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).     

Femtosecond midinfrared study of aggregation behavior in aqueous solutions of amphiphilic molecules

We study the spectral and orientational dynamics of HDO molecules in aqueous solutions of different concentrations of tertiary butyl alcohol (TBA) and trimethylamine-N-oxide (TMAO). The spectral dynamics is investigated with femtosecond two-dimensional infrared spectroscopy of the O-H stretch vibration of HDO:D(2)O, and the orientational dynamics is studied with femtosecond polarization-resolved pump-probe spectroscopy of the O-D stretch vibration of HDO:H(2)O. Both the spectral and orientational dynamics are observed to show bimodal behavior: part of the water molecules shows spectral and orientational dynamics similar to bulk liquid water and part of the water molecules displays a much slower dynamics. For low solute concentrations, the latter fraction of slow water increases linearly as a function of solute molality, indicating that the slow water is contained in the solvation shells of TBA and TMAO. At higher concentrations, the fraction of slow water saturates. The saturation behavior is much stronger for TBA solutions than for TMAO solutions, indicating the aggregation of the TBA molecules.     

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.     

A new method for the synthesis of the marine alkaloid fascaplysin

A new method for the synthesis of the marine alkaloid fascaplysin has been developed via a simple and practical approach to pyrido[1,2-a:3,4-b′]diindole ring system formation. Conversion of the marine alkaloid homofascaplysin C into fascaplysin is also described.     

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.     

Nonlinear quantum mode of terahertz electromagnetic wave amplification in resonant tunneling heterostructures

An analysis of high-frequency properties of the resonant tunneling diode (RTD) in a strong microwave electromagnetic field showed that the high-frequency current response increasing with the microwave power significantly more rapidly saturates out in the case of classical amplification mode, than in the case of “quantum” amplification mode. This makes the “quantum” mode even more attractive in comparison with the classical mode from the viewpoint of the possibility of amplification and generation in the range of subterahertz and terahertz frequencies and offers new opportunities to advance towards these frequencies.