Algebraic Bethe Ansatz for SO(N)-invariant transfer matrices

A matrix version of an algebraic Bethe Ansatz is proposed for R-matrices of a special structure. It is shown that SO(N)-invariant R-matrices in spinor representation possess this special structure. Eigenvalues of transfer matrices corresponding to these R-matrices are computed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 122–140, 1988.     

WAXS studies on block copolymers of ethylene and propylene

Wide-angle X-ray scattering from presumed block copolymers of polypropylene (PP) and ethylene-propylene copolymer (EPR), i.e., PP-EPR and PP-EPR-PP, synthesized by sequential polymerization with δ-TiCl₃? Et₂AlCl, was examined and compared with WAXS of mechanical blends and chain-transfer mixtures of PP and EPR with comparable compositions. The peak at 2θ = 20° for both the copolymers and the mixtures was attributed to the γ modification of PP in EPR. A strong variation in the ratio of diffraction intensities I₀₄₀/I₁₁₀ of PP in block copolymers and mixtures was explained in terms of crystallite growth in different directions. Analysis of the patterns and calculation of crystallinity, crystallite size, and lattice parameters led to the conclusion that block structure existed in the prepared copolymers.     

On the effect of longitude-dependent fields on convection in stellar atmospheres

In rotating stellar convective zones, heat transfer is shown to be associated with unbalanced azimuth forces arising in the radially ascending (heated) or descending (cold) matter. The presence of a longitude-dependent magnetic field generates additional azimuth forces, hence, new ways of compensating for the unbalanced forces. Generally speaking, this magnetic field is variable but may be nearly static in layers where convective equilibrium is replaced by radiative equilibrium. The condition for the coexistence of the static and usual fields is derived. To this end, an axisymmetric azimuth magnetic field of energy comparable to the energy of rotation should be introduced into models under consideration. In such configurations, conditions for magnetic field generation, as in the Sun, may appear.     

On a method for studying the norm and the stability of solutions

We present a new method (the method of unitary transformations), which differs from the existing ones, for studying the stability and the norm of solutions of regular and singularly perturbed initial-value problems for nonautonomous linear and quasilinear systems of ODE with normal and “almost normal” matrices. Our results generalize similar theorems for the corresponding systems with constant matrices. This method allows one to avoid rather cumbersome traditional analysis, including the Lyapunov function method. For special classes of singularly perturbed problems, the method provides estimates for the norms of solutions in the presence of exponential or power boundary layers; these observations enrich the collection of known results in this field.     

Lower bounds for positive and negative parts of measures and the arrangement of singularities of their Laplace transforms

For a real measure with variation V(x) satisfying the estimate V(x) ≤ c ₀ exp(Cx) and for the Laplace transform holomorphic in the disk {¦ -C¦ ≤ C} and having at least one pole of order m, we obtain lower bounds for the positive and negative parts of the measure V _± (x) > cx ^m , x > x ₀. We establish lower bounds for V _+- (x) on “short” intervals. Applications to number theory of the results obtained are considered.     

Ethylene–propylene copolymerization with bis(β‐enaminoketonato) titanium complexes activated with modified methylaluminoxane

Ethylene–propylene copolymerization, using [(Ph)NC(R₂)CHC(R₁)O]₂TiCl₂ (R₁ = CF₃, Ph, or t‐Bu; R₂ = CH₃ or CF₃) titanium complexes activated with modified methylaluminoxane as a cocatalyst, was investigated. High‐molecular‐weight ethylene–propylene copolymers with relatively narrow molecular weight distributions and a broad range of chemical compositions were obtained. Substituents R₁ and R₂ influenced the copolymerization behavior, including the copolymerization activity, methylene sequence distribution, molecular weight, and polydispersity. With small steric hindrance at R₁ and R₂, one complex (R₁ = CF₃; R₂ = CH₃) displayed high catalytic activity and produced copolymers with high propylene incorporation but low molecular weight. The microstructures of the copolymers were analyzed with ¹³C NMR to determine the methylene sequence distribution and number‐average sequence lengths of uninterrupted methylene carbons. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5846–5854, 2006     

Graft polymerization of vinyl monomers inside macroporous polyacrylamide gel,cryogel, in aqueous and aqueous‐organic media initiated by diperiodatocuprate(III) complexes

