Compact spreads and compact translation planes over locally compact fields

We prove that a spread S over a locally compact nondlscrete field F defines a topological translation plane if and only if the spread is compact. For F=R, this is implicit in Breuning's thesis [Bre], cf. [B 2]. For the proof, we describe the point set of the projective translation plane as a quotient space of some projective space, with identifications taking place in one hyperplane. This is new even for F=R.     

Rigorous calculation of pixel and inter-electrode capacitances of thin-film transistor liquid crystal displays using three-dimensional simulation

We have rigorously calculated for the first time all the inter-electrode and pixel capacitances of Thin-Film Transistor Liquid Crystal Displays using the electrical energy distribution inside a liquid crystal cell. The energy distribution is obtained from the three-dimensional profiles of potential distribution and molecular director. The dynamic equation of continuum theory for liquid crystals is described in a tensorial form in order to maintain the equivalence of n and -n . The effects of lateral fields generated by multiple electrodes of finite sizes are taken into account in the simulation. As a numerical technique, we used a finite difference method which is suitable for the highly non-linear equations. As a result, we confirmed that the pixel capacitance for our pixel structure is about 40% larger than that of the conventional approach. It is also revealed that the gate-common and gate-data inter-electrode capacitances are not negligible.     

Determinant formulas for class numbers in function fields

In this paper, by extending Kucera's idea to the function field case, we obtain several determinant formulas involving the real class number and the relative class number of any subfield of cyclotomic function fields. We also provide several examples using these determinant formulas.

     

Synthesis and characterization of new segmented polyurethanes with side‐chain,liquid‐crystalline chain extenders

Liquid‐crystalline, segmented polyurethanes with methoxy–biphenyl mesogens pendant on the chain extender were synthesized by the conventional prepolymer technique and esterification reaction. Two, side‐chain, liquid‐crystalline (SCLC) polyurethanes with mesogens having spacers of six and eight methylene units were prepared. The structures of the mesogenic units and SCLC polyurethanes were confirmed by Fourier transform infrared spectroscopy and ¹H NMR. Polymer properties were also examined by solubility tests, water uptakes, and inherent viscosity measurements. Differential scanning calorimetry studies indicated that the transition temperature of the isotropic to the liquid‐crystalline phase decreased with increasing spacer length. Wide‐angle X‐ray diffraction (WAXD) studies revealed the existence of liquid‐crystalline phases for both SCLC polyurethanes. Polarized optical microscopic investigations further confirmed the thermotropic liquid‐crystalline behaviors and nematic mesophases of both samples. Thermogravimetric analysis displayed better thermal stabilities for both SCLC polymers and indicated that the presence of mesogenic side chains may increase the thermal stability of segmented polyurethanes. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 290–302, 2004     

Effects of poly[styrene‐b‐(ethylene‐co‐butylene)‐b‐styrene] on the charge distributions of low‐density polyethylene/polystyrene blends

The effect of the triblock copolymer poly[styrene‐b‐(ethylene‐co‐butylene)‐b‐styrene] (SEBS) on the formation of the space charge of immiscible low‐density polyethylene (LDPE)/polystyrene (PS) blends was investigated. Blends of 70/30 (wt %) LDPE/PS were prepared through melt blending in an internal mixer at a blend temperature of 220 °C. The amount of charge that accumulated in the 70% LDPE/30% PS blends decreased when the SEBS content increased up to 10 wt %. For compatibilized and uncompatibilized blends, no significant change in the degree of crystallinity of LDPE in the blends was observed, and so the effect of crystallization on the space charge distribution could be excluded. Morphological observations showed that the addition of SEBS resulted in a domain size reduction of the dispersed PS phase and better interfacial adhesion between the LDPE and PS phases. The location of SEBS at a domain interface enabled charges to migrate from one phase to the other via the domain interface and, therefore, resulted in a significant decrease in the amount of space charge for the LDPE/PS blends with SEBS. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2813–2820, 2004     

