A SURVEY ON FREE OBJECTS IN DIVISION RINGS AND IN DIVISION RINGS WITH AN INVOLUTION

Let D be a division ring with center k, and let D-dagger be its multiplicative group. We investigate the existence of free groups in D-dagger, and free algebras and free group algebras in D. We also go through the case when D has an involution * and consider the existence of free symmetric and unitary pairs in D-dagger.

FREE GROUP ALGEBRAS IN DIVISION RINGS

Let k be an algebraically closed field of characteristic zero and let L be an algebraic function field over k. Let sigma : L -> L be a k-automorphism of infinite order, and let D be the skew field of fractions of the skew polynomial ring L[t; sigma]. We show that D contains the group algebra kF of the free group F of rank 2.

Canonical Objects in Classes of (n, V)-Groupoids

AMS Subj. Classification: 03C05, 08B20

Contributos do postal ilustrado para a história do Free Card

Dissertação de mestrado em Ciências da Comunicação (área de especialização em Publicidade e Relações Públicas)

Statistical properties of subgroups of free groups

The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k-tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so-called graph-based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the raph-based distribution, while they are exponentially generic in the word-based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group.

Development of Free Space Method for Material Characterisation and GPR Study & A Case Study on Biological Samples

The thesis mainly focuses on material characterization in different environments: freely available samples taken in planar fonn, biological samples available in small quantities and buried objects.Free space method, finds many applications in the fields of industry, medicine and communication. As it is a non-contact method, it can be employed for monitoring the electrical properties of materials moving through a conveyor belt in real time. Also, measurement on such systems at high temperature is possible. NID theory can be applied to the characterization of thin films. Dielectric properties of thin films deposited on any dielectric substrate can be determined. ln chemical industry, the stages of a chemical reaction can be monitored online. Online monitoring will be more efficient as it saves time and avoids risk of sample collection.Dielectric contrast is one of the main factors, which decides the detectability of a system. lt could be noted that the two dielectric objects of same dielectric constant 3.2 (s, of plastic mine) placed in a medium of dielectric constant 2.56 (er of sand) could even be detected employing the time domain analysis of the reflected signal. This type of detection finds strategic importance as it provides solution to the problem of clearance of non-metallic mines. The demining of these mines using the conventional techniques had been proved futile. The studies on the detection of voids and leakage in pipes find many applications.The determined electrical properties of tissues can be used for numerical modeling of cells, microwave imaging, SAR test etc. All these techniques need the accurate determination of dielectric constant. ln the modem world, the use of cellular and other wireless communication systems is booming up. At the same time people are concemed about the hazardous effects of microwaves on living cells. The effect is usually studied on human phantom models. The construction of the models requires the knowledge of the dielectric parameters of the various body tissues. lt is in this context that the present study gains significance. The case study on biological samples shows that the properties of normal and infected body tissues are different. Even though the change in the dielectric properties of infected samples from that of normal one may not be a clear evidence of an ailment, it is an indication of some disorder.ln medical field, the free space method may be adapted for imaging the biological samples. This method can also be used in wireless technology. Evaluation of electrical properties and attenuation of obstacles in the path of RF waves can be done using free waves. An intelligent system for controlling the power output or frequency depending on the feed back values of the attenuation may be developed.The simulation employed in GPR can be extended for the exploration of the effects due to the factors such as the different proportion of water content in the soil, the level and roughness of the soil etc on the reflected signal. This may find applications in geological explorations. ln the detection of mines, a state-of-the art technique for scanning and imaging an active mine field can be developed using GPR. The probing antenna can be attached to a robotic arm capable of three degrees of rotation and the whole detecting system can be housed in a military vehicle. In industry, a system based on the GPR principle can be developed for monitoring liquid or gas through a pipe, as pipe with and without the sample gives different reflection responses. lt may also be implemented for the online monitoring of different stages of extraction and purification of crude petroleum in a plant.Since biological samples show fluctuation in the dielectric nature with time and other physiological conditions, more investigation in this direction should be done. The infected cells at various stages of advancement and the normal cells should be analysed. The results from these comparative studies can be utilized for the detection of the onset of such diseases. Studying the properties of infected tissues at different stages, the threshold of detectability of infected cells can be determined.

