Group classification of unsteady boundary layer equations of a class of non-Newtonian fluids

Two dimensional unsteady boundary layer equations of a general model of non-Newtonian fluids were investigated in this study. In this model, the shear stress is taken as an arbitrary function of the velocity gradient. Group classification of the equations with respect to shear stress is done using two different approaches: (1) classical theory (2) equivalence transformations. Both approaches yield identical results. It is found that the principle Lie Algebra extends only for cases of Newtonian and Power-Law flows.     

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.     

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 .

     

Morphology and oxygen sensor response of luminescent Ir-labeled poly(dimethylsiloxane)/polystyrene polymer blend films

Polymer films consisting of a linear poly(dimethylsiloxane) end-functionalized with a luminescent Ir(III) complex (Ir-PDMS), blended with polystyrene (PS), function as optical oxygen sensors. The sensor response arises by quenching of the luminescence from the Ir(III) chromophore by oxygen that permeates into the polymer film. The morphology and luminescence oxygen sensor properties of blend films consisting of Ir-PDMS and PS have been characterized by fluorescence microscopy, atomic force microscopy, and scanning electron microscopy. The investigations demonstrate that microscale phase segregation occurs in the films. In blends that contain a relatively small amount of Ir-PDMS in PS (ca. 10 wt %), the Ir-PDMS exists as circular domains, with diameters ranging from 2 to 5 mum, surrounded by the majority PS phase. For larger weight fractions of Ir-PDMS in the blends, the film morphology becomes bicontinuous. A novel epifluorescence microscopy method is applied that allows the construction of Stern-Volmer quenching images that quantify the oxygen sensor response of the blend films with micrometer spatial resolution. These images provide a map of the oxygen permeability of the polymer blend films with a spatial resolution of ca. 1 mum. The results of this investigation show that the micrometer-sized Ir-PMDS domains display a 2-3-fold higher oxygen sensor response compared to the surrounding PS matrix. This result is consistent with the fact that PDMS is considerably more gas permeable compared to PS. The relationship of the microscale morphology of the blends to their performance as macroscale optical oxygen sensors is discussed.     

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.     

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.