Positive and Nontrivial Solutions for the Urysohn Integral Equation

We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation.     

Generators of KMS Symmetric Markov Semigroups on {\mathcal{B}({\rm h})} Symmetry and Quantum Detailed Balance

We find the structure of generators of norm-continuous quantum Markov semigroups on B(h){\mathcal{B}({\rm h})} that are symmetric with respect to the scalar product tr (ρ ^1/2 x*ρ ^1/2 y) induced by a faithful normal invariant state ρ and satisfy two quantum generalisations of the classical detailed balance condition related with this non-commutative notion of symmetry: the so-called standard detailed balance condition and the standard detailed balance condition with an antiunitary time reversal.     

Sub-Rayleigh imaging via N-photon detection

The Rayleigh diffraction bound sets the minimum separation for two point objects to be distinguishable in a conventional imaging system. We demonstrate sub-Rayleigh resolution by scanning a focused beam--in an arbitrary, object-covering pattern that is unknown to the imager--and using N-photon photodetection implemented with a single-photon avalanche detector array. Experiments show resolution improvement by a factor ～(N-N(max))(?) beyond the Rayleigh bound, where N(max) is the maximum average detected photon number in the image, in good agreement with theory.     

Precision and control in polymer synthesis why it's important and some recent examples of how to do it

This paper discusses some of the reasons why precision and control in polymer synthesis is of importance. By way of illustration it describes in outline recent results from the authors' laboratories in three areas. Namely; the controlled syntheses of poly(arylene vinylene)s and the influence of cis/trans vinylene content on luminescence in such polymers; the living polymerisation of highly functionalised polymers in water and the regulation of the crystallisation of calcium carbonate from water by the resultant well-defined water soluble polymers; and a simple route to hyperbranched polymers and the influence of the structure and topology of the products on solution properties. In each case the influence of control of architecture on properties will be discussed.     

Palladium complexes of 8-(di-tert-butylphosphinooxy) quinoline

The preparation of the new ligand 8-(di-tert-butylphosphinooxy)quinoline (1) and the palladium derivatives [PdCl₂(1)] (2), [Pd(η³-all)(1)]⁺ [all = C₃H₅ (3a), 1-PhC₃H₄ (3b) and 1,3-Ph₂C₃H₃ (3c)] and [Pd(η²-ol)(1)] [ol = dimethyl fumarate (4a) and fumaronitrile (4b)] is reported. The cationic species 3a-3c have been isolated as salts. The complex 3a(BF₄) is obtained either from the reaction of 1 with [Pd(μ-Cl)(η³-C₃H₅)]₂ or from the reaction of ClP(CMe₃)₂ with [Pd(η³-C₃H₅)(8-oxyquinoline)], followed in both cases by chloride abstraction with NaBF₄. In the complexes, the ligand 1 is P,N chelated to the central metal, as shown by the X-ray structural analysis of 3a(BF₄). At 25 °C in solution, 3a(BF₄) and 3b(BF₄) undergo a fast η³−η¹−η³ dynamic process which brings about a syn-anti exchange only for the allylic protons cis to phosphorus, while for 4a and 4b a slow rotation of the olefin around its bond axis to palladium takes place. The complexes 2 and 3a(BF₄) are efficient catalyst precursors in the coupling of the phenylboronic acid with aryl bromides and chlorides.     

Energies and spatial features for the rotationless bound states of 4He3+(2Sigmag+): a cationic core from helium cluster ionization

Ab initio quantum calculations have been carried out on the helium ionic trimer. The potential energy surface is accurately fitted, especially in the vicinity of the three equivalent minima. The spectrum of bound states for the zero angular momentum is computed and analyzed in detail. Energies and wave functions reveal several interesting features related to the fact that He3+ represents one of the few homonuclear ionic trimers that are linear in their ground vibrational state. At low energies, the triply degenerate eigenfunctions are localized at the potential minimum. With growing excitation energy, however, the wave functions exhibit stronger spatial delocalization.     

A toy model of polymer stretching

We present an extremely simplified model of multiple-domain polymer stretching in an atomic force microscopy experiment. We portray each module as a binary set of contacts and decompose the system energy into a harmonic term (the cantilever) and long-range interaction terms inside each domain. Exact equilibrium computations and Monte Carlo simulations qualitatively reproduce the experimental sawtooth pattern of force-extension profiles, corresponding (in our model) to first-order phase transitions. We study the influence of the coupling induced by the cantilever and the pulling speed on the relative heights of the force peaks. The results suggest that the increasing height of the critical force for subsequent unfolding events is an out-of-equilibrium effect due to a finite pulling speed. The dependence of the average unfolding force on the pulling speed is shown to reproduce the experimental logarithmic law.     

Laccase–polyazetidine prepolymer–MWCNT integrated system: Biochemical properties and application to analytical determinations in real samples

Bioelectrochemical properties of Trametes versicolor Laccase (TvL) and Trametes hirsuta Laccase (ThL) immobilized by using polyazetidine prepolymer (PAP) onto multi-walled carbon nanotubes (MWCNTs) screen printed electrode (SPE) surface, have been studied with several redox mediators by cyclic voltammetry (CV). The efficient entrapment of laccase in the PAP layer was confirmed by determination of both kinetic parameters (maximum current and Michaelis–Menten apparent constant) and analytical performances by chronoamperometry. The Laccase-modified MWCNTs electrode provides an effective biosensor for determination of polyphenols and catecholamines in real matrices; performances of the considered biosensors for real samples analysis are also compared and discussed.     

Nuclear magnetic resonance of benzobisheterocyclic compounds

The nuclear magnetic resonance spectra of forty-nine benzobisheterocyclic compounds, containing various heterocycles, were determined. The observed spectral data made possible the elucidation of the structure and also clarified the influences of the heterocyclic substituents and of heterocyclic rings on chemical shift values of the aromatic protons.     

Influence of curing conditions on the morphology and physical properties of epoxy resins modified with a liquid polyamine

A diglycidyl ether of bisphenol-A (DGEBA) epoxy resin has been stoichiometrically cured with cycloaliphatic amine 4,4′-diamino-3,3′-dimethylcyclohexylmethane (3DCM) and modified with an amine terminated oligomer polyoxypropylenetriamine (POPTA) at a concentration of 15 wt %. Mixtures, postcured at the same temperature, have been precured at different temperatures. Phase separation takes place before gelation at all precure temperatures used. The variation in the glass transition region of the mixtures has been analyzed by dynamic mechanical measurements. Mechanical properties and fracture toughness of the modified mixtures have been related to their microstructural spherical features. Results are compared to those for the unmodified mixtures cured with different precure temperatures. © 1997 John Wiley & Sons, Inc.