On approximately convex functions

A real valued function defined on a real interval is called -convex if it satisfies

The main results of the paper offer various characterizations for -convexity. One of the main results states that is -convex for some positive and if and only if can be decomposed into the sum of a convex function, a function with bounded supremum norm, and a function with bounded Lipschitz-modulus. In the special case , the results reduce to that of Hyers, Ulam, and Green obtained in 1952 concerning the so-called -convexity.

     

Synthesis of new sulfonic acid-containing oligosaccharide mimetics of sialyl Lewis A

Two trisaccharides as new sulfonic acid mimetics of the sialyl Lewis A tetrasaccharide were synthesized. The natural sialic acid residue is replaced by a C-sulfonic acid moiety attached to position C-3′ of the lactosamine unit of the mimetics. The l-fucose unit was also replaced by a d-arabinose ring in one of the analogues. Formation of the sulfonic acid moiety on the trisaccharide level could be successfully achieved by means of introduction of an acetylthio moiety into the galactose skeleton and subsequent oxidation. The equatorial arrangement of the acetylthio group linked to C-3 of the galactose ring could be achieved by double nucleophilic substitution; efficient formation of the gulo-triflate derivatives required low-power microwave activation. Oxidation of the acetylthio group was carried out using Oxone in acetic acid.     

Towards a superstatistical SU(2) Yang-Mills EoS

We study an SU(2) lattice gauge field system on a 10⁴ symmetric and on a 10³ × 2 asymmetric lattice in order to learn about the equation of state.     

On the volume of the convex hull of two convex bodies

In this note we examine the volume of the convex hull of two congruent copies of a convex body in Euclidean $n$ -space, under some subsets of the isometry group of the space. We prove inequalities for this volume if the two bodies are translates, or reflected copies of each other about a common point or a hyperplane containing it. In particular, we give a proof of a related conjecture of Rogers and Shephard.     

Asymmetric epoxidation of substituted chalcones and chalcone analogues catalyzed by α-d-glucose- and α-d-mannose-based crown ethers

The chiral monoaza-15-crown-5 lariat ethers annellated to methyl-4,6-O-benzylidene-α-d-glucopyranoside-1 or mannopyranoside 2 have been applied as phase-transfer catalysts in the epoxidation of substituted chalcones and chalcone analogues with tert-butylhydroperoxide resulting in significant asymmetric induction. It was found that the position of the substituents in the aromatic ring of the chalcone had an influence both on the chemical yields and enantiomeric excesses. The lowest enantioselectivities (62–83% ee) were found in the case of ortho-substituted model compounds. The highest ee values (ee of 83–97%) were obtained in the case of para-substituted models. From among the chalcone analogues, the maximum ee (90–92%) was detected for the model compound having α-tert-butyl- and β-aryl groups. Using glucose-based crown ether 1, formation of the (?)-enantiomer was preferred, while applying mannose-based 2 as the catalyst, the (+)-enantiomer was in excess.     

Maximum number of colors: C-coloring and related problems

We discuss problems and results on the maximum number of colors in combinatorial structures under the assumption that no totally multicolored sets of a specified type occur.     

Observation of a diamagnetic signal up to 132 K in a Tl−Ca−Ba−Cu−O compound

Tl–Ca–Ba–Cu–O compounds of the nominal composition of (1, 1, 1, 1) have been prepared from different starting materials and with the same heat treatment process. During the investigation of their properties a diamagnetic signal has been found up to the temperature of 132 K. This hints at the existence of a certain material content distributed into discrete superconducting domains. The parameters of it reflect a superstructure of the (2, 2, 2, 3) and (2, 1, 2, 2) compositions having a time-dependent behaviour. On the basis of the signal levels at 132 K and 4.2 K, the quantity of the high temperature superconducting material is about 0.01% of the total one at liquid He temperatures.