Scaled-oscillation and regularity

We give sufficient conditions for Sobolev and Lipschitz functions in terms of their lower scaled-oscillation. The sharpness of these conditions is shown by examples. Our examples also show that a Stepanov-type differentiability theorem does not hold under the boundedness assumption of the lower scaled-oscillation.

     

Unavoidable Traces Of Set Systems

Sauer, Shelah, Vapnik and Chervonenkis proved that if a set system on n vertices contains many sets, then the set system has full trace on a large set. Although the restriction on the size of the groundset cannot be lifted, Frankl and Pach found a trace structure that is guaranteed to occur in uniform set systems even if we do not bound the size of the groundset. In this note we shall give three sequences of structures such that every set system consisting of sufficiently many sets contains at least one of these structures with many sets.     

Global variations in peak bone mass as studied by dual-energy X-ray absorptiometry

In 1994, the International Atomic Energy Agency (IAEA) initiated a 5-year Co-ordinated Research Project (CRP) to determine geographical and racial differences in peak bone mineral density (BMD) in men and women aged 15-49 years. The study demonstrates that there are distinct global differences in BMD at the hip and spine in both men and women approximating to one population standard deviation between populations with the highest and lowest BMD. These differences persist following adjustments for age, sex and body size. Such information is valuable in understanding the reasons for global differences in fracture rate and predicting future trends in fracture incidence. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mineralogical analysis of auriferous ores from the El Diamante mine, Colombia

X-ray diffraction (XRD), Mössbauer spectrometry (MS), secondary ions mass spectroscopy (SIMS) and laser-ablation microprobe–inductively coupled plasma–mass spectrometry (LAM–ICP–MS) were used to study mineral samples of Colombian auriferous ores collected from the “El Diamante” mine, located in the municipality of Guachavez-Nariño, in Colombia. The samples were prepared as polished thin sections and polished sections. From XRD data, quartz, sphalerite and pyrite were detected and their respective cell parameters were estimated. From MS analyses, pyrite, arsenopyrite and chalcopyrite were identified; their respective hyperfine parameters and respective texture were deduced. Multiple regions of approximately 200 × 200 μm in each sample were analyzed with SIMS; the occurrence of “invisible gold” associated mainly with pyrite and secondarily with arsenopyrite could thus be assigned. It was also found that pyrite is of the arsenious type. Spots from 30 to 40 μm in diameter were analyzed with LAM–ICP–MS for pyrite, arsenopyrite and sphalerite; Au is “homogeneously” distributed inside the structure of the arsenious pyrite and the arsenopyrite (not as inclusions); the chemical composition indicates similarities of this “invisible gold”, forming a solid solution with arsenious pyrite and arsenopyrite. One hundred nineteen and 62 ppm of ‘invisible gold’ was quantified in 21 spots analyzed on pyrite and in 14 spots on arsenopyrite, respectively.     

Cyclic Markov equilibria in stochastic games

We examine a three-person stochastic game where the only existing equilibria consist of cyclic Markov strategies. Unlike in two-person games of a similar type, stationary ε-equilibria (ε > 0) do not exist for this game. Besides we characterize the set of feasible equilibrium rewards.     

Temperature dependence of the iron hyperfine field distribution in amorphous Fe-rich Fe-Zr alloys

The temperature dependence of the iron hyperfine field distribution is reported in melt-quenched amorphous Fe-Zr alloys. The most remarkable feature is the compositinal change in the shape of the average hyperfine field versus temperature curves. The unusual increase in the average hyperfine field below about 85 K is a characteristic feature of the RSG systems; however, no anomaly is observed in the width of the hyperfine field distribution as a function of temperature. The results cannot be properly explained in the framework of the existing spin glass models.     

Thickness dependence of the magnetic anisotropy of Fe layers separated by Al

Magnetic multilayers of ⁵⁷Fe with nominal thickness, T _nom, between 0.4 and 1.0 nm separated by 3.0 nm Al spacer layers were prepared by alternate deposition of the constituents in high vacuum. The samples were investigated at 4.2 K in external magnetic field. A fraction of Fe atoms corresponding to about 0.3 nm equivalent Fe-thickness was found to mix into the Al spacer. The extremely strong magnetic anisotropy observed for T _nom < 0.8 nm is attributed to Fe layers of approximately two atomic planes thick. The anisotropy decreases considerably after the building up of the third Fe atomic layer starts at T _nom = 0.8 nm, but full saturation was not achieved even for T _nom = 1 nm and 3 T magnetic field applied perpendicularly to the sample plane.     

Fourier transform ion cyclotron resonance study of ion-molecule reactions of [M – OCH3]+ ions of methyl 2,3,4,6-tetra-O-methyl-d-hexopyranosides with ammonia

Glycosidic oxocarbenium ions A₁⁺ were formed by isobutane chemical ionization from methyl 2,3,4,6-tetra-O-methyl-β-D -mannopyranoside, methyl 2,3,4,6-tetra-0-methyl-β-D -galactopyranoside and methyl 2,3,4,6-tetra-O-methyl-β-D -glucopyranoside (the ring - O-being converted into ? O ? ), and then- reaction with ammonia was studied by Fourier transform ion cyclotron resonance Spectrometry. Very slow formation (reaction efficiency 0.6-1.4%) of the adduct ion [A₁ + NH₃]⁴ was observed as the main process for carefully thermalized ions A₁⁺. Interestingly, the efficiency of the adduct ion formation depends on the sterochemistry of ions A₁⁺.     

Determination of Rb and Sr concentrations in rocks by radioisotope X-ray fluorescence analysis

A method is described for Rb and Sr concentration determinations in rocks by radioisotope X-ray fluorescence analysis. The yield/concentration ratios were established by increasing the concentrations of the examined elements in the sample and recording each spectrum. The analytical error in the 100-1,000 ppm concentration range was 2–4%, and for 50 ppm about 10%, and the detection limit was 5–10 ppm.