Connected signed graphs of fixed order,size, and number of negative edges with maximal index

In this paper we focus on connected signed graphs of fixed number of vertices, positive edges and negative edges that maximize the largest eigenvalue (also called the index) of their adjacency matrix. In the first step we determine these signed graphs in the set of signed generalized theta graphs. Concerning the general case, we use the eigenvector techniques for getting some structural properties of resulting signed graphs. In particular, we prove that positive edges induce nested split subgraphs, while negative edges induce double nested signed subgraphs. We observe that our concept can be applied when considering balancedness of signed graphs (the property that is extensively studied in both mathematical and non-mathematical context).     

Poly(ethylene glycol)-supported tetrahydroxyphenyl porphyrin: a convenient,recyclable catalyst for photooxidation reactions

[reaction: see text] A new poly(ethylene glycol)-supported porphyrin has been prepared and its ability as a promoter in photooxidation reactions has been studied. The PEG-supported catalyst exhibits high activity, comparable to that of a nonanchored sensitizer, and it is easily removable by filtration from the reaction mixture. The polymer-bound porphyrin has been recycled up to six times with no loss of chemical and stereochemical efficiency.     

Fluorescence in alkali-metal salts of some acyclic,resonance-stabilized carbanions

While fluorescence can be clearly observed in resonance-stabilized acyclic anions, its occurrence is insufficient for unambiguous assignment of either ion-pairing type or anion geometry. As in cyclic, aromatic anions, the requirement for contact ion-pairing is less severe in the excited state than in the ground state. The fluorescence lifetimes of acyclic anions are affected more by the associated cation than by the type of ion-pairing.     

Number and length of attractors in a critical Kauffman model with connectivity one

The Kauffman model describes a system of randomly connected nodes with dynamics based on Boolean update functions. Though it is a simple model, it exhibits very complex behavior for "critical" parameter values at the boundary between a frozen and a disordered phase, and is therefore used for studies of real network problems. We prove here that the mean number and mean length of attractors in critical random Boolean networks with connectivity one both increase faster than any power law with network size. We derive these results by generating the networks through a growth process and by calculating lower bounds.     

Experimental determination of human erythrocyte membrane permeability coefficients for a series of amides

Erythrocyte membrane permeability coefficients have been determined for a series of amides by a method based on the physical and mathematical modelling of hypotonic haemolysis process. The results show that penetration of the substances occurs by two alternative ways through aqueous pores formed by proteins and by the direct dissolving of the molecules in membrane lipids. This conclusion can be confirmed by the correlation analysis between permeability coefficients of native erythrocytes and those pre-incubated with the monosodium salt of p-chloromercuribenzenesulfonic acid (pCMBS), and the partition coefficients of the substances in hydrophilic-hydrophobic phases. Penetration of substances through hydrophilic channels is limited by the sterical factor and diameter in particular. Permeability coefficients for erythrocytes pre-incubated with pCMBS increase in an accordance with the rise of the partition coefficients with correlation coefficient of 0.94, thereby indicating a lipid route of permeation of molecules through erythrocyte membranes.     

Dopant-modulated pair interaction in cuprate superconductors

A comparison of recent experimental STM data with single-impurity and many-impurity Bogoliubov-de Gennes calculations strongly suggests that random out-of-plane dopant atoms in cuprates modulate the pair interaction locally. This type of disorder is crucial to understanding the nanoscale electronic inhomogeneity observed in BSCCO-2212, and can reproduce observed correlations between the positions of impurity atoms and various aspects of the local density of states such as the gap magnitude and the height of the coherence peaks. Our results imply that each dopant atom modulates the pair interaction on a length scale of order one lattice constant.     

Design of two-dimensional random surfaces with specified scattering properties

A method is proposed for designing a two-dimensional randomly rough Dirichlet surface that, when illuminated at normal incidence, scatters a scalar plane wave with a specified angular distribution of its intensity. The method is validated by computer simulation calculations.