Action of a finite quantum group on the algebra of complex NxN matrices

Using the fact that the algebra M := M_N(C) of NxN complex matrices can be considered as a reduced quantum plane, and that it is a module algebra for a finite dimensional Hopf algebra quotient H of U_q(sl(2)) when q is a root of unity, we reduce this algebra M of matrices (assuming N odd) into indecomposable modules for H. We also show how the same finite dimensional quantum group acts on the space of generalized differential forms defined as the reduced Wess Zumino complex associated with the algebra M.Comment: 11 pages, LaTeX, uses diagrams.sty, to be published in "Particles, Fields and Gravitation" (Lodz conference), AIP proceeding

Higher Coxeter graphs associated to affine su(3) modular invariants

The affine $su(3)$ modular invariant partition functions in 2d RCFT are associated with a set of generalized Coxeter graphs. These partition functions fall into two classes, the block-diagonal (Type I) and the non block-diagonal (Type II) cases, associated, from spectral properties, to the subsets of subgroup and module graphs respectively. We introduce a modular operator $\hat{T}$ taking values on the set of vertices of the subgroup graphs. It allows us to obtain easily the associated Type I partition functions. We also show that all Type II partition functions are obtained by the action of suitable twists $\vartheta$ on the set of vertices of the subgroup graphs. These twists have to preserve the values of the modular operator $\hat{T}$.Comment: Version 2. Abstract, introduction and conclusion rewritten, references added. 36 page

Financing health care in high-income countries

The main lesson from the experience of high-income countries with health care financing is a simple one: financing reforms should support the ultimate goal of universal coverage. Most high-income countries started with voluntary health insurance systems, which were then gradually extended to compulsory social insurance for certain groups and finally reached universal coverage, either as nationwide social health insurance schemes or as tax-financed national health services. The risk pooling and prepayment functions are essential. Moreover, the revenue collection mechanisms, whether as general tax revenues or payroll taxes, are secondary to the basic object of providing financial protection through effective risk pooling mechanisms. The experience of high-income countries indicates that private health insurance, medical savings accounts, and other forms of private resource collection are supplementary methods for increasing universal coverage.

From conformal embeddings to quantum symmetries: an exceptional SU(4) example

We briefly discuss several algebraic tools that are used to describe the quantum symmetries of Boundary Conformal Field Theories on a torus. The starting point is a fusion category, together with an action on another category described by a quantum graph. For known examples, the corresponding modular invariant partition function, which is sometimes associated with a conformal embedding, provides enough information to recover the whole structure. We illustrate these notions with the example of the conformal embedding of SU(4) at level 4 into Spin(15) at level 1, leading to the exceptional quantum graph E4(SU(4)).Comment: 22 pages, 3 color figures. Version 2: We changed the color of figures (ps files) in such a way that they are still understood when converted to gray levels. Version 3: Several references have been adde

From modular invariants to graphs: the modular splitting method

We start with a given modular invariant M of a two dimensional su(n)_k conformal field theory (CFT) and present a general method for solving the Ocneanu modular splitting equation and then determine, in a step-by-step explicit construction, 1) the generalized partition functions corresponding to the introduction of boundary conditions and defect lines; 2) the quantum symmetries of the higher ADE graph G associated to the initial modular invariant M. Notice that one does not suppose here that the graph G is already known, since it appears as a by-product of the calculations. We analyze several su(3)_k exceptional cases at levels 5 and 9.Comment: 28 pages, 7 figures. Version 2: updated references. Typos corrected. su(2) example has been removed to shorten the paper. Dual annular matrices for the rejected exceptional su(3) diagram are determine

Kinetic models for dilute solutions of dumbbells in non-homogeneous flows revisited

We propose a two fluid theory to model a dilute polymer solution assuming that it consists of two phases, polymer and solvent, with two distinct macroscopic velocities. The solvent phase velocity is governed by the macroscopic Navier-Stokes equations with the addition of a force term describing the interaction between the two phases. The polymer phase is described on the mesoscopic level using a dumbbell model and its macroscopic velocity is obtained through averaging. We start by writing down the full phase-space distribution function for the dumbbells and then obtain the inertialess limits for the Fokker-Planck equation and for the averaged friction force acting between the phases from a rigorous asymptotic analysis. The resulting equations are relevant to the modelling of strongly non-homogeneous flows, while the standard kinetic model is recovered in the locally homogeneous case

