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 $\nu$ \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

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

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