Note zu einem Borelschen Summationsverfahren

Ohne Zusammenfassung     

Gitterzahlen und innere Volumina

Ohne Zusammenfassung Hugo Hadwiger zum 70. Geburtstag gewidmet     

Research problems

Periodica Mathematica Hungarica - In this column Periodica Mathematica Hungarica publishes current research problems whose proposers believe them to be within the reach of existing methods....     

Zur simultanen homogenen diophantischen Approximation II

Ohne Zusammenfassung     

Ein Satz über konvexe Mengen und Gitterpunkte

Ohne ZusammenfassungHerrnGruber, Wien, verdanke ich den Hinweis (9. 11. 67) auf dieses Problem.     

Existence, positivity and contractivity for quantum stochastic flows with infinite dimensional noise

Quantum stochastic differential equations of the form

Behavior of polyethylene in a variable temperature density gradient column

Polymer morphology (phase size and phase density) of slow cooled and quenched polyethylene (HDPE, LDPE, and LLDPE) has been characterized over a range of temperatures. The characterization methodology includes variable-temperature density gradient column (VT-DGC), small-angle x-ray scattering (SAXS), wide-angle x-ray diffraction (WAXD) and differential scanning calorimetry (DSC). Using a novel technique, a VT-DGC was prepared and cycled over a range of service temperatures (20-60 °C) for 5 cycles to investigate the changes of slow cooled and quenched HDPE, LDPE and LLDPE. A significant change in bulk density was present in each sample between the first cycle and subsequent cycles. Morphological analysis was performed using both the two-phase and three-phase models. The two-phase model showed that, for a particular sample, the thickness of the crystalline and amorphous phases varied very little within the experimental temperature range. Using the three-phase model, differences in the interfacial layer thickness were measured and observed to be significant compared to the amorphous and crystalline phase changes. The amorphous and crystalline densities of all samples varied less than 2%. Overall, significant difference in crystalline density was observed between HDPE, LDPE and LLDPE due to molecular structure.     

Evaluation of the nanofibrillar structure of Dioscorea opposite extract for cell attachment

Dioscorea opposite has been widely used in traditional herbal medicine in the Far East, ameliorating symptoms ranging from abdominal swelling to pain. Previous studies have focused on understanding the chemical components that lead to the medicinal effects of the extract. In this study, we examined the nanostructures formed by the soluble and insoluble parts of the sticky excretion from the mucilaginous rhizome of Dioscorea opposite and evaluated their cellular response. Using atomic force microscopy, we found that the soluble extract of the excretion had the capacity to form a nanofibrillar scaffold composed of uniform ～10 nm nanofibers with a typical pore size of ～40 nm, while the insoluble extract formed some nanofibers without specific structure. Cellular response to the two types of nanostructures was tested by seeding with HeLa and MC3T3 cells. The observations suggested that the nanofibrillar scaffold formed from the soluble extract provided an excellent platform for HeLa cell attachment and growth and to a lesser degree for MC3T3 cells, while nanofibers from the insoluble extract displayed no cell attachment and growth. Further analysis by direct incubation of the soluble extract with growing cells indicated that components from the extract preferentially bound to HeLa cells, but not to MC3T3 cells, which might help explain the observed preference of HeLa cells on the nanofibrillar scaffold. The nanofibrillar scaffold created from the Dioscorea opposite extract and its ability to sustain the attachment of specific cell types demonstrate the potential for this natural nanomaterial in tissue engineering applications.     

An approach to phase behaviour in polymers

Aspects of phase transition will be surveyed such as are direct consequences of straightforward thermodynamic considerations yet are not normally taken count of in traditional treatments of phase behaviour even if, as is here shown, they can assume special significance in polymers. The central theme will be the common experience that in most materials, but especially in polymers, the state of ultimate thermodynamic stability is hardly ever attained, consequently that we are dealing with metastable states, the issue of metastability thus becoming the main theme of the present treatise. This metastability can manifest itself either through the phase transformation, even in the thermodynamically stable phase, not reaching completion and/or that phases other than those of ultimate stability appear first often taking on a dominant role. The above two strands are being followed through first separately and finally, with the example of polymer crystallisation, in combination. In the course of it all a variety of phase transformations and numerous potentially intriguing consequences are being touched upon. These are encompassing aspects of liquid-liquid phase separation, liquid-crystal formation and crystallisation, the intervention of glass transition, the significance of supercooling, the effect on and influence of the morphology and the connection and interrelation between thermodynamic stability (including metastability) and the rates of the phase transformation, with passing comments on gels and also on some aspects of chain conformation in solution. In the case of the most extensively covered item of crystallisation attention is being drawn to the possibility of stability inversion with phase (here crystal) size. The latter, in terms of ‘Phase Stability Diagrams’, offers a new approach to crystal growth, which in the case of polymers, creates both new perspectives and opens up the possibility of treating so far largely disconnected aspects of the subject within a unifying framework. The survey ends with reference to recent work on amorphisation through pressure pointing to new aspects of material behaviour and to some new and possibly surprising variants of otherwise familiar phase diagrams.