Sets of uniqueness for spherically convergent multiple trigonometric series

A subset of the -dimensional torus is called a set of uniqueness, or -set, if every multiple trigonometric series spherically converging to outside vanishes identically. We show that all countable sets are -sets and also that sets are -sets for every . In particular, , where is the Cantor set, is an set and hence a -set. We will say that is a -set if every multiple trigonometric series spherically Abel summable to outside and having certain growth restrictions on its coefficients vanishes identically. The above-mentioned results hold also for sets. In addition, every -set has measure , and a countable union of closed -sets is a -set.

     

VLPR study of the reaction Br + CH3CHO

The reaction \documentclass{article}\pagestyle{empty}\begin{document}${\rm Br} + {\rm CH}_3 {\rm CHO}\buildrel1\over\rightarrow{\rm HBr} + {\rm CH}_3 {\rm CO}$\end{document} has been studied by VLPR at 300 K. We find k₁ = 2.1 × 10¹² cm³/mol s in excellent agreement with independent measurements from photolysis studies. Combining this value with known thermodynamic data gives k_-1 = 1 × 10¹⁰ cm³/mol s. Observations of mass 42 expected from ketene suggest a rapid secondary reaction: in which step 2 is shown to be rate limiting under VLPR conditions and k₂ is estimated at 10^12.6 cm³/mol s from recent theoretical models for radical recombination. It is also shown that 0 ? E₁ ? 1.4 kcal/mol using theoretical models for calculation of A₁ and is probably closer to the lower limit. Reaction ?1 is negligible under conditions used.     

Electrophoresis of human salivary proteins: response to natural stimulation

Human saliva was analyzed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis and the response to different natural stimuli investigated. Serva Blue R revealed pink/violet-staining proteins ("lumicarmines"). These intensified following stimulation but in an unpredictable and sometimes disproportionate manner, causing pattern changes. This variable response undermines their potential forensic value for suspect identification.     

Backward photoproduction of ϱ° and f between 2.8 GeV and 4.8 GeV

A measurement of backward photoproduction of charged pion pairs on protons is reported. The pion pair mass spectrum shows strong ?° and f production. Data are presented on the u and s dependence for ?^O and f, together with the decay polarisation for the ?^O.     

Measurement of the fragmentation of hadronic systems of different flavour and colour selected by lepton pairs

A lepton-pair trigger was used to select a hadronic system in different flavour and colour states: properties of the transformation of this system into hadrons were measured in terms of charge flow, multiplicity distribution, and fragmentation function. It is observed that, while the effects of flavour are clearly seen, the colour degrees of freedom are not observed in the region of low p_T.