A refinement of the Strichartz inequality on the saddle and applications

We consider the nonlinear nonelliptic Schrödinger equation defined by with initial datum in L²(R²). We show that if the solution blows up in finite time, then there is a mass concentration phenomenon near the blow-up time. The key ingredient is a refinement of the Strichartz inequality on the saddle.     

Dynamics of ion exchange between self-assembled redox polyelectrolyte multilayer modified electrode and liquid electrolyte

A probe beam deflection (PBD) study of ion exchange between an electroactive polymer poly(allylamine)-bipyridyl-pyridine osmium complex film and liquid electrolyte is reported. The PBD measurements were made simultaneously to chronoamperometric oxidation-reduction cycles, to be able to detect kinetic effects in the ion exchange. Layer-by-layer (LbL) self-assembled redox polyelectrolyte films with osmium bipyridyl complex covalently attached to poly(allylamine) (PAH-Os) and poly(styrene sulfonate) (PSS) have been built by alternate electrostatic adsorption from soluble polyelectrolytes. The ionic exchange during initial conditioning of the film ("break-in") undergoing oxidation-reduction cycles and recovery after equilibration in the reduced state have shown an exchange of anions and cations with time lag between them. The effect of the nature of cation on the ionic exchange has been investigated with dilute HCl, LiCl, NaCl, and CsCl electrolytes. The ratio of anion to cation exchanged at the film-electrolyte interface has a strong dependence on the nature of charge in the topmost layer, that is, when negatively charged PSS is the capping layer, a larger proportion of cation exchange is observed. This demonstrates that the electrical potential distribution at the redox polyelectrolyte multilayer (PEM)/electrolyte interface determines the ionic flux in response to charge injection in the film.     

Apparent Molar Volumes of Some Sodium Sulfonamides in Water at Several Molalities and Temperatures

In this article, measured densities of aqueous solutions of sodium sulfadiazine, sodium sulfamerazine and sodium sulfamethazine are reported as a function of molality from 0.0500 to 0.5000 mol?kg^?1 and as a function of temperature at (278.15, 283.15, 288.15, 293.15, 298.15, 303.15, 308.15 and 313.15) K. The apparent molar volumes, partial molar volumes at infinite dilution and partial molar expansibilities were calculated. The dependence of these properties upon temperature is shown. The results are interpreted in terms of solute-solvent interactions.     

Shimura curves with many uniform dessins

A compact Riemann surface of genus g >?1 has different uniform dessins d’enfants of the same type if and only if its surface group S is contained in different conjugate Fuchsian triangle groups Δ and αΔα ^?1. Tools and results in the study of these conjugates depend on whether Δ is an arithmetic triangle group or not. In the case when Δ is not arithmetic the possible conjugators are rare and easy to classify. In the arithmetic case, i.e. for Shimura curves, the problem is much more complicated, but the arithmetic of quaternion algebras controls the growth of the number of uniform dessins of given type with respect to the genus. This number grows at most as O(g ^1/3) and this bound is sharp. As a tool, localization of the quaternion algebras and the representation of p-adic maximal orders as vertices of Serre–Bruhat–Tits trees turn out to be crucial. In low genera, the results shed a surprising new light on the uniformization of some classical curves like Klein’s quartic and other Macbeath–Hurwitz curves.     

A Simple Thermoelectric Droplet Generator

Experimental Techniques - A new design for a droplet generator capable of producing single droplets is presented. The design relies on thermoelectric heating to vaporize water at the interface...     

Synthesis and Characterization of HgII/Se/CuI Multinuclear Compounds from Mercury(II) Bis(p‐aminobenzeneselenolate) – Hg(SeC6H4NH2‐p)2

In this paper we explore an amino functionalized selenolate unit for the synthesis of new multinuclear compounds with promising interesting properties and potential precursors of semiconductors. We present for the first time the X‐ray crystallographic structure of [Hg(SeC₆H₄NH₂)₂]₂ · diox ( 1· diox) and its copper(I) derivatives: HgCu₂X₂(SeC₆H₄NH₂)₂(PPh₃)₄ · 4diox [X = Br ( 2· 4diox) and I ( 3· 4diox)]. The compounds 1 and 2 , 3 can be considered as the starting material and intermediates, respectively, for the synthesis of ternary Hg^II/Se/Cu^I nanoclusters. We also provide IR and NMR spectroscopic data and evaluate the optical features of these compounds by difuse reflectance UV/Vis spectroscopy.