COMPUTATION OF HOPF BRANCHES BIFURCATING FROM A HOPF/PITCHFORK POINT FOR PROBLEMS WITH Z_2-SYMMETRY

1.IntroductionThispaperisdevotedtothecalculatiollofT,ranchesofHopfpointswhichemallatefromacertaillsingularPointofatwopar:lmeterII()nlinearsystemwhereXisarealHillersspac(},Aabifllrcationparallleter,oranadditionalcontrolparameter,alldgisasnlootllmapping.\Nreassllllle(HI)gisA--synlnletric:thereexistsalillearoperators:X-Xsatisfying(I:identicaloperatorillX)Itiswellknottrnthat(1.2)irldllcestilesplittillgl)Th.firstauthorhasbeedsupportedbyar(>searchgralltoftileV'Olkswagen-StiftungWesaythatxiss…     

Gradient- and Sensitivity-Enhanced TOCSY Experiments

A pulsed field gradient version of the sensitivity-enhanced 2D TOCSY experiment is proposed which yields high-quality spectra with improved sensitivity and a minimum of two scans pert₁increment. For rapid acquisition of 1D TOCSY spectra, the 1D DPFGSE–TOCSY experiment was modified to include phase-encoded multiple-selective excitation followed by a simple spectral editing. Combination of these two building blocks is used in a sensitivity-enhanced 2D analog of the 3D TOCSY–TOCSY experiment which provides an efficient tool for resolving severely overlapped signals of oligomers in short experimental time.     

Contributions of Spin–Lattice Relaxation to the Echo Decay of Planar Cu in High-Temperature Superconductors

Measurement ofT_2G, the Gaussian component of the spin-echo envelope of planar Cu nuclei in high-temperature superconductors, gives important information about the real part of the Cu electron spin susceptibility. In the traditional picture of the planar Cu echo decay, the internuclear coupling is assumed to remain static with respect to spin–lattice relaxation and mutual exchange fluctuations. In some circumstances, however, this assumption breaks down. We calculate the internuclear corrections arising from spin–lattice relaxation to the conventional theory ofT_2Gand show thatT_2Gcan be easily corrected for these effects. We argue that mutual exchanges due to the perpendicular indirect couplings are suppressed in these materials. For YBa₂Cu₄O₈, we find a correction on the order of 10% inT_2Gand using the corrected values we find that the isotope ratio⁶³T_2G/⁶⁵T_2Gagrees with theory.     

Fluorinated,crosslinkable terpolymers based on vinylidene fluoride and bearing sulfonic acid side groups for fuel‐cell membranes

The radical terpolymerization of 8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene with vinylidene fluoride (VDF) and perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride is presented. Changing the feed compositions of these three fluorinated comonomers enabled us to obtain different random‐type poly[vinylidene fluoride‐ter‐perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride‐ter‐8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene] terpolymers containing various sulfonyl fluoride and brominated side groups. Yields higher than 70% were reached in all cases. The hydrolysis of the sulfonyl fluoride group into the ? SO₃Li function in the presence of lithium carbonate was quantitatively achieved without the content of VDF being affected, and so dehydrofluorination of the VDF base unit was avoided. These original terpolymers were then crosslinked via dangling bromine atoms in the presence of a peroxide/triallyl isocyanurate system, which produced films insoluble in organic solvents such as acetone and dimethylformamide (which totally dissolved uncured terpolymers). The acidification of ? SO₃Li into the ? SO₃H function enabled protonic membranes to be obtained. The thermal stabilities of the crosslinked materials were higher than those of the uncured terpolymers, and their electrochemical performances were investigated. According to the contents of the sulfonic acid side functions, the ion‐exchange capacities ranged from 0.6 to 1.5 mequiv of H⁺/g, whereas the water uptake and conductivities ranged from 5–26% (±11%) and from 0.5 to 6.0 mS/cm, respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4566–4578, 2006     

Operational characteristics and power scaling of a transverse flow transversely excited CW CO<Subscript>2</Subscript> laser

Transverse flow transversely excited (TFTE) CO₂ lasers are easily scalable to multikilowatt level. The laser power can be scaled up by increasing the volumetric gas flow and discharge volume. It was observed in a TFTE CW CO₂ laser having single row of pins as an anode and tubular cathode that the laser power was not increasing when the discharge volume and the gas volumetric flow were increased by increasing the electrode separation keeping the gas flow velocity constant. The discharge voltage too remained almost constant with the change of electrode separation at the same gas flow velocity. This necessitated revision of the scaling laws for designing this type of high power CO₂ laser. Experimental results of laser performance for different electrode separations are discussed and the modifications in the scaling laws are presented.     

Monte Carlo simulations on magnetic behavior of a spin-chain system in triangular lattice doped with antiferromagnetic bonds

A three-dimensional Ising-like model doped with anti-ferromagnetic (AFM) bonds is proposed to investigate the magnetic properties of a doped triangular spin-chain system by using a Monte-Carlo simulation. The simulated results indicate that a steplike magnetization behavior is very sensitive to the concentration of AFM bonds. A low concentration of AFM bonds can suppress the stepwise behavior considerably, in accordance with doping experiments on Ca₃Co₂O₆. The analysis of spin snapshots demonstrates that the AFM bond doping not only breaks the ferromagnetic ordered linear spin chains along the hexagonal c-axis but also has a great influence upon the spin configuration in the ab-plane.      

