Long time behaviour of a flow in infinite pipe conforming to slip boundary conditions

The paper analyses long time behaviour of solutions of the Navier–Stokes equations in a two‐dimensional pipe‐like domain. The system is studied with perfect slip boundary conditions with arbitrary inflow conditions at infinity. The main results show the existence of global in time solutions and of an attractor for the dynamical system generated by the model. The paper also establishes an upper bound for the Hausdorff dimension of the attractor. Copyright © 2005 John Wiley & Sons, Ltd.     

Pressure-temperature phase diagrams of smectogenic 4'-alkyl-4-cyanobiphenyls (9CB, 10CB, 11CB and 12CB)

The pressure-temperature ( p - T ) phase diagrams for four smectogenic members of the 4'-alkyl-4-cyanobiphenyl homologous series ( n CB, n =9, 10, 11 and 12) over the temperature range 320-410 K and pressure range 0.1-300 MPa (3 kbar) were constructed using DTA. At 1 atm 9CB exhibits nematic and smectic A d phases, while the other members show only the smectic A d phase. However, at elevated pressures the clearing line splits in the case of 10CB and 11CB which indicates the induction of a nematic phase. It was found that the triple point, where the isotropic, nematic and smectic phases coexist, is strongly shifted to higher pressures with increasing chain length. This was interpreted as being caused by a loss of the rod-like shape of the molecules containing longer alkyl tails which explore a range of conformations. The slope of the clearing line, d T /d p , depends strongly on the length of the alkyl chain for the n CB series, but does not show a step-wise change between the nematogenic and smectogenic members.     

On essential extensions of reduced rings and domains

A ring is said to be a left essential extension of a reduced ring (domain) if it contains a left ideal which is a reduced ring (domain) and intersects nontrivially every nonzero twosided ideal of the ring. We prove that every ring which is a left essential extension of a reduced ring is a subdirect sum of rings which are essential extensions of domains, but the converse implication does not hold. We give some applications of this result and discuss several related questions.Received: 6 January 2003     

Configurational and conformational preferences in stereoselective acylations of <Emphasis Type="Italic">N</Emphasis>-methyl-1,3-diaminopropane with acyl chlorides

Evidence for a stereoinduction profile of the reaction of N-methyl-1,3-diaminopropane with acyl chlorides has been provided. A possibility to engage in intramolecular CH₂⋯HN and Cl⋯H-N interactions and the proton migration process to the methylamino group leads to the E secondary amides carrying the N⋯H⁺⋯N or N-H⋯N bridges, that show unusual spectroscopic images. Empirical relations between the Δδ _C chemical shift differences, the polarizability of the CO(S) groups and hydrogen bonding strength have been found. Both ¹H-¹⁵N-GHSQC and GHMBC experiments provide insight into the nature of hydrogen bonding and confirm the cyclic array of atoms.     

Effect of Ga doping on magneto-transport properties in colossal magnetoresistive La0.7Ca0.3Mn1−xGaxO3 (0<x<0.1)

Samples of La_0.7Ca_0.3Mn_1−xGa_xO₃ with x=0, 0.025, 0.05 and 0.10 were prepared by standard solid-state reaction. They were first characterized chemically, including the microstructure. The magnetic properties and various transport properties, i.e. the electrical resistivity, magnetoresistivity (for a field below 8 T), thermoelectric power and thermal conductivity measured each time on the same sample, are reported. The markedly different behaviour of the x=0.1 sample from those with a smaller Ga content, is discussed. The dilution of the Mn³⁺/Mn⁴⁺ interactions with Ga doping considerably reduces the ferromagnetic double exchange interaction within the manganese lattice leading to a decrease of the Curie temperature. The polaron binding energy varies from 224 to 243 meV with increased Ga doping.     

Multinuclear magnetic resonance study of some mesoionic oxatriazoles containing nitrogenous exocyclic groups

¹H,¹³C,¹⁴N and¹⁵N NMR measurements are reported for four mesoionic 1-oxa-2, 3, 4-triazoles containing exocyclic nitrogenous groups. The NMR signal assignments are discussed and compared with those previously published for some corresponding oxatriazoles. The results obtained support the proposed cyclic mesoionic structures for the compounds studied. The questions of possible charge delocalization and valence tautomerism are addressed. Compound with N^– H as a exocyclic group (Fig. 1) is found to be relatively unstable, this is attributed to proton migration in the corresponding non-cyclic form of this molecule.Published in Khimiya Geterotsikiicheskikh Soedinenii, No. 9, pp. 1260–1263, September, 1995.     

On quartics with three-divisible sets of cusps

 We study the geometry and codes of quartic surfaces with many cusps. We apply Gr?bner bases to find examples of various configurations of cusps on quartics. Received: 10 May 2002 / Revised version: 11 November 2002 Published online: 3 March 2003 Permanent address: Institute of Mathematics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland. e-mail: rams@mi.uni-erlangen.de, rams@im.uj.edu.pl Research partially supported by the Schwerpunktprogramm ``Global methods in complex geometry' of the Deutsche Forschungsgemeinschaft, and by EAGER. Mathematics Subject Classification (2000): 14J25, 14J17     

Activity of TiO2 deposited by the CVD method on ammoxidized surface of a carbonaceous material in hydrogenation of styrene

Hydrogenation of styrene has been applied as a test reaction to study the catalytic activity of TiO₂ deposited by the CVD (chemical vapour deposition) method on the surface of a carbonaceous material enriched in nitrogen (C_N).     

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