13,246 research outputs found
Division algebras of prime degree with infinite genus
The genus gen(D) of a finite-dimensional central division algebra D over a
field F is defined as the collection of classes [D'] in the Brauer group Br(F),
where D' is a central division F-algebra having the same maximal subfields as
D. For any prime p, we construct a division algebra of degree p with infinite
genus. Moreover, we show that there exists a field K such that there are
infinitely many nonisomorphic central division K-algebras of degree p, and any
two such algebras have the same genus.Comment: 4 page
The Critical Crossover at the n-Hexane - Water Interface
According to estimates of the parameters of the critical crossover in
monolayers of long-chain alcohol molecules adsorbed at the n-hexane - water
interface, all systems in which this phenomenon is observed are characterized
by the same value of the critical exponent \approx 1.8.Comment: 5 pages, 2 pictures, 1 tabl
Partial measures
We study sigma-additive set functions defined on a hereditary subclass of a
sigma-algebra and taken values in the extended real line. Analogs of the Jordan
decomposition theorem and the Radon-Nikodym theorem are obtained.Comment: 4 pages. Submitted to Lobachevskii Journal of Mathematics (
http://ljm.ksu.ru
Compact Layer of Alkali Ions at the Surface of Colloidal Silica
The forces of electrical imaging strongly polarize the surface of colloidal
silica. I used X-ray scattering to study the adsorbed 2-nm-thick compact layer
of alkali ions at the surface of concentrated solutions of 5-nm, 7-nm, and
22-nm particles, stabilized either by NaOH or a mixture of NaOH and CsOH, with
the total bulk concentration of alkali ions ranging from 0.1- to 0.7-mol/L. The
observed structure of the compact layer is almost independent of the size of
the particles and concentration of alkali base in the sol; it can be described
by a two-layer model, i.e., an ~ 8 Angstrom thick layer of directly adsorbed
hydrated alkali ions with a surface concentration 3x10(18) m(-2), and a ~ 13
Angstrom thick layer with a surface concentration of sodium ions 8x10(18)
m(-2). In cesium-enriched sols, Cs+ ions preferentially adsorb in the first
layer replacing Na+; their density in the second layer does not depend on the
presence of cesium in the sol. The difference in the adsorption of Cs+ and Na+
ions can be explained by the ion-size-dependent term in the electrostatic Gibbs
energy equation derived earlier by others. I also discuss the surface charge
density and the value of surface tension at the sol's surface.Comment: 32 pages 10 figure
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