Stability control of the electrooptic effect with new maleimide copolymers containing photoreactive tricyanopyrrolidene‐based chromophores

New photocrosslinkable maleimide copolymers have been synthesized by the attachment of a tricyanopyrrolidene‐based chromophore. The 2‐(3‐cyano‐4‐(2‐{4‐[hexyl‐(6‐hydroxy‐hexyl)‐amino]‐phenyl}‐vinyl)‐5‐oxo‐1‐{4‐[4‐(3‐oxo‐3‐phenyl‐propenyl)‐ phenoxy]‐butyl}‐1,5‐dihydro‐pyrrol‐2‐ylidene)‐malononitrile chromophore exhibits nonlinear optical activity and contains a chalcone moiety that is sensitive to UV light (λ = 330–360 nm) for crosslink formation. The maleimide monomers have also been functionalized with chalcone moieties. The resultant copolymers exhibit great processability, and one of them shows a maximum electrooptic coefficient of 90 pm/V at 1300 nm. We could control the thermal stability of the electrooptic coefficient with the newly synthesized photoreactive copolymers successfully. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 531–542, 2007     

Cellulose dimethylphenylcarbamate-bonded carbon-clad zirconia for chiral separation in high performance liquid chromatography.

Porous zirconia particles are very robust material and have received considerable attention as a stationary phase support for HPLC. We prepared cellulose dimethylphenylcarbamate-bonded carbon-clad zirconia (CDMPCCZ) as a chiral stationary phase (CSP) for separation of enantiomers of a set of 14 racemic compounds in normal phase (NP) and reversed-phase (RP) liquid chromatography. Retention and enantioselectivity on CDMPCCZ were compared to those on CDMPC-coated zirconia (CDMPCZ) to see how the change in immobilization method of the chiral selector affects the retention and chiral selectivity. In NPLC, retention was longer and the number of resolved racemates was smaller on CDMPCCZ than on CDMPCZ. However, chiral selectivity factors for some resolved racemates were better on CDMPCCZ than on CDMPCZ. The longer retention on CDMPCCZ is likely due to strong, non-chiral discriminating interactions with the carbon layer on CDMPCZ. In RPLC only two racemates were resolved on CDMPCCZ, but retention times were shorter than, and resolutions were comparable to, those in NPLC, indicating a potential for improving chromatographic performance of the CDMPCCZ column in RPLC with optimized column preparation and separation conditions.     

Backward extensions of subnormal operators

The concept of backward extension for subnormal weighted shifts is generalized to arbitrary subnormal operators. Several differences and similarities in these contexts are explored, with emphasis on the structure of the underlying measures.

     

Determination of carbamazepine by chemiluminescence detection using chemically prepared tris(2,2'-bipyridine)ruthenium(III) as oxidant.

A new chemiluminescence method for the determination of carbamazepine (CBZ) has been developed. The method is based on the chemiluminescence produced in the reaction of tris(2,2'-bipyridine)ruthenium(III) and CBZ in an acidic medium. The chemiluminescence intensity was enhanced by organic solvents in the reaction system. Under the optimum experimental conditions, the calibration curve was linear over the range 4.0 x 10(-3)-8.6 x 10(-7) mol/L for CBZ. The detection limit (S/N = 3) was 2.5 x 10(-7) mol/L and the relative standard deviation of six replicate measurements was 2.6% for 4.0 x 10(-4) mol/L of CBZ. The possible reaction mechanism were also discussed. The chemiluminescence method was successfully applied to assay the CBZ contents in pharmaceutical tablets.     

Chern numbers for two families of noncommutative Hopf fibrations

We consider noncommutative line bundles associated with the Hopf fibrations of SU_q(2) over all Podle? spheres and with a locally trivial Hopf fibration of S³_pq. These bundles are given as finitely generated projective modules associated via 1-dimensional representations of U(1) with Galois-type extensions encoding the principal fibrations of SU_q(2) and S³_pq. We show that the Chern numbers of these modules coincide with the winding numbers of representations defining them. To cite this article: P.M. Hajac et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).