Isometries of the Dirichlet space among the composition operators

We show that every composition operator which is an isometry of the Dirichlet space is induced by a univalent full map of the disk into itself that fixes the origin. This is an analogue of the Hardy space result for inner functions due to Nordgren. The proof relies on the Stone-Weierstrass theorem and the Riesz representation theorem.

     

Polyelectrolyte complexes. VI. Polycation structure,polyanion molar mass,and polyion concentration effects on complex nanoparticles based on poly(sodium 2‐acrylamido‐2‐methylpropanesulfonate)

The formation and characterization of some interpolyelectrolyte complex (IPEC) nanoparticles based on poly(sodium 2‐acrylamido‐2‐methylpropanesulfonate) (NaPAMPS), as a function of the polycation structure, polyanion molar mass, and polyion concentration, were followed in this work. Poly(diallyldimethylammonium chloride) and two polycations (PCs) containing (N,N‐dimethyl‐2‐hydroxypropyleneammonium chloride) units in the backbone (PCA₅ and PCA₅D₁) were used as starting polyions. The complex stoichiometry, (n^?/n⁺)_iso, was pointed out by optical density at 500 nm (OD₅₀₀), polyelectrolyte titration, and dynamic light scattering. IPEC nanoparticle sizes were influenced by the polycation structure and polyanion molar mass only before the complex stoichiometry, which was higher for the more hydrophilic polycations (PCA₅ and PCA₅D₁) and for a higher NaPAMPS molar mass, and were almost independent of these factors after that, at a flow rate of the added polyion of about 0.28 mL × (mL PC)^?1 × h^?1. The IPEC nanoparticle sizes remained almost constant for more than 2 weeks, both before and after the complex stoichiometry, at low concentrations of polyions. NIPECs as stable colloidal dispersions with positive charges in excess were prepared at a ratio between charges (n^?/n⁺) of 0.7, and their storage colloidal stability, as a function of the polycation structure and polyion concentration (from 0.8 to ca. 7.8 mmol/L), was demonstrated. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2495–2505, 2004     

Electroacoustic oscillations of aluminum oxide particles in the thermal plasma

The frequencies of natural electroacoustic oscillations of aluminum oxide particles in a laminar disperse aluminum flame are determined experimentally using the capacitive method. A computational model is proposed for estimating the natural frequency of oscillations of charged particles in the smoky plasma taking into account the Doppler effect. It is shown that, for a natural frequency of oscillations of 51 kHz, two measured maxima at frequencies of 30 and 60 kHz in the oscillation spectrum correspond to the Doppler frequencies.     

On norms of composition operators acting on Bergman spaces

For arbitrary composition operators acting on a general Bergman space we improve the known lower bound for the norm and also generalize a related recent theorem of D.G. Pokorny and J.E. Shapiro. Next, we obtain a geometric formula for the norms of composition operators with linear fractional symbols, thus extending a result of C. Cowen and P. Hurst and revealing the meaning of their computation. Finally, we obtain a lower bound for essential norm of an arbitrary composition operator related to the well-known criterion of B. MacCluer and J.H. Shapiro. As a corollary, norms and essential norms are obtained for certain univalently induced noncompact composition operators in terms of the minimum of the angular derivative of the symbol.     

On the Seneta Sequences

In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc.     

A census of semisymmetric cubic graphs on up to 768 vertices

A list is given of all semisymmetric (edge- but not vertex-transitive) connected finite cubic graphs of order up to 768. This list was determined by the authors using Goldschmidt's classification of finite primitive amalgams of index (3,3), and a computer algorithm for finding all normal subgroups of up to a given index in a finitely-presented group. The list includes several previously undiscovered graphs. For each graph in the list, a significant amount of information is provided, including its girth and diameter, the order of its automorphism group, the order and structure of a minimal edge-transitive group of automorphisms, its Goldschmidt type, stabiliser partitions, and other details about its quotients and covers. A summary of all known infinite families of semisymmetric cubic graphs is also given, together with explicit rules for their construction, and members of the list are identified with these. The special case of those graphs having K_1,3 as a normal quotient is investigated in detail. Supported in part by N.Z. Marsden Fund (grant no. UOA 124) and N.Z. Centres of Research Excellence Fund (grant no. UOA 201) Supported in part by “Ministrstvo za šolstvo, znanost in šport Slovenije”, research program no. 101-506. Supported in part by research projects no. Z1-4186-0101 and no. Z1-3124-0101. The fourth author would like to thank the University of Auckland for hospitality during his visit there in 2003.     

