Isometric immersions of domains of Lobachevski space in Euclidean spaces

Immersions of domains of the n-dimensional Lobachevski space Lⁿ in the (2n−1)-dimensional Euclidean space E²ⁿ⁻¹ are studied. It is shown that the problem of isometric immersion of domains of Lⁿ in E²ⁿ⁻¹ is reduced to the study of a certain system of nonlinear partial differential equations, yielding the sine-Gordon equation as one of the special cases. Published inZapiski Nauchnykh Seminarov POMI, Vol. 234, 1996, pp. 11–16.     

Synthesis of adamantane by ionic liquid-promoted isomerization of tricyclo[5.2.1.02,6]decane and H2SO4-mediated hydroisomerization of pentacyclo[4.4.0.02,4.03,7.08,10]decane

Russian Chemical Bulletin - Adamantane was synthesized by skeletal isomerization of endo- and exo-tricyclo[5.2.1.02,6]-decanes in the presence of ionic liquid [Et3NH]+[Al2Cl7]?—CuSO4. A...     

Investigation of the Mn-doped compound CuGaTe<Subscript>2</Subscript> by <Superscript>63</Superscript>Cu AND <Superscript>69</Superscript>Ga nuclear magnetic resonance techniques

The synthesized base compound CuGaTe₂ and the Mn-doped compounds Cu_0.97Ga_0.97Mn_0.06Te₂ and Cu_0.93Ga_0.93Mn_0.14Te₂ have been investigated by using ⁶³Cu and ⁶⁹Ga NMR spectroscopy. The NMR spectra obtained testify to substantial structural distortions near the cationic positions in the crystal lattice of Mndoped samples. The constants of quadrupole coupling between ⁶³Cu and ⁶⁹Ga nuclei in the compounds investigated have been estimated.     

Superhyperfine structure in the EPR spectra and optical spectra of impurity f ions in dielectric crystals: A review

The results of observation and simulation of the superhyperfine (ligand hyperfine) structure (SHFS) of the electron paramagnetic resonance (EPR) spectra of rare-earth and uranium impurity ions in dielectric crystals have been systematized. The resolved SHFS of the EPR spectra of doped cubic crystals (with the fluorite and perovskite structures) has been observed for orientations of a constant magnetic field along the crystallographic axes. Most attention has been paid to tetragonal double fluorides LiRF₄ (R = Y, Lu, Tm), in which the SHFS of the EPR spectra has also been found for intermediate orientations of the magnetic field. For the LiYF₄: Nd³⁺ single crystal, the splitting of optical spectral lines due to the interaction of Nd³⁺ ions with nuclear magnetic moments of the nearest neighbor fluorine ions has been observed for the first time. The Van Vleck paramagnet LiTmF₄: U³⁺ is characterized by the SHFS with clearly distinguishable components due to the interaction of uranium ions both with nuclei of the fluorine ions and with enhanced magnetic moments of the thulium nuclei. The SHFS envelopes of the EPR spectra of Yb³⁺, Ce³⁺, Nd³⁺, and U³⁺ ions in LiYF₄ and LiLuF₄ crystals are well reproduced by numerical calculations based on the microscopic model using only three fitting parameters: the width of transitions between the electron-nuclear sublevels of the complex containing the paramagnetic ion and nuclei of the ligands and two constants of covalent bonding of the f electrons with 2s and 2p electrons of the nearest neighbor fluorine ions.     

Investigation of CuGaTe<Subscript>2</Subscript> semiconductor compounds doped with Mn by the EPR method

The EPR method is used to investigate the synthesized basic CuGaTe₂ compound and CuGaTe₂{Mn} compounds doped with Mn. The CuGaTe₂ EPR spectra obtained testify to the formation of the Jahn-Teller copper centers with g-tensors having axial symmetry that differ by values of the main g-tensor components (g_⎟⎪ and g_⊥). The intensive line with g_eff3 = 1.996 ± 0.001 registered for samples of CuGaTe₂{Mn} compounds is associated with the presence of centers formed by manganese.     

On the geometric results of A. V. Pogorelov

We present a survey of the principal results of A. V. Pogorelov in the field of geometry. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1116–1130, August, 2007.     

Cation distribution and exchange interactions in CuCr2S4:57Fe

The character of the distribution of Fe ions over tetrahedral and octahedral positions of the spinel structure was investigated in the magnetic-hardening range at 290 and 78 K in CuCr₂S₄:⁵⁷Fe with different degrees of doping with the isotope⁵⁷Fe. It was established that for degrees of substitution not greater than 0.1 per formula unit the Fe ions do not have a definite preference for either positions. The dependence of the effective magnetic field at the⁵⁷Fe nuclei on the degree and character of the embedding of Fe ions in the crystal lattice was determined. The features found are explained by the change in the indirect exchange of Cr ions via current carriers and the degree of delocalization of the 3d-electrons of Cr and Fe ions in the process of cationic substitution.A. N. Tupolev Aviation Institute, Kazan. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 71–74, October, 1992.