The r-mean curvature and rigidity of compact hypersurfaces in the Euclidean space

Annals of Global Analysis and Geometry - In this paper, we characterize round spheres in the Euclidean space under some suitable conditions on the r-mean curvature.     

Synthesis of β -Cyperone via Fungal Hydroxylation of thujone-derived tricyclic cyclopropanes

Synthesis of optically active sesquiterpenes with a eudesmane C-skeleton from the chiral starting material thujone involves transformation of a tricyclic intermediate (1R,2R,4S)-1,7-dimethyl-4-(1-methylethyl)tricyclo[4.4.0.0^2,4]dec-6-en-8-one ( 2 ) into the bicyclic compound β -cyperone ( 5 ). Hydroxylation of 2 at C(5) or C(11) permits subsequent opening of the cyclopropane ring and rearrangement to β -cyperone. In this publication, studies involving hydroxylation of 2 by fungal cultures are presented. The resultant products are useful intermediates in efficient synthesis of eudesmane sesquiterpenes. Of five fungi tested, Rhizopus oryzae ATCC 11145 proved most versatile. It hydroxylates at the exocyclic C(11) position in high yield (70%) and, to a lesser extent, at C(5) (5%). Enzymatic activity appears at the end of growth phase and at least 2.2 g of 2 per liter can be metabolized without significant loss of product yield. A second fungus, Cunninghamella echinulata ATCC 9244, proved most useful for hydroxylation of derivatives of 2 for the preparation of derivatives of β -cyperone, although product yields were low (2–20%), some derivatives were nonreactive, and hydroxylation at C(9) occurred. The relationship between precursor structure and enzyme affinity is discussed.     

Conceptual continuity as a mode of understanding complex systems: Applications to the dynamics sociopolitical systems

In complex biological systems, entities that are conceptually distinct but empirically related—such as sunlight and plant growth or antigene and immune response—are being explicitly linked through the identification of highly specific uninterrupted interaction sequences that take place between their macromolecular system components. These uninterrupted sequences of causation include common elements that are shared by the empirically related but conceptually distinct entities. Through the identification of specific shared elements, “conceptual continuity” is established between these entities. Examples are introduced to suggest that in sociopolitical systems, an analogous conceptual continuity can be established between distinct sociopolitical entities. The identification of specific shared elements, essential for the well being of each of the entities, can play a significant role in resolving conflicts between those separated by seemingly insurmountable obstacles such as race or religion or ideology. © 2006 Wiley Periodicals, Inc. Complexity 11:20–24, 2006     

Crystallization and morphology of poly(vinylidene fluoride)/poly(3‐hydroxybutyrate) blends. I. Spherulitic morphology and growth by polarized microscopy

The development of the poly(3‐hydroxybutyrate) (PHB) morphology in the presence of already existent poly(vinylidene fluoride) (PVDF) spherulites was studied by two‐stage solidification with two separate crystallization temperatures. PVDF formed irregular dendrites at lower temperatures and regular, banded spherulites at elevated temperatures. The transition temperature of the spherulitic morphology from dendrites to regular, banded spherulites increased with increasing PVDF content. A remarkable amount of PHB was included in the PVDF dendrites, whereas PHB was rejected into the remaining melt from the banded spherulites. When PVDF crystallized as banded spherulites, PHB could consequently crystallize only around them, if at all. In contrast, PHB crystallized with a common growth front, starting from a defined site in the interfibrillar regions of volume‐filling PVDF dendrites. It formed by itself dendritic spherulites that included a large number of PVDF spherulites. For blends with a PHB content of more than 80 wt %, for which the PVDF dendrites were not volume‐filling, PHB first formed regular spherulites. Their growth started from outside the PVDF dendrites but could later interpenetrate them, and this made their own morphology dendritic. These PHB spherulites melted stepwise because the lamellae inside the PVDF dendrites melted at a lower temperature than those from outside. This reflected the regularity of the two fractions of the lamellae because that of those inside the dendrites of PVDF was controlled by the intraspherulitic order of PVDF, whereas that from outside was only controlled by the temperature and the melt composition. The described morphologies developed without mutual nucleating efficiency of the components. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 873–882, 2003     

Real analyticity of topological pressure for parabolically semihyperbolic generalized polynomial-like maps

For arbitrary parabolically semihyperbolic generalized polynomial-like maps f, we prove that on a certain interval, which contains the interval (0, HD(J(f))), the pressure function t ? P(−t log |f|) is real-analytic. Our results generalize the work of Makarov and Smirnov in [3] and [7].