Existence of disjoint weakly mixing operators that fail to satisfy the Disjoint Hypercyclicity Criterion

Recently, Bès, Martin, and Sanders [11] provided examples of disjoint hypercyclic operators which fail to satisfy the Disjoint Hypercyclicity Criterion. However, their operators also fail to be disjoint weakly mixing. We show that every separable, infinite dimensional Banach space admits operators T1,T2,…,TN with N⩾2 which are disjoint weakly mixing, and still fail to satisfy the Disjoint Hypercyclicity Criterion, answering a question posed in [11]. Moreover, we provide examples of disjoint hypercyclic operators T1, T2 whose corresponding set of disjoint hypercyclic vectors is nowhere dense, answering another question posed in [11]. In fact, we explicitly describe their set of disjoint hypercyclic vectors. Those same disjoint hypercyclic operators fail to be disjoint topologically transitive. Lastly, we create examples of two families of d-hypercyclic operators which fail to have any d-hypercyclic vectors in common.

PHOTOPERTURBATION OF THE (1)A-][-(5)T SPIN EQUILIBRIUM IN AN IRON(II) COMPLEX IN SOLUTION VIA LIGAND-FIELD EXCITATION

Variable-temperature magnetic susceptibility measurements in the solid state of the bis complex of tris(1-pyrazolyl)-methane with Fe(II), [Fe(tpm)2](ClO4)2, suggest the existence of singlet-quintet spin crossover with the singlet isomer largely favored at room temperature. In acetonitrile solution, measurement of the absorption spectrum as a function of temperature reveals a spin equilibrium with the quintet population varying from ca. 6% at 233 K to ca. 30% at 295 K. When the complex in solution is irradiated with a laser pulse at wavelengths within the ligand field absorption band of the singlet isomer, ground-state depletion occurs within the pulse duration followed by fast recovery to the original absorbance level with a time constant of 25 +/- 5ns. The recovery time is virtually independent of temperature over the range +23 to -43-degrees-C, but the signal:noise ratio of the transient signals increases with decreasing temperature. The effect was observable at several monitoring wavelengths spanning the LF and MLCT absorption regions of the complex but only when the irradiation wavelength fell within the LF absorption region. Irradiation within the MLCT band produced no effect other than that of laser pulse scatter. The observations are interpreted in terms of photoperturbation of the singlet-quintet spin state equilibrium, which in this case occurs solely through excitation in the ligand field absorption region of the complex and is the first reported instance of this type for a spin-crossover complex in solution.

Fundamentals of steady state, non-Newtonian rimming flow

Rimming flow on the inner surface of a horizontal rotating cylinder is investigated. Using a scale analysis, a theoretical description is obtained for steady-state non-Newtonian flow. Simple lubrication theory is applied since the Reynolds number is small and the liquid film is thin. Since the Deborah number is very small the flow is viscometric. The shear-thinning number, which characterizes the shear-thinning effect, may be small or large. A general constitutive law for this kind of flow requires only a single function relating shear stress and shear rate that corresponds to a generalized Newtonian liquid. For this case the run-off condition for rimming flow is derived. Provided the run-off condition is satisfied, the existence of a continuous steady-state solution is proved. The rheological models, which show Newtonian behavior at low shear rates with transition to power-law shear thinning at moderate shear rates, are considered. Numerical results are carried out for the Carreau and Ellis models, which exhibit Newtonian behavior near the free surface and power-law behavior near the wall of the rotating cylinder.

First EXAFS studies on aurophilic interactions in solution

EXAFS has been used to directly show the existence of Au…Au interactions in dissolved Au(I) complexes for the first time; the information has been used to understand the optical properties of these materials.

Relevance of heterometallic binding energy for metal underpotential deposition

We present first-principles calculations for a number of metals adsorbed on several different metallic substrates. Some of these systems are very relevant in electrochemistry, especially in the field of underpotential deposition phenomena. The present studies reveal the existence of a relationship between the excess binding energy and the surface energy difference between substrate and adsorbate. Comparisons with experimental underpotential shifts show that excess binding energies are systematically underestimated. By analyzing experimental information on different systems, we conclude that this discrepancy between our vacuum calculations and experiments carried out in an electrolytic solution is likely to be due to anion adsorption and/or solvent effects.

Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

On the mobility of a one-dimensional damped Frenkel-Kontorova chain: Commensurate versus incommensurate

The mobility of a one-dimensional damped Frenkel-Kontorova chain under a de driving force is studied numerically and analytically For the commensurate case, the particles in the chain me synchronized st high driving force. For the incommensurate chain, a single mode solution dominates st high mobility regime. We are able to calculate the mobilities for both the cases analytically, and a good agreement with numerical results is found. The mobility hysteresis for the incommensurate chain is explained by the existence of two branches of physical solutions, and transitions occur when one of them breaks up.

