Seven Classes of Harmonic Diffeomorphisms

We deduce two necessary and sufficient conditions for a diffeomorphism $f : M \to \overline{M}$ of a Riemannian manifold (M,g) onto a Riemannian manifold $(\overline{M},\bar g)$ to be harmonic. Using the representation theory of groups, we define in an intrinsic way seven classes of such harmonic diffeomorphisms and partly describe the geometry of each class.     

Several Constructions of Exact Sequences

The article presents a construction of a 5-term relative exact sequence in purely categorical terms and the Mayer–Vietoris sequence for weak -groupoids of R. Street. In the first half of the paper, it is shown that several well-known exact sequences can be obtained, using the Z-diagram described at the beginning of the article. There are number of categories that are close to the category of topological spaces in the sense of homotopy theory. The objects of such a category can be viewed as weak -groupoids in a very intuitive way. Therefore, the language of weak -groupoids seems to be very convenient to make explicit constructions in categories of this type. The article presents a combinatorial construction of the path space of a weak -groupoid and applies the machinery of Sec. 1 to obtain the long exact sequence of a homotopy fiber. The construction is quite natural and gives information on the structure of the relative terms. In the last section, the Mayer–Vietoris sequence of a fiber square of weak -groupoids is obtained under some conditions. Of course, this construction makes sense for topological spaces or for any category mentioned above. But the statement of the conditions is more natural in terms of weak -groupoids. This sequence generalizes the sequence of fibration, and in this case the conditions given in the article are equivalent to the homotopy lifting property. Bibliography: 6 titles.     

Orbital frustration at the origin of the magnetic behavior in LiNiO2

We report on the ESR, magnetization, and magnetic susceptibility measurements performed over a large temperature range, from 1.5 to 750 K, on high-quality stoichiometric LiNiO2. We find that this compound displays two distinct temperature regions where its magnetic behavior is anomalous. With the help of a statistical model based on the Kugel'-Khomskii Hamiltonian, we show that below T(of) approximately 400 K, an orbitally frustrated state characteristic of the triangular lattice is established. This then gives a solution to the long-standing controversial problem of the magnetic behavior in LiNiO2.     

High-temperature electron paramagnetic resonance in magnets with the Dzyaloshinskii-Moriya interaction

We analyze the high-temperature electron paramagnetic resonance (EPR) absorption in a weakly anisotropic Heisenberg magnet having two distinct types of anisotropy, represented, respectively, by a symmetric term and the Dzyaloshinskii-Moriya (DM) term. Contrary to the widespread opinion that the latter is responsible for the excessive linewidth observed in the EPR spectra of many oxides, we prove that its contribution to the linewidth is only of the same level as that of the symmetric anisotropy. This gives a solution to the long-standing controversial problem of the high-temperature magnetic relaxation in quantum-spin systems with the DM interaction.     

Josephson effect in MgB(2) break junctions

We present the first observation of the dc and ac Josephson effect in MgB(2) break junctions. The junctions, obtained at 4.2 K in high-quality, high-density polycrystalline metallic MgB(2) samples, show a nonhysteretic dc Josephson effect. By irradiating the junctions with microwaves we observe clear Shapiro steps spaced by the ideal Delta V value. The temperature dependence of the dc Josephson current and the dependence of the height of the steps on the microwave power are obtained. These results directly prove the existence of pairs with charge 2e in MgB(2) and give evidence of the superconductor-normal metal-superconductor weak link character of these junctions.     

Control of radiation parameters of pulse-periodic tunable diode lasers based on lead salts with double heterostructure

Spectral and power properties of the pulse-periodic tunable diode lasers based on lead salts with double heterostructure grown by MBE are considered. Procedure and criteria of preliminary selection of the laser samples are discussed. Typical characteristics of such lasers are presented. Methods for controlling the spectral and power properties in the pulse mode are considered. General mechanisms of laser wavelength tuning by current and temperature variations are demonstrated on the basis of experimental data. Methods for optimizing these parameters are considered.     

Intermodulation of transverse magnetoresistance oscillations in structures with strong intersubband interaction

In the Shubnikov–de Haas oscillation spectrum of doped InAs/AlSb structures, high-amplitude peaks are established at combination frequencies. It is demonstrated that they are caused by a significant contribution of intersubband scattering to the processes of electron-electron interaction. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 32–38, December, 2008.