Higher order Ito product formula and generators of evolutions and flows

A simple combinatorial formula is found for the product of two iterated quantum stochastic integrals, and used to find conditions that such an integral represent a unitary-valued or^*-algebra homomorphism-valued process.     

Synthesis of cross-conjugated polyketones by the crossed-aldol condensation of cyclic ketones with aromatic dialdehydes

Insoluble cross-conjugated polyketones were prepared from terephthalaldehyde and a variety of cycloaliphatic ketones by the crossed-aldol condensation. Elemental analyses and infrared spectra suggest that the polymeric aldol intermediates were not completely dehydrated. Evidence is also presented that suggests conjugate addition of the base to the α,β-unsaturated ketone may occur. Soluble cross-conjugated polyketones were prepared from terephthalaldehyde and 2-indanone, which contains no beta hydrogens, and from cycloaliphatic ketones and 1,2-bis(4-formylphenoxy)ethane, a dialdehyde containing isolated aldehyde groups. It is proposed, therefore, that the lack of solubility in the terephthalaldehyde-based polyketones arises from crosslinking via enolate anions formed at the beta position of the cyclic ketones, which are delocalized through the carbonyl groups of neighboring backbone repeating units. © 1995 John Wiley & Sons, Inc.     

Science Teacher Supply in the United States

The purpose of this study was to describe the supply and potential shortages of science teachers in the United States. Ninety-six percent of the State Science Consultants of the 50 State Boards of Education responded to a 1992 survey to assess the supply of science teachers. This survey was modeled after Howe and Gerlovich's 1982 study to provide an assessment of changes in science teacher supply over the last 10 years. Although there were improvements in the supply of science teachers, shortages were reported in all science subjects and were particularly critical in physics, chemistry, and earth science. In addition to providing a needed update on science teacher supply, this study analyzed 45 previous studies of science teacher supply and found convincing evidence to support the hypothesis that there is a persistent but fluctuating long term shortage of science teachers. This shortage is attributed to competition with business and industry. To alleviate critical shortages of science teachers, it is recommended that salaries be raised to be more competitive with industry and a national database be established to facilitate monitoring the supply of science teachers.     

Definitive evidence that the ESR spectrum observed during photolysis of Mn2(CO)10 in THF is due to octahedral high-spin (d5) manganese(II)

The reassignment to a manganese(0) quartet state by C.L. Kwan and J.K. Kochi (J. Organometal. Chem., 101 (1975) C9) of the ESR spectrum obtained during photolysis of Mn₂(CO)₁₀ in THF is shown to be in error; computer simulation of the X-band spectrum and observation of the S-band spectrum confirm our previous assignment to sextet manganese(II) and chemical and IR evidence indicate the presence of [Mn(CO)₅]^? as a counter ion.     

Novel mercury(II) complexes of meso-tetraphenylporphyrin and N-methylporphyrins

Treatment of meso-tetraphenylporphyrin, H₂TPP, with just over one equivalent of mercury(II) acetate in methylene chloride-THF gives mercury(II) meso-tetraphenylporphyrin, HgTPP. With excess of mercury(II) acetate, H₂TPP and HgTPP afford a novel dimetallic mononuclear porphyrin, AcOHgTPPHgOAc. In contrast, HgTPP reacts with mercury(II) chloride to give the chloro-analogue, ClHgTPPHgCl, but there is no reaction between H₂TPP and mercury(II) chloride. Demetallation of HgTPP in methylene chloride containing small amounts of hydrogen chloride proceeds via the dimetallic compound, ClHgTPPHgCl, to give free base HTPP. The reaction rate is dependent upon acid concentration suggesting that the rate determining step is protonation, but dilution causes no decrease in the rate; a mechanism which invokes the intermediacy of monohydrogen-meso-tetraphenylporphyrinatomercury(II) chloride, H(TPP)HgCl, in the formation of ClHgTPPHgCl and in its subsequent decomposition into H₂TPP, is proposed.N-Methylporphyrins react with mercury(II) acetate in methylene chloride-tetrahydrofuran to give the corresponding N-methylporphyrinatomercury(II) acetates, Me(P)HgOAc.