Generalizations of the odd degree theorem and applications

LetV ⊂ ℙℝ ⁿ be an algebraic variety, such that its complexificationV _ℂ ⊂ ℙ ⁿ is irreducible of codimensionm ≥ 1. We use a sufficient condition on a linear spaceL ⊂ ℙℝ ⁿ of dimensionm + 2r to have a nonempty intersection withV, to show that any six dimensional subspace of 5 × 5 real symmetric matrices contains a nonzero matrix of rank at most 3.     

Durability of polyurethanes elastomers

The effect of thermal aging on three different elastomeric polyurethane adhesives was studied. Consequently, an attempt was made to predict the polyurethanes' service lifetimes from the changes in tensile properties, hardness of bulk specimens and adhesion strength properties (lap shear and butt joints) of polycarbonate bonded joints. Aging temperatures ranged from ambient to 70 °C (at 50% relative humidity) for durations from 20 days to 18 months. Experimental results were analyzed according to a kinetic rate theory and using limit values for the various properties. Consequently, service lifetimes were determined and compared to results from actual service life. Predictions of long-term performance from accelerated tests proved to be reasonable for the properties and materials studied.     

Some rigorous results for electromagnetic mass splittings in QCD

Written proved recently that m_π⁺m_π⁰. We note that this result is a consequence of the Green's function inequalities generalized to include EM as background fields. We also suggest that all ΔI = 2EM mass splittings can be proved to be positive.     

Some mappings of pfriodic groups

For the rational integera and the rational primeb, letP(a,b) be the set of primesp such that . A natural integerq satisfies (i) iffq is a power product fromP(a,b). In the (additively written) Abelian groupG, g→ag permutes the elements ofG ^# in cycles whose lengths are multiples ofb, but not ofb ², iffG is aπ-group withπ⊂P (a,b). The casea=−2,b=2 has combinational applications.     

Research problems

This section appears in nearly every issue. Contributions are invited, and should be submitted to R. C. Thompson, Mathematics Department, University of California, Santa Barbara, CA. 93106, USA.     

Remarks on a principle of localization

We prove that the Brauer class of a crossed product is a sum of symbols iff its “local” components are. Analogously we show that a solution of the “Goldie rank conjecture” would follow from the “local” statements; an extension of a result of Cliff-Sehgal is an easy corollary.     

Charmonium production inB-decays

We calculate partial widths for the decay of theB-meson into all possible charmonium states and estimate the corresponding branching ratios.     

Dipole moment of interacting rare-gas atoms

The translational absorption spectra of HeAr and NeAr have been analyzed with a hard-sphere potential to obtain the explicit dependence of the interaction dipoles on interatomic distance. The dipoles were found to consist of a short-range part varying almost exponentially with the distance and of a long-range part which varies more slowly. ^μHe Ar^(r) exhibited an unexpected maximum at small distances.