Ergodicity of eigenfunctions for ergodic billiards

We give a simple proof of ergodicity of eigenfunctions of the Laplacian with Dirichlet boundary conditions on compact Riemannian manifolds with piecewise smooth boundaries and ergodic billiards. Examples include the Bunimovich stadium, the Sinai billiard and the generic polygonal billiard tables of Kerckhoff, Masur and Smillie.     

Alkoxy/siloxy group exchange in the system vinyltrialkoxysilane-iridium(I) siloxide complex

A study of reactions of dimeric siloxide iridium complex, [[(cod)Ir(mu-OSiMe3)]2] (1) with vinyltriethoxysilane and vinyltrimethoxysilane has revealed a new type of the reation--alkoxy group transfer from silicon to iridium with a simultaneous transfer of a siloxy group from iridium to silicon--as a result of which vinyldialkoxytrimethyldisiloxane and dimeric alkoxide iridium complex [[(cod)Ir(mu-OR)]2] (3) are formed. The structure of [[(cod)Ir(mu-OEt)]2] (3a) has been solved by X-ray diffraction.     

Crystal Structures of 1,5,9,18,22,26-Hexaaza[11.11]-p-cyclophane Adducts; Two-dimensional Supramolecular Networks

Two newly identified supramolecular structures arise from self-assembly of the macrocyclic 1,5,9,18,22,26- hexaaza[11.11]-p-cyclophane salts with o-nitrophenol (C₂₈H₅₀N₆)⁴⁺·4(C₆H₄NO₂O)⁻ (1) and with HCl (C₂₈H₅₂N₆)⁶⁺·6Cl^-·4H₂O (2). In both cases two-dimensional supramolecular sheets are formed.     

Laser-Induced Fluorescence (LIF) Probe for <Emphasis Type="Italic">In-situ</Emphasis> Nitric Oxide Concentration Measurement in a Non-thermal Pulsed Corona Discharge Plasma Reactor

Laser-induced fluorescence (LIF) is an effective in-situ probe for NO concentrations below 300 ppm in a non-thermal plasma reactor. A new method has been developed to measure in-situ NO concentration in the reactor discharge region using a long-time—on the order of seconds—averaged fluorescence detection. This method, for quantifying NO concentration in a nonthermal plasma reactor, is simpler than a short-time—on the order of nanoseconds—fluorescence detection. For accurate measurement based on the new method, the LIF intensity must be close to the corona-induced fluorescence (CIF) intensity; the CIF intensity serves as a guide in selecting the LIF intensity. We find that a kinetic model proposed earlier works for two-tube reactors and represents the NO concentration in the middle of the reactor, which verifies the assumption of gas plug flow.     

Highly stereoselective synthesis, structure, and application of (E)-9-[2-(silyl)ethenyl]-9H-carbazoles

(E)-N-(Silyl)vinylcarbazole has been easily prepared via a new catalytic route, silylative coupling (SC) of vinylcarbazole with vinyltrisubstituted silanes catalyzed by [RuH(Cl)(CO)(PCy3)2]. X-ray structures of two silylvinylcarbazoles as first N-vinylcarbazole derivatives have been resolved. The Pd-catalyzed Hiyama coupling reaction (also as the tandem reaction with SC) of synthesized (E)-N-(triethoxysilyl)vinylcarbazole with iodobenzene has been performed to afford (E)-N-(phenylvinyl)carbazole with high yield and stereoselectivity.     

Interaction with glycine increases stability of a mutagenic tautomer of uracil. A density functional theory study

The most stable structures for the gas-phase complexes of minor tautomers of uracil (U) with glycine (G) were characterized at the density functional B3LYP/6-31++G level of theory. These are cyclic structures stabilized by two hydrogen bonds. The relative stability of isolated tautomers of uracil was rationalized by using thermodynamic and structural arguments. The stabilization energies for complexes between the tautomers of U and G result from interplay between the stabilizing two-body interaction energies and destabilizing one-body terms. The latter are related to the energies of (i) tautomerization of the unperturbed moieties and (ii) distortions of the resulting rare tautomers in the complex. The two-body term describes the interaction energy between distorted tautomers. The two-body interaction energy term correlates with perturbations of length of the proton-donor bonds as well as with deprotonation enthalpies and proton affinities of the appropriate monomer sites. It was demonstrated that the relative instability of rare tautomers of uracil is diminished due to their interactions with glycine. In particular, the instability of the third most stable tautomer (U(III)) is decreased from 11.9 kcal/mol for non-interacting uracil to 6.7 kcal/mol for uracil in a complex with the zwitterionic tautomer of glycine. A decrease of instability by 5.2 kcal/mol could result in an increase of concentration of U(III) by almost 5 orders of magnitude. This is the tautomer with proton donor and acceptor sites matching guanine rather than adenine. Moreover, kinetic characteristics obtained for the glycine-assisted conversion of the most stable tautomer of uracil (U(I)) to U(III) indicate that the U(I)<-->U(III) thermodynamic equilibrium could be easily attained at room temperature. The resulting concentration of this tautomer falls in a mutationally significant range.     

