Closed expressions for Lie algebra invariants and finite transformations

A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements requires the use of projectors, whose coefficients are invariant polynomials. The detailed general forms of these projectors are given. Closed expressions for finite Lorentz transformations, both homogeneous and inhomogeneous, as well as for Galilei transformations, are found as examples.

Identification of lattices from genus of compact surface

In this work we propose procedures for the identification of structure of group associate lattices from fundamental region F4g of regular tessellations {4g; 4g} in the Euclidian plane and hyperbolic plane, where g denote genus of compact surface. © 2006 SBrT.

Fluxo do grupo de renormalização dos modelos-'alfa' e as álgebras de Lie contínuas

Pós-graduação em Física - IFT

A new method for calculating the convergent point of a moving group

Context. Convergent point (CP) search methods are important tools for studying the kinematic properties of open clusters and young associations whose members share the same spatial motion. Aims. We present a new CP search strategy based on proper motion data. We test the new algorithm on synthetic data and compare it with previous versions of the CP search method. As an illustration and validation of the new method we also present an application to the Hyades open cluster and a comparison with independent results. Methods. The new algorithm rests on the idea of representing the stellar proper motions by great circles over the celestial sphere and visualizing their intersections as the CP of the moving group. The new strategy combines a maximum-likelihood analysis for simultaneously determining the CP and selecting the most likely group members and a minimization procedure that returns a refined CP position and its uncertainties. The method allows one to correct for internal motions within the group and takes into account that the stars in the group lie at different distances. Results. Based on Monte Carlo simulations, we find that the new CP search method in many cases returns a more precise solution than its previous versions. The new method is able to find and eliminate more field stars in the sample and is not biased towards distant stars. The CP solution for the Hyades open cluster is in excellent agreement with previous determinations.

Galaxy triplets in Sloan Digital Sky Survey Data Release 7: II. A connection with compact groups?

We analyse a sample of 71 triplets of luminous galaxies derived from the work of O’Mill et al. We compare the properties of triplets and their members with those of control samples of compact groups, the 10 brightest members of rich clusters and galaxies in pairs. The triplets are restricted to have members with spectroscopic redshifts in the range 0.01 ≤ z ≤ 0.14 and absolute r-band luminosities brighter than Mr = −20.5. For these member galaxies, we analyse the stellar mass content, the star formation rates, the Dn(4000) parameter and (Mg − Mr) colour index. Since galaxies in triplets may finally merge in a single system, we analyse different global properties of these systems. We calculate the probability that the properties of galaxies in triplets are strongly correlated. We also study total star formation activity and global colours, and define the triplet compactness as a measure of the percentage of the system total area that is filled by the light of member galaxies. We concentrate in the comparison of our results with those of compact groups to assess how the triplets are a natural extension of these compact systems. Our analysis suggests that triplet galaxy members behave similarly to compact group members and galaxies in rich clusters. We also find that systems comprising three blue, star-forming, young stellar population galaxies (blue triplets) are most probably real systems and not a chance configuration of interloping galaxies. The same holds for triplets composed of three red, non-star-forming galaxies, showing the correlation of galaxy properties in these systems. From the analysis of the triplet as a whole, we conclude that, at a given total stellar mass content, triplets show a total star formation activity and global colours similar to compact groups. However, blue triplets show a high total star formation activity with a lower stellar mass content. From an analysis of the compactness parameter of the systems we find that light is even more concentrated in triplets than in compact groups. We propose that triplets composed of three luminous galaxies, should not be considered as an analogous of galaxy pairs with a third extra member, but rather they are a natural extension of compact groups.

