A Note on Caterpillar-Embeddings with No Two Parallel Edges

Let G be a set of n points in general position (i.e., no three points are on a line) in the plane, and let C be a caterpillar on n vertices. We show that one can always find a rectilinear embedding of C in the plane such that the vertices of C are the points of G and no two edges of C go to parallel segments. This proves a conjecture of Robert E. Jamison.     

Calculation of cyclodextrin-mediated enantiomer ratio shifting of racem norgestrel in aqueous solutions

Enantioselective solubility of rac-norgestrel was found in the presence of γ-cyclodextrin or hydroxypropyl-γ-cyclodextrin. In both cases the efficacious enantiomer was dissolved in greater extent. Calculating the molar absorptivity and molar ellipticity spectra of the γ- and hydroxypropyl-γ-cyclodextrin aqueous complexes, a simple and rapid direct circular dichroism (CD) spectrometric method was obtained for the determination of the enantiomer ratio in aqueous solutions.     

Growth of Sb-Bi gradient single crystals

The growth conditions and structural quality of Sb-Bi gradient single crystals with Bi content from 2 to 18 at %, grown by the Czochralski method with solid phase feed, are investigated. Bi distribution in the crystals along their pulling direction are studied by electron probe microanalysis and the change in the interplanar spacing is analyzed by double-crystal X-ray diffraction. It is established that the pulling rate and feed mass affect the Bi distribution in Sb-Bi single crystals.     

At Least n – 1 Intersection Points in a Connected Family of n Unit Circles in the Plane

Let C be a family of n different unit circles in the plane. We show that C determines at least n - c intersection points, where c is the number of connected components in ∪_{C ∈ C}C. This proves a conjecture of A. Bezdek.     

On the effect of montmorillonite in the curing reaction of epoxy nanocomposites

The procedure for the fabrication of epoxy-based polymer layered silicate nanocomposites is important in respect of the nanostructure that is developed. To further our understanding of this, the influence of an organically modified clay (montmorillonite, MMT) on the curing kinetics of an epoxy resin has been studied by differential scanning calorimetry. Clay loadings of 10 and 20 mass% are used, and isothermal as well as dynamic cures have been investigated. For both cure schedules the effect of the MMT is to advance the reaction. Kinetic analysis yields values for the activation energy, but shows that the reaction cannot be described simply by the usual autocatalytic equation. The glass transition of the cured nanocomposites is lower than that for the cured neat resin, a result that is attributed to homopolymerisation taking place in addition to the epoxy–amine reaction.     

Synthetic reactions catalyzed by immobilized lipase from oilseed rape (Brassica napus L.)

Lipase from rape (Brassica napus L., immobilized onto celite, catalyzes esterification and transesterification reactions in hexane. The activity of the lipase is stimulated up to 35 fold by the addition of water (1.3% w/v). The activity of the lipase in hydrolysis is about 8 times higher than in the esterification reactions in hexane. Interesteri-fication reactions between mono- and diacylglycerols and transesterification reactions of mono- and diacylglycerols with alcohols were also catalyzed at relatively high rates but transesterification/esterification of these acylglycerols with fatty acids was comparatively slow. In transesterification reactions, triacylglycerols reacted rather slowly.     

Übergangsformen zwischen Einkristall- und Sphärolithwachstum im Polyäthylen

Zusammenfassung Steigert man für das Poly?thylen die Kristallisationstemperatur, so findet man Kristallformen in der folgenden Reihenfolge: rautenf?rmige Einkristalle— rautenf?rmige Einkristalle mit abgeschnittenen spitzen Ecken (“truncated lozenge crystals”)-l?ngliche sechseckf?rmige Einkristalle, bei denen die kristallographische b-Achse der orthorhombischen Elementarzelle in Richtung der l?ngsten Ausdehnung des Kristalls liegt. Diese l?nglichen Sechsecke lagern sich zu Sph?rolithen zusammen, und zwar so, da? die kristallographische b-Achse radial liegt, wie es auch bei den aus der Schmelze gewachsenen Sph?rolithen der Fall ist. Damit sind für das Poly?thylen übergangsformen zwischen den Einkristallen und Sph?rolithen aufgezeigt. Sph?rolithe, die aus der L?sung gewachsen sind, zeigen im Polarisationsmikroskop nur dann ein konzentrisches Ringsystem, wenn bei der Bildung der Sph?rolithe ein Mindestangebot an Substanz vorhanden ist. Die Ringbreite nimmt dann mit steigender Kristallisationstemperatur zu. Bei aus der Schmelze gewachsenen Poly?thylen-Sph?rolithen ist mit der Bildung von nicht-kristallographischen Verzweigungen eine Drehung der Indikatrix verbunden. Vermutlich wird also auch bei aus der L?sung gewachsenen Sph?rolithen das Ringsystem auf dem Auftreten von Verzweigungen infolge hohen Angebotes von kristallisierender Substanz beruhen.

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Summary With increasing temperature of crystallization polyethylene crystallizes from solution as lozenge single crystals, truncated lozenge crystals and longish hexagonal crystals, with the crystallographic b-axis along the long diagonal. In the solutions longish hexagonal crystal plates are able to cluster and to form spherulites, in which their crystallographic b-axes are oriented radially like the b-axes in spherulites grown from the melt. Various transition species have been observed. In polarised light the spherulites grown from solution show a concentric ring-system only, if during the crystallization a sufficient quantity of polyethylene is present. The ring-width increases with increasing crystallization temperature. Further it is shown that in polyethylene spherulites grown from the melt the rotation of the indicatrix is connected with a non-crystallographic branching. We suppose, that also for the solution-grown spherulites the ring-system depends on branching.