Exponential mapping for non semisimple quantum groups

The concept of universal T matrix, recently introduced by Fronsdal and Galindo in the framework of quantum groups, is here discussed as a generalization of the exponential mapping. New examples related to inhomogeneous quantum groups of physical interest are developed, the duality calculations are explicitly presented and it is found that in some cases the universal T matrix, like for Lie groups, is expressed in terms of usual exponential series.Comment: 12 page

Lie Algebroid Yang Mills with Matter Fields

Lie algebroid Yang-Mills theories are a generalization of Yang-Mills gauge theories, replacing the structural Lie algebra by a Lie algebroid E. In this note we relax the conditions on the fiber metric of E for gauge invariance of the action functional. Coupling to scalar fields requires possibly nonlinear representations of Lie algebroids. In all cases, gauge invariance is seen to lead to a condition of covariant constancy on the respective fiber metric in question with respect to an appropriate Lie algebroid connection. The presentation is kept in part explicit so as to be accessible also to a less mathematically oriented audience.Comment: 24 pages, accepted for publication in J. Geom. Phy

Free q-Schrodinger Equation from Homogeneous Spaces of the 2-dim Euclidean Quantum Group

After a preliminary review of the definition and the general properties of the homogeneous spaces of quantum groups, the quantum hyperboloid qH and the quantum plane qP are determined as homogeneous spaces of Fq(E(2)). The canonical action of Eq(2) is used to define a natural q-analog of the free Schro"dinger equation, that is studied in the momentum and angular momentum bases. In the first case the eigenfunctions are factorized in terms of products of two q-exponentials. In the second case we determine the eigenstates of the unitary representation, which, in the qP case, are given in terms of Hahn-Exton functions. Introducing the universal T-matrix for Eq(2) we prove that the Hahn-Exton as well as Jackson q-Bessel functions are also obtained as matrix elements of T, thus giving the correct extension to quantum groups of well known methods in harmonic analysis.Comment: 19 pages, plain tex, revised version with added materia

Experimental cannibalization of plagioclase by alkaline basalt magmas

Time-series crystallization/dissolution experiments were conducted on a natural potassic basalt seeded with bytownitic plagioclases (Plg) at atmospheric pressure, in air, at 1180- 1240 °C and isothermal dwell time up to 20 hours. Plg-seed presence promotes the early formation of new-Plg, dampening the clinopyroxene (Cpx) crystallization. New-Plgs grow at a rate from 10-6 up to 10-8 cm·s-1 as the dwell time increases. Seeds overgrow at similar rate. Cpx crystallizes with a delay of at least 3 hours; this has a significant impact on the composition of both residual melt and new-Plgs. For undercooling >35 °C the Cpx delay causes a strong supersaturation of this phase in the melt resulting in a decrease in the new-Plg nucleation rate by 2 orders of magnitude in the 3 h-experiment. In the 15h-run, Cpx coarsening and the decrease of crystallinity suggest the achievement of a near-equilibrium conditions. Cpx growth rate is in the order of 10-7 cm·s-1 showing very limited variation. Finally, for the investigated superheating (5-15 °C) only the long lasting experiments allows an estimation of Plg dissolution rate (10-9 cm·s-1) although changes in the melt composition are already detectable in the 3h-runs. As a whole our results suggest that in natural systems, the takeover of antecrysts/ xenocrysts by a magma can induce on a short time scales, changes in its initial nucleation behavior with remarkable petrological implications for the solidification paths and eruptive dynamics of potassic magmatic systems

Base cation mobility in vineyard soils of the Colli Albani volcanic district (Central Italy)

The quality of the Colli Albani volcanic soils has certainly contributed to the vine cultivars hence the name of one of the oldest wines (i.e., Alban wine). The alkali up to 15 wt%, SiO2 ≤ 52 wt% and the emplacement at high temperature (≤ 600 °C) are the bedrock features that have deeply influenced the soil-forming processes in the vineyards. However, the peculiar features of the Colli Albani soils are not well known. Field survey and textural, mineralogical, and chemical data obtained with SEM, EMP, XRD, and ICP-OES were used to characterize the vineyard soils of the Colli Albani. Leucite (Lct)-bearing soils and quartz (Qz)-bearing soils occur in the studied vineyard. The Qz-bearing soils represent more weathered volcanic material, depleted in primary minerals and enriched in clays, which show a lower cation exchange capacity (CEC) than the Lct-bearing soils. CEC is a misleading definition for the Colli Albani soils because the base cation mobility in the vineyard is independent from clay mineral enrichment in the soil. Actually, the release of K, Na, Ca, and Mg depends by (i) the complete dissolution of leucite and analcime, (ii) the oxy-reaction affecting the phlogopite, which releases K + Mg, and (iii) the incongruent dissolution of clinopyroxene characterized by the “gothic texture.” This texture highlights the capacity of clinopyroxene to release Ca and Mg in volcanic soils. Quantification of the texture and abundance of the primary minerals are mandatory for the management of the vineyard soils in the Colli Albani and, in general, it is significative for the vineyards in volcanic areas

