A remark on divisibility of definable groups

We show that if G is a definably compact, definably connected definable group defined in an arbitrary o‐minimal structure, then G is divisible. Furthermore, if G is defined in an o‐minimal expansion of a field, k ∈ ? and p_k : G → G is the definable map given by p_k (x ) = x^k for all x ∈ G , then we have |(p_k )^–1(x )| ≥ k^r for all x ∈ G , where r > 0 is the maximal dimension of abelian definable subgroups of G . (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Novel,organosoluble, light‐colored fluorinated polyimides based on 2,2′‐bis(4‐amino‐2‐trifluoromethylphenoxy)biphenyl or 2,2′‐bis(4‐amino‐2‐trifluoromethylphenoxy)‐1,1′‐binaphthyl

Two series of fluorinated polyimides were prepared from 2,2′‐bis(4‐amino‐2‐trifluoromethylphenoxy)biphenyl ( 2 ) and 2,2′‐bis(4‐amino‐2‐trifluoromethylphenoxy)‐1,1′‐binaphthyl ( 4 ) with various aromatic dianhydrides via a conventional, two‐step procedure that included a ring‐opening polyaddition to give poly(amic acid)s, followed by chemical or thermal cyclodehydration. The inherent viscosities of the polyimides ranged from 0.54 to 0.73 and 0.19 to 0.36 dL/g, respectively. All the fluorinated polyimides were soluble in many polar organic solvents, such as N,N‐dimethylacetamide and N‐methylpyrrolidone, and afforded transparent and light‐colored films via solution‐casting. These polyimides showed glass‐transition temperatures in the ranges of 222–280 and 257–351 °C by DSC, softening temperatures in the range of 264–301 °C by thermomechanical analysis, and a decomposition temperature for 10% weight loss above 520 °C both in nitrogen and air atmospheres. The polyimides had low moisture absorptions of 0.23–0.58%, low dielectric constants of 2.84–3.61 at 10 kHz, and an ultraviolet–visible absorption cutoff wavelength at 351–434 nm. Copolyimides derived from the same dianhydrides with an equimolar mixture of 4,4′‐oxydianiline and diamine 2 or 4 were also prepared and characterized. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2416–2431, 2004     

Soluble,saturated‐red‐light‐emitting poly(p‐phenylenevinylene) containing triphenylamine units and cyano groups

A conjugated poly(p‐CN‐phenylenevinylene) (PCNPV) containing both electron‐donating triphenylamine units and electron‐withdrawing cyano groups was prepared via Knoevenagel condensation in a good yield. Gel permeation chromatography suggested that the soluble polymer had a very high weight‐average molecular weight of 309,000. A bright and saturated red emission was observed under UV excitation in solution and film. Cyclic voltammetry showed that the polymer presented quasi‐reversible oxidation with a relatively low potential because of the triphenylamine unit. A single‐layer indium tin oxide/PCNPV/Mg–Ag device emitted a bright red light (633 nm). © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3947–3953, 2004     

New liquid‐crystalline poly(ester amide)s: The role of nitro groups in the phase behavior

New hydrogen‐bonded liquid‐crystalline poly(ester amide)s (PEA)s were obtained from 1,4‐terephthaloyl[bis‐(3‐nitro‐N‐anthranilic acid)] (5) or 1,4‐terephthaloyl[bis‐(N‐anthranilic acid)] (6), with or without nitro groups, respectively, through the separate condensation of each with hydroquinone or dihydroxynaphthalene. The dicarboxylic monomers were synthesized from 2‐aminobenzoic acid. The phase behavior of the monomers and polymers were studied with differential scanning calorimetry, polarized light microscopy, and wide‐angle X‐ray diffraction methods. Monomer 5, containing nitro groups, exhibited a smectic liquid‐crystalline phase, whereas the texture of monomer 6 without nitro groups appeared to be nematic. The PEAs containing nitro groups exhibited polymorphism (smectic and nematic), whereas those without nitro groups exhibited only one phase transition (a nematic threaded texture). The changes occurring in the phase behavior of the polymers were explained by the introduction of nitro groups. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1289–1298, 2004     

The intertwining lifting theorem for ordered groups

Sz.-Nagy's dilation theorem for a contraction on a Hilbert space has been extended by Mlak to the case of a contraction semigroup whose indices are the positive elements of a totally ordered discrete group. We generalize to this case the intertwining lifting theorem of Sz.-Nagy and Foias. Some previous interpolation results on ordered groups are obtained as consequences.     