Formation of Kinneyia via shear-induced instabilities in microbial mats

Kinneyia are a class of microbially mediated sedimentary fossils. Characterized by clearly defined ripple structures, Kinneyia are generally found in areas that were formally littoral habitats and covered by microbial mats. To date, there has been no conclusive explanation of the processes involved in the formation of these fossils. Microbial mats behave like viscoelastic fluids. We propose that the key mechanism involved in the formation of Kinneyia is a Kelvin–Helmholtz-type instability induced in a viscoelastic film under flowing water. A ripple corrugation is spontaneously induced in the film and grows in amplitude over time. Theoretical predictions show that the ripple instability has a wavelength proportional to the thickness of the film. Experiments carried out using viscoelastic films confirm this prediction. The ripple pattern that forms has a wavelength roughly three times the thickness of the film. This behaviour is independent of the viscosity of the film and the flow conditions. Laboratory-analogue Kinneyia were formed via the sedimentation of glass beads, which preferentially deposit in the troughs of the ripples. Well-ordered patterns form, with both honeycomb-like and parallel ridges being observed, depending on the flow speed. These patterns correspond well with those found in Kinneyia, with similar morphologies, wavelengths and amplitudes being observed

Orders and dimensions for sl(2) or sl(3) module categories and Boundary Conformal Field Theories on a torus

After giving a short description, in terms of action of categories, of some of the structures associated with sl(2) and sl(3) boundary conformal field theories on a torus, we provide tables of dimensions describing the semisimple and co-semisimple blocks of the corresponding weak bialgebras (quantum groupoids), tables of quantum dimensions and orders, and tables describing induction - restriction. For reasons of size, the sl(3) tables of induction are only given for theories with self-fusion (existence of a monoidal structure).Comment: 25 pages, 5 tables, 9 figures. Version 2: updated references. Typos corrected. Several proofs added. Examples of ADE and generalized ADE trigonometric identities have been removed to shorten the pape

Twisted partition functions for ADE boundary conformal field theories and Ocneanu algebras of quantum symmetries

For every ADE Dynkin diagram, we give a realization, in terms of usual fusion algebras (graph algebras), of the algebra of quantum symmetries described by the associated Ocneanu graph. We give explicitly, in each case, the list of the corresponding twisted partition functionsComment: 47 pages, 25 figures and 17 tables. Several typos are corrected. References adde

Root exudation of phloridzin by apple seedlings (Malus x domestica Borkh.) with symptoms of apple replant disease

This study investigates the occurrence of the flavonoid phloridzin (phloretin-2'-O-β-D-glucoside) in root exudates of apple seedlings showing growth reduction related to apple replant disease (ARD). The disease is most likely caused by a complex of soil-borne fungi and bacteria, but the etiology remains to be elucidated. Information on specific exudation processes in the rhizosphere of apple seedlings could contribute to our understanding of the conditions triggering ARD development.To procure ARD symptoms, apple seedlings (Malus x domestica Borkh.) were grown in ARD-conductive soil. Root exudates were collected by submerging the roots in a solution of 0.05 mM CaCl2 for a period of 4 h. The fraction of phenolic root exudates was analyzed using HPLC/DAD (high performance liquid chromatography/diode array detector).Results suggest that (i) phloridzin is a constant root exudate of apple seedlings. It was the most abundant phenol in the collected exudates from replant-diseased as well as healthy seedlings. (ii) Phloridzin exudation, related to root dry matter, was the most intensive at the onset of ARD symptom development and lower during the period when symptoms were most severe or outgrown. (iii) In comparison to healthy seedlings, the phloridzin exudation of apple replantdiseased seedlings was significantly higher only at the onset of ARD symptom development, suggesting a response of the plants to infection.The finding of phloridzin in the root exudates of Malus x domestica Borkh. might have consequences for research on the etiology of ARD. Specialized pathogenic microorganisms could be attracted by this distinct compound. Since it is very characteristic of apple plants, phloridzin might be the compound that ARD-causing microorganisms utilize to recognize their host. For practical applications, phloridzin root exudation could therefore be a parameter in evaluating ARD-susceptibility of different rootstocks