The Enhanced Single-dish Control System and wide surveys of compact sources

The Italian radio telescopes currently undergo a major upgrade period in response to the growing demand for deep radio observations, such as surveys on large sky areas or observations of vast samples of compact radio sources. The optimised employment of the Italian antennas, at first constructed mainly for VLBI activities and provided with a control system (FS – Field System) not tailored to single-dish observations, required important modifications in particular of the guiding software and data acquisition system. The production of a completely new control system called ESCS (Enhanced Single-dish Control System) for the Medicina dish started in 2007, in synergy with the software development for the forthcoming Sardinia Radio Telescope (SRT). The aim is to produce a system optimised for single-dish observations in continuum, spectrometry and polarimetry. ESCS is also planned to be installed at the Noto site. A substantial part of this thesis work consisted in designing and developing subsystems within ESCS, in order to provide this software with tools to carry out large maps, spanning from the implementation of On-The-Fly fast scans (following both conventional and innovative observing strategies) to the production of single-dish standard output files and the realisation of tools for the quick-look of the acquired data. The test period coincided with the commissioning phase for two devices temporarily installed – while waiting for the SRT to be completed – on the Medicina antenna: a 18-26 GHz 7-feed receiver and the 14-channel analogue backend developed for its use. It is worth stressing that it is the only K-band multi-feed receiver at present available worldwide. The commissioning of the overall hardware/software system constituted a considerable section of the thesis work. Tests were led in order to verify the system stability and its capabilities, down to sensitivity levels which had never been reached in Medicina using the previous observing techniques and hardware devices. The aim was also to assess the scientific potential of the multi-feed receiver for the production of wide maps, exploiting its temporary availability on a mid-sized antenna. Dishes like the 32-m antennas at Medicina and Noto, in fact, offer the best conditions for large-area surveys, especially at high frequencies, as they provide a suited compromise between sufficiently large beam sizes to cover quickly large areas of the sky (typical of small-sized telescopes) and sensitivity (typical of large-sized telescopes). The KNoWS (K-band Northern Wide Survey) project is aimed at the realisation of a full-northern-sky survey at 21 GHz; its pilot observations, performed using the new ESCS tools and a peculiar observing strategy, constituted an ideal test-bed for ESCS itself and for the multi-feed/backend system. The KNoWS group, which I am part of, supported the commissioning activities also providing map-making and source-extraction tools, in order to complete the necessary data reduction pipeline and assess the general system scientific capabilities. The K-band observations, which were carried out in several sessions along the December 2008-March 2010 period, were accompanied by the realisation of a 5 GHz test survey during the summertime, which is not suitable for high-frequency observations. This activity was conceived in order to check the new analogue backend separately from the multi-feed receiver, and to simultaneously produce original scientific data (the 6-cm Medicina Survey, 6MS, a polar cap survey to complete PMN-GB6 and provide an all-sky coverage at 5 GHz).

Diffusion maps in the Subriemannian motion group and perceptual grouping

Il presente lavoro è motivato dal problema della constituzione di unità percettive a livello della corteccia visiva primaria V1. Si studia dettagliatamente il modello geometrico di Citti-Sarti con particolare attenzione alla modellazione di fenomeni di associazione visiva. Viene studiato nel dettaglio un modello di connettività. Il contributo originale risiede nell'adattamento del metodo delle diffusion maps, recentemente introdotto da Coifman e Lafon, alla geometria subriemanniana della corteccia visiva. Vengono utilizzati strumenti di teoria del potenziale, teoria spettrale, analisi armonica in gruppi di Lie per l'approssimazione delle autofunzioni dell'operatore del calore sul gruppo dei moti rigidi del piano. Le autofunzioni sono utilizzate per l'estrazione di unità percettive nello stimolo visivo. Sono presentate prove sperimentali e originali delle capacità performanti del metodo.

Canonical group quantization and boundary conditions

In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

Contribution to the Analysis, Design and Assessment of Compact Antenna Test Ranges At Millimeter Wavelengths - Contribución al Análisis, Diseño y Caracterización de Sistemas de Medida de Antenas en Rango Compacto para Frecuencias Milimétricas

