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…     

Infinite classes of anti‐mitre and 5‐sparse Steiner triple systems

In this paper, we present three constructions for anti‐mitre Steiner triple systems and a construction for 5‐sparse ones. The first construction for anti‐mitre STSs settles two of the four unsettled admissible residue classes modulo 18 and the second construction covers such a class modulo 36. The third construction generates many infinite classes of anti‐mitre STSs in the remaining possible orders. As a consequence of these three constructions we can construct anti‐mitre systems for at least 13/14 of the admissible orders. For 5‐sparse STS(υ), we give a construction for υ ≡ 1, 19 (mod 54) and υ ≠ 109. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 237–250, 2006     

Interactions between kinetic and radiative processes inside moving absorbing fluids

The aim of this paper is to present several features of the couplings occurring between radiative transfer and the kinetics of a moving dielectric. After determining how the velocity field affects the apparent thermo-optical properties of matter, the energy transport problem is investigated in instationary regime and the general form of transient radiative transfer equation inside a moving medium is built. Then, the model is applied to the particular case of turbulent flows: a system of two equations for mean and fluctuating radiative energies is presented, and the resolution of this system is finally carried out.     

A comparative XPS and UPS study of VOx layers on mineral TiO2(001)‐anatase supports

Four vanadium oxide layers on mineral TiO₂(001)‐anatase supports with different thickness (3–33 Å) were prepared with reactive d.c. magnetron sputtering and were extensively studied with photoelectron spectroscopy. Al Kα radiation and 150 eV synchrotron radiation were used as excitation sources. The evolution of the 2p, 3s and 3p core level line shapes of V and Ti as a function of the vanadium oxide thickness was studied, as well as the O1s and O2s core lines and the valence band. All the V2p spectra of the deposited vanadium oxide layers consist of at least 60% V⁵⁺, the rest being V⁴⁺. The V3p region is complicated by multiplet splitting, which prevents the determination of the vanadium oxidation state. The V3p multiplet splitting is different for the two excitation energies. No reduction of the titania support surface due to the vanadium oxide deposition was observed. Copyright © 2006 John Wiley & Sons, Ltd.     

GPS/SINS组合导航系统在运载火箭中的应用

针对运载火箭特点,着重研究在发射惯性坐标系下,位置、速度组合模式的GPS/SINS组合导航算法,推导了该坐标系下的惯导一阶误差传播方程,建立了该坐标系下GPS/SINS组合导航系统的状态方程和观测方程,并进行了相关数学仿真验证。仿真结果表明,在该坐标系中,GPS/SINS组合导航算法能较准确地给出运载火箭的位置、速度和姿态信息,提高运载火箭制导精度。     

Effect of reaction conditions on the molecular weight and polydispersity of linear poly(arylene ether phosphine oxide)s prepared from an AB monomer

A thorough study of the polymerization behavior of 4‐fluoro‐4′‐hydroxytriphenyl‐phosphine oxide, 2 , under nucleophilic aromatic substitution reactions has been carried out. The synthesis of 2 was achieved in excellent yields by the reaction of bis(4‐fluorophenyl)phenylphosphine oxide, 1 , with one equivalent of potassium hydroxide in DMSO/water. The structure and purity of 2 were confirmed via ¹H, ¹³C, and ³¹P NMR spectroscopy along with elemental analysis. Polymerization reactions of 2 in NMP or DMSO at 180 °C provided the corresponding linear poly(arylene ether phosphine oxide)s, PAEPOs, with number average molecular weights, M_n, ranging from 11,700 to 36,500 Da. All of the polymer samples were completely soluble in chloroform, tetrahydrofuran, DMSO, NMP, and DMAc. The polymerization reactions were accompanied by a competing intramolecular process that resulted in the formation of cyclic oligomeric species that were removed via a final precipitation from methanol. Analysis using ³¹P NMR spectroscopy and size exclusion chromatography (SEC) confirmed that the majority of the lower molecular weight cyclic species were removed via this process. The polymer samples formed tough films when chloroform solutions were slowly evaporated on a glass slide. The PAEPO samples prepared in this study exhibited excellent thermal stability with T_d (5%) values between 503 and 542 in air while the glass transition temperatures ranged from 223 to 237 °C. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2099–2106, 2006     

Heterograft copolymers of poly(ε‐caprolactone) prepared by combination of ATRA “grafting onto” and ATRP “grafting from” processes