Thermochemically induced binding of methyl orange to polycations containing primary amine groups

The thermochemical transformation of electrostatically formed complexes of methyl orange (MO) with polycations containing primary amine groups such as ammonium salts afforded new polymers with a high concentration of covalently bound 4‐N,N‐dimethylaminoazobenzene groups in the side chain. Poly(allylamine hydrochloride) and poly(β‐aminoethylene acrylamide hydrochloride) were employed as support polycations for MO. The transformation of sulfonate–ammonium ion pairs into sulfonamide bonds, via heating at an elevated temperature, was supported by the polymer properties before and after the thermal treatment. The polymer structure changes were monitored with elemental analysis, Fourier transform infrared, ¹H NMR, and ultraviolet–visible absorption spectroscopy, and thermogravimetric analysis. The spacer length between the backbone and azobenzene structures used as side chains strongly influenced the polymer properties before and after the heat‐induced reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5898–5908, 2006     

Energetics of radical transfer in DNA photolyase

Charge separation and radical transfer in DNA photolyase from Escherichia coli is investigated by computing electrostatic free energies from a solution of the Poisson-Boltzmann equation. For the initial charge separation 450 meV are available. According to recent experiments [Aubert et al. Nature 2000, 405, 586-590] the flavin receives an electron from the proximal tryptophan W382, which consequently forms a cationic radical WH(*)(+)382. The radical state is subsequently transferred along the triad W382-W359-W306 of conserved tryptophans. The radical transfer to the intermediate tryptophan W359 is nearly isoenergetic (58 meV uphill); the radical transfer from the intermediate W359 to the distal W306 is 200 meV downhill in energy, funneling and stabilizing the radical state at W306. The resulting cationic radical WH(*)(+)306 is further stabilized by deprotonation, yielding the neutral radical W(*)306, which is 214 meV below WH(*)(+)306. The time scale of the charge recombination process yielding back the resting enzyme with FADH(*) is governed by reprotonation of W306, with a calculated lifetime of 1.2 ms that correlates well with the measured lifetime of 17 ms. In photolyase from Anacystis nidulans the radical state is partially transferred to a tyrosine [Aubert et al. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 5423-5427]. In photolyase from Escherichia coli, there is a tyrosine (Y464) close to the distal tryptophan W306 that could play this role. We show that this tyrosine cannot be involved in radical transfer, because the electron transfer from tyrosine to W306 is much too endergonic (750 meV) and a direct hydrogen transfer is likely too slow. Coupling of specific charge states of the tryptophan triad with protonation patterns of titratable residues of photolyase is small.     

Ferromagnetism in Metallocene-Doped Fullerenes

 Ferromagnetism in fullerene-based systems doped with metallocenes is reviewed. These compounds form a ferromagnetic state by spin-coupling between π electrons on fullerene units, while the metallocene molecules do not contribute to the spin ordering. One of these compounds has the highest critical temperature (19 K) for this class of compound. The magnetic properties of these materials are very strongly dependent on the crystallization conditions. Corresponding author. E-mail: Dragan.Mihailovic@ijs.si Received September 4, 2002; accepted September 6, 2002     

Cobalt(II) Chloride Complex Formation in Acetamide–Calcium Nitrate Tetrahydrate Melts

The absorption spectra of Co(II) chloride complexes, containing variable concentrations of chloride ligand, in a molten mixture of 80 mol% acetamide–20 mol% calcium nitrate tetrahydrate, were studied at 313, 333, 353, and 363 K, in the wavelength range 400-800 nm. The melt contains three possible ligands (CH₃CONH₂, H₂O, and NO₃ ^-) for competition with added chloride ligand. Addition of chloride caused a shift of the absorption maximum of octahedral cobalt(II) nitrate towards lower energies and pronounced changes in the shape of the initial spectrum of cobalt(II) nitrate. The effect of temperature changes on the molar absorption coefficient of the Co(II) species was dependent on the chloride concentration and was attributed to the structural changes occurring in the cobalt(II) species. The STAR and STAR FA programs were applied to identify the complex ionic species and to calculate the stability constants of Co(II) complexes formed in this solvent. The results indicate the highest probability of formation of the following complex species: Co(NO₃)₄ ^2-, Co(NO₃)₂Cl₂ ^2-, and CoCl₄ ^2-. Stability constants of each complex were presented for the equilibria occurring at 313, 333, 353, and 363 K. Distribution of the Co(II) species was also calculated over the ranges of chloride concentration and temperature investigated.