Selectively protected galactose derivatives for the synthesis of branched oligosaccharides

Synthesis and characterization of several new anomerically pure galactose derivatives, based on simple and effective protective group manipulations of benzyl β-d-galactopyranoside, are reported. The monosaccharides described contain selectively protected/deprotected hydroxyl functionalities at their 1,2,3,4- and 6-positions rendering them useful as building blocks for construction of branched oligosaccharides.     

Synthesis of new thermosetting poly(2,6‐dimethyl‐1,4‐phenylene oxide)s containing epoxide pendant groups

A new class of thermosetting poly(2,6‐dimethyl‐1,4‐phenylene oxide)s containing pendant epoxide groups were synthesized and characterized. These new epoxy polymers were prepared through the bromination of poly(2,6‐dimethyl‐1,4‐phenylene oxide) in halogenated aromatic hydrocarbons followed by a Wittig reaction to yield vinyl‐substituted polymer derivatives. The treatment of the vinyl‐substituted polymers with m‐chloroperbenzoic acid led to the formation of epoxidized poly(2,6‐dimethyl‐1,4‐phenylene oxide) with variable pendant ratios, and the structures and properties were studied with nuclear magnetic resonance spectroscopy, Fourier transform infrared spectroscopy, differential scanning calorimetry, thermogravimetric analysis, and gel permeation chromatography. The ratios of pendant functional groups were tailored for the polymer properties, and the results showed that the glass‐transition temperatures increased as the benzylic protons were replaced by bromo‐, vinyl‐, or epoxide‐functional groups, whereas the thermal stability decreased in comparison with the original polymer. Within a molar fraction of 20–50%, the degree of functionalization had little effect on the glass‐transition temperature; however, it correlated inversely with the thermal stability of each functionalized polymer. The thermal curing behavior of the epoxide‐functionalized polymer was enhanced by the increment of the pendant functionality, which resulted in a significant increase in the glass‐transition temperature as well as the thermal stability after the curing reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5875–5886, 2006     

Synthesis and cationic photopolymerization of new fluorinated,polyfunctional propenyl ether oligomers

New fluorinated, polyfunctional propenyl ether functionalized resins were synthesized, and their behavior in cationic photopolymerization was investigated. The photopolymerization proceeded efficiently with a high double‐bond conversion (>90%), giving rise to UV‐cured coatings characterized by low glass‐transition temperatures (?33 °C ≤ glass‐transition temperature ≤ ?15 °C) and hydrophobic surface properties. A fluorinated additive was also employed as a reactive additive in the cationic photopolymerization of trimethylolpropane tripropenyl ether, increasing the double‐bond conversion, polymer network flexibility, thermal stability, and surface hydrophobicity. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6943–6951, 2006     

Protection of immobilized sulfhydryl groups against autooxidation by alterations in their microenvironment

Immobilized sulfhydryl groups were prepared by partial thiolation of NH₂-glass beads. The microenvironment of the immobilized SH groups was varied by different chemical modifications of neighboring NH₂ groups. Introduction of a strong charge in the surroundings of immobilized sulfhydryls results in their dramatic stabilization against autooxidation. This effect is due to the salting of O₂ from the surface microlayer of the thiolated beads.     

Compact flat manifolds with holonomy group

In this paper we construct a family of compact flat manifolds, for all dimensions , with holonomy group isomorphic to and first Betti number zero.