There are 3155 nonisomorphic perfect one‐factorizations of K16

We enumerate all nonisomorphic perfect one‐factorizations of $K_{16}$.     

Crystallographic, vibrational and theoretical studies of 2,3-diaminopyridinium selenate

The new organic–inorganic salt, 2,3-diaminopyridinium selenate, has been synthesized and characterized by means of single-crystal X-ray crystallography, FT-IR and FT-Raman spectroscopy. A diprotonated organic ligand, H₂^1,3L²⁺, existing in the crystal structure was theoretically shown to be the most stable cationic species of 2,3-diaminopyridine. The weak non-covalent forces of N–H?O type between the hydrogen atoms of the amino and ammonio groups of 2,3-diaminopyridinium cation and oxygen atoms of tetrahedral selenate anions determine three-dimensional arrangement with complex network of intermolecular interactions of hydrogen bond type (donor–acceptor distances from 2.697(3) Å to 3.088(3) Å). Vibrational spectra have been discussed in comparison with X-ray results. Juxtaposition of spectra of the complex with the pure organic ligand and deuterated analogue of the title compound allowed to give reliable assignments of most observed vibrational bands. Presented data can be useful in elucidation of molecular mechanism of uptake of tetrahedral SeO₄²⁻ anion by the living organisms.     

On the Equivalence of Solutions for a Class of Stochastic Evolution Equations in a Banach Space

We study a class of stochastic evolution equations in a Banach space E driven by cylindrical Wiener process. Three different analytical concepts of solutions: generalised strong, weak and mild are defined and the conditions under which they are equivalent are given. We apply this result to prove existence, uniqueness and continuity of weak solutions to stochastic delay evolution equations. We also consider two examples of these equations in non-reflexive Banach spaces: a stochastic transport equation with delay and a stochastic delay McKendrick equation.     

Diophantine properties of measures invariant with respect to the Gauss map

Motivated by the work of D. Y. Kleinbock, E. Lindenstrauss, G. A. Margulis, and B. Weiss [8, 9], we explore the Diophantine properties of probability measures invariant under the Gauss map. Specifically, we prove that every such measure which has finite Lyapunov exponent is extremal, i.e., gives zero measure to the set of very well approximable numbers. We show, on the other hand, that there exist examples where the Lyapunov exponent is infinite and the invariant measure is not extremal. Finally, we construct a family of Ahlfors regular measures and prove a Khinchine-type theorem for these measures. The series whose convergence or divergence is used to determine whether or not µ-almost every point is ψ-approximable is different from the series used for Lebesgue measure, so this theorem answers in the negative a question posed by Kleinbock, Lindenstrauss, and Weiss [8].     

Theoretical description of dihydrogen/hydride and trihydride molybdocene complexes: An insight from static and molecular dynamics simulations

