Sublimation of atomic layers from a chromium surface

We employ low-energy electron microscopy to study the kinetics of thermal etching, or sublimation, of Cr(001) at approximately 1100 K. Atomic layers are removed from the surface by spontaneous nucleation and growth of two-dimensional vacancy islands, by rotation of spiral steps, and by island decay. The growth rates of vacancy islands and the rotation frequencies of double spirals are measured as a function of temperature, and the results are correlated with activation barriers of surface processes. Mass transport between the surface and bulk is shown to be unimportant.     

On Integrable Delta Functions on the Levi-Civita Field

In this paper, we develop a theory of integrable delta functions on the Levi-Civita field R as well as on R² and R³ with similar properties to the one-dimensional, two-dimensional and three-dimensional Dirac Delta functions and which reduce to them when restricted to points in R, R² and R³, respectively. First we review the recently developed Lebesgue-like measure and integration theory over R, R² and R³. Then we introduce delta functions on R, R² and R³ that are integrable in the context of the aforementioned integration theory; and we study their properties and some applications.     

High-load, ROMP-generated oligomeric bis-acid chlorides: design of soluble and insoluble nucleophile scavengers

[reaction: see text] An efficient strategy for scavenging a host of nucleophiles utilizing an oligomeric bis-acid chloride (OBAC), generated from the ROM polymerization of trans-bicyclo[2.2.1]hept-5-ene-2,3-dicarbonyl dichloride, is described. The reactivity and high load of the OBAC reagent is exploited in the scavenging of amines, alcohols, and thiols that are present in excess following a common benzoylation event. Following the scavenging event, these oligomers can be precipitated with EtOAc and filtered (SiO(2)), leaving benzoylated nucleophiles in excellent yield and purity.     

Iodine-induced reaction cascades for the rapid construction of variously substituted benzothiophenes

[reaction: see text] Readily accessible propynols with a 2-thioxyphenyl substituent selectively undergo 5-exo-iodocyclization followed by tandem rearrangement and elimination or substitution processes to give selective access to either 2-acyl- or 2-(1-iodoalkeny)-benzo[b]thiophene systems.     

The Dielectrophoretic Behavior of Submicron Latex Spheres: Influence of Surface Conductance

An analysis of the dielectrophoretic crossover frequency as a function of medium conductivity has been made for submicron spheres with different surface functionalities. It is shown that the AC electrokinetic behavior of the particles can be explained by modeling the surface conductivity of the particle as the sum of two surface conductance components: one due to charge motion behind the slip plane (the Stern layer) and the other due to charge motion in front of the slip plane.     

An oxidation with thionyl chloride

The reaction of the 2-methylquinoline-3-carboxylic acid 1b with thionyl chloride gave the dichlorothiolactone 2 , the structure of which was confirmed by chemical transformations.     

ROMP-generated oligomeric sulfonyl chlorides as versatile soluble scavenging agents

[reaction: see text] A new method for homogeneous nucleophilic scavenging employing oligomeric sulfonyl chloride (OSC) reagents is described. The method utilizes OSC to rapidly scavenge a variety of amines that are present in excess. The OSC reagents are generated from ROM polymerization of 2-chlorosulfonyl-5-norbornene utilizing the second generation Grubbs catalyst to produce oligomers of varying size as stable, free-flowing powders. Following the scavenging event, these oligomers are precipitated with ethyl acetate leaving products in excellent yield and purity.     

Quantitative measurement of the polydispersity in the extent of functionalization of glass‐forming calix[4]resorcinarenes

The polydispersity in the degree of functionalization for two calix[4]resorcinarenes was determined by measuring quantitatively their molecular mass distribution with matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry. A mathematical method for polydisperse materials is described that creates a calibration curve to correct the ion signal intensities in the mass spectrum to give a more reliable molecular mass distribution. Correction is required due to various sample preparation and instrumental effects that may produce a systematic mass bias in the number of oligomers measured. This method employs gravimetric mixtures of analytes with different degrees of functionalization. One calix[4]resorcinarene was found to give accurate molecular mass distributions with little correction, while another, having a very similar molecular structure, was found to exhibit strong over‐counting of the oligomers having a high degree of functionalization. Copyright © 2009 John Wiley & Sons, Ltd.     

Towers of 2-covers of hyperelliptic curves

In this article, we give a way of constructing an unramified Galois-cover of a hyperelliptic curve. The geometric Galois-group is an elementary abelian -group. The construction does not make use of the embedding of the curve in its Jacobian, and it readily displays all subcovers. We show that the cover we construct is isomorphic to the pullback along the multiplication-by- map of an embedding of the curve in its Jacobian.

We show that the constructed cover has an abundance of elliptic and hyperelliptic subcovers. This makes this cover especially suited for covering techniques employed for determining the rational points on curves. In particular the hyperelliptic subcovers give a chance for applying the method iteratively, thus creating towers of elementary abelian 2-covers of hyperelliptic curves.

As an application, we determine the rational points on the genus curve arising from the question of whether the sum of the first fourth powers can ever be a square. For this curve, a simple covering step fails, but a second step succeeds.