Synthesis and characterization of model 3‐miktoarm star copolymers of poly(dimethylsiloxane) and poly(2‐vinylpyridine)

3‐Miktoarm star copolymers, 3μ‐D₂V, with two poly(dimethylsiloxane) (PDMS) and one poly(2‐vinylpyridine) (P2VP) arm, were synthesized by using anionic polymerization–high vacuum techniques and (chloromethylphenylethyl)methyl dichlorosilane, heterofunctional linking agent, with two SiCl groups and one CH₂Cl group. The synthetic strategy involves the selective reaction of the two ? SiCl groups with PDMSOLi living chains, followed by reaction of the remaining chloromethyl group with P2VPLi. Combined molecular characterization results (size exclusion chromatography, membrane osmometry, and ¹H NMR spectroscopy) revealed a high degree of structural and compositional homogeneity. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 614–619, 2006     

Air‐stable and recoverable catalyst for copper‐catalyzed controlled/living radical polymerization of styrene; In situ generation of Cu(I) species via electron transfer reaction

Copper‐catalyzed controlled/living radical polymerization (LRP) of styrene (St) was conducted using the silica gel‐supported CuCl₂/N,N,N′,N′,N″‐pentamethyldiethylenetriamine (SG‐CuCl₂/PMDETA) complex as catalyst at 110 °C in the presence of a definite amount of air. This novel approach is based on in situ generation and regeneration of Cu(I) via electron transfer reaction between phenols and Cu(II). Sodium phenoxide or p‐methoxyphenol was used as a reducing agent of Cu(II) complexes in LRP. The number–average molecular weight, M_n,GPC, increases linearly with monomer conversion and agrees well with the theoretical values up to 85% conversion The molecular weight distribution, M_w/M_n, decreases as the conversion increases and reaches values below 1.2. The catalyst was recovered in aerobic condition and reused in copper‐catalyzed LRP of St. For the second run, the number–average molecular weights increased with monomer conversion and the polydispersities decreased as the polymerization proceeded and reached to the value <1.3 at 81% conversion. The recycled catalyst retained 90% of its original activity in the subsequent polymerization. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 77–87, 2006     

Nitroxide‐mediated radical polymerization of 2‐(dimethylamino)ethyl acrylate and its sequential block copolymerization with styrene and N‐butyl acrylate

Nitroxide‐mediated radical polymerization (NMRP) of 2‐(dimethylamino)ethyl acrylate (DMAEA) was carried out at 100–120 °C, initiated by MONAMS, an alkoxyamine based on N‐tert‐butyl‐N‐(1‐diethyl phosphono‐2,2‐dimethylpropyl)nitroxide, SG1. Controlled polymerization can be achieved by the addition of free SG1 (the initial molar ratio of SG1 to MONAMS ranged from 0.06 to 0.12), giving a linear first‐order kinetic plot up to 55–70% conversion depending on the reaction conditions. The molecular weights show a near linear increase with conversion; however, they deviate to some extent with theoretical values. SG1‐mediated polymerization of DMAEA at 112 °C is also controlled in organic solvents (N,N‐dimethylformide, anisole, xylene). Polymerization rate increases with increasing solvent polarity. Chain transfer to polymer produces ～1 mol % branches in bulk and 1.2–1.9 mol % in organic solvents, typical of those for acrylates. From poly(styrene) (pS) and poly(n‐butyl acrylate) (pBA) macroinitiators, amphiphilic di‐ and triblock copolymers p(S‐b‐DMAEA), p(DMAEA‐b‐S‐b‐DMAEA), p(BA‐b‐DMAEA), and p(DMAEA‐b‐BA‐b‐DMAEA) were synthesized via NMRP at 110 °C. Polymers were characterized by GPC, NMR, surface tension measurements, and DSC. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 414–426, 2006     

Glycopolymeric inhibitors of β‐glucuronidase. III. Configurational effects of hydroxy groups in pendant glyco‐units in polymers upon inhibition of β‐glucuronidase

Two kinds of new glycopolymers, (P(VB‐1‐GlcaH‐co‐AAm), 9 ) and (P(VB‐1‐Glco‐co‐AAm), 10 ), were synthesized through the radical copolymerization of styrene derivatives bearing pendant D ‐glucaric and D ‐gluconic moieties, N‐(p‐vinylbenzyl)‐1‐D ‐glucaramide (VB‐1‐GlcaH, 7 ), and N‐(p‐vinylbenzyl)‐D ‐gluconamide (VB‐1‐Glco, 8 ), with acrylamide (AAm). Glycopolymer 9 bearing the pendant glucaric moiety at the first position inhibited the hydrolysis of a model compound for xenobiotics‐β‐glucuronide conjugates, p‐nitrophenyl β‐D ‐glucuronide, uncompetitively, in contrast to the competitive inhibition in the presence of the corresponding isomeric glycopolymer bearing the pendant D ‐glucaric unit at the sixth position (P(VB‐6‐GlcaH‐co‐AAm), 3 ) reported in our previous article. On the other hand, another copolymer 10 bearing the gluconic moiety was found not to inhibit the hydrolysis as well as the corresponding copolymer bearing pendant gulonic unit (P(VB‐6‐Glco‐co‐AAm), 4 ). These results indicate that the hydrolysis is influenced not only by existence of pendant carboxyl units but also by the direction on the linkage of the glyco‐units to the polymer frame. Therefore the configurational position of hydroxy groups in pendant glyco‐units in macromolecular inhibitors may be essential for the interaction with β‐glucuronidase. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4895–4903, 2006