos). [ABSTRACT FROM AUTHOR]