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.     

Sensitivity analysis for minimum Hamiltonian path and traveling salesman problems

Given the minimum Hamiltonian path (or traveling salesman tour) H⁰ in an undirected weighted graph, the sensitivity analysis problem consists in finding by how much we can perturb each edge weight individually without changing the optimality of H⁰.

The maximum increment and decrement of the edge weight that preserve the optimality of H⁰ is called edge tolerance with respect to the solution H⁰. A method of computing lower bounds of edge tolerances based on solving the sensitivity analysis problem for appropriate relaxations of the minimum Hamiltonian path and traveling salesman problems is presented.     

Bifractional inequalities and convex cones

In this paper we give a systematic study of a class of linear inequalities related to convex cones in linear spaces. In particular, Chebyshev and Andersson type inequalities are discussed. Some classical and new inequalities are derived from the results.     

Optimal portfolio choice under a liability constraint

The problem of characterizing the least expensive bond portfolio that enables one to meet his/her liability to pay C dollars K years from now is dealt with in this article. Bond prices are allowed to be either overpriced or underpriced at the purchase time, while at the sale time the bonds are suppose to be fairly priced. Assuming shifts in spot rates to occur instantly after the acquisition of a bond portfolio Z and to follow fairly general type of behavior described by the condition (2), we give both necessary and sufficient conditions for Z to solve the immunization problem above. Our model is general enough to cover situations with twists in the yield curve. Making use of the K-T conditions, we explain in remark 7 why we focus on search of an optimal portfolio in the class of barbell strategies. Finally, by means of the K-T conditions we find an optimal bond portfolio which solves the immunization problem. This revised version was published online in June 2006 with corrections to the Cover Date.     

Structural studies on aryl‐substituted enaminoketones and their thio analogues. Part I. Analysis of high‐resolution 1H, 13C NMR and 13C CP MAS spectra combined with GIAO‐DFT calculations

A series of aryl‐substituted enaminoketones and their thio analogues in CDCl₃ solution and in the solid state were studied by the use of high‐resolution ¹H and ¹³C as well as ¹³C cross polarization magic angle spinning (CP MAS) NMR spectra in combination with gauge including atomic orbitals‐density functional theory (GIAO‐DFT) calculations performed at the B3PW91/6–311 + + G(d,p) level of theory using the B3PW91/6‐311 + + G(d,p)‐optimized geometries. The analysis of the ¹³C NMR spectra in solution was done by using the Incredible Natural Abundance DoublE QUAntum Transfer Experiment (INADEQUATE) technique, whereas trends observed in the ¹³C shielding constants, calculated for the compounds studied, were a great help in assigning most of the signals in the ¹³C CP MAS NMR spectra. It was established on the basis of the experimental and theoretical NMR data that both groups of compounds exist in the form of Z‐s‐Z‐s‐E isomers in CDCl₃ solution as well as in the solid state, with the NH hydrogen atom involved in intramolecular hydrogen bonding. This conclusion is in agreement with the fact that some of the compounds studied reveal liquid‐crystalline properties. Three‐bond H, H and C, H coupling constants measured in solution played a crucial role in the structure elucidation. Copyright © 2009 John Wiley & Sons, Ltd.     

Sparse hamiltonian 2-decompositions together with exact count of numerous Hamilton cycles

We construct multigraphs of any large order with as few as only four 2-decompositions into Hamilton cycles or only two 2-decompositions into Hamilton paths. Nevertheless, some of those multigraphs are proved to have exponentially many Hamilton cycles (Hamilton paths). Two families of large simple graphs are constructed. Members in one class have exactly 16 hamiltonian pairs and in another class exactly four traceable pairs. These graphs also have exponentially many Hamilton cycles and Hamilton paths, respectively. The exact numbers of (Hamilton) cycles and paths are expressed in terms of Lucas- or Fibonacci-like numbers which count 2-independent vertex (or edge) subsets on the n-path or n-cycle. A closed formula which counts Hamilton cycles in the square of the n-cycle is found for n≥5. The presented results complement, improve on, or extend the corresponding well-known Thomason’s results.     

A generalized Jacobian based Newton method for semismooth block-triangular system of equations

This paper will consider the problem of solving the nonlinear system of equations with block-triangular structure. A generalized block Newton method for semismooth sparse system is presented and a locally superlinear convergence is proved. Moreover, locally linear convergence of some parameterized Newton method is shown.     

Conditions for blow-up of solutions of some nonlinear Volterra integral equations

In this paper we give necessary and sufficient conditions for blow-up of solutions for a particular class of nonlinear Volterra equations. We also give some examples.