New Ln[B6O9(OH)3] borates (Ln = Sm-Lu): Structure, properties, and structural relation to cationic Li4[B7O12]Cl conductors (Li-Boracites)

Crystals of new rare earth borates of the composition Ln[B₆O₉ (OH)₃] (Ln = Sm-Lu), sp. gr. R3c are synthesized under hydrothermal conditions. Their crystal structures are determined on single crystals with Ln = Ho, Gd without preliminary determination of their chemical formulas. The polar anionic framework of the crystals consists of BO₃ triangles and BO₄ tetrahedra and has wide channels along the threefold axis of the structure, which are similar to the channels along the a, b, and c axes in cubic Li₄[B₇O₁₂]Cl boracite with Li conductivity. Rare earth atoms are arranged in the structure over the cubic F pseudolattice, whereas the analogous positions in Li boracites are filled with Cl anions. The squared optical nonlinearity of the new crystals is comparable with the nonlinearity of quartz, whereas the electrical conductivity in borates at 300°C exceeds 10⁻⁶ S/cm. __________ Translated from Kristallografiya, Vol. 49, No. 4, 2004, pp. 681–691. Original Russian Text Copyright ? 2004 by Belokoneva, Ivanova, Stefanovich, Dimitrova, Kurazhkovskaya.     

在白噪声分析中的广义维里拉普拉斯

一类广义维里拉普拉斯，把在白噪声分析构架中通常定义的维里拉普拉斯作为特殊情形而包含。     

Regioorientation in the reaction of side chain activated alkylpyridines with electrophiles

X-ray structural data has shown that condensation of sym-3-nitrocollidine with benzaldehyde occurs at the 6-methyl group. The presence of an acceptor group in the side chain of 2,6-dimethyl-4-cyanomethyl-3-nitropyridine causes condensation to occur at the activated methylene group in the 4-position.M. V. Lomonosov State University, Moscow 119899. A. N. Nesmeyanov Institute of Organoelemental Compounds, Moscow 117813. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11. pp. 1543–1550, November, 1995. Original article submitted June 10, 1995.     

A notch filter for 140 GHz microwave radiation

The construction of a notch-filter for 140 GHz with very low passband insertion loss is described. It is based on a single-mode rectangular waveguide and cylindrical cavities matched to it. The typical transmission characteristic is also presented.     

Minimax estimates for functionals of solutions of wave equations with time-periodic right-hand sides

Minimax mean-square estimates for the velocity potential in the steady regime, as well as for the intensities of harmonic ponts sources, are obtained from the results of inaccurate measurements of the potential. Bibliography: 4 titles. Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 77, 1993, pp 87–96.     

Simulated cosmic strings in a “big bang” in superfluid3He at 100 μK

During studies of the impact of single neutrons on superfluid³He at around 100μK we have measured the thermal energy released in the superfluid following the nuclear reaction, n+³He→p+³H+764keV. However, we find that the measured energy deposited in the quasiparticle system shortly after this reaction is substantially less than what we expect. We believe that this energy deficit represents that energy which has gone into the creation of vortices, in analogy to the creation of cosmic strings in the early universe via the Kibble mechanism. Furthermore, from the magnitude of the deficit, we can infer the vortex density which compares favorably with that predicted in Zurek’s scenairo.     

Spinor norms of local autometries of generalized quadratic lattices

It is proved that the group of spinor norms of autometries of a generalized quadratic lattice ℒ over the ring of integral elements v _p of a local field k _p , in the case wherep∤2 and ℒ is a generalized translation, is generated by the spinor norms of symmetries contained in the group of autometries of ℒ. As a corollary, an extension to the case of generalized quadratic lattices is given for known sufficient conditions of coincidence of the genus and the spinor genus of a quadratic lattice. Bibliography: 9 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 161–173. Translated by Yu. G. Teterin.