Analysis and finite element simulations of a second‐order fluid model in a bounded domain

This article is concerned with the equations governing the steady motion of a viscoelastic incompressible second‐order fluid in a bounded domain. A new proof of existence and uniqueness of strong solutions is given. In addition, using appropriate finite element methods to approximate a coupled equivalent problem, sharp error estimates are obtained using a fixed point argument. The method is applied to the two‐dimensional lid‐driven cavity problem, at low Reynolds number and in a certain range of values of the viscoelastic parameters, to analyze the combined effects of inertia and viscoelasticity on the flow. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Benzyne cyclisation with carbanion activated aromatic rings1

Attempts to cyclise o-chlorophenyl benzyl ether, sulphide, sulphoxide and sulphone by treatment with KNH₂/NH₃ were unsuccessful. Similar reaction of 1-(o-chlorophenyl)-2,2-diphenylethane led to amination whereas α-(o-chlorobenzyl)phenylacetic acid gave a dihydrocoumarin. Reaction of 4- and 2-(o-chlorophenethyl)-pyridines, however, afforded products comprising benzisoquinolines and 1-pyridylbenzocyclobutenes.     

All-Solid-State PVC Membrane Ag+-Selective Electrodes Based on Diaza-18-Crown-6 Compounds

Two diaza-crown ether compounds were synthesized and evaluated as Ag⁺-selective carriers in polyvinylchloride (PVC) membrane electrodes of solid-state type. The all-solid-state PVC membrane electrode based on N,N-Dibenzyl-dibenzo-diaza-18-crown-6 exhibited a super-Nernstian response (75±10mV per decade) over the concentration range of 1×10^–1 to 7×10^–6M of Ag⁺ ion and a detection limit of 3×10^–6M, at a wide range of pH (pH 4–7). The response time of the electrode was fast (less than 10s), and it can be used for three months without any significant deviation in potential. The proposed all-solid-state PVC membrane electrodes revealed high selectivity toward Ag⁺ ion with respect to alkali, alkaline earth, heavy and transition metal ions. A flow-through cell of all-solid-state PVC membrane Ag⁺-selective electrode based on N,N-Dibenzyl-dibenzo-diaza-18-crown-6 has also been prepared and applied for flow-injection analysis of Ag⁺ ion in solution.     

Sol–gel synthesis of IPTES and D10H consisting fluorinated silane system for hydrophobic applications

In this study, new fluorinated silane system was prepared by adding hydroxyl terminated Fluorolink D10H oligomer to 3-isocyanatopropyltrietoxysilane. The obtained silane system was independently composed with 3-Glycidyloxypropyltrimethoxysilane and 3-Glycidyloxy-propyltriethoxysilane. Then the prepared two different coating solutions were applied to glass surface by spin-coating method. The chemical bonding between groups in system was investigated by FTIR analysis. The elemental composition of coatings was determined by using EDX analysis. Their structure and surface properties were analyzed by scanning electron microscopy, atomic force microscopy, contact angle measurement and UV–vis spectrophotometer. The amounts of fluorine on the coatings prepared with IPTES-D10H-GLYEO and IPTES-D10H-GLYMO were 33 and 34 %wt, respectively. Transparent coatings with smooth surface and uniform thickness were obtained. The coatings had nanoscale roughness. The contact angles of coatings for water were range from 103° to 110°, and for n-hexadecane were range from 59° to 62°.     

Effect of amine catalysts on preparation of nanometric SiO<Subscript>2</Subscript> particles and antireflective films via sol–gel method

SiO₂ sols were prepared by hydrolysis and condensation reactions of tetraethyl orthosilicate through a one step acid or a two step acid + base catalysis process, in the presence of nitric acid and four different base catalyzers, namely trimethylamine, triethylamine, tripropylamine and tributylamine. Hydrolysis of TEOS was followed by FT-IR analyses. Particle size distributions of the sols were evaluated after predetermined durations in 1–22 days. Particle growth was seen to be faster in amine catalyzed systems than in one step acid catalyzed system. The highest rate of growth was in triethylamine catalyzed system. Glass substrates were dip coated with the prepared SiO₂ sols. Effect of sol aging duration on film thickness and on light transmittance properties of the films was investigated with respect to type of base catalyst. Thicknesses of the films which were measured to be in the range of 100–400 nm, were seen to increase with aging duration of the sols. Triethylamine catalyzed system presented the highest film thickness. Films obtained from one step acid catalyzed system presented an increase of 4.8%; whereas acid + base catalyzed films provided an increase in the light transmittance of 5.7% in the first 4 days of aging. Surfaces of films were examined by FESEM and AFM. The antireflective character of the films was verified by diffuse reflectance analyses.     

Distinguished representations and exceptional poles of the Asai-L-function

Let K/F be a quadratic extension of p-adic fields. We show that a generic irreducible representation of GL(n, K) is distinguished if and only if its Rankin-Selberg Asai L-function has an exceptional pole at zero. We use this result to compute Asai L-functions of principal series representations of GL(2, K), hence completing the computation of these functions for generic representations of this group.     

Steady Flows of Shear-Dependent Oldroyd-B Fluids around an Obstacle

This work is concerned with the study of steady flows of an incompressible viscoelastic fluid of Oldroyd type, with viscosity depending on the second invariant of the rate of deformation tensor in an exterior domain. We establish a result of existence and uniqueness of strong solutions for sufficiently small data and give estimates relating these solutions to those of the corresponding generalized Newtonian fluid.     

Synthesis of Novel Chiral C 2-symmetric Diaza-18-crown-6 Ether Derivatives and their Enantioselective Recognition of Amino Acid Derivatives

New chiral diaza-18-crown-6 ether derivatives, 5 and 6 were synthesized from (R)-(-)-2-amino-1-bütanol. These chiral artificial receptors exhibit pronounced chiral recognition toward the enantiomers of l- and d- amino acid derivatives. The highest enantioselectivity was observed in the case of Trp-OMe·HCl (K_D/K_L=12.5).     

On the operations of sequences in rings and binomial type sequences

Given a commutative ring with identity R, many different and interesting operations can be defined over the set \(H_R\) of sequences of elements in R. These operations can also give \(H_R\) the structure of a ring. We study some of these operations, focusing on the binomial convolution product and the operation induced by the composition of exponential generating functions. We provide new relations between these operations and their invertible elements. We also study automorphisms of the Hurwitz series ring, highlighting that some well-known transforms of sequences (such as the Stirling transform) are special cases of these automorphisms. Moreover, we introduce a novel isomorphism between \(H_R\) equipped with the componentwise sum and the set of the sequences starting with 1 equipped with the binomial convolution product. Finally, thanks to this isomorphism, we find a new method for characterizing and generating all the binomial type sequences.