Algorithms for Sat and Upper Bounds on Their Complexity

We survey recent algorithms for the propositional satisfiability problem. In particular, we consider algorithms having the best current worst-case upper bounds on their complexity. We also discuss some related issues: a derandomization of the algorithm of Paturi, Pudlák, Saks, and Zane, the Valiant–Vazirani lemma, and random walk algorithms with the back button. Bibliography: 47 titles.     

New phosphonium salts based on 3-(diphenylphosphino)propanoic and ω-haloalkanoic acids

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Diophantine representations of linear recurrent sequences. II

Direct constructions of Diophantine representations for linear recurrent sequences are considered. Diophantine representations of the sets of values for third-order sequences with negative discriminants are found. As an auxiliary problem, we study the structure of the multiplicative group of the ringZ[λ], where λ is an invertible algebraic integer (unit) in a real quadratic field or in a cubic field of negative discriminant. The index of the subgroup {±λ ⁿ ∣n ∈Z} in the group (Z[λ])^* and the generator of (Z[λ])^* are evaluated explicitly. Bibliography: 14 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 241, 1997, pp. 5–29. This research was supported in part by the ISSEP, grants a96-1965 and a97-2261. Translated by M. A. Vsemirnov     

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.