Mutation Symmetries in BPS Quiver Theories: Building the BPS Spectra

We study the basic features of BPS quiver mutations in 4D $\mathcal{N}=2$ supersymmetric quantum field theory with $G=ADE$ gauge symmetries.\ We show, for these gauge symmetries, that there is an isotropy group $\mathcal{G}_{Mut}^{G}$ associated to a set of quiver mutations capturing information about the BPS spectra. In the strong coupling limit, it is shown that BPS chambers correspond to finite and closed groupoid orbits with an isotropy symmetry group $\mathcal{G}_{strong}^{G}$ isomorphic to the discrete dihedral groups $Dih_{2h_{G}}$ contained in Coxeter$(G)$ with $$ the Coxeter number of G. These isotropy symmetries allow to determine the BPS spectrum of the strong coupling chamber; and give another way to count the total number of BPS and anti-BPS states of $\mathcal{N}=2$ gauge theories. We also build the matrix realization of these mutation groups $\mathcal{G}_{strong}^{G}$ from which we read directly the electric-magnetic charges of the BPS and anti-BPS states of $\mathcal{N}=2$ QFT$_{4}$ as well as their matrix intersections. We study as well the quiver mutation symmetries in the weak coupling limit and give their links with infinite Coxeter groups. We show amongst others that $\mathcal{G}_{weak}^{su_{2}}$ is contained in ${GL}({2,}\mathbb{Z})$; and isomorphic to the infinite Coxeter ${I_{2}^{\infty}}$. Other issues such as building $\mathcal{G}$ and $\mathcal{G}_{weak}^{su_{3}}$ are also studied.Comment: LaTeX, 98 pages, 18 figures, Appendix I on groupoids adde

On the oxygen reduction reaction mechanism catalyzed by pd complexes on 2d carbon. A theoretical study

Oxygen Reduction Reaction (ORR) is the bottle-neck strategic reaction ruling the fuel cell efficiency process. The slow kinetics of the reaction require highly effective electrocatalysts for proper boosting. In this field, composite catalysts formed by carbon nanotubes functionalized with palladium(II) complexes showed surprising catalytic activity comparable to those of a commercial Pt electrode, but the catalytic mechanisms of these materials still remain open to discussion. In this paper, we propose the combination of experimental and theoretical results to unfold the elementary reaction steps underlying the ORR catalysis

Effects and Mechanisms Activated by Treatment with Cationic, Anionic and Zwitterionic Liposomes on an In Vitro Model of Porcine Pre-Pubertal Sertoli Cells

: Liposomes have been successfully used as drug-delivery vehicles, but there are no clinical studies on improved fertility and the few reported experimental studies have been performed in animal models far from humans. The aim of this paper was to study the effects of treatment with cationic, anionic and zwitterionic liposomes on our superior mammalian model of porcine prepubertal Sertoli cells (SCs) to find a carrier of in vitro test drugs for SCs. Porcine pre-pubertal SCs cultures were incubated with different liposomes. Viability, apoptosis/necrosis status (Annexin-V/Propidium iodide assay), immunolocalisation of β-actin, vimentin, the phosphorylated form of AMP-activated protein Kinase (AMPK)α and cell ultrastructure (Transmission Electron Microscopy, TEM) were analysed. Zwitterionic liposomes did not determine changes in the cell cytoplasm. The incubation with anionic and cationic liposomes modified the distribution of actin and vimentin filaments and increased the levels of the phosphorylated form of AMPKα. The Annexin/Propidium Iodide assay suggested an increase in apoptosis. TEM analysis highlighted a cytoplasmic vacuolisation. In conclusion, these preliminary data indicated that zwitterionic liposomes were the best carrier to use in an in vitro study of SCs to understand the effects of molecules or drugs that could have a clinical application in the treatment of certain forms of male infertility

Projective representation of k-Galilei group

The projective representations of k-Galilei group G_k are found by contracting the relevant representations of k-Poincare group. The projective multiplier is found. It is shown that it is not possible to replace the projective representations of G_k by vector representations of some its extension.Comment: 15 pages Latex fil

Ehrenfest times for classically chaotic systems

We describe the quantum mechanical spreading of a Gaussian wave packet by means of the semiclassical WKB approximation of Berry and Balazs. We find that the time scale $\tau$ on which this approximation breaks down in a chaotic system is larger than the Ehrenfest times considered previously. In one dimension \tau=\fr{7}{6}\lambda^{-1}\ln(A/\hbar), with $\lambda$ the Lyapunov exponent and $A$ a typical classical action.Comment: 4 page