Divergent coordination mode of magnesium and zinc alkyls supported by the bifunctional pyrrolylaldiminato ligand

The first magnesium and zinc alkyls derived from N-(iso-propyl)-pyrrolylaldimine have been synthesised and structurally characterised: both tBuM(N,N')-type compounds exist as three-coordinate monomers in benzene solution, but in the solid state the magnesium complex is a centrosymmetric dimer with Mg2(mu-N)2 bridges, whereas the zinc complex is a Zn...pi bonded dimer with a pi-coordinated pyrrole unit.     

X-ray structures and homolysis of some alkylcobalt(III) phthalocyanine complexes

The first crystallographic data for sigma-bonded alkylcobalt(III) phthalocyanine complexes are reported. A single-crystal X-ray structure of CH(3)CH(2)Co(III)Pc (Pc = dianion of phthalocyanine) reveals that the solid consists of centrosymmetric face-to-face dimers in which the CH(3)CH(2)Co(III)Pc units retain their square pyramidal geometry. The structure appears to be the first one reported for a five-coordinate RCo(III)(chelate) complex with an electron-deficient equatorial system. The Co-C bond in CH(3)CH(2)Co(III)Pc (2.031(5) A) is the longest found in five-coordinate RCo(III)(chel) complexes (R = simple primary alkyl group). Another X-ray study demonstrates that CH(3)Co(III)Pc(py) has a distorted octahedral geometry with axial bonds of very similar length to those in methylcobalamin. The axial bonds are shorter than those in its octaethylporphyrin analogue, in accordance with a weaker trans axial influence in six-coordinate complexes containing an electron-deficient phthalocyanine equatorial ligand. A different trend has been observed for five-coordinate RCo(III)(chel) complexes: electron-rich equatorial systems seem to make the Co-C axial bond shorter. Kinetic data for the homolysis of RCo(III)Pc complexes (R = Me, Et) in dimethylacetamide are also reported. Homolysis of ethyl derivatives is faster. The Co-C bond dissociation energies (BDEs) for the pyridine adducts of the methyl and the ethyl derivative are 30 +/- 1 and 29 +/- 1 kcal/mol, respectively. The BDE for CH(3)CoPc(py) is considerably lower than that for MeCbl despite the very similar lengths of the axial bonds in the two complexes. The results of this work do not support any correlation between the Co-C bond length and the bond strength as defined by BDE.     

Renormalization group and high-temperature series for the two-dimensional ising model

We employ high-temperature series to investigate a two-parameter class of renormalization group transformations for the two-dimensional Ising model on the triangular lattice. For the static case we identify an optimal organization of the high-temperature expansion and an optimal transformation matrix and thus find, in second order, =0.96 and the magnetic eigenvaluey=2-/2=1.76.From recursion relations for flip rates we find the dynamic exponent to be the same for all transformations in our two-parameter class,z=2.32.Our fixed-point flip rates do not describe a Markov process even though the corresponding master equation for the single-event probability displays no explicit memory effects. The non-Markovian nature shows up only in a violation of the Markovian detailed balance conditions.     

Polyurethane anionomers synthesised with aromatic, aliphatic or cycloaliphatic diisocyanates, polyoxyethylene glycol and 2,2-bis-(hydroxymethyl)propionic acid. Part II. Supermolecular structure. Thermal properties

Small angle X-ray scattering and differential scanning calorimetry methods were employed to characterise the internal order of structural phases present in polyurethane coatings obtained as a result of water evaporation from anionomer dispersions. Those anionomers were produced in the reaction of aromatic, cycloaliphatic and aliphatic diisocyanates with polyoxyethylene glycol, 2,2-bis-(hydroxymethyl)propionic acid and 1,6-hexamethylenediamine. The decisive effects were found from ionic and polar structures within the rigid urethane and urea segments on the ordered arrangement degree of the supermolecular structures in the obtained anionomers. That becomes apparent in differential scanning calorimetry thermograms and contributes to improved thermal stability of the produced polyurethane coatings.