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.     

Influence of Musa acuminate bio-filler on the thermal,mechanical and visco-elastic behavior of poly (propylene) carbonate biocomposites

Biocomposites were fabricated using poly(propylene) carbonate as matrix and cellulosic polysaccharide banana (Musa acuminate) peel powder as filler in varying concentrations (5–25?wt.%) and were characterized for their functional properties. Microscopic analysis indicated the uniform distribution and existence of microfibrils in the filler. The thermal stability of the composites was lower than the matrix till 320?°C, beyond which it increased. The visco-elastic and mechanical behavior of the biocomposites was found to be enhanced with the addition of fillers. Thus, with better thermal, visco-elastic, and mechanical properties, the biocomposite films can be a replacement for the non-biodegradable polymers for packaging applications.     

On minimal non-M_rC-groups

A group $G$ is said to be a minimax group if it has a finite series whose factors satisfy either the minimal or the maximal condition. Let $D(G)$ denotes the subgroup of $G$ generated by all the Chernikov divisible normal subgroups of $G$ . If $G$ is a soluble-by-finite minimax group and if $D(G)=1$ , then $G$ is said to be a reduced minimax group. Also $G$ is said to be an $ M_{r}C$ -group (respectively, $PC$ -group), if $G/C_{G} \left(x^{G}\right)$ is a reduced minimax (respectively, polycyclic-by-finite) group for all $x\in G$ . These are generalisations of the familiar property of being an $FC$ -group. Finally, if $\mathfrak X $ is a class of groups, then $G$ is said to be a minimal non- $\mathfrak X $ -group if it is not an $\mathfrak X $ -group but all of whose proper subgroups are $\mathfrak X $ -groups. Belyaev and Sesekin characterized minimal non- $FC$ -groups when they have a non-trivial finite or abelian factor group. Here we prove that if $G$ is a group that has a proper subgroup of finite index, then $G$ is a minimal non- $M_{r}C$ -group (respectively, non- $PC$ -group) if, and only if, $G$ is a minimal non- $FC$ -group.     

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.     

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.