Holomorphic structures on the quantum projective line

We show that much of the structure of the 2-sphere as a complex curve survives the q-deformation and has natural generalizations to the quantum 2-sphere - which, with additional structures, we identify with the quantum projective line. Notably among these is the identification of a quantum homogeneous coordinate ring with the coordinate ring of the quantum plane. In parallel with the fact that positive Hochschild cocycles on the algebra of smooth functions on a compact oriented 2-dimensional manifold encode the information for complex structures on the surface, we formulate a notion of twisted positivity for twisted Hochschild and cyclic cocycles and exhibit an explicit twisted positive Hochschild cocycle for the complex structure on the sphere.Comment: 22 pages, no figures. Published in IMR

Moduli Spaces of Instantons on Toric Noncommutative Manifolds

We study analytic aspects of U(n) gauge theory over a toric noncommutative manifold $M_\theta$. We analyse moduli spaces of solutions to the self-dual Yang-Mills equations on U(2) vector bundles over four-manifolds $M_\theta$, showing that each such moduli space is either empty or a smooth Hausdorff manifold whose dimension we explicitly compute. In the special case of the four-sphere $S^4_\theta$ we find that the moduli space of U(2) instantons with fixed second Chern number $k$ is a smooth manifold of dimension $8k-3$.Comment: 44 pages, no figure

The Image of the Hyper City

Since the nineteenth and twentieth century, information has been pivotal both in the cultural tradition and then in the economic tradition. While the Fordism economic model and its specialisation requirements originated a simplistic zoning and single-use development approach to the design of a city. It, however, determined a fragmented growth of cities. Inevitably, the zoning as an urban strategy affected the architectural scale. Nevertheless, the idea of information, commercial goods and thereby people freely able to flow through the city allowed architects and urban designer to conceive new types of urban infrastructures. For example, trains, which were designed on the model of urban “arteries and veins.” Over time, the persistence of urban and architectural segmentation has strengthened social and economic inequalities among urban society. In addition, information has played a more vital role in this strengthening process. The technological achievements of the twenty-first century such as information technologies have significantly affected cities. The new informational patterns have provided new ways of designing, and in turn how societies experience cities. These “quantified cities” consist of digital data that dynamically interacts with “quantified human beings.” Consequently, a renewed urban semiotics is established, which is built around an alternate sociological comprehension. Is this new urban semiotics able to heal an ill and divided urban body? The paper will investigate a new concept of “quantified city” based on the notion of “Hyper-Reality,” and its inhabitants who are entering in a “post-human” condition while living in a dynamic urban environment. In particular, the critical analysis will be used as a “tool” for redefining the perception of the city (i.e., the image of the Hyper City) through inhabitants’ (post-humans’) relational patterns which are technologically mediated (i.e., Google Maps, Uber, Instagram, etc.). The more traditional notion of urbanisation is questioned with a focus on how the an urban society is embedded within the digital condition and the notion of a city

‘The Open Typology’: Towards Socially Sustainable Architectural and Care Types

One aspect that characterises the twenty-first century is its accomplishments such as better health-care systems, improved economies, a reduction in infant mortality and a growing number of adults living longer. However, these accomplishments can have a downside. For example, people are living longer while at the same time dementia rates are increasing significantly. With the increase in demand for high-dependency-related services, while at the same time costs are spiralling possibly out of control of societal budgets, there is a need for a shift in the care model. Additionally, difficulties in defining a clear dividing line between normal ageing and pathological ageing have led to a stigmatisation of older adults as a social and economic burden. This type of segregation and stigmatisation must be addressed to ensure future care delivery is inclusive. The positive benefits of an inclusive care system are both social and economic, and at an individual level it can positively impact upon an older adult’s mental and physical well-being

Noncommutative families of instantons

We construct $\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\theta(2,H)$ by $Sp_\theta(2)$.Comment: v2: Minor changes; computation of the pairing at the end of Sect. 5.1 improve

Sub-structure formation in starless cores

Motivated by recent observational searches of sub-structure in starless molecular cloud cores, we investigate the evolution of density perturbations on scales smaller than the Jeans length embedded in contracting isothermal clouds, adopting the same formalism developed for the expanding Universe and the solar wind. We find that initially small amplitude, Jeans-stable perturbations (propagating as sound waves in the absence of a magnetic field), are amplified adiabatically during the contraction, approximately conserving the wave action density, until they either become nonlinear and steepen into shocks at a time $t_{\rm nl}$, or become gravitationally unstable when the Jeans length decreases below the scale of the perturbations at a time $t_{\rm gr}$. We evaluate analytically the time $t_{\rm nl}$ at which the perturbations enter the non-linear stage using a Burgers' equation approach, and we verify numerically that this time marks the beginning of the phase of rapid dissipation of the kinetic energy of the perturbations. We then show that for typical values of the rms Mach number in molecular cloud cores, $t_{\rm nl}$ is smaller than $t_{\rm gr}$, and therefore density perturbations likely dissipate before becoming gravitational unstable. Solenoidal modes grow at a faster rate than compressible modes, and may eventually promote fragmentation through the formation of vortical structures.Comment: 8 pages, 4 figure

