Structure and atropisomerisation of new diastereomeric gossypol Schiff bases with (R)-(+)-2-amino-3-benzyloxy-1-propanol studied by NMR,ECD and DFT methods

Gossypol Schiff base with (R)-(+)-2-amino-3-benzyloxy-1-propanol 1 was synthesised and resolved by HPLC method into diastereomers to study their atropisomerisation process. The spectroscopic analysis performed by one- and two-dimensional NMR, UV–vis and FT-IR methods indicated that the compound exists in solution as an enamine-oxo tautomer. The ECD measurements and TD-DFT calculations allowed us to unambiguously determine the configuration about the axially chiral biaryl moiety of 1. The conditions of the atropisomerisation processes of diastereopure gossypol Schiff bases (S_AX,R)-1 and (R_AX,R)-1 were determined on the basis of ECD and NMR measurements. Exposure of the diastereomers of 1 to sunlight and to the light at λ = 254 nm significantly accelerated the atropisomerisation when compared to its rate in the dark.     

Situations in traffic — how quickly they change

Spatio-temporal correlations of traffic intensity are analyzed employing data collected for the motorway M-30 around Madrid during one week in January 2009. We found that the lifetime of these correlations is the shortest in the evening between 6:00 p.m. and 8:00 p.m. This lifetime represents a new indicator for the amount of attention that is demanded by drivers in given traffic conditions.     

Correlation between the surface free energy of modified and non-modified glasses with controlled porosity and their sorption properties

Summary Contact angles for water and diiodomethane drops were measured on the surface of thermally and chemically (by Carbowax 20M bonding) modified porous glasses and on the surface of naphthalene, diphenyl and anthracene. Using the obtained results to a modified Young equation, dispersion and nondispersion components of the surface free energy of these glasses and organic substances were calculated. The work of adhesion (W_A) for benzene, naphthalene, diphenyl, anthracene, nitrobenzene was estimated and correlated with the capacity factors, (k′) of these substances. On the basis of experimental and calculated data it can be stated that the thermal treatment of porous glasses increases, their hydrophobicity but the Carbowax layer causes hydrophilicity. There is a linear relationship between k′ and W_A which can be helpful for predicting retention data of chromatographed substances on the base of surface free energy which can be calculated from contact angle measurements.     

Sard's theorem for mappings in Hölder and Sobolev spaces

We prove various generalizations of classical Sard's theorem to mappings f:M ^m →N ⁿ between manifolds in Hölder and Sobolev classes. It turns out that if f ∈ C ^k,λ (M ^m ,N ⁿ ), then—for arbitrary k and λ—one can obtain estimates of the Hausdorff measure of the set of critical points in a typical level set f ^?1(y). The classical theorem of Sard holds true for f ∈ C ^k with sufficiently large k, i.e., k>max(m?n,0); our estimates contain Sard's theorem (and improvements due to Dubovitskii and Bates) as special cases. For Sobolev mappings between manifolds, we describe the structure of f ^?1(y).     

The effect of cholesterol on the adsorption of phenyltin compounds onto phosphatidylcholine and sphingomyelin liposome membranes

Organometallic compounds are widely spread in the human environment sometimes, causing a substantial health risk. Their amphiphilic character enables them to intercalate and penetrate cell membranes, potentially affecting various vital cell functions. Compound adsorption onto the membrane depends on the compound properties, as well as on the membrane composition and state. When adsorbing onto the lipidic surface, phenyltins localize at areas where lipid bilayer organization is compatible with compound spatial requirements. The lipid bilayer is a dynamic and laterally nonuniform structure with complex local and global architecture correlated with a variety of cell functions. The selective binding of a toxic compound to selected membrane areas may, therefore, interfere with some types of cellular process. We present experimental results concerning phenyltin adsorption onto the lipid bilayer surface measured with the fluorescent probe fluorescein‐PE. Model lipid bilayers were formed from lipid mixtures mimicking various plasma membrane regions. The adsorption of Ph₃SnCl and P₂SnCl₂ onto the phosphatidylcholine–cholesterol bilayer was qualitatively different from sphingomyelin–cholesterol. The results presented indicate that phenyltins are likely to accumulate in areas containing phosphatidylcholine, outside of lipid rafts. Copyright © 2004 John Wiley & Sons, Ltd.     

On relations between non-Archimedean power series spaces

The power series spaces of finite type, A₁(α), and infinite type, A_∞(α), are the most known and important examples of non-Archimedean nuclear Fréchet spaces. We study when Aπ (α) has a subspace (or quotient) isomorphic to A_q(b).     

Extending partial isometries

We show that a finite metric spaceA admits an extension to a finite metric spaceB so that each partial isometry ofA extends to an isometry ofB. We also prove a more precise result on extending a single partial isometry of a finite metric space. Both these results have consequences for the structure of the isometry groups of the rational Urysohn metric space and the Urysohn metric space. Research supported by NSF grant DMS-0400931. I would like to thank Ward Henson and Alekos Kechris for conversations and emails regarding the paper. Part of this work was done when I visited Caltech in May 2004. I thank the mathematics department there for support