Pluripolar hulis and holomorphic coverings

The aim of the paper is to study the behavior of (complete) pluripolar sets under special holomorphic mappings (proper mappings and coverings). Research was supported in part by the KBN Grant 2 P03A 017 14. The author is a fellow of the Foundation for Polish Science.     

Mixed Aggregates of the Dilithiated Koga Tetraamine: NMR Spectroscopic and Computational Studies

A combination of ¹H, ⁶Li, ¹³C, and ¹⁵N NMR spectroscopies and density functional theory computations explores the formation of mixed aggregates by a dilithium salt of a C₂‐symmetric chiral tetraamine (Koga's base). Lithium halides, acetylides, alkoxides, and monoalkylamides form isostructural trilithiated mixed aggregates with few exceptions. ⁶Li–¹³C and ⁶Li–¹⁵N couplings reveal heretofore undetected transannular contacts (laddering) with lithium acetylides and lithium monoalkylamides. Marked temperature‐dependent ¹⁵N chemical shifts seem to be associated with this laddering. Computational studies shed light on the general structures of the aggregates, their penchant for laddering, and the stereochemical consequences of aggregation.     

Total synthesis of (+)-pinnatoxin A

A convergent enantioselective total synthesis of (+)-pinnatoxin A is described. The synthesis capitalizes on the highly diastereoselective Ireland-Claisen rearrangement of an acyclic alpha-branched allylic ester to set the quaternary stereogenic center at the core of the spiroimine ring system along with the adjacent tertiary stereocenter. The all-carbon macrocyclic ring system was formed by ring-closing metathesis.     

Solution of Vizing's Problem on Interchanges for the case of Graphs with Maximum Degree 4 and Related Results

Let G be a Class 1 graph with maximum degree 4 and let be an integer. We show that any proper t‐edge coloring of G can be transformed to any proper 4‐edge coloring of G using only transformations on 2‐colored subgraphs (so‐called interchanges). This settles the smallest previously unsolved case of a well‐known problem of Vizing on interchanges, posed in 1965. Using our result we give an affirmative answer to a question of Mohar for two classes of graphs: we show that all proper 5‐edge colorings of a Class 1 graph with maximum degree 4 are Kempe equivalent, that is, can be transformed to each other by interchanges, and that all proper 7‐edge colorings of a Class 2 graph with maximum degree 5 are Kempe equivalent.     

Redox sensing by Escherichia coli: effects of copper ions as oxidizers on proton-coupled membrane transport

Escherichia coli is able to grow under anaerobic fermentation conditions upon a decrease in redox potential (E(h)). Indeed, upon a transition of E. coli MC4100 wild-type culture to stationary growth phase a decrease in E(h) from the positive values ( approximately +100 mV) to the negative ones ( approximately -520 mV) was observed, the acidification of the medium and the H(2) production were obtained. An oxidizer, copper ions (Cu(2+)) affected a bacterial growth in a concentration-dependent manner (of 0.1 mM to 10 mM) increasing latent (lag) growth phase duration, delaying logarithmic (log) growth phase and decreasing specific growth rate. Acidification of the medium and the N,N'-dicyclohexylcarbodiimide (DCCD)- and azide-sensitive proton-potassium exchange by bacteria were inhibited, H(2) production upon growth and under assays disappeared with Cu(2+) (0.1 mM). These effects were observed with hycE but not hyfR and hyc(A-H) mutants and under aerobic conditions. Cu(2+) also increased membrane proton conductance. Copper ions are suggested to affect directly the F(0)F(1)-ATPase associated with potassium uptake transport system and/or formate hydrogenlyase composed with hydrogenase 4. A role of the F(0)F(1)-ATPase in redox sensing under fermentation is proposed.     

Three-dimensional phase field microelasticity theory of a multivoid multicrack system in an elastically anisotropic body: Model and computer simulations

The phase field microelasticity theory of a three-dimensional, elastically anisotropic system of voids and cracks is proposed. The theory is based on the equation for the strain energy of the continuous elastically homogeneous body presented as a functional of the phase field, which is the effective stress-free strain. It is proved that the stress-free strain minimizing the strain energy of this homogeneous modulus body fully determines the elastic strain and displacement of the body with voids and/or cracks. The proposed phase field integral equation describing the elasticity of an arbitrary system of voids and cracks is exact. The geometry and evolution of multiple voids and/or cracks are described by the phase field, which is the solution of the time-dependent Ginzburg-Landau equation. Other defects, such as dislocations and precipitates, are trivially integrated into this theory. The proposed model does not impose a priori constraints on possible void and crack configurations or their evolution paths. Examples of computations of elastic equilibrium of systems with voids and/or cracks and the evolution of cracks under applied stress are considered.     

3,3]-Sigmatropic rearrangement/5-exo-dig cyclization reactions of benzyl alkynyl ethers: synthesis of substituted 2-indanones and indenes

Substituted benzyl alkynyl ethers, prepared from the corresponding α-alkoxy ketones in a two-step sequence involving enol triflate formation and KOtBu-induced E2 elimination, undergo [3,3]-sigmatropic rearrangement/intramolecular 5-exo-dig cyclization at 60 °C to form substituted 2-indanones in good overall yields. 1,3-cis-Disubstituted-2-indanones are formed preferentially when the benzylic substituent R(1) is bulky. Substituted indenes may be prepared from 2-indanones in high yields by Horner-Wadsworth-Emmons reaction.     

Laser Raman Spectrum of Triglycine Sulfate

Abstract

The laser Raman spectrum of ferroelectric triglycine sulfate has been determined by the use of an argon ion gas laser. The observed Raman lines are compared with reported assignments in the literature by Taurel¹ and Krishnan², Determination of depolarization ratio of the sulfate line at 980 cm^?1 shows that the Raman band is highly polarizable and the molecular vibration is totally symmetrical v₁.

The role played by the glycine groups in the spontaneous polarization and its reversal can be indirectly confirmed by Raman spectrum of TGS. Interpretation of the Raman spectrum indicates that the SO₄ groups do not have tetrahedral symmetry at roan temperature. Ferroelectric behavior of TGS is attributed to the glycine groups.     

The spherical sector of the Calogero model as a reduced matrix model

We investigate the matrix-model origin of the spherical sector of the rational Calogero model and its constants of motion. We develop a diagrammatic technique which allows us to find explicit expressions of the constants of motion and calculate their Poisson brackets. In this way we obtain all functionally independent constants of motion to any given order in the momenta. Our technique is related to the valence-bond basis for singlet states.