ON ALGEBRAIC VOLUME DENSITY PROPERTY

A smooth affine algebraic variety X equipped with an algebraic volume form ω has the algebraic volume density property (AVDP) if the Lie algebra generated by complete algebraic vector fields of ω-divergence zero coincides with the space of all algebraic vector fields of ω-divergence zero. We develop an effective criterion of verifying whether a given X has AVDP. As an application of this method we establish AVDP for any homogeneous space X = G/R that admits a G-invariant algebraic volume form where G is a linear algebraic group and R is a closed reductive subgroup of G.     

Hydrogels from phospholipid vesicles

It is shown that phospholipid dispersions with a few percent of diacylphosphocholine PC in water can be swollen to single-phase lyotropic liquid crystalline L_α-phases by the addition of co-solvents like glycerol, 1,3-butyleneglycol BG or 1,2-propyleneglycol PG. The birefringent L_α-phases contain small unilamellar and multilamellar vesicles if the temperature of the samples is above the Krafft-Temperature T_m of the phospholipid. When such transparent birefringent viscous samples are cooled down below T_m the samples are transformed into birefringent gels. Cryo-TEM and FF-TEM measurements show that the bilayers of the vesicles are transformed from the liquid to the crystalline state during the transformation while the vesicle structure remains. The bilayers of the crystalline vesicles form adhesive contacts in the gel. Pulsed-field gradient NMR measurements show that two different kinds of water or co-solvent can be distinguished in the gels. One type of solvent molecules can diffuse like normal solvent in a continuous bulk phase. A second type of water diffuses much more slowly. This type of solvent is obviously trapped in the vesicles. The permeability of the crystalline vesicles for water and solvent molecules is much lower in the crystalline state than in the fluid state.     

Determination of Particle Size,Core and Shell Size Distributions of Core–Shell Particles by Analytical Ultracentrifugation

In core–shell nanoparticle analysis, the determination of size distributions of the different particle parts is often complicated, especially in liquid media. Density matching is introduced as a method for analyzing core–shell nanoparticles using Analytical Ultracentrifugation (AUC), making it possible to obtain the core size distribution in liquid dispersions. For this approach, the density of the dispersion is adjusted to the density of the shell. Oil filled nanocapsules are utilized with component densities of around 1 g mL⁻¹ to demonstrate this technique. The shell size distribution is calculated supposing the particle size distribution as a convolution of the shell- and core size distributions. Finally, the distributions of core size, shell thickness, particle size, and particle density and thus particle composition are obtained. To clarify the effect of swelling, AUC measurements are combined with further size characterization methods like Particle Tracking Microscopy and Dynamic Light Scattering.     

A Relation Between Closure Operators on a Small Category and Its Category of Presheaves

In this paper we show that each factorization structure on a small category , satisfying certain conditions, yields a presheaf on and a morphism of presheaves . We then give connections, and set up one to one correspondences, between subclasses of the following classes: (a) closure operators on (b) subobjects of (c) morphisms from to (d) weak Lawvere–Tierney topologies (e) weak Grothendieck topologies (f) closure operators on .     

Influence of anionic substitutions on hyperfine interactions and ionic ordering in ferrites

Hyperfine Interactions -     

Probes for Narcotic Receptor Mediated Phenomena

The synthesis of a series of epoxy 5‐phenylmorphans is being explored in order to determine the conformational requirements of the phenolic ring in a phenylmorphan molecule that may be needed both for binding to a specific opioid receptor and for exhibiting opioid agonist or antagonist activity. Of the twelve possible ortho‐ and para‐bridged isomers (a–f) (Fig. 1), we now report the synthesis of the para‐d isomer, rac‐(3R,6aS,11aR)‐2‐methyl‐1,3,4,5,6,11a‐hexahydro‐2H‐3,6a‐methanobenzofuro[2,3‐c]azocin‐8‐ol ( 3 ). Compound 3 was synthesized via construction of the 5‐phenylazabicyclo[3.3.1]non‐3‐ene skeleton (Scheme 1) and subsequent closure of the epoxy bridge (Scheme 2). As determined by an X‐ray diffraction study, the epoxy bridge, restricting the phenyl‐ring rotation, fixed the dihedral angle between the least‐squares planes through the phenyl ring and atoms N(2), C(3), C(11a), and C(6a) of the piperidine ring (Fig. 2) at 43.0°, and the torsion angle C(12)? C(6a)? C(6b)? C(10a) at ?95.0°.