The 1H and 13C NMR chemical shifts of Strychnos alkaloids revisited at the DFT level

The density functional theory calculation of ¹H and ¹³C NMR chemical shifts in a series of ten 10 classically known Strychnos alkaloids with a strychnine skeleton was performed at the PBE0/pcSseg-2//pcseg-2 level. It was found that calculated ¹H and ¹³C NMR chemical shifts provided a markedly good correlation with experiment characterized by a mean absolute error of 0.08 ppm in the range of 7 ppm for protons and 1.67 ppm in the range of 150 ppm for carbons, so that a mean absolute percentage error was as small as ~1% in both cases.     

Multinomial permutations on a circle

Multinomial permutations on a circle are considered in the framework of combinatorics. Different cases are presented and shown to agree with previously derived formula for the number of cyclic necklaces. Two applied examples are discussed with a view to illustrate the implications of derived formulas. Copyright © 2006 John Wiley & Sons, Ltd.     

Super-Brownian motion with reflecting historical paths. II. Convergence of approximations

We prove that the sequence of finite reflecting branching Brownian motion forests defined by Burdzy and Le Gall ([1]) converges in probability to the “super-Brownian motion with reflecting historical paths.” This solves an open problem posed in [1], where only tightness was proved for the sequence of approximations. Several results on path behavior were proved in [1] for all subsequential limits–they obviously hold for the unique limit found in the present paper.Mathematics Subject Classification (2000): Primary 60H15, Secondary 35R60Supported in part by NSF Grant DMS-0071486, Israel Science Foundation Grants 12/98 and 116/01 - 10.0, and the U.S.-Israel Binational Science Foundation (grant No. 2000065).     

Gromov's K-area and symplectic rigidity

Supported by the United States-Israel Binational Science Foundation grant 94-00302     

Enumerating disjunctions and conjunctions of paths and cuts in reliability theory

Let G=(V,E) be a (directed) graph with vertex set V and edge (arc) set E. Given a set P of source-sink pairs of vertices of G, an important problem that arises in the computation of network reliability is the enumeration of minimal subsets of edges (arcs) that connect/disconnect all/at least one of the given source-sink pairs of P. For undirected graphs, we show that the enumeration problems for conjunctions of paths and disjunctions of cuts can be solved in incremental polynomial time. Furthermore, under the assumption that P consists of all pairs within a given vertex set, we also give incremental polynomial time algorithm for enumerating all minimal path disjunctions and cut conjunctions. For directed graphs, the enumeration problem for cut disjunction is known to be NP-complete. We extend this result to path conjunctions and path disjunctions, leaving open the complexity of the enumeration of cut conjunctions. Finally, we give a polynomial delay algorithm for enumerating all minimal sets of arcs connecting two given nodes s₁ and s₂ to, respectively, a given vertex t₁, and each vertex of a given subset of vertices T₂.     

On Uniform Boundedness and Uniform Asymptotics for Orthogonal Polynomials on the Unit Circle

The known conditions due to G. Baxter, Ya. L. Geronimus, and B. L. Golinskii which guarantee the uniform boundedness and/or uniform asymptotic representation for orthonormal polynomials on the unit circle are under consideration. We show that these conditions are in general not necessary. We discuss the relation between the orthonormal polynomials on the unit circle, the best approximations, and absolutely convergent Fourier series.     

Dzyaloshinsky-Moriya antisymmetric exchange coupling in cuprates: Oxygen effects

We reconsider the conventional Moriya approach to the Dzyaloshinsky-Moriya antisymmetric exchange coupling for a single Cu₁-O-Cu₂ bond in cuprates using a perturbation scheme that provides an optimal way to account for intra-atomic electron correlations, low-symmetry crystal field, and local spin-orbital contributions with a focus on the oxygen term. The Dzyaloshinsky vector and the corresponding weak ferromagnetic moment are shown to be a superposition of comparable and, sometimes, competing local Cu and O contributions. We predict the effect of oxygen staggered spin polarization in the antiferromagnetic edge-shared CuO₂ chains due to the uncompensated oxygen Dzyaloshinsky vectors. The polarization is perpendicular to both the main chain antiferromagnetic vector and the CuO₂ chain normal. The intermediate ¹⁷O NMR is shown to be an effective tool to inspect the effects of Dzyaloshinsky-Moriya coupling in an external magnetic field. In particular, we argue that the puzzling planar ¹⁷O Knight shift anomalies observed in the paramagnetic phase of the generic Dzyaloshinsky-Moriya antiferromagnetic cuprate La₂CuO₄ can be assigned to the effect of the field-induced staggered magnetization. Finally, we revisit the effects of symmetric spin anisotropy, in particular, those directly induced by the Dzyaloshinsky-Moriya coupling. The perturbation scheme generalizes the well-known Moriya approach and presents a basis for reliable quantitative estimates for the symmetric partner of the Dzyaloshinsky-Moriya coupling. In contrast to the conventional standpoint, the parameters of the effective two-ion spin anisotropy are shown to incorporate the contributions of a single-ion anisotropy for two-hole configurations at both Cu and O sites. The text was submitted by the author in English.     

Azines and Azoles: CXXII. New Regioselective Synthesis of 1-Substituted 6-Alkyluracils

Readily available 5-acyl-4-hydroxy-3,6-dihydro-2H-1,3-thiazine-2,6-diones with primary alkyl- and arylamines in mild conditions (boiling in propan-2-ol) to give Schiff bases. In more rigid conditions (boiling in DMF), the reaction is accompanied by COS liberation and provides 1-substituted 6-alkyluracils. This previously unknown reaction possesses a considerable synthetic potential and can be considered as a new, general, and regioselective synthetic approach to 1-substituted 6-alkyluracils.__________Translated from Zhurnal Obshchei Khimii, Vol. 75, No. 1, 2005, pp. 146–158.Original Russian Text Copyright © 2005 by Yuskovets, Moskvin, Mikhailov, Ivin.For communication CXXI, see [1].