PHOTOMINERALIZATION OF SALICYLIC-ACID - A KINETIC-STUDY

The kinetics of the photomineralization of salicylic acid (SA) sensitized by Degussa P25 titanium dioxide (TiO2) dispersions in oxygenated aqueous solution are reported as a function of the following experimental parameters: [TiO2], percentage of O-2, [SA], temperature (T) and light intensity (I). The kinetics of SA photomineralization conform to a Langmuir-Hinshelwood kinetic scheme with SA and O-2 adsorbed at different sites with apparent Langmuir adsorption coefficients of (6.1 +/- 1.2) x 10(4) mol(-1) dm(3) and 0.061 +/- 0.007 kPa(-1) respectively. The overall activation energy for the system was determined as 4.6 +/- 0.2 kJ mol(-1). Two major stable reaction intermediates are identified (dihydroxybenzoic acids (DHBA) and catechol (C)) and the existence of a further pathway involving one or more very unstable and, as yet, unidentified reaction intermediates is proposed. A kinetic model is presented which describes the temporal behaviour of the concentrations of SA, CO2 and the major photogenerated intermediates (DHBA and C). This model is used to predict successfully the temporal behaviour of the major intermediates in the photomineralization of SA under non-standard conditions.

Adsorption and aggregation properties of norovirus GI and GII virus-like particles demonstrate differing responses to solution chemistry

The transport properties (adsorption and aggregation behavior) of virus-like particles (VLPs) of two strains of norovirus ("Norwalk" GI.1 and "Houston" GII.4) were studied in a variety of solution chemistries. GI.1 and GII.4 VLPs were found to be stable against aggregation at pH 4.0-8.0. At pH 9.0, GI.1 VLPs rapidly disintegrated. The attachment efficiencies (a) of GI.1 and GII.4 VLPs to silica increased with increasing ionic strength in NaCl solutions at pH 8.0. The attachment efficiency of GI.1 VLPs decreased as pH was increased above the isoelectric point (pH 5.0), whereas at and below the isoelectric point, the attachment efficiency was erratic. Ca(2+) and Mg(2+) dramatically increased the attachment efficiencies of GI.1 and GII.4 VLPs, which may be due to specific interactions with the VLP capsids. Bicarbonate decreased attachment efficiencies for both GI.1 and GII.4 VLPs, whereas phosphate decreased the attachment efficiency of GI.1, while increasing GII.4 attachment efficiency. The observed differences in GI.1 and GII.4 VLP attachment efficiencies in response to solution chemistry may be attributed to differential responses of the unique arrangement of exposed amino acid residues on the capsid surface of each VLP strain.

Removal of ortho-phosphate from aqueous solution by adsorption onto dolomite

An experimental study on the adsorption of phosphate onto cost effective fine dolomite powder is presented. The effect of solution pH, solution ionic strength and adsorption isotherm were examined. The adsorption of phosphate was pH dependent and phosphate adsorption favoured acidic conditions. The adsorption was significantly influenced by solution ionic strength indicating outer-sphere complexation reactions. The experimental data further indicated that the removal of phosphate increased with increase in the ionic strength of solution. The experimental data were modelled with different isotherms: Langmuir, Freundlich and Redlich–Peterson isotherms. It was found that the Redlich–Peterson isotherm depicted the equilibrium data most accurately. The overall kinetic data fitted very well the pseudo-first-order rate model.

Sound Synthesis for Contact-Driven Musical Instruments via Discretisation of Hamilton's Equations

Physical modelling of musical instruments involves studying nonlinear interactions between parts of the instrument. These can pose several difficulties concerning the accuracy and stability of numerical algorithms. In particular, when the underlying forces are non-analytic functions of the phase-space variables, a stability proof can only be obtained in limited cases. An approach has been recently presented by the authors, leading to unconditionally stable simulations for lumped collision models. In that study, discretisation of Hamilton’s equations instead of the usual Newton’s equation of motion yields a numerical scheme that can be proven to be energy conserving. In this paper, the above approach is extended to collisions of distributed objects. Namely, the interaction of an ideal string with a flat barrier is considered. The problem is formulated within the Hamiltonian framework and subsequently discretised. The resulting nonlinearmatrix equation can be shown to possess a unique solution, that enables the update of the algorithm. Energy conservation and thus numerical stability follows in a way similar to the lumped collision model. The existence of an analytic description of this interaction allows the validation of the model’s accuracy. The proposed methodology can be used in sound synthesis applications involving musical instruments where collisions occur either in a confined (e.g. hammer-string interaction, mallet impact) or in a distributed region (e.g. string-bridge or reed-mouthpiece interaction).

The solution structure of 1:2 phenol/N-methylpyridinium bis{(trifluoromethyl)sulfonyl}imide liquid mixtures

Neutron diffraction has been used to investigate the liquid structure of a 1:2 solution of phenol in the ionic liquid N-methylpyridinium bis{(trifluoromethyl)sulfonyl}imide at 60 ◦C, using the empirical potential structure refinement (EPSR) process to model the data obtained from the SANDALS diffractometer at ISIS. Addition of phenol results in suppression of the melting point of the pyridinium salt and formation of a room temperature solution with aromatic phenol–cation and phenol-OH to anion hydrogen-bonding interactions.