The Neumann problem for the Laplace equation on general domains

The solution of the weak Neumann problem for the Laplace equation with a distribution as a boundary condition is studied on a general open set G in the Euclidean space. It is shown that the solution of the problem is the sum of a constant and the Newtonian potential corresponding to a distribution with finite energy supported on ∂G. If we look for a solution of the problem in this form we get a bounded linear operator. Under mild assumptions on G a necessary and sufficient condition for the solvability of the problem is given and the solution is constructed. The research was supported by the Academy of Sciences of the Czech Republic, Institutional Research Plan No. AV0Z10190503.     

A homological approach to representations of algebras II: tame hereditary algebras

We determine the pure global dimension of finite dimensional hereditary or radical-squared zero algebras over algebraically closed fields. The results are applied to algebras of dimension four and to the incidence algebras of critical ordered sets studied by Loupias. We further prove that the path algebra of an oriented cycle shares with Dedekind domains the Kulikov property (submodules of pure-projective modules are pure-projective).     

Light scattering characterization of thermodynamic interaction of polymers in dilute solution. Effect of solvent and molecular weight

Interaction of nonidentical polymer molecules in a dilute solution of a mixture of two polymers is quantitatively characterized by A₂₄, the second virial coefficient for interaction of unlike species. This parameter is related to the compatibility of the two polymers in solution and is obtainable experimentally, e.g., by light scattering. With chemically markedly different polymers, A₂₄ depends neither on the molecular weight of the polymers nor on the solvent and becomes characteristic of the polymer pair. For a mixture of two copolymers or of a homopolymer and a copolymer with similar compositions, A₂₄ depends both on the solvent and on the molecular weight of polymers. Under such circumstances A₂₄ ceases to be a quantity given only by the chemical structure of the two polymers; however, under suitable conditions it remains a sensitive function of the difference between the chemical nature of polymer components.     

Treatment of citrate-capped Au colloids with NaCl, NaBr and Na2SO4: a TEM, EAS and EPR study of the accompanying changes

In the present study, effects of the treatment of citrate-reduced Au sols with NaCl, NaBr and Na₂SO₄ are described. The particles are characterized by transmission electron microscopy (TEM) and spectroscopic methods, suggesting an exchange of the citrate capping by the anions of the Na salts. Under electron beam exposure the capping of the NaCl- and NaBr-treated particles disappears. The specific electronic properties of the Na salt-treated particles are studied by electron absorption spectroscopy (EAS) and electron paramagnetic resonance (EPR). A discussion of the results in comparison with the spectroscopic responses from the original particles is given. A correlation between the data of EAS and EPR is found. The respective electron-withdrawing effect of the capping anions towards the Au core seems to be of considerable significance regarding the orbital situation around the Fermi level.     

Preparation and configurational stability of chiral chloro-[D1]methyllithiums of 98% enantiomeric excess

Enantiopure stannyl-[D1]methanol was converted to chloro-[D1]methylstannane under complete inversion of configuration using Ph3P/N-chlorosuccinimide in THF. It was transmetalated to stereospecifically give chloro-[D1]methyllithium (ee up to 98%). Its microscopic configurational stability was tested by performing tin-lithium exchange in the presence of benzaldehyde as the electrophile under various conditions. The macroscopic configurational stability was addressed by using the same electrophile but by adding it 30 s after the addition of MeLi used for transmetalation. Chloro-[D1]methyllithium is chemically very labile, however completely configurationally stable on both time scales up to the temperature of rapid decomposition (-78 degrees C).     

Covalent bonding of azoles to quaternary protoberberine alkaloids

Adducts of the quaternary protoberberine alkaloids (QPA) berberine, palmatine, and coptisine were prepared with nucleophiles derived from pyrrole, pyrazole, imidazole, and 1,2,4-triazole. The products, 8-substituted 7,8-dihydroprotoberberines, were identified by mass spectrometry and 1D and 2D NMR spectroscopy, including (1)H--(15)N shift correlations at natural abundance. In addition, two adducts of QPA with chloroform and methanethiolate were characterized by using NMR data. Single-crystal X-ray structures of 8-pyrrolyl-7,8-dihydroberberine, 8-pyrazolyl-7,8-dihydroberberine, and 8-imidazolyl-7,8-dihydroberberine are also presented.     

Spectroscopic investigations of high-power laser-induced dielectric breakdown in gas mixtures containing carbon monoxide

Large-scale plasma was created in gas mixtures containing carbon monoxide by high-power laser-induced dielectric breakdown (LIDB). The composition of the mixtures used corresponded to a cometary and/or meteoritic impact into the Earth's early atmosphere. A multiple-centimeter-sized fireball was created by focusing a single 85 J, 450 ps near-infrared laser pulse into the center of a 15 L gas cell. The excited reaction intermediates that formed in various stages of the LIDB plasma chemical evolution were investigated by optical emission spectroscopy (OES) with temporal resolution. Special attention was paid to any OES signs of molecular ions. However, carbon monoxide cations were registered only if their production was enhanced by Penning ionization, i.e., excess He was added to the CO. The chemical consequences of laser-produced plasma generation in a CO-N 2-H 2O mixture were investigated using high resolution Fourier-transform infrared absorption spectroscopy (FTIR) and gas chromatography (GC). Several simple inorganic and organic compounds were identified in the reaction mixture exposed to ten laser sparks. H 2 (18)O was used to avoid possible contamination. The large laser spark triggered more complex reactivity originating in carbon monoxide than expected, when taking into account the strong triple bond of carbon monoxide causing typically inefficient dissociation of this molecule in electrical discharges.     

syn‐Tri‐μ‐chlorido‐bis{[(R,R)/(S,S)‐2,2′‐bis(diphenylphosphino)‐1,1′‐biphenyl]hydridoiridium(III)} tetrafluoridoborate dichloromethane disolvate

In the structure of the title compound, [Ir₂Cl₃H₂(C₃₆H₂₈P₂)₂]BF₄·2CH₂Cl₂, the bimetallic cation features a confacial bioctahedral structure that is held together by three bridging chloride ions and is very close to C₂ symmetric. The hydrides are in a syn orientation (trans to the same halide bridge), and the chelating bis(phosphine) atropisomers display a racemic (R,R)/(S,S) configuration. Because of the high trans‐bond‐weakening influence of the hydride ligands, the Ir—Cl bonds trans to Ir—H [2.5262 (7) and 2.5365 (7) Å] are significantly longer than those opposite the Ir—P linkages [2.4287 (7)–2.4672 (8) Å]. The Ir—P distances vary between 2.2464 (9) and 2.2565 (8) Å. This study illustrates the usefulness of sterically demanding biaryl‐based P₂ ligands in the synthesis of halide‐bridged Ir₂ complexes, which are valuable precursors of versatile catalysts for homogeneous C=O hydrogenation.