Walsh's Brownian Motion-Type of Extensions

Let (X _t ) be a rotation invariant Feller process on the state space F R²{} consisting of finite number of rays, meeting at 0. We study a certain class of possible strong Markov extensions of (X _t ) to F ,{} given the corresponding radial extension to [0, ). A well-known example is the class of Walsh's Brownian motions, in the case where (X _t ) is the Brownian motion on F. It turns out that while the symmetric extension of Walsh's Brownian motion-type always exists, the non-symmetric extension exists iff (X _t ), roughly speaking, does not jump from one ray to another before hitting 0.     

Unique representation in number systems and L codes

An algorithm is presented for deciding whether or not the representation according to a given number system is unique.     

Determination of antimony in geochemical samples by graphite furnace atomic absorption spectrometry using different matrix modifiers

Determination of antimony by graphite furnace atomic absorption spectrometry using five different matrix modifiers, viz. nitric acid, copper, nickel, molybdenum and palladium, together with L'vov platform was studied. Without matrix modification, antimony was lost in a 1.2-M HCl solution when the thermal pretreatment temperature exceeded 700°C. By using 1.4 M HNO₃ or $\text{1μg}\text{20μl}$ copper solution the thermal pretreatment temperature could be increased up to 900°C. The matrix modification with $\text{2μg}\text{20μl}$ palladium, $\text{4μg}\text{20μl}$ molybdenum, or $\text{20μg}\text{20μl}$ nickel allowed the use of 1300°C as the pretreatment temperature. The best results were obtained with palladium when its concentration exceeded $\text{0.8μg}\text{20μl}$. Chemical interferences were studied with standard solutions spiked with different metal chlorides. The severe interference caused by iron chloride was avoided with ascorbic acid (2.5 %, $\text{w}\text{v}$). The method was tested on some geochemical reference samples.     

Variational principles for differential equations with symmetries and conservation laws

This research was supported in part by NSF grant DMS 91-00674     

4-Aryl-8-hydroxyquinolines from 4-chloro-8-tosyloxyquinoline using a Suzuki-Miyaura cross-coupling approach

4-Chloro-8-tosyloxyquinoline was successfully cross-coupled with various arylboronic acids in anhydrous Suzuki-Miyaura conditions. The protective tosyl group was stable during the anhydrous coupling. The use of tosyl protection in association with anhydrous Suzuki-Miyaura reaction conditions allows the use of commercially available but relative inert 5-chloro-8-hydroxyquinoline for the synthesis of 5-phenyl-8-hydroxyquinoline. Deprotection could easily be made by using suitable nucleophiles to afford the final 5-phenyl and 4-aryl-8-hydroxyquinolines in high yields. Under acidic conditions the tosyloxy group is sufficiently stable to allow selective further modification of acid labile functional groups.     

Calculation of isotropic Compton profiles with Gaussian basis sets

In this paper we present an adaptive algorithm for calculating the isotropic Compton profile (ICP) for any type of Gaussian basis set. The ICP is a measure of the momentum density of electrons and it can be obtained from inelastic X-ray scattering experiments employing synchrotron radiation. We have performed calculations of the ICP for water and helium monomers and dimers using density-functional theory, Hartree-Fock and post-Hartree-Fock methods, with Dunning-type ((d-)aug-)cc-p(C)VXZ basis sets. We have examined the convergence of the Compton profile as a function of the basis set and the level of theory used for the formation of the density matrix. We demonstrate that diffuse basis functions are of utmost importance to the calculation of Compton profiles. Basis sets of at least triple-ζ quality appended by diffuse functions should be used in Compton profile calculations in order to obtain sufficient convergence with regard to the current, experimentally feasible accuracy for systems consisting of light elements.     

Muckenhoupt Ap-properties of Distance Functions and Applications to Hardy–Sobolev -type Inequalities

Potential Analysis - Let X be a metric space equipped with a doubling measure. We consider weights w(x) = dist(x,E)?α, where E is a closed set in X and $alpha in mathbb {R}$ . We...