Graphs that are not complete pluripolar

Let be domains in . Under very mild conditions on we show that there exist holomorphic functions , defined on with the property that is nowhere extendible across , while the graph of over is not complete pluripolar in . This refutes a conjecture of Levenberg, Martin and Poletsky (1992).

     

Hidden symmetries of integrable conformal mechanical systems

We split the generic conformal mechanical system into a “radial” and an “angular” part, where the latter is defined as the Hamiltonian system on the orbit of the conformal group, with the Casimir function in the role of the Hamiltonian. We reduce the analysis of the constants of motion of the full system to the study of certain differential equations on this orbit. For integrable mechanical systems, the conformal invariance renders them superintegrable, yielding an additional series of conserved quantities originally found by Wojciechowski in the rational Calogero model. Finally, we show that, starting from any N=4 supersymmetric “angular” Hamiltonian system one may construct a new system with full N=4 superconformal D(1,2;α) symmetry.     

Concise Synthesis of (+)-[13C4]-Anatoxin-a by Dynamic Kinetic Resolution of a Cyclic Iminium Ion

An asymmetric total synthesis of [¹³C₄]-anatoxin-a ([¹³C₄]- 1 ) has been developed from commercially available ethyl [¹³C₄]-acetoacetate ([¹³C₄]- 15 ). The unique requirements associated with isotope incorporation inspired a new, robust, and highly scalable route, providing access to 0.110 g of this internal standard for use in the detection and precise quantification of anatoxin-a in freshwater. A highlight of the synthesis is a method that leverages a cyclic iminium ion racemization to achieve dynamic kinetic resolution in an enantioselective Morita–Baylis–Hillman (MBH) cyclization.     

10‐Step Asymmetric Total Synthesis and Stereochemical Elucidation of (+)‐Dragmacidin D

The asymmetric synthesis of dragmacidin D ( 1 ) was completed in 10 steps. Its sole stereocenter was set by using direct asymmetric alkylation enabled by a C₂‐symmetric tetramine and lithium N‐(trimethylsilyl)‐tert‐butylamide as the enolization reagent. A central Larock indole synthesis was employed in a convergent assembly of the heterocyclic subunits. The stereochemical evidence from this work strongly supports the predicted S configuration at the 6′′′ position, which is consistent with other members of the dragmacidin family of natural products.     

Long-chain alkyl sulfonate micelle fission: a molecular dynamics study

In this study, we investigate micelle fission of long-chain alkyl sulfonate molecules using atomistic scale simulation. GROMACS software code with the united atom force field was applied. 0.5-μs parallel molecular dynamics simulation study was conducted for a surfactant/water system consisting of 192 sodium pentadecyl sulfonate and 40,553 water molecules. The large preassembled micelle was ruptured at Krafft above T?=?323-K temperature, and we track two ellipsoid-like micelles over the course of the production run. To estimate the micelle shape, we determined the principal moments of inertia and the eccentricity, which proved that the micelles have a pronounced prolate spheroid shape, which agrees well with our previous experimental data. The mechanism of micelle fission was explored in detail. The aggregation number, ionization degree, and other parameters obtained from simulation were consistent with existing experimental finding. The determined parameters in addition to simple visual inspection of trajectories revealed monomer-micelle exchange—with the estimated relaxation time τ ₁?=?10^??9s. We assume that the exchange process is conditioned by the unequal size of micelles leading to adjustment of aggregation number.     

Copper(II)-selective fluorimetric bulk optode membrane based on a 1-hydroxy-9,10-anthraquinone derivative having two propenyl arms as a neutral fluorogenic ionophore

A new optical chemical sensor has been developed for the selective determination of copper(II) ions in aqueous solutions. The reversible sensing system was prepared by incorporating 1-hydrpxy-2-(prop-2'-enyl)-4-(prop-2'-enyloxy)-9,10-anthraquinone (AQ) as a neutral Cu2+-selective fluoroionophore in the plasticized PVC membrane with potassium tetrakis(p-chlorophenyl borate) as an anionic additive. The response of the sensor is based on the fluorescence quenching of AQ by Cu2+ ions. At a pH 5.5, the proposed sensor displays a calibration response for Cu2+ over a wide concentration rang of 1.0 x 10(-2) to 1.0 x 10(-6) M, with a relatively fast response of less than 40 s. In addition to high stability and reproducibility, the sensor shows a unique selectivity towards Cu2+ ion with respect to common co-existing cations. The proposed fluorescence optode was applied successfully to the determination of copper(II) in black tea samples.     

Harmonic maps into loop spaces of compact Lie groups

We study harmonic maps from Riemann surfaces M to the loop spaces ΩG of compact Lie groups G, using the twistor approach. We conjecture that harmonic maps of the Riemann sphere ℂℙ¹ into ΩG are related to Yang-Mills G-fields on ℝ⁴. This work was partly supported by the RFBR (Grant Nos. 04-01-00236, 06-02-04012), by the program of Support of Scientific Schools (Grant No. 1542.2003.1), and by the Scientific Program of RAS “Nonlinear Dynamics”     

Freudenthal duality and generalized special geometry

Freudenthal duality, introduced in Borsten et al. (2009) [1] and defined as an anti-involution on the dyonic charge vector in d=4 space-time dimensions for those dualities admitting a quartic invariant, is proved to be a symmetry not only of the classical Bekenstein-Hawking entropy but also of the critical points of the black hole potential.Furthermore, Freudenthal duality is extended to any generalized special geometry, thus encompassing all N>2 supergravities, as well as N=2 generic special geometry, not necessarily having a coset space structure.