Wigner-Weyl isomorphism for quantum mechanics on Lie groups

The Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group $G$ is developed in detail. Several New features are shown to arise which have no counterparts in the familiar Cartesian case. Notable among these is the notion of a `semiquantised phase space', a structure on which the Weyl symbols of operators turn out to be naturally defined and, figuratively speaking, located midway between the classical phase space $T^*G$ and the Hilbert space of square integrable functions on $G$. General expressions for the star product for Weyl symbols are presented and explicitly worked out for the angle-angular momentum case.Comment: 32 pages, Latex2

Unexpected Architectures. Restorations in Romagna Between the Two World Wars

The research here presented is a critical appraisal of some restoration works carried out between the two World Wars in a particular geographic context, which is the Romagna district, in the Northeast of Italy. Starting from two case studies (the Casa del Fascio in Forl\uec and the Malatesta Library in Cesena) and thanks to the analysis of bibliographical sources, archival documents, and drawings, this research aims at understanding how broader and major theories about architectural restoration are articulated in peripheral background. What emerges are unexpected results: Late and deeply contextualized operations, strongly linked with the national panorama but at the same time chasing for the revival of their own history

The Schwinger Representation of a Group: Concept and Applications

The concept of the Schwinger Representation of a finite or compact simple Lie group is set up as a multiplicity-free direct sum of all the unitary irreducible representations of the group. This is abstracted from the properties of the Schwinger oscillator construction for SU(2), and its relevance in several quantum mechanical contexts is highlighted. The Schwinger representations for $SU(2), SO(3)$ and SU(n) for all $n$ are constructed via specific carrier spaces and group actions. In the SU(2) case connections to the oscillator construction and to Majorana's theorem on pure states for any spin are worked out. The role of the Schwinger Representation in setting up the Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group is brought out.Comment: Latex, 17 page

Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients

We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank approximations and the cyclic reduction method. The setup and application phases of the preconditioner achieve log-linear complexity in memory footprint and number of operations, and numerical experiments exhibit good weak and strong scalability at large processor counts in a distributed memory environment. Numerical experiments with linear systems that feature symmetry and nonsymmetry, definiteness and indefiniteness, constant and variable coefficients demonstrate the preconditioner applicability and robustness. Furthermore, it is possible to control the number of iterations via the accuracy threshold of the hierarchical matrix approximations and their arithmetic operations, and the tuning of the admissibility condition parameter. Together, these parameters allow for optimization of the memory requirements and performance of the preconditioner

Topology and quantum states: The electron-monopole system

This paper starts by describing the dynamics of the electronmonopole system at both classical and quantum level by a suitable reduction procedure. This suggests, in order to realise the space of states for quantum systems which are classically described on topologically non-trivial configuration spaces, to consider Hilbert spaces of exterior differential forms. Among the advantages of this formulation, we present—in the case of the group SU(2), how it is possible to obtain all unitary irreducible representations on such a Hilbert space, and how it is possible to write scalar Dirac-type operators, following an idea by K¨ahler

Noncommutative differential calculus for Moyal subalgebras

We build a differential calculus for subalgebras of the Moyal algebra on R^4 starting from a redundant differential calculus on the Moyal algebra, which is suitable for reduction. In some cases we find a frame of 1-forms which allows to realize the complex of forms as a tensor product of the noncommutative subalgebras with the external algebra Lambda^*.Comment: 13 pages, no figures. One reference added, minor correction

Expression patterns of cytokines, p53 and nitric oxide synthase enzymes in corpora lutea of pseudopregnant rabbits during spontaneous luteolysis