This paper aims at reporting on the synthesis of a heterograft copolymer by combining the “grafting onto” process based on atom transfer radical addition (ATRA) and the “grafting from” process by atom transfer radical polymerization (ATRP). The statistical copolymerization of ε‐caprolactone (εCL) and α‐chloro‐ε‐caprolactone (αClεCL) was initiated by 2,2‐dibutyl‐2‐stanna‐1,3‐dioxepane (DSDOP), followed by ATRA of parts of the chlorinated units of poly(αClεCL‐co‐εCL) on the terminal double bond of α‐MeO,ω‐CH₂?CH? CH₂? CO₂‐poly(ethylene oxide) (PEO). The amphiphilic poly(εCL‐g‐EO) graft copolymer collected at this stage forms micelles as supported by dynamic light scattering (DLS) and transmission electron microscopy (TEM). The unreacted pendant chloro groups of poly(εCL‐g‐EO) were used to initiate the ATRP of styrene with formation of copolymer with two populations of randomly distributed grafts, that is PEO and polystyrene. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6015–6024, 2006     

Synthesis and characterization of mid‐ and end‐chain functional telechelics by controlled polymerization methods and coupling processes

Well‐defined polystyrene‐ (PSt) or poly(ε‐caprolactone) (PCL)‐based polymers containing mid‐ or end‐chain 2,5 or 3,5‐ dibromobenzene moieties were prepared by controlled polymerization methods, such as atom transfer radical polymerization (ATRP) or ring opening polymerization (ROP). 1,4‐Dibromo‐2‐(bromomethyl)benzene, 1,3‐dibromo‐5‐(bromomethyl)benzene, and 1,4‐dibromo‐2,5‐di(bromomethyl)benzene were used as initiators in ATRP of styrene (St) in conjunction with CuBr/2,2′‐bipyridine as catalyst. 2,5‐Dibromo‐1,4‐(dihydroxymethyl)benzene initiated the ROP of ε‐caprolactone (CL) in the presence of stannous octoate (Sn(Oct)₂) catalyst. The reaction of these polymers with amino‐ or aldehyde‐functionalized monoboronic acids, in Suzuki‐type couplings, afforded the corresponding telechelics. Further functionalization with oxidable groups such as 2‐pyrrolyl or 1‐naphthyl was attained by condensation reactions of the amino or aldehyde groups with low molecular weight aldehydes or amines, respectively, with the formation of azomethine linkages. Preliminary attempts for the synthesis of fully conjugated poly(Schiff base) with polymeric segments as substituents, by oxidative polymerization of the macromonomers, are presented. All the starting, intermediate, or final polymers were structurally analyzed by spectral methods (¹H NMR, ¹³C NMR, and IR). © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 727–743, 2006     

Effect of the pore surface modification of an inorganic substrate on the plasma‐grafting behavior of pore‐filling‐type organic/inorganic composite membranes

We have investigated the effect of the surface state and surface treatment of the pores of an inorganic substrate on the plasma‐grafting behavior of pore‐filling‐type organic/inorganic composite membranes. Shirasu porous glass (SPG) was used as the inorganic substrate, and methyl acrylate was used as the grafting monomer. The grafting rate increased as the density of silanol on the SPG substrate increased. This result suggests that radicals are generated mainly at the silanol groups on the pore surface by plasma irradiation. The SPG substrates were treated with silane coupling agents used to control the mass of organic material bonded to the pore surface. The thickness of the grafted layer became thinner as the mass of organic material bonded to the pore surface of SPG increased. This decrease in the thickness of the grafted layer could be explained by the decrease in the penetration depth of vacuum ultraviolet rays contained in plasma having a wavelength of less than 160 nm that generated radicals in the pores of the substrate. The thickness of the grafted layer inside the SPG substrates could be controlled through the control of the mass of organic material bonded to the pore surface of the SPG substrate. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 846–856, 2006     

Synthesis and characterization of poly(dimethylsiloxane‐urethane) elastomers: Effect of hard segments of polyurethane on morphological and mechanical properties

A series of poly(dimethylsiloxane‐urethane) elastomers based on hexamethylenediisocyanate, toluenediisocyanate, or 4,4′‐methylenediphenyldiisocyanate hard segment and polydimethylsiloxane (PDMS) soft segment were synthesized. In this study, a new type of soft‐segmented PDMS crosslinker was synthesized by hydrosilylation reaction of 2‐allyloxyethanol with polyhydromethylsiloxane, using Karstedt's catalyst. The synthesized soft‐segmented crosslinker was characterized by FT‐IR, ¹H, and ¹³C NMR spectroscopic techniques. The mechanical and thermal properties of elastomers were characterized using tensile testing, thermogravimetric analysis, differential scanning calorimetry (DSC), and dynamical mechanical analysis measurements. The molecular structure of poly(dimethylsiloxane‐urethane) membranes was characterized by ATR‐FTIR spectroscopic techniques. Infrared spectra indicated the formation of urethane/urea aggregates and hydrogen bonding between the hard and soft domains. Better mechanical and thermal properties of the elastomers were observed. The restriction of chain mobility has been shown by the formation of hydrogen bonding in the soft and hard segment domains, resulting in the increase in the glass‐transition temperature of soft segments. DSC analysis indicates the phase separation of the hard and soft domains. The storage modulus (E′) of the elastomers was increasing with increase in the number of urethane connections between the hard and soft segments. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2980–2989, 2006