On the Curvature of the Indicatrix Surface in Three-Dimensional Minkowski Spaces

Periodica Mathematica Hungarica - As it is well-known a Minkowski space is a finite dimensional real vector space equipped with a Minkowski functional F. If the square of the Minkowski functional...     

On the number of conjugacy classes of a finite solvable group II

We prove that a finite solvable group G has at least (49p+1)/60 conjugacy classes whenever p is a prime such that p² divides the order of G. We also construct an infinite family of finite solvable groups, where this bound is attained.     

Indistinguishability of particles or independence of the random variables?

After establishing the formula of information, we turn to two cases: to the independent case and to the dependent case. If the characteristics of the particles (e.g., the energy) as random variables are independent, we come in the discrete case to the Boltzmann distribution, while in the continuous case we come to the Gibbs formula-irrespectively of whether the particles are distinguishable or not. Our effort is nimed at clarity of the ideas, not at their mathematical completeness. Supported by the Hungarian National Foundation for Scientific Research (grant No. T 016384 and No. 4007-016237) Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russian, 1995, Part III.     

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.     

Sodium-23 Nuclear Magnetic Resonance Spectroscopy

With the availability of Fourier transform spectrometers, ²³Na-NMR spectroscopy has become an important tool. It affords direct insight into solvation and ion pairing phenomena, both in organic and in bio-inorganic systems. Monitoring the chemical shifts and linewidths of ²³Na signals gives access to binding constants, reorientational correlation times and the microdynamics of the sodium coordination shell. The binding of other cations can also be studied by ²³Na-NMR spectroscopy, in competition experiments.     

Enhancement of phosphoprotein analysis using a fluorescent affinity tag and mass spectrometry

A fluorescent affinity tag (FAT) was synthesized and was utilized to selectively modify phosphorylated serine and threonine residues via beta-elimination and Michael addition chemistries in a 'one-step' reaction. This labeling technique was used for covalent modification of both phosphoproteins and phosphopeptides, allowing identification of these molecular species by fluorescence imaging after solution- or gel-based separation methods. In addition to the strong fluorescence of the rhodamine tag, a commercially available antibody can be used to enrich low-abundance post-labeled phosphopeptides present in complex mixtures. Application of this methodology to phosphorylation-site mapping has been evaluated for a phosphoprotein standard, bovine beta-casein. Initial results demonstrated low femtomole detection limits after fluorescence image analysis of FAT-labeled proteins or peptides.     

Investigating bidentate and tridentate carbamoylmethylphosphine oxide ligand interactions with rare-Earth elements using electrospray ionization quadrupole ion trap mass spectrometry

Electrospray ionization (ESI) quadrupole ion trap mass spectrometry (QIT-MS) and collisionally activated dissociation (CAD) were used to evaluate the rare-earth binding properties of two hydrophobic carbamoylmethylphosphine oxide (CMPO) ligands, the normal bidentate variety, (t-BuC6H4)2P(O)CH2C(O)N(i-Bu)2 (A), a new potentially tridentate extractant, (t-BuC6H4)2P(O)CH[CH2C(O)N(i-Bu)2]C(O)N(i-Bu)2 (B), and tributyl phosphate. The mass spectral results obtained from analysis of 1% HNO3/methanol solution containing the ligands and dissolved lanthanide salts reveal that the favorable stoichiometries of the ligand/metal/nitrate complexes are 2:1:2 for the bidentate ligand A, 1:1:2 for the tridentate ligand B, and 3:1:2 for the monodentate tributyl phosphate. These observed stoichiometries correlate with the number of available binding sites on each ligand as well as with potential steric effects. Energy-variable collisionally activated dissociation experiments showed that for the 2:1:2 complexes involving ligand A or B, as the ionic radius of the bound metal decreased, the removal of nitric acid required less energy and resulted in less extensive spontaneous solvent coordination. This experimental trend suggests that, as the ionic radius of the lanthanide ion decreases, a pair of the carbamoylmethylphosphine ligands is able to more completely solvate the bound metal ion thereby weakening the nitrate-metal interaction.     

Direct Clay-Catalyzed Friedel-Crafts Arylation and Chlorination of the Hydrocarbon Adamantane

Multiple chlorinations and arylations at the tertiary positions of adamantane are promoted by FeCl₃-doped K10 montmorillonite in CCl₄ or in aromatic solvents. The process, remarkably easy to implement, can be tailored to selective formation of monosubstituted 1-adamantyl derivatives or 1,3-disubstituted adamantanes. The process achieves alkylation at the meta- and para-positions of toluene leading to a purely statistical distribution and displays no substrate specificity in competition experiments between toluene and benzene.