On K-stability of reductive varieties

G. Tian and S.K. Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kähler metric of constant scalar curvature. In [D3] Donaldson partially confirmed it in the case of projective toric varieties. In this paper we extend Donaldson’s results and computations to a new case, that of reductive varieties.Received: November 2003 Revision: January 2004 Accepted: January 2004     

Symmetry of the Barochronous Motions of a Gas

We study the system of nonlinear differential equations which expresses the constancy of the algebraic invariants of the Jacobian matrix for smooth vector fields in three-dimensional space. This system is equivalent to the equations of gas dynamics which describe the barochronous motions of a gas (the pressure and density depend only on the time). We present the results of computation of the admissible local Lie group and construction of the general solution of the system. We mention a few new problems that arise here.     

Rapid magnetization reversal in magnetic small particles induced by non-static bias field

Magnetization reversal processes by a switching field in single-domain nano-sized magnetic particles in the presence of a small transverse non-static bias field are studied. Applying an oscillating bias field instead of a static field, the reversal time becomes much shorter when the switching field is slightly stronger than the effective anisotropy field. A pulsed bias field of a suitably chosen duration in the nanosecond scale is found to induce a rapid switching, even when the switching field is smaller than the anisotropy field. The dependence of the reversal time on the frequency of an oscillating bias field and the duration of a pulsed bias field are studied. The present work thus complement the earlier studies on switching in the presence of a static bias field.     

Analysis of iron storage proteins in chicken liver and spleen tissues in comparison with human liver ferritin by Mössbauer spectroscopy

Summary Characterization of iron storage proteins in liver and spleen from normal chicken and chicken with lymphoid leukemia in comparison with human liver ferritin were considered by M?ssbauer spectroscopy (preliminary results). Small differences in M?ssbauer hyperfine parameters for both normal and lymphoid leukemia chicken liver and spleen were observed. The value of quadrupole splitting for human liver ferritin was higher than those for chicken tissues. A decrease of iron content in lymphoid leukemia chicken tissues was also found, however, the reason of this fact (pathology or feeding) was not clear yet.     

Some nucleophilic substitution reactions of s-triazolo[1,5-c]pyrimidines

Nucleophilic substitution of 5-methylthio- and 5-cyanomethylthio-7-amino-s-triazolo[1,5-c]pyrimidines has been carried out using sodium hydroxide, ammonia, hydrazine hydrate, and four amines. The cyanomethyl group is particularly reactive under these conditions and 5-cyanomethylthiotriazolopyrimidine can be used to functionalize this heterocycle.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 382–385, March, 1992.     

Muon spin resonance and repolarization in amorphous silicon monoxide (a-SiO)

Studies of the muonium fractions in the amorphous oxide a-SiO have been carried out by RF resonance at TRIUMF, Canada and LF repolarization techniques at RAL, U.K. The resonance measurements confirm the presence of the interstitial Mu centre in this intermediate oxide of silicon. Analysis of the data gathered at RAL, using a recently-developed fitting technique, reveals that the Mu^* state is present here as well, but with lower relative fractions than in a-Si. However, as in the latter material, but in contrast to c-Si, this bond-centre species appears to be stable up to room temperature.     

Structure and reactivity of 2-methyl-9-hydroxy-4H-pyrido[1,2-a]pyrimidin-4-one

It has been shown that the alkylation of 2-methyl-9-hydroxy-4H-pyrido[1,2-a]pyrimidin-4-one takes place at the oxygen atom, but electrophilic substitution takes place mainly at position 8 of the molecule (the ortho position relative to the hydroxy group).Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 12, pp. 1660–1666, December, 1992.