Synthesis and chiroptical properties of two new planar-chiral macrocycles

Could simple intraannular-arm macrocyclic systems exist in enantiopure stable forms? The effective synthesis of two representative compounds of such a class, their resolution into enantiomers, and experiments justifying their stability toward racemization are presented.     

On characterization of Poisson and Jacobi structures

We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids.     

An invariance of geometric mean with respect to Lagrangian means

The invariance of the geometric mean G with respect to the Lagrangian mean-type mapping (Lf,Lg), i.e. the equation G○(Lf,Lg)=G, is considered. We show that the functions f and g must be of high class regularity. This fact allows to reduce the problem to a differential equation and determine the second derivatives of the generators f and g.     

The Transition Products in Substitutional Photochemistry of [Mo(CN)8]4− – Theoretical Approach. X-ray Crystal Structure of (AsPh4)[W(bpy)(CN)6]

The single crystal X-ray structure of (AsPh₄)[W(bpy)(CN)₆] is described. The structure of octa- and hepta-coordinated intermediates of substitutional photolysis of [Mo(CN)₈]⁴⁻ ion in aqueous media were determined by performing semi-empirical calculations. On the basis of obtained results as well as on empirical data the photolysis scheme has been postulated.     

Uniform persistence for nonautonomous and random parabolic Kolmogorov systems

The purpose of this paper is to investigate uniform persistence for nonautonomous and random parabolic Kolmogorov systems via the skew-product semiflows approach. It is first shown that the uniform persistence of the skew-product semiflow associated with a nonautonomous (random) parabolic Kolmogorov system implies that of the system. Various sufficient conditions in terms of the so-called unsaturatedness and/or Lyapunov exponents for uniform persistence of the skew-product semiflows are then provided. Among others, it is shown that if the associated skew-product semiflow has a global attractor and its restriction to the boundary of the state space has a Morse decomposition which is unsaturated or whose external Lyapunov exponents are positive, then it is uniformly persistent. More specific conditions are discussed for uniform persistence in n-species, particularly 3-species, random competitive systems.     

Exchange interaction and spin dynamics in pentanuclear clusters, Cu3Ln2(ClCH2COO)12(H2O)8 (Ln = Nd3+, Sm3+, Pr3+)

New compounds, [Cu₃Ln₂(ClCH₂COO)₁₂(H₂O)₈]·2H₂O with Ln = Nd³⁺ (I), Sm³⁺ (II), Pr³⁺ (III), built up of pentanuclear clusters were synthesized and studied by means of X-ray analysis and electron paramagnetic resonance (EPR). X-ray data show that all compounds are isostructural and the pentanuclear clusteres may be considered as a linear system with alternating Cu(II) and Ln(III) ions: Cu(2)-L¹-Ln-L²-Cu(1)-L²-Ln-L²-Cu(2) with L¹ and L² being bridging fragments and Cu(1) and Cu(2) being structurally nonequivalent copper complexes. EPR studies demonstrate that in the temperature range of 100–293 K the signals due to only one type of the copper complexes are observed in the spectra of I–III. AtT<100 K the spectral temperature dependence is nontrivial. AtT<30 K new signals are detected in the spectra of I and II. The temperature dependence of the EPR spectra is interpreted under the assumption that the parameter of the exchange interaction Cu(2)-Ln considerably exceeds the parameter of the interaction Cu(1)-Ln. EPR spectra are calculated for the fragments of five paramagnetic centers in the frames of the model taking into account the nonequivalence of two copper complexes, short longitudinal and transverse paramagnetic relaxation times of the rare-earth ions at room temperature and the change of the relaxation rates when the temperature decreases. The results of the calculations show that it is possible to obtain information about the interactions in the system on the basis of the analysis of the temperature dependence of the EPR spectra of the central copper complex. The parameter of the isotropic part of the exchange interaction between copper and neodymium ions (for the interaction Cu(2)-Nd) is estimated as about 15 cm⁻¹. A considerable rearrangement of the spin states when the temperature changes is found for all complexes.     

