Pseudo-rotations of the open annulus

In this paper, we study pseudo-rotations of the open annulus, \emph{i.e.} conservative homeomorphisms of the open annulus whose rotation set is reduced to a single irrational number (the angle of the pseudo-rotation). We prove in particular that, for every pseudo-rotation $h$ of angle $\rho$, the rigid rotation of angle $\rho$ is in the closure of the conjugacy class of $h$. We also prove that pseudo-rotations are not persistent in $C^r$ topology for any $r\geq 0$.Comment: 25 page

Conformational Control of Exciton-Polariton Physics in Metal - Poly(9,9-dioctylfluorene) - Metal Cavities

Control is exerted over the exciton-polariton physics in metal - Poly(9,9-dioctyl fluorene) - metal microcavities via conformational changes to the polymer backbone. Using thin-film samples containing increasing fractions of $\beta$-phase chain segments, a systematic study is reported for the mode characteristics and resulting light emission properties of cavities containing two distinct exciton sub-populations within the same semiconductor. Ultrastrong coupling for disordered glassy-phase excitons is observed from angle-resolved reflectivity measurements, with Rabi splitting energies in excess of 1.05 eV (more than 30% of the exciton transition energy) for both TE- and TM-polarized light. A splitting of the lower polariton branch is then induced via introduction of $\beta$-phase excitons and increases with their growing fraction. In all cases, the photoluminescence emanates from the lowermost polariton branch, allowing conformational control to be exerted over the emission energy and its angular variation. Dispersion-free cavities with highly saturated blue-violet emission are thus enabled. Experimental results are discussed in terms of the full Hopfield Hamiltonian generalized to the case of two exciton oscillators. The importance of taking account of the molecular characteristics of the semiconductor for an accurate description of its strong coupling behaviour is directly considered, in specific relation to the role of the vibronic structure

Modelling the microfiltration of lactic acid fermentation broths and comparison of operating modes

clarification of fermentation broths by cross-flow microfiltration. Microfiltration experiments conducted under constant transmembrane pressure and under constant permeate fluxes (higher and lower than the critical flux) were represented by the resistance in series model in which the membrane resistance, the adsorption resistance, the bacteria cake resistance and the soluble compounds concentration polarisation resistance were taken into account. The different operating modes were compared in terms of two industrial interest criteria: the productivity and fouling rates. Higher productivities were obtained during constant transmembrane pressure runs whereas the lowest fouling rate was observed during the run conducted with a constant permeate flux lower than the critical flux. However, this fouling was mainly due to adsorption and solute components concentration polarisation. Key words

Fast inactivation in Shaker K+ channels. Properties of ionic and gating currents.

Fast inactivating Shaker H4 potassium channels and nonconducting pore mutant Shaker H4 W434F channels have been used to correlate the installation and recovery of the fast inactivation of ionic current with changes in the kinetics of gating current known as "charge immobilization" (Armstrong, C.M., and F. Bezanilla. 1977. J. Gen. Physiol. 70:567-590.). Shaker H4 W434F gating currents are very similar to those of the conducting clone recorded in potassium-free solutions. This mutant channel allows the recording of the total gating charge return, even when returning from potentials that would largely inactivate conducting channels. As the depolarizing potential increased, the OFF gating currents decay phase at -90 mV return potential changed from a single fast component to at least two components, the slower requiring approximately 200 ms for a full charge return. The charge immobilization onset and the ionic current decay have an identical time course. The recoveries of gating current (Shaker H4 W434F) and ionic current (Shaker H4) in 2 mM external potassium have at least two components. Both recoveries are similar at -120 and -90 mV. In contrast, at higher potentials (-70 and -50 mV), the gating charge recovers significantly more slowly than the ionic current. A model with a single inactivated state cannot account for all our data, which strongly support the existence of "parallel" inactivated states. In this model, a fraction of the charge can be recovered upon repolarization while the channel pore is occupied by the NH2-terminus region

Some fossil ginkgophytes and a possible vojnovskyalean element from the Glossopteris flora of Vereeniging, Transvaal

Main articleA short historical review is given of previously described sites where plant fossils occur in Lower Karroo beds at Vereeniging in the Southern Transvaal. Reference is made to the importance of these sites because of the outstanding discoveries made here in the past. Some new material from the same sites is described and several unusual elements in the Glossopteris flora of Vereeniging are recorded for the first time. Leaves of a plant not previously recorded from Gondwanaland are provisionally described under the term cf. Nephropsis on account of a strong resemblance to leaves of the Russian Permian genus Nephropsis Zalessky. The remaining specimens in the assemblage are tentatively placed in the genera Ginkgoites Seward and Psygmophyllum Schimper respectively. Owing to the paucity of material, type numbers are assigned in certain cases, instead of specific names. Specific identification is attempted, however, in the case of four of the specimens, which are provisionally assigned to Psygmophyllum kidstoni Seward.Non

On some "northern" elements in the Lower Gondwana flora of Vereeniging, Transvaal

Main articleA small assemblage of plant elements from the Lower Permian of Vereeniging, in the southern Transvaal, is described here. The assemblage is constituted of form-genera normally only found in the palaeo floristic regions of the northern hemisphere. The genera concerned are: Pecopteris (Asterotheca), Cladophlebis, Sphenophyllum and Psygmophyllum. The intermingling of these "Northern" elements with the Glossopteris flora of Vereeniging serves to illustrate the mixed nature of this flora. Reference is made to similar mixed Gondwana floras elsewhere in Africa and also in South America.Non

Scattering by a toroidal coil

In this paper we consider the Schr\"odinger operator in ${\mathbb R}^3$ with a long-range magnetic potential associated to a magnetic field supported inside a torus ${\mathbb{T}}$. Using the scheme of smooth perturbations we construct stationary modified wave operators and the corresponding scattering matrix $S(\lambda)$. We prove that the essential spectrum of $S(\lambda)$ is an interval of the unit circle depending only on the magnetic flux $\phi$ across the section of $\mathbb{T}$. Additionally we show that, in contrast to the Aharonov-Bohm potential in ${\mathbb{R}}^2$, the total scattering cross-section is always finite. We also conjecture that the case treated here is a typical example in dimension 3.Comment: LaTeX2e 17 pages, 1 figur