Bijectivity of the canonical map for the noncommutative instanton bundle

It is shown that the quantum instanton bundle introduced in Commun. Math. Phys. 226, 419-432 (2002) has a bijective canonical map and is, therefore, a coalgebra Galois extension.Comment: Latex, 12 pages. Published versio

Spatial and temporal variability of mobile macro-invertebrate assemblages associated to coralligenous habitat

The study aimed to investigate patterns of spatial and temporal variability of mobile macroinvertebrate assemblages associated to coralligenous habitat. A multi-factorial sampling design was used to test the hypotheses that the structure of assemblages and their spatial and temporal variability changed in relation to substrate inclination. Moreover, macroalgae and sessile macro-invertebrates were also investigated in order to detect eventual relationship between sessile and mobile assemblages. A total of 236 mobile macro-invertebrate taxa were identified, among them 2 Platyhelminthes, 4 Sipuncula, 6 Nemertea, 27 Mollusca, 86 Annelida, 103 Arthropoda, 8 Echinodermata. Results of the study showed that mobile macro-invertebrate assemblages of coralligenous habitat were little influenced by the inclination of substrate and by the morphology of sessile organisms, as patterns of variation were different between the two assemblages. Mobile macro-invertebrate assemblages changed among sampling dates within one year period and they showed high variability at the spatial scale examined

Free-Field Representation of Group Element for Simple Quantum Group

A representation of the group element (also known as ``universal ${\cal T}$-matrix'') which satisfies $\Delta(g) = g\otimes g$, is given in the form $$g = \left(\prod_{s=1}^{d_B}\phantom.^>\ {\cal E}_{1/q_{i(s)}}(\chi^{(s)}T_{-i(s)})\right) q^{2\vec\phi\vec H} \left(\prod_{s=1}^{d_B}\phantom.^<\ {\cal E}_{q_{i(s)}}(\psi^{(s)} T_{+i(s)})\right)$$ where $d_B = \frac{1}{2}(d_G - r_G)$, $q_i = q^{|| \vec\alpha_i||^2/2}$ and $H_i = 2\vec H\vec\alpha_i/||\vec\alpha_i||^2$ and $T_{\pm i}$ are the generators of quantum group associated respectively with Cartan algebra and the {\it simple} roots. The ``free fields'' $\chi,\ \vec\phi,\ \psi$form a Heisenberg-like algebra:$\psi^{(s)}\psi^{(s')} = q^{-\vec\alpha_{i(s)} \vec\alpha_{i(s')}} \psi^{(s')}\psi^{(s)}, & \chi^{(s)}\chi^{(s')} = q^{-\vec\alpha_{i(s)}\vec\alpha_{i(s')}} \chi^{(s')}\chi^{(s)}& {\rm for} \ s<s', \\ q^{\vec h\vec\phi}\psi^{(s)} = q^{\vec h\vec\alpha_{i(s)}} \psi^{(s)}q^{\vec h\vec\phi}, & q^{\vec h\vec\phi}\chi^{(s)} = q^{\vec h \vec\alpha_{i(s)}}\chi^{(s)}q^{\vec h\vec\phi}, & \\ &\psi^{(s)} \chi^{(s')} = \chi^{(s')}\psi^{(s)} & {\rm for\ any}\ s,s'.$We argue that the$d_G$-parametric ``manifold'' which$g$spans in the operator-valued universal envelopping algebra, can also be invariant under the group multiplication$g \rightarrow g'\cdot g''$. The universal${\cal R}$-matrix with the property that${\cal R} (g\otimes I)(I\otimes g) = (I\otimes g)(g\otimes I){\cal R}$is given by the usual formula$${\cal R} = q^{-\sum_{ij}^{r_G}||\vec\alpha_i||^2|| \vec\alpha_j||^2 (\vec\alpha\vec\alpha)^{-1}_{ij}H_i \otimes H_j}\prod_{ \vec\alpha > 0}^{d_B}{\cal E}_{q_{\vec\alpha}}\left(-(q_{\vec\alpha}- q_{\vec\alpha}^{-1})T_{\vec\alpha}\otimes T_{-\vec\alpha}\right).$$Comment: 68 page

Differential calculus on the quantum Heisenberg group

The differential calculus on the quantum Heisenberg group is conlinebreak structed. The duality between quantum Heisenberg group and algebra is proved.Comment: AMSTeX, Pages

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

Quantum Double and Differential Calculi

We show that bicovariant bimodules as defined by Woronowicz are in one to one correspondence with the Drinfeld quantum double representations. We then prove that a differential calculus associated to a bicovariant bimodule of dimension n is connected to the existence of a particular (n+1)--dimensional representation of the double. An example of bicovariant differential calculus on the non quasitriangular quantum group E_q(2) is developed. The construction is studied in terms of Hochschild cohomology and a correspondence between differential calculi and 1-cocycles is proved. Some differences of calculi on quantum and finite groups with respect to Lie groups are stressed.Comment: Revised version with added cohomological analysis. 14 pages, plain te

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

Green function on the quantum plane

Green function (which can be called the q-analogous of the Hankel function) on the quantum plane E_q^2= E_q(2)/U(1) is constructed.Comment: 8 page

Spatial Resolution of Double-Sided Silicon Microstrip Detectors for the PAMELA Apparatus

The PAMELA apparatus has been assembled and it is ready to be launched in a satellite mission to study mainly the antiparticle component of cosmic rays. In this paper the performances obtained for the silicon microstrip detectors used in the magnetic spectrometer are presented. This subdetector reconstructs the curvature of a charged particle in the magnetic field produced by a permanent magnet and consequently determines momentum and charge sign, thanks to a very good accuracy in the position measurements (better than 3 um in the bending coordinate). A complete simulation of the silicon microstrip detectors has been developed in order to investigate in great detail the sensor's characteristics. Simulated events have been then compared with data gathered from minimum ionizing particle (MIP) beams during the last years in order to tune free parameters of the simulation. Finally some either widely used or original position finding algorithms, designed for such kind of detectors, have been applied to events with different incidence angles. As a result of the analysis, a method of impact point reconstruction can be chosen, depending on both the particle's incidence angle and the cluster multiplicity, so as to maximize the capability of the spectrometer in antiparticle tagging.Comment: 28 pages, 18 figures, submitted to Nuclear Instruments and Methods in Physics Research