Viehwegʼs hyperbolicity conjecture is true over compact bases

We prove Viehweg?s hyperbolicity conjecture over compact bases and over bases with non-uniruled compactification. The most general case of the conjecture states that the base space of a maximal variation family of smooth projective manifolds with semi-ample canonical sheaf is of log-general type.     

Self-association-driven transition of the β-peptidic H12 helix to the H18 helix

Various patterns of foldameric oligomers formed by trans-ABHC ((1S,2S,3S,5S)-2-amino-6,6-dimethylbicyclo[3.3.1]heptane-3-carboxylic acid) and β(3)-hSer residues were studied. NMR, ECD and molecular modelling demonstrated that octameric and nonameric sequences with multiple i-i+3 ABHC pair repulsions attain the β-H18 helix in CD(3)OH. As a close relative of the α-helix, this helix type is stabilized by i-i+4 backbone H-bond interactions. The formation of the β-H18 helix was found to be solvent- and concentration-dependent. Upon dilution, the β-H18 → β-H12 helix transition was revealed by concentration-dependent ECD, DOSY-NMR and TEM measurements.     

On the equality of two-variable general functional means

Aequationes mathematicae - Given two functions $$f,g:I\rightarrow \mathbb {R}$$ and a probability measure $$\mu $$ on the Borel subsets of [0, 1], the two-variable mean $$M_{f,g;\mu...     

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.     

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.     

Bin covering with a general profit function: approximability results

In the recent paper (Benk? et al. 2010) we introduced a new problem that we call Bin Packing/Covering with Delivery, or BP/CD for short. Mainly we mean under this expression that we look for not only a good, but a “good and fast” packing or covering. In the present paper we investigate the offline case. For the analysis, a novel view on “offline optimum” is introduced, which appears to be relevant concerning all problems where a final solution is ordering-dependent. We prove that if the item sizes are not allowed to be arbitrarily close to zero, then an optimal offline solution can be found in polynomial time. On the other hand, for unrestricted problem instances, no polynomial-time algorithm can achieve an asymptotic approximation ratio better than 6/7 if $P\ne NP$ .     

Adoption of the Numerical Method of Chebyshev Polynomials to the Stability Analysis of Delayed DEs

We propose a new way of the application of the numerical method based on Chebyshev approximation concerning the stability analysis of (periodic) delay‐differential equations. The technique is tested on the delayed Mathieu equation.     

Smart nanocomposite polymer gels

The combination of polymers with nanomaterials displays novel and often enhanced properties compared to the traditional materials. They can open up possibilities for new technological applications. The magnetic polymer gel represents a new type of composites consisting of small magnetic particles, usually from the nanometer range to the micron range, dispersed in a highly elastic polymeric gel matrix. Combination of magnetic and elastic properties leads to a number of striking phenomena that are exhibited in response to impressed magnetic fields. Giant deformational effects, high elasticity, anisotropic properties, temporary reinforcement and quick response to magnetic field open new opportunities for using such materials for various applications.     

On the invariance equation for two-variable weighted nonsymmetric Bajraktarević means

Aequationes mathematicae - The purpose of this paper is to investigate the invariance of the arithmetic mean with respect to two weighted Bajraktarević means, i.e., to solve the functional...     

Foreword

Journal of Radioanalytical and Nuclear Chemistry -