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.     

Optical Spectroscopy and Theoretical Studies in Calixarene Chemistry

This review summarizes different applications of optical spectroscopic methods in calixarene chemistry including UV/Vis spectrometry, vibrational spectroscopic techniques (FTIR and Raman spectroscopy), luminescence spectroscopy (including fluorescence and phosphorescence), ellipsometry and various optical microscopic methods. Moreover, the results of theoretical studies (AM1, PM3, DFT, ab initio, etc.) are summarized based on selected papers in the field of conformational studies, thermodynamics and complexation features. About 300 references are processed systematically from the results reported mainly in the recent years with emphasis on the potential of practical application of these molecules.     

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.     

Magnetic properties of HITPERM-type alloys at high temperature

(Fe,Co)–Zr,Hf)–Cu–B (HITPERM-type) alloys with variable Hf, Zr and Co content were isothermally crystallised at 500–650 °C for 1 h, and the optimum nanocrystallisation temperature was selected on the basis of the minimum coercive field at room temperature. The quasistatic hysteresis loops were measured at temperature from 20 to 650 °C. Subsequently, the optimally annealed alloys were subjected to long-term annealing at 500, 550 and 600 °C. Working temperature of 600°C is too high for the investigated alloys to maintain stable magnetic properties. Temperature of 550 or 500 °C permits the material to be magnetically stable for a long period. The magnetic hysteresis loops recorded for the nanocrystalline alloys, where Fe:Co ratio is close to 1 and refractory metals content is 7 at.%, prove that coercive field increases slightly with temperature, but remains in the range of 20–40 A/m (depending on the alloy composition) from 20 to 550 °C. This proves that the investigated alloys, after optimisation of chemical composition, may be suitable for high temperature use.     

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.     

Synthesis of cephalosporins carrying isoxazolyl acetamido and related side chains

Starting from 3,5-dimethylisoxazole the carboxylic acids I and V, the amino acids VIII (L-) and IX (D-), and the ureido acids X (L-) and XI (D-) were prepared, which were used for the synthesis of the new cephalosporins XVIIb, XXa-c (L-), and XXIb (D-). Thein vitro antibacterial activity of these semi-synthetic antibiotics was studied. The resorption of XVIIb was investigated in mice.Research Group for Antibiotics of the Hungarian Academy of Sciences, H-4010 Debrecen, P.O. Box 70, Hungary. Published in Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1524–1535, November, 1998.     

Conflict resolution in fuzzy environment

Conflict resolution methodology is discussed with fuzzified Pareto frontier. Four solution concepts, namely, the Nash solution, the generalized Nash solution, the Kalai-Smorodinsky concept, and a solution method based on a special bargaining process are examined. The solutions are also fuzzy, the corresponding payoff values are fuzzy numbers, the membership functions of which are determined. Three particular cases are considered in the paper. Linear, quadratic, and general nonlinear Pareto frontiers with known shape are examined.     

Change of geometry of polyacetylene upon charge transfer

Crystal orbital calculations on cis- and trans-polyacethylene chains indicate two kinds of geometry changes on charge transfer. (1) increase (decrease) of the CC bond lenght and CCC bond angles in the trans conformer taking up (losing) electrons, and $\text{(u)}\text{?}$ a tendency towards bond-length equalization on electron uptake and loss for both conformers.     

Stereochemical studies—76 saturated heterocycles—63 : synthesis of cis- and trans-n-methyl- and n-benzyl-4.5- and 5,6-tetramethylenetetrahydro-1,3-oxazines; an x-ray study of n-benzyl-cis-4,5-tetramethylenetetrahydro-1,-3-oxazinium- picrate

- The corresponding $\text{cis}$- and $\text{trans-N}$-methyl- and $\text{N}$-benzyl-5,6- and 4,5-tetramethylenetetrahydro-l,3-oxazines $\text{(5a,b-8a,b)}$were synthesized from $\text{cis}$- and $\text{trans-N}$-methyl and$\text{N}$-benzyl-2- aminomethyl-1-cyclohexanols $\text{1a,b,2a,b}$, from $\text{cis}$- and $\text{trans-N}$-methyl- and $\text{N}$benzyl -2-hydroxymethyl-1-cyclohexylamines$\text{(3a,b,4a,b)}$ by reaction with formaldehyde. The aminoalcohols $\text{1a,2a,3a,b}$and $\text{4a,b}$ were prepared in considerably higher yields than in earlier procedures. NMR spectroscopy showed that the $\text{cis}$ isomers of the synthesized oxazines were conformationally homogeneous in solution, and their preferred conformation (inside or outside) depended on the steric requirement of the groups attached to the anellation points, whereas a bulky C-2 substituent had no influence on the predominant conformation. The structure of $\text{N}$-benzyl-$\text{cis}$-4,5-tetramethylenetetrahydro-1,3-oxaziniumpicrate $\text{(7b)}$. determined by X-ray diffraction analysis, was in agreement with the predominant N-outside conformation of the corresponding base, established by means of NMR spectroscopy.