Dirac operators on all Podles quantum spheres

We construct spectral triples on all Podles quantum spheres. These noncommutative geometries are equivariant for a left action of $U_q(su(2))$ and are regular, even and of metric dimension 2. They are all isospectral to the undeformed round geometry of the 2-sphere. There is also an equivariant real structure for which both the commutant property and the first order condition for the Dirac operators are valid up to infinitesimals of arbitrary order.Comment: 24 pages, no figures; v2: minor correction

ADAS analysis of the differential emission measure structure of the inner solar corona. II. A study of the `quiet Sun' inhomogeneities from SOHO CDS-NIS spectra

We present a study of the differential emission measure (DEM) of a `quiet Sun' area observed in the extreme ultraviolet at normal incidence by the Coronal Diagnostic Spectrometer (CDS) on the SOHO spacecraft. The data used for this work were taken using the NISAT_S observing sequence. This takes the full wavelength ranges from both the NIS channels (308-381 Angtr. and 513-633 Angst.) with the 2 arcsec by 240 arcsec slit, which is the narrowest slit available, yielding the best spectral resolution. In this work we contrast the DEM from subregions of 2 by 80 arcsec$^2$ with that obtained from the mean spectrum of the whole raster (20 by 240 arcsec$^2$). We find that the DEM maintains essentially the same shape in the subregions, differing by a constant factor between 0.5 and 2 from the mean DEM, except in areas were the electron density is below $2 \times 10^7$ cm$^{-3}$ and downflow velocities of 50 km/s are found in the transition region. Such areas are likely to contain plasma departing from ionisation equilibrium, violating the basic assumptions underlying the DEM method. The comparison between lines of Li-like and Be-like ions may provide further evidence of departure from ionisation equilibrium. We find also that line intensities tend to be lower where velocities of the order of 30 km/s or higher are measured in transition region lines. The DEM analysis is also exploited to improve the line identification performed by Brooks et al (1999) and to investigate possible elemental abundance variations from region to region. We find that the plasma has composition close to photospheric in all the subregions examined.Comment: 18 pages, 9 figures, 7 tables. Table 5 is available only online. A copy of Table 5 can be found at http://webusers.ct.astro.it/acl/table5.dat. The ReadMe file is at http://webusers.ct.astro.it/acl/ReadMe. Accepted by Astronomy and Astrophysic

A Method for the Measurement of Digitizers’ Absolute Phase Error

A lot of engineering applications, from telecommunications to power systems, require accurate measurement of phase angles. Some of them, like synchrophasor measurement and calibration of instrument transformers with digital output, in order to reach high phase measurement accuracy, require the knowledge of phase error of digitizers. Therefore, in this paper a method for the measurement of digitizers’ absolute phase errors is proposed. It adopts a sinewave and two square waves, that are the digitizer sample clock and a phase reference signal. Combining the measurements of the relative phase differences between the adopted signals it is possible to accurately evaluate the absolute phase error of a digitize

A new approach to analyzing solar coronal spectra and updated collisional ionization equilibrium calculations. II. Additional ionization rate coefficients

We have reanalyzed SUMER observations of a parcel of coronal gas using new collisional ionization equilibrium (CIE) calculations. These improved CIE fractional abundances were calculated using state-of-the-art electron-ion recombination data for K-shell, L-shell, Na-like, and Mg-like ions of all elements from H through Zn and, additionally, Al- through Ar-like ions of Fe. They also incorporate the latest recommended electron impact ionization data for all ions of H through Zn. Improved CIE calculations based on these recombination and ionization data are presented here. We have also developed a new systematic method for determining the average emission measure ($EM$) and electron temperature ($T_e$) of an isothermal plasma. With our new CIE data and our new approach for determining average $EM$ and $T_e$, we have reanalyzed SUMER observations of the solar corona. We have compared our results with those of previous studies and found some significant differences for the derived $EM$ and $T_e$. We have also calculated the enhancement of coronal elemental abundances compared to their photospheric abundances, using the SUMER observations themselves to determine the abundance enhancement factor for each of the emitting elements. Our observationally derived first ionization potential (FIP) factors are in reasonable agreement with the theoretical model of Laming (2008).Comment: 147 pages (102 of which are online only tables and figures). Submitted to ApJ. Version 2 is updated addressing the referee's repor