Distributions with Heavy Tails in Orlicz Spaces

This paper relies on the application of Kantorovich functionals on quasi-interior points of the positive cone for certain classes of Orlicz spaces. Particularly we provide the asymptotic calculation of the ruin probability in the renewal risk model under heavy-tailed claims in the Orlicz spaces. This application assures the extension of classical asymptotic theory of regular variation.     

A Monoidal Category for Perturbed Defects in Conformal Field Theory

Starting from an abelian rigid braided monoidal category C{\mathcal{C}} we define an abelian rigid monoidal category C_F{\mathcal{C}_F} which captures some aspects of perturbed conformal defects in two-dimensional conformal field theory. Namely, for V a rational vertex operator algebra we consider the charge-conjugation CFT constructed from V (the Cardy case). Then C = Rep(V){\mathcal{C} = {\rm Rep}(V)} and an object in C_F{\mathcal{C}_F} corresponds to a conformal defect condition together with a direction of perturbation. We assign to each object in C_F{\mathcal{C}_F} an operator on the space of states of the CFT, the perturbed defect operator, and show that the assignment factors through the Grothendieck ring of C_F{\mathcal{C}_F}. This allows one to find functional relations between perturbed defect operators. Such relations are interesting because they contain information about the integrable structure of the CFT.     

A simple and effective method for phosphoryl transfer using TiCl(4) catalysis

[reaction: see text] A number of Lewis acids have been evaluated as catalysts for the phosphoryl transfer, the most efficient being TiCl(4). Application of this methodology to the phosphorylation of a number of representative target alcohols is presented     

Nonlocal dynamics of spontaneous imbibition fronts

We have studied spontaneous imbibition fronts generated by capillary rise between two roughened glass plates, the separation d of which varied between 10 and 50 microm. Perfect agreement with Washburn's law was obtained. We have determined the roughness exponent chi of the fronts, and found chi=0.81+/-0.01 for small length scales. Above a certain crossover length xi, it reached chi=0.58+/-0.04, as predicted by the quenched noise Kardar-Parisi-Zhang equation. The crossover length is found to scale with the plate separation as sqrt[d], as predicted by recent models which properly include nonlocal dynamics effects on the front. We believe this to be the first clear identification of crossover from nonlocal to local dynamics.     

Irreversibility and polymer adsorption

Physisorption or chemisorption from dilute polymer solutions often entails irreversible polymer-surface bonding. We present a theory of the resultant nonequilibrium layers. While the density profile and loop distribution are the same as for equilibrium layers, the final layer comprises a tightly bound inner part plus an outer part whose chains make only fN surface contacts where N is chain length. The contact fractions f follow a broad distribution, P(f) approximately f(-4/5), in rather close agreement with strong physisorption experiments [H. M. Schneider, Langmuir 12, 994 (1996)]].     

Interactive resonant scattering by a cluster of air bubbles in water

An exact, analytical solution is developed for the problem of acoustic-wave scattering from a cluster of ideal, gaseous, spherical bubbles in an unbounded, homogeneous, host fluid. This solution takes into account all modes of oscillation of the bubbles as well as all interactions between them; it is applicable to a wide range of bubble sizes and excitation frequencies. In the low frequency regime, the theory of this paper is shown to reduce to the "monopole" approximation, the effect of higher-order modes being non-negligible only for very small bubble-to-bubble separations. A numerical study of interactive backscattering from small clusters, comprising up to three ideal bubbles, is presented. Interactions between the bubbles are shown to produce downward shifts in the resonance frequency of the cluster, when the scattering configuration is symmetric. Furthermore, asymmetries of the scattering configuration are shown to generate sharp resonances at frequencies above the resonance of the symmetric mode. The results of this paper agree with previous theoretical and experimental work.     

The ultrasensitivity of living polymers

Synthetic and biological living polymers are self-assembling chains whose chain length distributions (CLDs) are dynamic. We show these dynamics are ultrasensitive: Even a small perturbation (e.g., temperature jump) nonlinearly distorts the CLD, eliminating or massively augmenting short chains. The origin is fast relaxation of mass variables (mean chain length, monomer concentration) which perturbs CLD shape variables before these can relax via slow chain growth rate fluctuations. Viscosity relaxation predictions agree with experiments on the best-studied synthetic system, alpha-methylstyrene.     

Anion recognition by functionalized single wall carbon nanotubes

Amidoferrocenyl-functionalised single wall carbon nanotubes (Fc-SWNT) are efficient exoreceptors for the redox recognition of H2PO4-.     

Synthesis,Spectral Properties,and Crystal Structure of {Methoxo[4-phenylbutane-2,4-dione(p-nitrobenzoyl) hydrazonato(2-)]oxovanadium(V)}

The hydrazino complex {methoxo[4-phenylbutane-2,4-dione(p-nitrobenzoyl)hydrazonato(2-)]oxovanadium(V)}, VO(p-NO₂bhbzac)OCH₃, (1), has been prepared by the direct reaction of bis(benzoylacetonato) oxovanadium(IV), VO(bza)₂, with p-NO₂-C₆H₄C(O)NHNH₂, p-NO₂bh, in CH₃OH. The resulting compound contains benzoylacetone-(p-NO₂)benzoyl hydrazone as tridentate Schiff base-type ligand and OCH₃ group as Lewis base, both ligated to vanadium. The crystals are orthorhombic, with Z = 8, space group Pbca, a = 11.699(5) Å, b = 14.035(5) Å, c = 22.564(5) Å, R1 = 0.0756 and wR2 = 0.1302. The crystal structure demonstrated the square-pyramidal geometry of the VO_oxo(ONO)O coordination sphere with the oxo ligand at the apical position. The electronic absorption spectra revealed a ligand-to-metal charge-transfer (LMCT) band in the near UV region at _max = 23,700 cm^–1 (B = 5640 dm³ mol^–1 cm^–1) in CH₃CN, _max = 23,420 cm^–1 (B = 5550 dm³ mol^–1 cm^–1) in DMSO, and _max near 26,950 (sh) cm^–1 (B = 10,550 dm³ mol^–1 cm^–1) in CH₂Cl₂. The FT-IR spectra of (1) show the characteristic strong (V = O) stretching vibration at 993 cm^–1 and support the view that the oxovanadium complex is pentacoordinated and monomeric.