Deformation Quantization of Algebraic Varieties

The paper is devoted to peculiarities of the deformation quantization in the algebro-geometric context. A direct application of the formality theorem to an algebraic Poisson manifold gives a canonical sheaf of categories deforming coherent sheaves. The global category is very degenerate in general. Thus, we introduce a new notion of a semiformal deformation, a replacement in algebraic geometry of an actual deformation (versus a formal one). Deformed algebras obtained by semiformal deformations are Noetherian and have polynomial growth. We propose constructions of semiformal quantizations of projective and affine algebraic Poisson manifolds satisfying certain natural geometric conditions. Projective symplectic manifolds (e.g. K3 surfaces and Abelian varieties) do not satisfy our conditions, but projective spaces with quadratic Poisson brackets and Poisson–Lie groups can be semiformally quantized.     

ChemInform Abstract: A New n = 4 Layered Ruddlesden—Popper Phase K2.5Bi2.5Ti4O13 Showing Stoichiometric Hydration.

Polycrystalline K_2.5Bi_2.5Ti₄O₁₃ (I) is prepared by solid state reaction of KNO₃, Bi₂O₃, and TiO₂ (Al₂O₃ crucible, 750 °C, 16 h).     

ChemInform Abstract: YCa3(CrO)3(BO3)4: A Cr3+ Kagome Lattice Compound Showing No Magnetic Order Down to 2 K.

Polycrystalline gaudefroyite‐type YCa₃(CrO)₃(BO₃)₄ with Cr³⁺ ions (3d³, S = 3/2) forming an undistorted Kagome lattice is prepared by reaction of a stoichiometric mixture of Y₂O₃, CaCO₃, Cr₂O₃, H₃BO₃ in a KCl flux (Al₂O₃ crucible, 1000 °C, 1 d) followed by re‐grinding and further annealing (1000 °C, 2 d, 95% yield).     

Cospectral polymers: Differentiation via semiflexibility

We consider polymer structures which are known in the mathematical literature as "cospectral." Their graphs have (in spite of the different architectures) exactly the same Laplacian spectra. Now, these spectra determine in Gaussian (Rouse-type) approaches many static as well as dynamical polymer characteristics. Hence, in such approaches for cospectral graphs many mesoscopic quantities are predicted to be indistinguishable. Here we show that the introduction of semiflexibility into the generalized Gaussian structure scheme leads to different spectra and hence to distinct macroscopic patterns. Moreover, particular semiflexible situations allow us to distinguish well between cospectral structures. We confirm our theoretical results through Monte Carlo simulations.     

Ion Interactions with the Carbon Nanotube Surface in Aqueous Solutions: Understanding the Molecular Mechanisms

We study the molecular mechanisms of alkali halide ion interactions with the single‐wall carbon nanotube surface in water by means of fully atomistic molecular dynamics simulations. We focus on the basic physical‐chemical principles of ion–nanotube interactions in aqueous solutions and discuss them in light of recent experimental findings on selective ion effects on carbon nanotubes.     

Underwound DNA under tension: structure, elasticity, and sequence-dependent behaviors

DNA melting under torsion plays an important role in a wide variety of cellular processes. In the present Letter, we have investigated DNA melting at the single-molecule level using an angular optical trap. By directly measuring force, extension, torque, and angle of DNA, we determined the structural and elastic parameters of torsionally melted DNA. Our data reveal that under moderate forces, the melted DNA assumes a left-handed structure as opposed to an open bubble conformation and is highly torsionally compliant. We have also discovered that at low forces melted DNA properties are highly dependent on DNA sequence. These results provide a more comprehensive picture of the global DNA force-torque phase diagram.     

Transannular additions of selectfluor and xenon difluoride: regioselectivity and mechanism

The addition of 1‐chloromethyl‐4‐fluoro‐1,4‐diazoniabicyclo[2.2.2]octane bis‐tetrafluoroborate (F‐TEDA) to unsaturated systems was modelled computationally at the ab initio levels and studied experimentally. The reaction of olefins with F‐TEDA is driven exclusively by charge transfer and displays the antibonding orbital picture in the transition structure for F‐transfer, similarly to that for the reactions of olefins with F‐radical. In contrast, the electrophilic and concerted fluorinations, respectively with H₂O???F⁺ complex and with F₂, show strong bonding interactions between the fluorine and olefin moieties in the transition structures. The reaction with F‐TEDA involves an initial formation of highly delocalized charge‐transfer complexes in the first step with further low‐barrier (ca 4 kcal) migration of fluorine and is best described as an inner‐sphere electron transfer. This nonelectrophilic mechanism is operative for the transannular addition of F‐TEDA to 3‐methylene‐7‐ethylidenebicyclo[3.3.1]nonane studied experimentally. The addition mode is determined by the formation of a more stable complex via the ethylidene fragment and demonstrates selectivities that differ from conventional electrophilic additions. This mechanistic scenario may be extended to the fluorination with xenon difluoride where similar products are formed in high yields. Copyright © 2010 John Wiley & Sons, Ltd.     

Kilohertz laser frequency sensing with Brillouin mutually modulated cross-gain modulation

Using mutually modulated cross-gain modulation, Stokes optical frequency changes are converted into modulation phase changes with high sensitivity. In the slow-light transition regime, we demonstrate kilohertz sensitivity to the Stokes optical carrier frequency. The sensitivity is inversely proportional to the modulation frequency of the pump and Stokes beams.