This Doctoral Thesis entitled Contribution to the analysis, design and assessment of compact antenna test ranges at millimeter wavelengths aims to deepen the knowledge of a particular antenna measurement system: the compact range, operating in the frequency bands of millimeter wavelengths. The thesis has been developed at Radiation Group (GR), an antenna laboratory which belongs to the Signals, Systems and Radiocommunications department (SSR), from Technical University of Madrid (UPM). The Radiation Group owns an extensive experience on antenna measurements, running at present four facilities which operate in different configurations: Gregorian compact antenna test range, spherical near field, planar near field and semianechoic arch system. The research work performed in line with this thesis contributes the knowledge of the first measurement configuration at higher frequencies, beyond the microwaves region where Radiation Group features customer-level performance. To reach this high level purpose, a set of scientific tasks were sequentially carried out. Those are succinctly described in the subsequent paragraphs. A first step dealed with the State of Art review. The study of scientific literature dealed with the analysis of measurement practices in compact antenna test ranges in addition with the particularities of millimeter wavelength technologies. Joint study of both fields of knowledge converged, when this measurement facilities are of interest, in a series of technological challenges which become serious bottlenecks at different stages: analysis, design and assessment. Thirdly after the overview study, focus was set on Electromagnetic analysis algorithms. These formulations allow to approach certain electromagnetic features of interest, such as field distribution phase or stray signal analysis of particular structures when they interact with electromagnetic waves sources. Properly operated, a CATR facility features electromagnetic waves collimation optics which are large, in terms of wavelengths. Accordingly, the electromagnetic analysis tasks introduce an extense number of mathematic unknowns which grow with frequency, following different polynomic order laws depending on the used algorithmia. In particular, the optics configuration which was of our interest consisted on the reflection type serrated edge collimator. The analysis of these devices requires a flexible handling of almost arbitrary scattering geometries, becoming this flexibility the nucleus of the algorithmia’s ability to perform the subsequent design tasks. This thesis’ contribution to this field of knowledge consisted on reaching a formulation which was powerful at the same time when dealing with various analysis geometries and computationally speaking. Two algorithmia were developed. While based on the same principle of hybridization, they reached different order Physics performance at the cost of the computational efficiency. Inter-comparison of their CATR design capabilities was performed, reaching both qualitative as well as quantitative conclusions on their scope. In third place, interest was shifted from analysis - design tasks towards range assessment. Millimetre wavelengths imply strict mechanical tolerances and fine setup adjustment. In addition, the large number of unknowns issue already faced in the analysis stage appears as well in the on chamber field probing stage. Natural decrease of dynamic range available by semiconductor millimeter waves sources requires in addition larger integration times at each probing point. These peculiarities increase exponentially the difficulty of performing assessment processes in CATR facilities beyond microwaves. The bottleneck becomes so tight that it compromises the range characterization beyond a certain limit frequency which typically lies on the lowest segment of millimeter wavelength frequencies. However the value of range assessment moves, on the contrary, towards the highest segment. This thesis contributes this technological scenario developing quiet zone probing techniques which achieves substantial data reduction ratii. Collaterally, it increases the robustness of the results to noise, which is a virtual rise of the setup’s available dynamic range. In fourth place, the environmental sensitivity of millimeter wavelengths issue was approached. It is well known the drifts of electromagnetic experiments due to the dependance of the re sults with respect to the surrounding environment. This feature relegates many industrial practices of microwave frequencies to the experimental stage, at millimeter wavelengths. In particular, evolution of the atmosphere within acceptable conditioning bounds redounds in drift phenomena which completely mask the experimental results. The contribution of this thesis on this aspect consists on modeling electrically the indoor atmosphere existing in a CATR, as a function of environmental variables which affect the range’s performance. A simple model was developed, being able to handle high level phenomena, such as feed - probe phase drift as a function of low level magnitudes easy to be sampled: relative humidity and temperature. With this model, environmental compensation can be performed and chamber conditioning is automatically extended towards higher frequencies. Therefore, the purpose of this thesis is to go further into the knowledge of millimetre wavelengths involving compact antenna test ranges. This knowledge is dosified through the sequential stages of a CATR conception, form early low level electromagnetic analysis towards the assessment of an operative facility, stages for each one of which nowadays bottleneck phenomena exist and seriously compromise the antenna measurement practices at millimeter wavelengths.

Compact steep-spectrum sources and the unified scheme.

The compact steep-spectrum sources (CSSs) are an interesting class of objects which are of subgalactic dimensions; they occur more frequently in high-frequency surveys because their spectra often turn over at lower frequencies. We have estimated the symmetry parameters of a well-defined sample of CSSs and compared these with the larger 3CR sources of similar luminosity to understand the evolution and the consistency of CSSs with the unified scheme. We suggest that the majority of CSSs are likely to be young sources advancing outward through an asymmetric, inhomogeneous environment to form the larger ones. The radio properties of the CSSs are consistent with the unified scheme, where the axes of the quasars are seen closer to the line of sight while the radio galaxies lie closer to the plane of the sky. We discuss how radio polarization observations may be used to probe whether the physical conditions in the central regions of the CSSs are different from the larger ones. We present a simple scenario where the depolarization and high rotation measures seen in many CSSs can be consistent with the low rotation measures of cores in the more extended quasars and suggest further observations to test this scenario.