Graft polymerization initiated by diperiodatocuprate(III) complex (Cu(III)) initiator was found to be an effective and convenient method for graft polymerization of vinyl monomers onto macroporous polyacrylamide gels, the so‐called cryogels (pAAm‐cryogels). The effect of time, temperature, monomer and initiator concentration during the graft polymerization in aqueous and aqueous‐organic media was studied. The graft polymerization of water‐soluble monomers as [2‐(methacryloyloxy)ethyl]‐trimethylammonium chloride, 2‐hydroxyethyl methacrylate, N‐isopropylacrylamide, and N,N‐dimethylacrylamide proceeds with higher grafting yield in aqueous medium, as compared with that in aqueous‐organic media. Graft polymerization in aqueous‐organic media such as water–DMSO solutions allows grafting of water‐insoluble monomers such as glycidyl methacrylate and N‐tert‐butylacrylamide with high grafting degrees of 100 and 410%, respectively. It was found that the deposition of initiator on the pore surface of cryogels promoted graft polymerization by facilitating the formation of the redox couple Cu(III)‐acrylamide group. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1952–1963, 2006     

Highly soluble and optically transparent poly (ether imide)s based on 2,6‐ or 2,7‐bis(3,4‐dicarboxyphenoxy)naphthalene dianhydride and aromatic bis(ether amine)s bearing trifluoromethyl groups

Two series of novel fluorinated poly(ether imide)s (coded IIIA and IIIB ) were prepared from 2,6‐bis(3,4‐dicarboxyphenoxy)naphthalene dianhydride and 2,7‐bis(3,4‐dicarboxyphenoxy)naphthalene dianhydride, respectively, with various trifluoromethyl‐substituted aromatic bis(ether amine)s by a standard two‐step process with thermal or chemical imidization of the poly(amic acid) precursors. These fluorinated poly(ether imide)s showed good solubility in many organic solvents and could be solution‐cast into transparent, flexible, and tough films. These films were nearly colorless, with an ultraviolet–visible absorption edge of 364–386 nm. They also showed good thermal stability with glass‐transition temperatures of 221–298 °C, 10% weight loss temperatures in excess of 489 °C, and char yields at 800 °C in nitrogen greater than 50%. The 2,7‐substituted IIIB series also showed better solubility and higher transparency than the isomeric 2,6‐substituted IIIA series. In comparison with nonfluorinated poly (ether imide)s, the fluorinated IIIA and IIIB series showed better solubility, higher transparency, and lower dielectric constants and water absorption. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5909–5922, 2006     

Synthesis and luminescence characteristics of conjugated dendrimers with 2,4,6‐triaryl‐1,3,5‐triazine periphery

We have synthesized conjugated dendrimer with triazine peripheries, and their luminescence properties were investigated. The dendrimers consist of dendritic triazine wedges for electron transport, distyrylbenzene core as an emitting moiety, and t‐butyl peripheral groups for good processing properties. The dendrimers have LUMO values of about ?2.7 eV possibly because of the triazine moiety with high electron affinity. Photoluminescence study indicates that energy transfer occurs from the triazine wedges to the stilbene bridge, and finally to the core chromophore units due to a cascade decrease of bandgap from the peripheral wedge to core moiety. Therefore, the emission wavelength was determined by the structure of the core unit. The energy transfer efficiency of distyrylbenzene‐cored dendrimers was about 75 and 55% for Trz‐1GD‐DSB and Trz‐2GD‐DSB, respectively. A preliminary electroluminescence property also was investigated. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 254–263, 2006     

Synthesis and application as polymer electrolyte of hyperbranched polyether made by cationic ring‐opening polymerization of 3‐{2‐[2‐(2‐hydroxyethoxy)ethoxy]ethoxymethyl}‐3′‐methyl‐oxetane

A novel cyclic ether monomer 3‐{2‐[2‐(2‐hydroxyethoxy)ethoxy]ethoxy‐methyl}‐3′‐methyloxetane (HEMO) was prepared from the reaction of 3‐hydroxymethyl‐3′‐methyloxetane tosylate with triethylene glycol. The corresponding hyperbranched polyether (PHEMO) was synthesized using BF₃·Et₂O as initiator through cationic ring‐opening polymerization. The evidence from ¹H and ¹³C NMR analyses revealed that the hyperbranched structure is constructed by the competition between two chain propagation mechanisms, i.e. active chain end and activated monomer mechanism. The terminal structure of PHEMO with a cyclic fragment was definitely detected by MALDI‐TOF measurement. A DSC test implied that the resulting polyether has excellent segment motion performance potentially beneficial for the ion transport of polymer electrolytes. Moreover, a TGA assay showed that this hyperbranched polymer possesses high thermostability as compared to its liquid counterpart. The ion conductivity was measured to reach 5.6 × 10^?5 S/cm at room temperature and 6.3 × 10^?4 S/cm at 80 °C after doped with LiTFSI at a ratio of Li:O = 0.05, presenting the promise to meet the practical requirement of lithium ion batteries for polymer electrolytes. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3650–3665, 2006