In this study ab initio Car–Parrinello molecular dynamics simulations, extended transition state (ETS)‐natural orbitals for chemical valence (NOCV) and QTAIM bonding analyses, were performed to characterize the ansa‐bridged molybdocene complexes [(C₅H₄)₂XMe₂MoH₃]⁺ for X = C, Si, Ge, Sn, Pb, and nonbridged Cp₂MoH system. The results have shown that the [(C₅H₄)₂CMe₂MoH(H₂)]⁺ complex exhibits nonclassical dihydrogen/hydride (H₂/H) conformation (97.6% of time of simulation), contrary to trihydride (H₃) structure noted for nonbridged Cp₂MoH (86.9%) and ansa‐bridged [(C₅H₄)₂SnMe₂MoH₃]⁺ (84.8%), [(C₅H₄)₂PbMe₂MoH₃]⁺ (84.9%) systems. Further, [(C₅H₄)₂SiMe₂MoH₃]⁺ and [(C₅H₄)₂GeMe₂MoH₃]⁺ complexes, appeared to exist in both conformations (H₂/H—55.4%, H₃—44.6% for Si‐based system and H₂/H—36.2%, H₃—63.8 % for germanium congener). It has been proven that the “steric availability” of the metal center, measured by the changes in the Cp? Mo? Cp angle (α), determines the existence of a given conformation—namely, the smaller value of the angle (molybdenum is sterically more accessible) the larger preference for the formation of dihydrogen/hydride structure. ETS‐NOCV method allowed to conclude that increase in the Cp? Mo? Cp angle (from α ca. 120° to α ca. 150°) leads to the enhancement of donation from H₂ and back‐donation from Mo to the σ*(H? H), what consequently leads to breaking of the H? H bond and formation of the trihydride structure. Systematical increase in the charge depletion from the σ‐bonding orbital of H₂ can be related to the reduction of the energy gap between the major orbitals involved in this contribution, namely highest occupied molecular orbital (HOMO) of H₂ with lowest unoccupied molecular orbital (LUMO) of [MoHL]⁺; ΔE = 0.0868 a.u. [for L =(C₅H₄)₂C], ΔE = 0.0827a.u. [for L = (C₅H₄)₂Si] ΔE = 0.0638 a.u. [for L = Cp₂]. Further, the relatively low energetic barrier to hydrogen exchange (ΔE^# = 3.3 kcal/mol) for carbon‐bridged complex, [(C₅H₄)₂CMe₂MoH_c(H_aH_b)]⁺ → [(C₅H₄)₂ CMe₂MoH_a(H_bH_c)]⁺, is related to strengthening of the Mo–H bonds when going from the substrate to the transition state (TS). Notably higher barrier to hydrogen rotation (ΔE^# = 10.1 kcal/mol) in [(C₅H₄)₂CMe₂MoH(H₂)]⁺ is due to lowering in the electrostatic stabilization as well as weakening of the donation (H₂ → Mo charge transfer) and practically lack‐of back‐donation (Mo → H₂) in the rotated TS. © 2012 Wiley Periodicals, Inc.     

Synthesis of Resorcinarene Derivatives by the Catalyzed Mannich Reaction,Part 2: Resorcinarene Derivatives with Unsaturated Bonds

The conditions of a simple synthesis of alkenyloxymethyl and the alkynyloxymethyl derivatives of resorcinarene by the Mannich reaction catalyzed with iminodiacetic acid are described. The synthesis presented in this article is effective and uses readily available and inexpensive substrates.     

Efficient and chemoselective direct reductive amination of aromatic aldehydes catalyzed by oxo–rhenium complexes containing heterocyclic ligands

This work describes the catalytic activity of 17 oxo–rhenium complexes containing heterocyclic ligands in the direct reductive amination of 4-nitrobenzaldehyde with 4-chloroaniline, using phenylsilane as reducing agent. In general, all of the catalysts tested gave excellent yields of the secondary amine, although, the best result was obtained with the catalytic system PhSiH₃/ReOBr₂(Hhmpbta)(PPh₃) (2.5 mol %). This system was also applied to the synthesis of a large variety of secondary amines in good to excellent yields and tertiary amines in moderate yields, with tolerance of different functional groups.     

The Use of Lypolitic Microorganisms Pseudomonas fluorescens and Penicillium citrinum for the Preparation of Optically Active 1 -Hydroxyalkylphosphonates

Abstract

Lipases are perhaps the most widely used biocatalysts in organic synthesis. In this study lipases were found to catalyse the acetylation of diethyl 1-hydroxyalkylphosphonates, as well as 1-aminoalkylphosphonates. Unfortunately the lack of enantioselectivity was observed despite of the source of enzyme, as well as the type of organic solvent used as the reaction medium. Also the use of lipases for the enantioselective hydrolysis of diethyl O-butyryloxyalkylphosphonates in aqueous media was unsucceful. Qulte oppositively the hydrolysis of these substrates by wide-type strain of Pseudomonas fluorescens yielded optically active diethyl 1-hydroxyalkylphosphonates with moderate or good yields and of satisfactory optical purity, as determined by means of n.m.r. analysis of Mosher derivatives. The use of other lypolitic microorganism - Penicillium citrinum -was also succesful providing enantiomeric forms of the products obtained from the reaction catalyzed by Pseudomoms fluorescens. The substrate specificity of these two microorganisms, is discussed in some detail.