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.     

Thermodynamic and kinetic investigations of PO3-4 adsorption on blast furnace slag

The kinetics of adsorption of PO(3-)(4) by blast furnace slag were found to be fast, reaching equilibrium in 20 min and following a pseudo-second-order rate equation. The adsorption behavior of PO(3-)(4) on blast furnace slag has been studied as a function of the solution agitation speed, pH, and temperature. Results have been analyzed by Freundlich, Langmuir, BET, and Dubinin-Radushkevich (D-R) adsorption isotherms. The mean energy of adsorption, 10.31 kJ mol(-1), was calculated from the D-R adsorption isotherm. The rate constants were calculated for 293, 298, 303, and 308 K using a pseudo-second-order rate equation and the activation energy (E(a)) was derived using the Arrhenius equation. Thermodynamic parameters such as DeltaH(0), DeltaS(0), and DeltaG(0) were calculated from the slope and intercept of linear plot of lnK(D) against 1/T. The DeltaH(0) and DeltaG(0) values of PO(3-)(4) adsorption on the blast furnace slag show endothermic heat of adsorption. But there is a negative free energy value, indicating that the process of PO(3-)(4) adsorption is favored at high temperatures.     

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 .

     

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.     

Monitoring the Instant Creation of a New Fluorescent Signal for Evaluation of DNA Conformation Based on Intercalation Complex

Here we report the monitoring the instant creation of a new fluorescent signal (FS) aroused from a positively charged water-soluble fluorogenic probe, ethidium bromide (EtBr) in the presence of a radical initiator, ammonium persulfate (APS) and an accelerator, tetraethylmetilendiamine (TEMED) for evaluation of deoxyribonucleic acid (DNA) conformation. The results revealed that the occurred FS (λ_ex?=?430 nm; λ_max?=?525 nm) is a reduced form of EtBr (λ_ex?=?480 nm; λ_max?=?617 nm) and it is completely distinct from hydroethidine (λ_ex?=?350 nm; λ_max?=?430 nm), which is two-electron reduced form of EtBr. It was noticed that EtBr was reduced to a new FS during the polymerization of N, N dimethyacrylamide (DMAA) too, at 25 °C in the presence of APS and TEMED or at 55 °C with only APS, and the rate of formation of FS was increased upon treatment time. The effect of nanoclays such as Laponite XLG® and Laponite XLS®, which provide a protective environment for DNA in nature, were also investigated through the reduction process of EtBr in the absence and presence of a water soluble monomer DMAA. We demonstrated that DNA conformation might be evaluated by monitoring FS effectuated during the reduction of EtBr in the presence of nanoclays having positively and negatively charged surfaces. Protective property of DNA against the formation of reduced product was elucidated by carrying out the polymerization at 55 °C. The results revealed that the monitoring of formation of FS in the presence of radical initiator could lead to elucidate the conformation of DNA upon formation of intercalator complex.     

A relationship between three analytical approaches to nonlinear problems

In this work, the relationship between three analytical techniques is demonstrated. The direct relationship between the variational approach (VA) and the Hamiltonian approach (HA) is illustrated for a first approximation, and subsequently the relationship between the variational approach and the harmonic balance method (HBM) is concluded. Moreover, the relationship between HA and VA is investigated for higher order solutions.     

A practical access to new pyrrolizine carboxylates via KHMDS-catalyzed carbocyclizations

Easy and effective preparation of new 1H-pyrrolizine carboxylates was achieved with high efficiency via KHMDS-induced carbocyclization of N-alkynyl proline carboxylates under substantially mild conditions. Meanwhile, some trans-diiodoallylic N-proline carboxylates were obtained from N-propargyl proline carboxylates using molecular I₂ with or without KHMDS. This method is quite feasible in terms of practical and quick access to the pyrrolizines and their derivatives over the formation of carbanions.