Crystallographic report: Bis[bis(N,N‐dibenzyldithiocarbamato)cadmium(II)]

The centrosymmetric structure of {Cd[S₂CN(CH₂Ph)₂]₂}₂ features both bridging and chelating dithiocarbamate ligands so that a square pyramidal S₅ coordination geometry results. Copyright © 2004 John Wiley & Sons, Ltd.     

On a dynamic fractional game

Consider a two-person zero-sum game constructed by a dynamic fractional form. We establish the upper value as well as the lower value of a dynamic fractional game, and prove that the dual gap is equal to zero under certain conditions. It is also established that the saddle point function exists in the fractional game system under certain conditions so that the equilibrium point exists in this game system.     

Bundles, Handcuffs, and Local Freedom

We answer a question of J. Anderson's by producing infinitely many commensurability classes of fibered hyperbolic 3-manifolds whose fundamental groups contain subgroups that are locally free and not free. These manifolds are obtained by performing 0–surgery on a collection of knots with the same properties.     

Effects of the H-bond donor structure on the properties of supramolecular side chain liquid crystalline polymers based on poly(3-carboxypropylmethylsiloxane-co-dimethylsiloxane)s and stilbazoles

Supramolecular side chain liquid crystalline polymers (SCLCPs) based on poly(3-carboxypropylmethylsiloxane-co-dimethylsiloxane) (PSIX, X=100, 76, 60, 41 or 23, denoting the mole percentage of 3-carboxypropylmethylsiloxane unit in the polymer) and stilbazole derivatives have been obtained through intermolecular hydrogen bonding (H-bonding) interactions between the carboxylic acid and the pyridyl moieties. The formation of H-bonding and self-assembly results in the formation of new mesogenic units, in which H-bonds function as molecular connectors. FTIR shows the existence of H-bonding in the complexes. The polymeric complexes behave as single component liquid crystalline polymers and exhibit stable and enantiotropic mesophases. The liquid crystalline properties of the supramolecular SCLCPs were studied using differential scanning calorimetry, polarizing optical microscopy and X-ray diffraction, and were found to exhibit smectic A phases with focal-conic textures. The thermal stability of the SCLCP increases on increasing the carboxylic acid content in the polysiloxane and the concentration of the stilbazole derivative in the complex. However, the thermal stability decreases on increasing the chain length of the stilbazole derivative. The crystal phase was not formed even on cooling to the glass transition temperature of the polymeric complex.     

Formation, isolation and characterization of an AB-biaryl atropisomer of oritavancin

Oritavancin is a semi-synthetic glycopeptide antibiotic which is structurally related to vancomycin. When oritavancin bisphosphate is dried in vacuo with heat, a new compound forms. This new compound is stable only in the solid state and reverts to oritavancin in solution. Highly enriched samples of this compound were obtained by preparative HPLC and the structure of this compound was elucidated by using one and two-dimensional (¹H and ¹³C) NMR spectroscopy in conjunction with computer-assisted molecular modeling. It has been determined that oritavancin adopts a conformation similar to that of vancomycin in solution, while the new compound is the unnatural R-AB-biaryl atropisomer of oritavancin. This is the first observation and isolation of an AB-biaryl atropisomer in an intact member of the vancomycin family of glycopeptide antibiotics.     

多元整系数多项式因式分解的一种理论和算法

本文将ｔ（ｔ是大于２的整数）元整系数多项式看成为系数为ｔ－２元整系数多项式的二元多项式，建立了多元整系数多项式因式分解的一种新理论，进而得到了分解多元整系数多项式的一个有力的算法。     

一种实现光源与光纤耦合的方法

本文介绍了一种用显微镜筒与透镜构成的光学系统来实现光源与光纤耦合的方法。该方法具有光路系统小巧方便、耐用、耦合效率高等优点。     

Sulfonated poly(aryl ether ether ketone ketone)s containing fluorinated moieties as proton exchange membrane materials

A series of sulfonated poly(aryl ether ether ketone ketone)s statistical copolymers with high molecular weights were synthesized via an aromatic nucleophilic substitution polymerization. The sulfonation content (SC), defined as the number of sulfonic acid groups contained in an average repeat unit, could be controlled by the feed ratios of monomers. Flexible and strong membranes in sodium sulfonate form could be prepared by the solution casting method, and readily transformed to their proton forms by treating them in 2 N sulfuric acid. The polymers showed high T_gs, which increased with an increase in SC. Membranes prepared from the present sulfonated poly(ether ether ketone ketone) copolymers containing the hexafluoroisopropylidene moiety (SPEEKK‐6F) and copolymers containing the pendant 3,5‐ditrifluoromethylphenyl moiety (SPEEKK‐6FP) had lower water uptakes and lower swelling ratios in comparison with previously prepared copolymers containing 6F units. All of the polymers possessed proton conductivities higher than 1 × 10^?2 S/cm at room temperature, and proton conductivity values of several polymers were comparable to that of Nafion at high relative humidity. Their thermal stability, oxidative stability, and mechanical properties were also evaluated. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2299–2310, 2006