9‐Methyl‐3‐phenyl­diazenyl‐9H‐carbazole: X‐ray and DFT‐calculated structures

The title compound, C₁₉H₁₅N₃, was prepared by condensation of 3‐nitroso­carbazole and aniline with subsequent methyl­ation. The structure is built up of stacks of almost planar mol­ecules. Density functional theory (DFT) calculations predict a completely planar conformation, different from that observed in the crystal lattice. HOMA (harmonic oscillator model of aromaticity) indices, calculated for three aromatic rings, demonstrate the small influence of the azo substituent on π electrons in the carbazole system.     

Synthesis of biodegradable copolymers with low‐toxicity zirconium compounds. V. Multiblock and random copolymers of L‐lactide with trimethylene carbonate obtained in copolymerizations initiated with zirconium(IV) acetylacetonate

Using zirconium(IV) acetylacetonate as an initiator of lactide/trimethylene carbonate copolymerization allowed us to obtain high‐molecular‐weight copolymers with high efficiency. The reactivity ratios of the comonomers were 13.0 for lactide and 0.53 for trimethylene carbonate. Despite the large differences between the values of the reactivity ratios, copolymers with randomized chain structures were obtained. This phenomenon occurred as a result of an intensive intermolecular transesterification process proceeding along with the reaction of copolymer chain growth and modifying its final structure. Conducting the copolymerization at the relatively low temperature of about 110 °C, which minimized the influence of intermolecular transesterification, made it possible to obtain semicrystalline copolymers with multiblock structures. Increasing the temperature of copolymerization up to 180 °C was associated with strong intensification of the transesterification reactions. At this temperature, amorphous copolymers were obtained with identical compositions but highly randomized chain structures. An analysis of the chain microstructures of the obtained copolymers, determining the average length of the blocks, the intermolecular transesterification ratio, and the degree of chain randomization, was conducted by means of NMR spectroscopy. For this purpose, very specific signal assignment in the carbonyl and methylene carbon regions of the ¹³C NMR spectra to appropriate comonomer sequences of polymeric chains was performed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3184–3201, 2006     

Synthesis of biodegradable copolymers with low‐toxicity zirconium compounds. IV. Copolymerization of glycolide with trimethylene carbonate and 2,2‐dimethyltrimethylene carbonate: Microstructure analysis of copolymer chains by high‐resolution nuclear magnetic resonance spectroscopy

The results of the copolymerization of glycolide with cyclic trimethylene carbonate and 2,2‐dimethyltrimethylene carbonate are described. The copolymerization was conducted in the presence of low‐toxicity zirconium(IV) acetylacetonate as an initiator. With this kind of initiator, the composition of the comonomer units in the copolymer chains was assumed to be obtained with high efficiency. Despite significant differences in the comonomer reactivity, in copolymers containing comparable amounts of glycolidyl and carbonate sequences, highly randomized chain structures were observed. This effect resulted from strong intermolecular transesterification that proceeded during the studied copolymerization and caused glycolidyl microblock randomization. The assignment of the spectral NMR lines to appropriate comonomer sequences of polymeric chains was performed in the region of methylene protons of glycolidyl units in ¹H NMR spectra of the copolymers and in the carbonyl region of carbon spectra. The equations were formulated for a detailed characterization of the obtained copolymer chains, the average lengths of the blocks, and the transesterification and randomization coefficients. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 98–114, 2006     

Filament sets and homogeneous continua

New tools are introduced for the study of homogeneous continua. The subcontinua of a given continuum are classified into three types: filament, non-filament, and ample, with ample being a subcategory of non-filament. The richness of the collection of ample subcontinua of a homogeneous continuum reflects where the space lies in the gradation from being locally connected at one extreme to indecomposable at another. Applications are given to the general theory of homogeneous continua and their hyperspaces.