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.     

Study of the reaction238U (α, α′f) atE α=480 MeV

The excitation function of the fission probability P _E E _x) for²³⁸U has been measured in the reaction²³⁸U(α, α′ f) at 480 MeV bombarding energy. The reaction mechanism of this reaction is discussed for excitation energies belowB _nf , the threshold for second chance fission, and aboveB _nf up toE _x =37 MeV. In comparing with results from fission induced by photons and by particle transfer reactions the (α, α′f) reaction gives too low values for the fission probabilityP _f at excitation energies well aboveB _nE . The role of the quasi-elastic knock-out process in this reaction 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     

Ground-state properties of LiV2O4 and Li1-xZnx(V1-yTiy)2O4

We present susceptibility, microwave resistivity, NMR and heat-capacity results for Li_1-xZn_x(V_1-yTi_y)₂O₄ with 0 ? x ? 0.3 and 0 ? y ? 0.3. For all doping levels the susceptibility curves can be fitted with a Curie-Weiss law. The paramagnetic Curie-Weiss temperatures remain negative with an average value close to that of the pure compound Θ≈ - 36 K. Spin-glass anomalies are observed in the susceptibility, heat-capacity and NMR measurements for both type of dopants. From the temperature dependence of the spin-lattice relaxation rate we found critical-dynamic behavior in the Zn doped compounds at the freezing temperatures. For the Ti-doped samples two successive freezing transitions into disordered low-temperature states can be detected. The temperature dependence of the heat capacity for Zn-doped compounds does not resemble that of canonical spin glasses and only a small fraction of the total vanadium entropy is frozen at the spin-glass transitions. For pure LiV₂O₄ the spin-glass transition is completely suppressed. The temperature dependence of the heat capacity for LiV₂O₄ can be described using a nuclear Schottky contribution and the non-Fermi liquid model, appropriate for a system close to a spin-glass quantum critical point. Finally an ( x / y , T )-phase diagram for the low-doping regime is presented. Received 16 March 2001 and Received in final form 30 October 2001     

Structure of neutron-rich Be and C isotopes

The structure of neutron-rich beryllium isotopes has been investigated using different heavy-ion-induced transfer reactions. In neutron transfer reactions, the population of final states shows a strong sensitivity to the chosen core nucleus, i.e., the target nuclei ⁹Be or ¹⁰Be, respectively. Molecular rotational bands up to high excitation energies are observed with ⁹Be as the core due to its pronounced 2α-cluster structure, whereas only a few states at low excitation energies are populated with ¹⁰Be as the core. For ¹¹Be, a detailed investigation has been performed for the three states at 3.41, 3.89, and 3.96 MeV, which resulted in the most probable spin-parity assignments 3/2⁺, 5/2^?, and 3/2^?, respectively. Furthermore, we have studied particle-hole states of ¹⁶C using the ¹³C(¹²C, ⁹C)¹⁶C reaction and found 14 previously unknown states. Using the ¹²C(¹²C, ⁹C)¹⁵C reaction, five new states were observed for ¹⁵C.