Die Gebilde ersten und zweiten Grades der liniengeometrie in synthetischer Behandlung.

Available on demand as hard copy or computer file from Cornell University Library.

The modern preceptor or a general course of education : containing introductory treatises on language, arithmetic, bookkeeping, algebra, geometry, geography, astronomy, chronology, navigation, drawing, painting, &c., agriculture, geology, moral philosophy : for the use of schools /

Mode of access: Internet.

An introductory account of certain modern ideas and methods in plane analytical geometry,

Mode of access: Internet.

Re-thinking home economics : from modern to postmodern accounts of pedagogical bodies

Two perceptions of the marginality of home economics are widespread across educational and other contexts. One is that home economics and those who engage in its pedagogy are inevitably marginalised within patriarchal relations in education and culture. This is because home economics is characterised as women's knowledge, for the private domain of the home. The other perception is that only orthodox epistemological frameworks of inquiry should be used to interrogate this state of affairs. These perceptions have prompted leading theorists in the field to call for non-essentialist approaches to research in order to re-think the thinking that has produced this cul-de-sac positioning of home economics as a body of knowledge and a site of teacher practice. This thesis takes up the challenge of working to locate a space outside the frame of modernist research theory and methods, recognising that this shift in epistemology is necessary to unsettle the idea that home economics is inevitably marginalised. The purpose of the study is to reconfigure how we have come to think about home economics teachers and the profession of home economics as a site of cultural practice, in order to think it otherwise (Lather, 1991). This is done by exploring how the culture of home economics is being contested from within. To do so, the thesis uses a 'posthumanist' approach, which rejects the conception of the individual as a unitary and fixed entity, but instead as a subject in process, shaped by desires and language which are not necessarily consciously determined. This posthumanist project focuses attention on pedagogical body subjects as the 'unsaid' of home economics research. It works to transcend the modernist dualism of mind/body, and other binaries central to modernist work, including private/public, male/female,paid/unpaid, and valued/unvalued. In so doing, it refuses the simple margin/centre geometry so characteristic of current perceptions of home economics itself. Three studies make up this work. Studies one and two serve to document the disciplined body of home economics knowledge, the governance of which works towards normalisation of the 'proper' home economics teacher. The analysis of these accounts of home economics teachers by home economics teachers, reveals that home economics teachers are 'skilled' yet they 'suffer' for their profession. Further,home economics knowledge is seen to be complicit in reinforcing the traditional roles of masculinity and femininity, thereby reinforcing heterosexual normativity which is central to patriarchal society. The third study looks to four 'atypical'subjects who defy the category of 'proper' and 'normal' home economics teacher. These 'atypical' bodies are 'skilled' but fiercely reject the label of 'suffering'. The discussion of the studies is a feminist poststructural account, using Russo's (1994) notion of the grotesque body, which is emergent from Bakhtin's (1968) theory of the carnivalesque. It draws on the 'shreds' of home economics pedagogy,scrutinising them for their subversive, transformative potential. In this analysis, the giving and taking of pleasure and fun in the home economics classroom presents moments of surprise and of carnival. Foucault's notion of the construction of the ethical individual shows these 'atypical' bodies to be 'immoderate' yet striving hard to be 'continent' body subjects. This research captures moments of transgression which suggest that transformative moments are already embodied in the pedagogical practices of home economics teachers, and these can be 'seen' when re-looking through postmodemist lenses. Hence, the cultural practices ofhome economics as inevitably marginalised are being contested from within. Until now, home economics as a lived culture has failed to recognise possibilities for reconstructing its own field beyond the confines of modernity. This research is an example of how to think about home economics teachers and the profession as a reconfigured cultural practice. Future research about home economics as a body of knowledge and a site of teacher practice need not retell a simple story of oppression. Using postmodemist epistemologies is one way to provide opportunities for new ways of looking.

Computational information geometry and its applications

Digitization is the main feature of modern Information Science. Conjoining the digits and the coordinates, the relation between Information Science and high-dimensional space is consanguineous, and the information issues are transformed to the geometry problems in some high-dimensional spaces. From this basic idea, we propose Computational Information Geometry (CIG) to make information analysis and processing. Two kinds of applications of CIG are given, which are blurred image restoration and pattern recognition. Experimental results are satisfying. And in this paper, how to combine with groups of simple operators in some 2D planes to implement the geometrical computations in high-dimensional space is also introduced. Lots of the algorithms have been realized using software.

A Modern Differential Geometric Approach to Shape from Shading

How the visual system extracts shape information from a single grey-level image can be approached by examining how the information about shape is contained in the image. This technical report considers the characteristic equations derived by Horn as a dynamical system. Certain image critical points generate dynamical system critical points. The stable and unstable manifolds of these critical points correspond to convex and concave solution surfaces, giving more general existence and uniqueness results. A new kind of highly parallel, robust shape from shading algorithm is suggested on neighborhoods of these critical points. The information at bounding contours in the image is also analyzed.

A numerical study of automotive turbocharger mixed flow turbine inlet geometry for off design performance

Mixed flow turbines represent a potential solution to the increasing requirement for high pressure, low velocity ratio operation in turbocharger applications. While literature exists for the use of these turbines at such operating conditions, there is a lack of detailed design guidance for defining the basic geometry of the turbine, in particular, the cone angle – the angle at which the inlet of the mixed flow turbine is inclined to the axis. This investigates the effect and interaction of such mixed flow turbine design parameters.
Computational Fluids Dynamics was initially used to investigate the performance of a modern radial turbine to create a baseline for subsequent mixed flow designs. Existing experimental data was used to validate this model.
Using the CFD model, a number of mixed flow turbine designs were investigated. These included studies varying the cone angle and the associated inlet blade angle.
The results of this analysis provide insight into the performance of a mixed flow turbine with respect to cone and inlet blade angle.

