Spectral Density of Jacobi Matrices with Small Deviations

We present several new asymptotic trace formulas for Jacobi matrices whose coefficients satisfy a small deviation condition. Our results extend most of the existing trace formulas for Jacobi matrices.     

The pressure–volume–temperature relationship of cellulose

Pressure–volume–temperature (PVT) measurements of α-cellulose with different water contents, were performed at temperatures from 25 to 180 °C and pressures from 19.6 to 196 MPa. PVT measurements allowed observation of the combined effects of pressure and temperature on the specific volume during cellulose thermo-compression. All isobars showed a decrease in cellulose specific volume with temperature. This densification is associated with a transition process of the cellulose, occurring at a temperature defined by the inflection point T _t of the isobar curve. T _t decreases from 110 to 40 °C with pressure and is lower as moisture content increases. For isobars obtained at high pressures and high moisture contents, after attaining a minimum, an increase in volume is observed with temperature that may be related to free water evaporation. PVT α-cellulose experimental data was compared with predicted values from a regression analysis of the Tait equations of state, usually applied to synthetic polymers. Good correlations were observed at low temperatures and low pressures. The densification observed from the PVT experimental data, at a temperature that decreases with pressure, could result from a sintering phenomenon, but more research is needed to actually understand the cohesion mechanism under these conditions.     

Central limit theorems for the zeros of Lamé polynomials

In a recent paper, it was shown that the zeros of Lamé polynomials satisfy a strong law of large numbers. In this paper, we show that the zeros also satisfy two central limit theorems.     

Analysis of diffuse-layer effects on time-dependent interfacial kinetics

We investigate the subtle effects of the diffuse charged layer on interfacial kinetics by solving the governing equations for ion transport (Nernst–Planck) with realistic boundary conditions representing reaction kinetics (Butler–Volmer) and compact-layer capacitance (Stern) in the asymptotic limit =λ_D/L→0, where λ_D is the Debye screening length and L is the distance between the working and counter electrodes. Using the methods of singular perturbation theory, we derive the leading-order steady-state response to a nonzero applied current in the case of the oxidation of a neutral species into cations, without any supporting electrolyte. In certain parameter regimes, the theory predicts a reaction-limited current smaller than the classical diffusion-limited current; this over potential effect is not due to ohmic drop effects in the bulk of the cell but rather to antagonist processes involved in the surface charge transfer and diffuse layer charging respectively. We demonstrate that the charging of diffuse charge, since it is intimately coupled to the surface reaction and cannot be considered independently, plays a fundamental role in nonequilibrium surface reactions when the transport of one of the reacting species is coupled to the total interfacial response of the compact and diffuse layers.     

Self-induced "electroclick" immobilization of a copper complex onto self-assembled monolayers on a gold electrode

We report the self-induced "electroclick" immobilization of the [Cu(II)(6-ethynyl-TMPA)(H(2)O)](2+) complex, by its simple electro-reduction, onto a mixed azidoundodecane-/decane-thiol modified gold electrode. The redox response of the grafted [Cu(II/I)(TMPA)] at the modified electrode is fully reversible indicating no Cu coordination change and a fast electron transfer.     

Comparative dissociation of peptide polyanions by electron impact and photo-induced electron detachment

We compare product-ion mass spectra produced by electron detachment dissociation (EDD) and electron photodetachment dissociation (EPD) of multi-deprotonated peptides on a Fourier transform and a linear ion trap mass spectrometer, respectively. Both methods, EDD and EPD, involve the electron emission-induced formation of a radical oxidized species from a multi-deprotonated precursor peptide. Product-ion mass spectra display mainly fragment ions resulting from backbone cleavages of C_α-C bond ruptures yielding a and x ions. Fragment ions originating from N-C_α backbone bond cleavages are also observed, in particular by EPD. Although EDD and EPD methods involve the generation of a charge-reduced radical anion intermediate by electron emission, the product ion abundance distributions are drastically different. Both processes seem to be triggered by the location and the recombination of radicals (both neutral and cation radicals). Therefore, EPD product ions are predominantly formed near tryptophan and histidine residues, whereas in EDD the negative charge solvation sites on the backbone seem to be the most favorable for the nearby bond dissociation.