Tilting theory and the finitistic dimension conjectures

Let be a right noetherian ring and let be the class of all finitely presented modules of finite projective dimension. We prove that findim iff there is an (infinitely generated) tilting module such that pd and . If is an artin algebra, then can be taken to be finitely generated iff is contravariantly finite. We also obtain a sufficient condition for validity of the First Finitistic Dimension Conjecture that extends the well-known result of Huisgen-Zimmermann and Smalø.

     

The Second Boundary-Value Problem for Pseudoparabolic Equations in Noncylindrical Domains

This paper is devoted to the study of the solvability of the second mixed problem in a noncylindrical domain for the nonstationary equation $${\text{div}}(k(x){\text{ grad }}u_t ) - c(x)u_t - b(x)u(x,t) = f(x,t)$$ called the pseudoparabolic equation. We prove existence and uniqueness theorems for the solution in the case of contracting (as time t increases) domains.     

Jahn-Teller effect in low-spin Ni3+ in the LaAlO3 ceramic

This paper reports on an EPR study of LaAl_1?x Ni_xO₃ solid solutions with x≤0.12 made in the 4.2-to 300-K temperature range. In the X range, the broadening of the single EPR line with g _eff=2.148 was observed at temperatures below ～40 K. In the Q range, a slightly anisotropic EPR line with g _⊥ ^′ =2.145±0.002 and g _‖ ^′ =2.154±0.002 transforms to a rhombic-symmetry spectrum with g ₁=2.183±0.002, g ₂=2.143±0.002, and g ₃=2.118±0.002. It is shown that the observed low-temperature effects are due to the lowered symmetry of the complex under the combined action of the tetragonal Jahn-Teller distortions and of the trigonal component of the crystal field.     

Sensitivity enhancement in structural measurements by solid state NMR through pulsed spin locking

Free induction decay (FID) signals in solid state NMR measurements performed with magic angle spinning can often be extended in time by factors on the order of 10 by a simple pulsed spin locking technique. The sensitivity of a structural measurement in which the structural information is contained in the dependence of the integrated FID amplitude on a preceding evolution period can therefore be enhanced substantially by pulsed spin locking in the signal detection period. We demonstrate sensitivity enhancements in a variety of solid state NMR techniques that are applicable to selectively isotopically labeled samples, including 13C-15N rotational echo double resonance (REDOR), 13C-13C dipolar recoupling measurements using the constant-time finite-pulse radio-frequency-driven recoupling (fpRFDR-CT) and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) techniques, and torsion angle measurements using the double quantum chemical shift anisotropy (DQCSA) technique. Further, we demonstrate that the structural information in the solid state NMR data is not distorted by pulsed spin locking in the detection period.     

Synthesis and liquid-crystalline properties of 4-(heptyloxy)-n-(aryl)benzaldimin-2-ols

The synthesis and liquid-crystalline properties of 4-(heptyloxy)-N-(aryl)benzaldimin-2-ols have been described. The compounds obtained have smectic and nematic mesomorphism. Alternation of the bleaching temperatures (T_bl) with variation of the length of the alkyl radical in the N-aryl fragment has been noted. The dependence of T_bl on the contribution of the substituent to the polarizability of the molecule ² is expressed by the equation T_bl=9.7+1.7².Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 9, pp. 1997–2001, September, 1989.     

Invariants and radiation of some nonstationary systems

In this paper formulas are obtained by means of the coherent-state method for calculating the radiation power of a nonstationary quantum system ofN charged particles whose Hamiltonian is a general quadratic form with respect to coordinates and momenta. The transitions between the coherent states and the Fock states of this system are discussed. The radiation is calculated both in the dipole approximation and strictly. As an example, the radiation of a charge in homogeneous varying electric and magnetic fields is found. The classical limit is considered.