A Note on Boundary Unique Contination for Harmonic Functions in Non-Smooth Domains

In this note, we prove the boundary unique continuation property for harmonic function dfined on convex domain     

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.     

Flatness of domains and doubling properties of measures supported on their boundary,with applications to harmonic measure

Journal of Fourier Analysis and Applications -     

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 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.