Equations of state and shock-induced transformations in solid I-solid II-liquid bismuth

An equation of state is determined for each phase in the solid I-solid II-liquid region of bismuth. Equality of the Gibbs free energy for each pair of phases determines the phase boundaries and triple point in the temperature-pressure plane. From the complete equation of state, the shock-wave response of bismuth preheated to 493 °K. is calculated and comparison is made with experimental data obtained by means of quartz transducer instrumentation. These results suggest that bismuth undergoes a certain degree of melting on the microsecond time scale of the shock-wave experiment. This is contrary to previous results and conclusions drawn from data on the shock-wave propagation in bismuth. These seemingly contradictory results may be due to microstructural differences in the samples or to differences in measuring techniques.     

Eigenvalue inequalities for principal submatrices

For a polynomial with real roots, inequalities between those roots and the roots of the derivative are demonstrated and translated into eigenvalue inequalities for a hermitian matrix and its submatrices. For example, given an n-by-n positive definite hermitian matrix with maximum eigenvalue λ, these inequalities imply that some principal submatrix has an eigenvalue exceeding $\text{[(}\text{n?1)}\text{n}\text{]λ}$.     

Heterocyclic studies—XXIX: Mass spectra of some 1,2-dihydro-5-trifluoromethyl-pyrimido(5,4-E)AS-triazines

Mass spectra of five 7-substituted-1,2-dihydro-5-trifluoromethylpyrimido(5,4-e)as-triazine derivatives are recorded. Fragmentation pathways, elucidation of which was assisted by deuterium labelling and accurate mass measurements, are compared with those of corresponding heteroaromatic compounds. Loss of HF initiated the major breakdown pathways, unless a large 7-substituent was present, which then fragmented preferentially.     

An invariant subspace theorem

In this paper it is proved that every operator on a complex Hilbert space whose spectrum is a spectral set has a nontrivial invariant subspace.     

Syntheses of some mixed AuOs and PtOs clusters and the X-ray structure of [Os4H2(CO)12(AuPPh3)2]

Some reactions of [Os₄H₃(CO)₁₂AuPR₃] (R = Et, Ph) resulting in the formation of [Os₄H₂(CO)₁₂(AuPR₃)₂] are presented. A single-crystal X-ray structure of [Os₄H₂(CO)₁₂(AuPPh₃)₂] is reported and reveals a novel Ph₃PAuAuPPh₃ unit asymmetrically bridging one edge of an Os₄ tetrahedron, the first example of a mixed gold-metal carbonyl cluster with an AuAu bond.