On Extracting Maximum Stable Sets in Perfect Graphs Using Lovász's Theta Function

We study the maximum stable set problem. For a given graph, we establish several transformations among feasible solutions of different formulations of Lovász's theta function. We propose reductions from feasible solutions corresponding to a graph to those corresponding to its induced subgraphs. We develop an efficient, polynomial-time algorithm to extract a maximum stable set in a perfect graph using the theta function. Our algorithm iteratively transforms an approximate solution of the semidefinite formulation of the theta function into an approximate solution of another formulation, which is then used to identify a vertex that belongs to a maximum stable set. The subgraph induced by that vertex and its neighbors is removed and the same procedure is repeated on successively smaller graphs. We establish that solving the theta problem up to an adaptively chosen, fairly rough accuracy suffices in order for the algorithm to work properly. Furthermore, our algorithm successfully employs a warm-start strategy to recompute the theta function on smaller subgraphs. Computational results demonstrate that our algorithm can efficiently extract maximum stable sets in comparable time it takes to solve the theta problem on the original graph to optimality. This work was supported in part by NSF through CAREER Grant DMI-0237415. Part of this work was performed while the first author was at the Department of Applied Mathematics and Statisticsat Stony Brook University, Stony Brook, NY, USA.     

Electrochemical Polymerization of Aniline at Low Supporting-Electrolyte Concentrations and Characterization of Obtained Films

Conductive polymers of aniline were synthesized in aqueous acidic media such as perchloric, sulfuric, hydrochloric, phosphoric, and trifluoroacetic acids and the effect of supporting electrolyte was investigated. The conductivity of each polyaniline (PAn) sample was determined by the four-probe technique. PAn (H₂SO₄) sample was shown to have the highest conductivity, specifically, 3.55 S cm^–1. The effect of concentrations of monomers and acids on the conductivity of PAn's was studied. It was observed that the conductivity decreased with increasing aniline concentration and increased with increasing sulfuric acid concentration. The conductivities of PAn (CF₃COOH) were also investigated in different supporting electrolytes and highly good increments of its conductivities were obtained. Magnetic properties of the PAn salts were analyzed by Gouy balance measurements and it was found that their conducting mechanisms are of bipolaron nature. From the FTIR analysis it was found that polymerization occurs via the –NH₂ group in a head-to-tail mechanism. The thermal analyses revealed that PAn (HCl) among the PAn salts studied shows the highest thermal stability. Surface analyses of polymers were clarified by scanning electron microscopy. From elemental analysis results, PAn salts were concluded to be in emeraldine structure.     

Gas phase ion/molecule reactions in laser desorption mass spectrometry

The desorption of neutrals, alkali ions and quasimolecular ions of sucrose was studied as function of substrate temperature in laser desorption mass spectrometry. These phenomena were also investigated in thermal desorption experiments. It was concluded that in these experiments gas phase cationization is the major ionization process.     

Monolayers as models for supported catalysts: zirconium phosphonate films containing manganese(III) porphyrins

Organized monolayer films of a manganese tetraphenylporphyrin have been prepared and used as supported oxidation catalysts. Manganese 5,10,15,20-tetrakis(tetrafluorophenyl-4'-octadecyloxyphosphonic acid) porphyrin (1) has been immobilized as a monolayer film by a combination of Langmuir-Blodgett (LB) and self-assembled monolayer techniques that use zirconium phosphonate linkages to bind the molecule to the surface. Analysis by FTIR, XPS, UV-vis and polarized optical spectroscopy show that the films consist of noninteracting molecules effectively anchored and oriented nearly parallel to the surface. The monolayer films are stable to the solvent and temperature conditions needed to explore organic oxidations. The activity of films of 1 toward the epoxidation of cyclooctene using iodosylbenzene as the oxidant was compared to that of Manganese 5,10,15,20-tetrakis(pentafluorophenyl) porphyrin (2) and 1 under equivalent homogeneous conditions. The immobilized porphyrin 1 shows an enhanced activity relative to either homogeneous reaction. The main difference between 1 and 2 is the four alkyl phosphonate arms in 1 designed to incorporate the porphyrin within the films. The increased activity of immobilized 1 is a combination of the porphyrin structure, which prohibits the formation of mu-oxo dimers even in solution, and a change in conformation when anchored to the surface. The study demonstrates that careful monolayer studies can provide useful models for the design and study of supported molecular catalyst systems.     

High-performance liquid chromatography with post-column derivatisation and fluorescence detection for sensitive determination of aflatoxin M1 in milk and cheese

A new HPLC method with fluorescence detection using pyridinium hydrobromide perbromide as a post-column derivatising agent has been developed to determine aflatoxin M1 in milk and cheese. The detection limits were 1 ng/kg for milk and 5 ng/kg for cheese. The calibration curve was linear from 0.001 to 0.1 ng injected. The method includes a preliminary C18-SPE clean-up and the average recoveries of Aflatoxin M1 from milk and cheese, spiked at levels of 25-75 ng/kg and 100-300 ng/kg, respectively, were 90 and 76%; the precision (RSDr) ranged from 1.7 to 2.6% for milk and from 3.5 to 6.5% for cheese. The method is rapid, easily automatable and therefore useful for accurate and precise screening of aflatoxin M1 in milk and cheese.     

New glyoxime derivatives and their transition metal complexes

Two new vic-dioxime ligands and their complexes with Co⁺², Ni⁺², Cu⁺², Cd⁺², and Zn⁺² ions were synthesized. Primer amines (3,4-methylenedioxaaniline and 4-methylbenzylamine) reacted with antichloroglyoxime to give 3,4-methylenedioxaphenylaminoglyoxime (H₂L¹) and N-(4-methylbenzyl)aminoglyoxime (H₂L²) ligands. Structures of the ligands and their complexes are proposed based on elemental analyses, IR, UV-Vis, and ¹H NMR spectra, magnetic susceptibility measurements, and thermogravimetric analyses (TGA). The article was submitted by the authors in English.     

A note on

There is only one pair of non-real zeros of , and of , in the left half-plane. The Riemann Hypothesis implies that and have no zeros in the strip .

     

Calcium oxalate monohydrate precipitation at membrane lipid rafts

The precipitation of calcium oxalate monohydrate (COM) was monitored at a Langmuir monolayer containing lipid raft domains. The raft-forming monolayer consists of a 2:1:1 mixture of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine/sphingomyelin/dihydrocholesterol, where the raft liquid ordered phase is enriched in sphingomyelin and the sterol. COM crystals, monitored by Brewster angle microscopy, appear at the phase boundary between the raft domains and the expanded phase.     

Bioadhesion to solids: contact angle hysteresis effect

It was recently reported that the ease of removal of sporelings of green seaweed Ulva under shear stress from the polymer surfaces was found to be linearly and positively correlated with contact angle and wetting hysteresis, i.e., the higher the hysteresis, the greater the removal. Motivated by this report, we examined the relationship between the bioadhesion of blood platelets and proteins with contact angle hysteresis of solid substrates using the data of published papers. It was determined that there is a linear and positive relationship between the contact angle hysteresis and bioadhesion of both blood platelets and γ-globulin protein contacting the solid substrates, i.e., the higher the hysteresis, the greater the bioadhesion. The reasons are discussed and it is proposed that testing the effect of CAH on the adhesion strengths of biomaterials on surfaces is useful in order to gain a better insight on the bioadhesion mechanism.