Synthesis and Characterization of Large Stereoregular Organosiloxane Cycles

The large stereoregular phenyltrimethylsiloxysiloxane macrocycles of general formula [PhSi(OSiMe3)O]n (n=6 and 12) have been selectively obtained with high yields by trimethylsilylation of cage-like oligophenylmetallasiloxanes (OPMS) which we described earlier. The compounds 3 (n=6) and 4 (n=12) have been characterized by NMR-spectroscopy method and by single crystal X-ray analysis. This investigation showed unambiguously that the siloxane macrocycles keep their size and configuration (the same as in the initial OPMS) during the trimethylsilylation. Thus a synthetic route for obtaining large stereoregular siloxane macrocycles has been developed

On algebraic classification of quasi-exactly solvable matrix models

We suggest a generalization of the Lie algebraic approach for constructing quasi-exactly solvable one-dimensional Schroedinger equations which is due to Shifman and Turbiner in order to include into consideration matrix models. This generalization is based on representations of Lie algebras by first-order matrix differential operators. We have classified inequivalent representations of the Lie algebras of the dimension up to three by first-order matrix differential operators in one variable. Next we describe invariant finite-dimensional subspaces of the representation spaces of the one-, two-dimensional Lie algebras and of the algebra sl(2,R). These results enable constructing multi-parameter families of first- and second-order quasi-exactly solvable models. In particular, we have obtained two classes of quasi-exactly solvable matrix Schroedinger equations.Comment: LaTeX-file, 16 pages, submitted to J.Phys.A: Math.Ge

Peculiarities of electronic heat capacity of thulium cuprates in pseudogap state

Precise calorimetric measurements have been carried out in the 7 - 300 K temperature range on two ceramic samples of thulium 123 cuprates TmBa2Cu3O6.92 and TmBa2Cu3O6.70. The temperature dependence of the heat capacity was analyzed in the region where the pseudogap state (PGS) takes place. The lattice contribution was subtracted from the experimental data. The PGS component has been obtained by comparing electronic heat capacities of two investigated samples because the PGS contribution for the 6.92 sample is negligible. The anomalous behavior of the electronic heat capacity near the temperature boundary of PGS was found. It is supposed that this anomaly is due to peculiarities in N(E) function where N is the density of electronic states and E is the energy of carriers of charge.Comment: 12 pages, 3 Postscript figure