On formality of Sasakian manifolds

We investigate some topological properties, in particular formality, of compact Sasakian manifolds. Answering some questions raised by Boyer and Galicki, we prove that all higher (than three) Massey products on any compact Sasakian manifold vanish. Hence, higher Massey products do obstruct Sasakian structures. Using this, we produce a method of constructing simply connected K-contact non-Sasakian manifolds. On the other hand, for every n > 3, we exhibit the first examples of simply connected compact Sasakian manifolds of dimension 2n + 1 that are non-formal. They are non-formal because they have a non-zero triple Massey product. We also prove that arithmetic lattices in some simple Lie groups cannot be the fundamental group of a compact Sasakian manifold.

Paleoecology, Diagenesis and Biological Affinity of Tetradiids in the Upper Ordovician (Sandbian) Black River Group of the Kingston Area, Ontario, Canada

Tetradiids are a group of colonial, tubular fossils that occur globally in Middle to Upper Ordovician strata. Tetradiids were first described as a type of tabulate coral; however, based on their four-fold symmetry, division, and presence of a central-sparry canal, they were recently reinterpreted as a florideophyte rhodophyte algae, a reinterpretation that is tested in this thesis. This study focused on understanding the affinity and taphonomy of this order of fossil. Research was conducted by stratigraphic and petrographic analyses of the Black River Group in the Kingston, Ontario region. Tetradiid occurrences were divided into fragment or colonial, with three morphologies of tetradiids described (Tetradium, Phytopsis and Paratetradium). Morphology is specific to depositional environment, with compact Tetradium consistently within ooid grainstones and open branching Phytopsis and chained Paratetradium consistently within mudstones. Two types of patch reefs were recognized: a Paratetradium bioherm, and a Paratetradium, Phytopsis, stromatolite bioherm. The presence of bioherms implies that tetradiids were capable of hypercalcifying. Preservation styles of tetradiids were investigated, and were compared to brachiopods, echinoderms, mollusks, and ooids. Tetradiids were preferentially preserved as molds and demonstrated complete dissolution of skeletal material. Rare specimens, however, demonstrated preserved horizontal partitions, central plates, and a double wall. Skeletal molds were filled with either calcite spar, mud or encrusted by a cryptomicrobial colony. Both calcitic and aragonitic ooids were discovered. The co-occurrence of aragonitic ooids, aragonitic crytodontids, and the evolution of aragonitic, hypercalcifying tetradiids is interpreted as representing the geochemical favoring of aragonite and HMC in a time of global calcite seas. The geochemical favoring of aragonite is interpreted to be independent to global Mg: Ca ratios, but was the result of increased saturation levels and temperature driven by high atmospheric pCO2. Based on the presence of epitheca, tabulae, septa, and the commonality of growth forms, tetradiids are interpreted as an order of Cnidaria. The evolution of an aragonitic skeleton in tetradiids is interpreted to be the result of de novo acquisition of a skeleton from an unmineralized clade.

Operator, organizational, DS, and GS maintenance manual : air conditioner, compact, vertical, 208V, 3 phase, 18,000 BTUH cooling, 12,000 BTUH heating, (Trane models), 50/60 hertz model CE20VAL6, FSN 4120-973-4589, 400 hertz model CE20VAL4, FSN 4120-858-5795.

"November 1969."

Jazz Innovations II with Kidz Boplicity Enso and the Ted Poor Group May 19, 2016

Concert Program

Galaxy threshing and the origin of ultra-compact dwarf galaxies in the Fornax cluster

A recent all-object spectroscopic survey centred on the Fornax cluster of galaxies has discovered a population of subluminous and extremely compact members, called 'ultra-compact dwarf' (UCD) galaxies. In order to clarify the origin of these objects, we have used self-consistent numerical simulations to study the dynamical evolution a nucleated dwarf galaxy would undergo if orbiting the centre of the Fornax cluster and suffering from its strong tidal gravitational field. We find that the outer stellar components of a nucleated dwarf are removed by the strong tidal field of the cluster, whereas the nucleus manages to survive as a result of its initially compact nature. The developed naked nucleus is found to have physical properties (e. g. size and mass) similar to those observed for UCDs. We also find that although this formation process does not have a strong dependence on the initial total luminosity of the nucleated dwarf, it does depend on the radial density profile of the dark halo in the sense that UCDs are less likely to be formed from dwarfs embedded in dark matter haloes with central 'cuspy' density profiles. Our simulations also suggest that very massive and compact stellar systems can be rapidly and efficiently formed in the central regions of dwarfs through the merging of smaller star clusters. We provide some theoretical predictions on the total number and radial number density profile of UCDs in a cluster and their dependencies on cluster masses.