Buried-object detection using free-space time-domain near-field measurements

The detection of buried objects using time-domain freespace measurements was carried out in the near field. The location of a hidden object was determined from an analysis of the reflected signal. This method can be extended to detect any number of objects. Measurements were carried out in the X- and Ku-bands using ordinary rectangular pyramidal horn antennas of gain 15 dB. The same antenna was used as the transmitter and recei er. The experimental results were compared with simulated results by applying the two-dimensional finite-difference time-domain(FDTD)method, and agree well with each other. The dispersi e nature of the dielectric medium was considered for the simulation.

CETL's Re-Usable Learning Objects

Completed, available and free to use Learning Objects listed by subject area

Comparison of preferences for object properties in the rat using paired- and free-choice paradigms

A common method for testing preference for objects is to determine which of a pair of objects is approached first in a paired-choice paradigm. In comparison, many studies of preference for environmental enrichment (EE) devices have used paradigms in which total time spent with each of a pair of objects is used to determine preference. While each of these paradigms gives a specific measure of the preference for one object in comparison to another, neither method allows comparisons between multiple objects simultaneously. Since it is possible that several EE objects would be placed in a cage together to improve animal welfare, it is important to determine measures for rats' preferences in conditions that mimic this potential home cage environment. While it would be predicted that each type of measure would produce similar rankings of objects, this has never been tested empirically. In this study, we compared two paradigms: EE objects were either presented in pairs (paired-choice comparison) or four objects were presented simultaneously (simultaneous presentation comparison). We used frequency of first interaction and time spent with each object to rank the objects in the paired-choice experiment, and time spent with each object to rank the objects in the simultaneous presentation experiment. We also considered the behaviours elicited by the objects to determine if these might be contributing to object preference. We demonstrated that object ranking based on time spent with objects from the paired-choice experiment predicted object ranking in the simultaneous presentation experiment. Additionally, we confirmed that behaviours elicited were an important determinant of time spent with an object. This provides convergent evidence that both paired choice and simultaneous comparisons provide valid measures of preference for EE objects in rats. (C) 2007 Elsevier B.V. All rights reserved.

Threshold-free object and ground point separation in LIDAR data

Light Detection And Ranging (LIDAR) is an important modality in terrain and land surveying for many environmental, engineering and civil applications. This paper presents the framework for a recently developed unsupervised classification algorithm called Skewness Balancing for object and ground point separation in airborne LIDAR data. The main advantages of the algorithm are threshold-freedom and independence from LIDAR data format and resolution, while preserving object and terrain details. The framework for Skewness Balancing has been built in this contribution with a prediction model in which unknown LIDAR tiles can be categorised as “hilly” or “moderate” terrains. Accuracy assessment of the model is carried out using cross-validation with an overall accuracy of 95%. An extension to the algorithm is developed to address the overclassification issue for hilly terrain. For moderate terrain, the results show that from the classified tiles detached objects (buildings and vegetation) and attached objects (bridges and motorway junctions) are separated from bare earth (ground, roads and yards) which makes Skewness Balancing ideal to be integrated into geographic information system (GIS) software packages.

Holographic imaging with multimode, large free spectral range lasers in photorefractive sillenite crystals

The holographic imaging of rigid objects with diode lasers emitting in many wavelengths in a sillenite Bi12TiO20 photorefractive crystal is both theoretically an experimentally investigated. It is shown that, due to the multi-wavelength emission and the typically large free spectral range of this light source, contour fringes appear on the holographic image corresponding to the surface relief, even in single-exposure recordings. The influence of the number of emitted modes on the fringe width is analysed, and the possible applications of the contour fringes in the field of optical metrology are pointed out.