The gene expressions for macrophage chemoattractant protein-1 (MCP-1), interleukin (IL)-1 beta, IL-2 and p53 were examined by semi-quantitative RT-PCR in corpora lutea (CL) of rabbits during spontaneous luteolysis at days 13, 15, 18 and 22 of pseudopregnancy. In the same luteal tissue, total activity of nitric oxide (NO) synthase (NOS) and genes for both endothelial (eNOS) and inducible (iNOS) isoforms were also analysed. From day 13 to 15, MCP-1 and IL-1 beta mRNA levels rose (P < or = 0.01) almost 2-fold, and the transcript for p53 almost 8-fold, but then all dropped (P < or = 0.05) from day 18 onward. IL-2 mRNA abundance was higher (P < or = 0.01) on day 13 and then gradually declined. During luteolysis, eNOS mRNA decreased 40% (P < or = 0.05) by day 15, but thereafter remained unchanged, while iNOS mRNA was barely detectable and did not show any clear age-related pattern throughout the late luteal stages. Total NOS activity progressively increased (P < or = 0.01) from day 13 to 18 of pseudopregnancy and then dropped to the lowest (P < or = 0.01) levels on day 22. Luteal progesterone content also declined during CL regression from 411 to 17 pg/mg found on days 13 and 22 respectively, in parallel with the decrease in blood progesterone concentrations. These data further support a physiological role of NO as modulator of luteal demise in rabbits. Locally, luteal cytokines may be involved in the up-regulation of NOS activity, while downstream NO may inhibit steroroidogenesis and induce expression of p53 gene after removal of the protective action of progesterone

Prostaglandin receptors and role of G protein-activated pathways on corpora lutea of pseudopregnant rabbit in vitro

Studies were conducted to characterize receptors for prostaglandin (PG) F(2alpha) (PGF(2alpha)) and PGE(2), and the signalling pathways regulating total nitric oxide synthase activity and progesterone production in rabbit corpora lutea (CL) of different luteal stages. CL were obtained at days 4, 9 and 13 of pseudopregnancy and cultured in vitro for 2 h with PGF(2alpha) or PGE(2) and with activators and inhibitors of G protein (Gp), phospholipase C (PLC), protein kinase C (PKC), adenylate cyclase (AC) and protein kinase A (PKA). High affinity PGF(2alpha) receptor (K(d)=1.9+/-0.6 nM mean+/-s.e.m. ) concentrations increased (P< or =0.01) four- to five-fold from early to mid- and late-luteal phases (50.6+/-8.5, 188.3+/-36.1 and 231.4+/-38.8 fmol/mg protein respectively). By contrast, PGE(2) receptor (K(d)=1.6+/-0.5 nM) concentrations decreased (P< or =0.01) from day 4 to day 9 and 13 (27.5+/-7.7, 12.4+/-2.4 and 16.5+/-3.0 fmol/mg protein respectively). The Gp-dependent AC/PKA pathway was triggered only on day 4 CL, mimicking the PGE(2) treatment and increasing progesterone production. In both day 9 and day 13 CL, the Gp-activated PLC/PKC pathway evoked a luteolytic effect similar to that induced by PGF(2alpha). The time-dependent selective resistance to PGF(2alpha) and PGE(2) by rabbit CL is mediated by factors other than a lack of luteal receptor-ligand interactions

The beat of a fuzzy drum: fuzzy Bessel functions for the disc

The fuzzy disc is a matrix approximation of the functions on a disc which preserves rotational symmetry. In this paper we introduce a basis for the algebra of functions on the fuzzy disc in terms of the eigenfunctions of a properly defined fuzzy Laplacian. In the commutative limit they tend to the eigenfunctions of the ordinary Laplacian on the disc, i.e. Bessel functions of the first kind, thus deserving the name of fuzzy Bessel functions.Comment: 30 pages, 8 figure

DISCOVERING AND COMMUNICATING THE RATIONALIST ARCHITECTURE OF FORLÌ. AN INTEGRATED PROCESS

A partnership between the Department of Architecture of the University of Bologna and ATRIUM aimed at enhancing the knowledge and communication of the rationalist architecture, built in the city of Forlì during the Fascist regime. The importance of finding an interpretative key for this dissonant heritage, bearers of an “uncomfortable” memory but at the same time able to strongly characterize the architectural quality of cities, was a primary goal.The cooperation started with the development of a pilot project regarding three architectures considered iconic for this context but also able to foster more complex urban policies. The first deliverable of the programme was the search, record, and management of the archival materials related to the whole history of these buildings. The enormous amount of data acquired revealed the importance of working on a dual track, aimed at both the stakeholders involved in the management process of this heritage and those who experience it.For what concerns the “technical level” which is related to the knowledge field, the first challenge was to understand how to manage information boosting interoperability, guaranteeing easy access and above all making the research implementable. According to the “touristic level” instead, a further objective of the project was related to the communication of this heritage to a varied audience of visitors.</p