Instability of nonminimally coupled scalar fields in the spacetime of slowly rotating compact objects

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The Extremely Red, Young L Dwarf PSO J318.5338-22.8603: a Free-Floating Planetary-Mass Analog to Directly Imaged Young Gas-Giant Planets

We have discovered using Pan-STARRS1 an extremely red late-L dwarf, which has (J - K)(MKO) = 2.78 and (J - K) (2MASS) = 2.84, making it the reddest known field dwarf and second only to 2MASS J1207-39b among substellar companions. Near-IR spectroscopy shows a spectral type of L7 +/- 1 and reveals a triangular H-band continuum and weak alkali (K I and Na I) lines, hallmarks of low surface gravity. Near-IR astrometry from the Hawaii Infrared Parallax Program gives a distance of 24.6 +/- 1.4 pc and indicates a much fainter J-band absolute magnitude than field L dwarfs. The position and kinematics of PSO J318.5-22 point to membership in the beta Pic moving group. Evolutionary models give a temperature of 1160(-40)(+30) K and a mass of 6.5(-1.0)(+1.3) M-Jup, making PSO J318.5-22 one of the lowest mass free-floating objects in the solar neighborhood. This object adds to the growing list of low-gravity field L dwarfs and is the first to be strongly deficient in methane relative to its estimated temperature. Comparing their spectra suggests that young L dwarfs with similar ages and temperatures can have different spectral signatures of youth. For the two objects with well constrained ages (PSO J318.5-22 and 2MASS J0355+11), we find their temperatures are approximate to 400 K cooler than field objects of similar spectral type but their luminosities are similar, i.e., these young L dwarfs are very red and unusually cool but not "underluminous." Altogether, PSO J318.5-22 is the first free-floating object with the colors, magnitudes, spectrum, luminosity, and mass that overlap the young dusty planets around HR 8799 and 2MASS J1207-39

VISUAL-INERTIAL INTEGRATION FOR HUMAN MOTION TRACKING AND NAVIGATION IN FREE-LIVING ENVIRONMENTS

The aging population has become a burning issue for all modern societies around the world recently. There are two important issues existing now to be solved. One is how to continuously monitor the movements of those people having suffered a stroke in natural living environment for providing more valuable feedback to guide clinical interventions. The other one is how to guide those old people effectively when they are at home or inside other buildings and to make their life easier and convenient. Therefore, human motion tracking and navigation have been active research fields with the increasing number of elderly people. However, motion capture has been extremely challenging to go beyond laboratory environments and obtain accurate measurements of human physical activity especially in free-living environments, and navigation in free-living environments also poses some problems such as the denied GPS signal and the moving objects commonly presented in free-living environments. This thesis seeks to develop new technologies to enable accurate motion tracking and positioning in free-living environments. This thesis comprises three specific goals using our developed IMU board and the camera from the imaging source company: (1) to develop a robust and real-time orientation algorithm using only the measurements from IMU; (2) to develop a robust distance estimation in static free-living environments to estimate people’s position and navigate people in static free-living environments and simultaneously the scale ambiguity problem, usually appearing in the monocular camera tracking, is solved by integrating the data from the visual and inertial sensors; (3) in case of moving objects viewed by the camera existing in free-living environments, to firstly design a robust scene segmentation algorithm and then respectively estimate the motion of the vIMU system and moving objects. To achieve real-time orientation tracking, an Adaptive-Gain Orientation Filter (AGOF) is proposed in this thesis based on the basic theory of deterministic approach and frequency-based approach using only measurements from the newly developed MARG (Magnet, Angular Rate, and Gravity) sensors. To further obtain robust positioning, an adaptive frame-rate vision-aided IMU system is proposed to develop and implement fast vIMU ego-motion estimation algorithms, where the orientation is estimated in real time from MARG sensors in the first step and then used to estimate the position based on the data from visual and inertial sensors. In case of the moving objects viewed by the camera existing in free-living environments, a robust scene segmentation algorithm is firstly proposed to obtain position estimation and simultaneously the 3D motion of moving objects. Finally, corresponding simulations and experiments have been carried out.