Fluctuating commutative geometry

We use the framework of noncommutative geometry to define a discrete model for fluctuating geometry. Instead of considering ordinary geometry and its metric fluctuations, we consider generalized geometries where topology and dimension can also fluctuate. The model describes the geometry of spaces with a countable number n of points. The spectral principle of Connes and Chamseddine is used to define dynamics. We show that this simple model has two phases. The expectation value , the average number of points in the universe, is finite in one phase and diverges in the other. Moreover, the dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2. We also address another discrete model defined on a fixed d = 1 dimension, where topology fluctuates. We comment on a possible spontaneous localization of topology.

Euclid and his modern rivals (1879), Lewis Carrol: tradução e crítica

Pós-graduação em Educação para a Ciência - FC

The Islamic Crossed-Arch Domes in Cordoba: Geometry and Structural Analysis of the “Capilla de Villaviciosa”

Crossed-arch domes are a singular type of ribbed vaults. Their characteristic feature is that the ribs that form the vault are intertwined, forming polygons or stars, leaving an empty space in the centre. The earliest known vaults of this type are found in the Great Mosque of Córdoba, built ca. 960 a.C. The type spread through Spain, and the north of Africa in the 10th to the 16th Centuries, and was used by Guarini and Vittone in the 17th and 18th Centuries in Italy. However, it was used only in a few buildings. Though the literature about the structural behaviour of ribbed Gothic vaults is extensive, so far no structural analysis of crossed arch domes has been made. The purpose of this work is, first to show the way to attack such an analysis within the frame of Modern Limit Analysis of Masonry Structures (Heyman 1995), and then to apply the approach to study the stability of the dome of the Capilla de Villaviciosa. The work may give some clues to art and architectural historians to understand better the origin and development of Islamic dome architecture.

Geodesics without differential equations: general relativistic calculations for introductory modern physics classes

Introductory courses covering modem physics sometimes introduce some elementary ideas from general relativity, though the idea of a geodesic is generally limited to shortest Euclidean length on a curved surface of two spatial dimensions rather than extremal aging in spacetime. It is shown that Epstein charts provide a simple geometric picture of geodesics in one space and one time dimension and that for a hypothetical uniform gravitational field, geodesics are straight lines on a planar diagram. This means that the properties of geodesics in a uniform field can be calculated with only a knowledge of elementary geometry and trigonometry, thus making the calculation of some basic results of general relativity accessible to students even in an algebra-based survey course on physics.

Learning and Exploiting Camera Geometry for Computer Vision

This work explores the use of statistical methods in describing and estimating camera poses, as well as the information feedback loop between camera pose and object detection. Surging development in robotics and computer vision has pushed the need for algorithms that infer, understand, and utilize information about the position and orientation of the sensor platforms when observing and/or interacting with their environment.

The first contribution of this thesis is the development of a set of statistical tools for representing and estimating the uncertainty in object poses. A distribution for representing the joint uncertainty over multiple object positions and orientations is described, called the mirrored normal-Bingham distribution. This distribution generalizes both the normal distribution in Euclidean space, and the Bingham distribution on the unit hypersphere. It is shown to inherit many of the convenient properties of these special cases: it is the maximum-entropy distribution with fixed second moment, and there is a generalized Laplace approximation whose result is the mirrored normal-Bingham distribution. This distribution and approximation method are demonstrated by deriving the analytical approximation to the wrapped-normal distribution. Further, it is shown how these tools can be used to represent the uncertainty in the result of a bundle adjustment problem.

Another application of these methods is illustrated as part of a novel camera pose estimation algorithm based on object detections. The autocalibration task is formulated as a bundle adjustment problem using prior distributions over the 3D points to enforce the objects' structure and their relationship with the scene geometry. This framework is very flexible and enables the use of off-the-shelf computational tools to solve specialized autocalibration problems. Its performance is evaluated using a pedestrian detector to provide head and foot location observations, and it proves much faster and potentially more accurate than existing methods.

Finally, the information feedback loop between object detection and camera pose estimation is closed by utilizing camera pose information to improve object detection in scenarios with significant perspective warping. Methods are presented that allow the inverse perspective mapping traditionally applied to images to be applied instead to features computed from those images. For the special case of HOG-like features, which are used by many modern object detection systems, these methods are shown to provide substantial performance benefits over unadapted detectors while achieving real-time frame rates, orders of magnitude faster than comparable image warping methods.

The statistical tools and algorithms presented here are especially promising for mobile cameras, providing the ability to autocalibrate and adapt to the camera pose in real time. In addition, these methods have wide-ranging potential applications in diverse areas of computer vision, robotics, and imaging.

Coccosphere geometry measurements from culture experiments on the coccolithophore species Calcidiscus leptoporus, Calcidiscus quadriperforatus and Helicosphaera carteri

Coccolithophores are a key phytoplankton group that exhibit remarkable diversity in their biology, ecology, and calcitic exoskeletons (coccospheres). An understanding of the physiological processes that underpin coccosphere architecture is essential for maximizing the information that can be retrieved from their extensive fossil record. Using culturing experiments on four modern species from three long-lived families, we investigate how coccosphere architecture responds to population shifts from rapid (exponential) to slowed (stationary) growth phases as nutrients become depleted. These experiments reveal statistical differences in cell size and the number of coccoliths per cell between these two growth phases, specifically that cells in exponential-phase growth are typically smaller with fewer coccoliths, whereas cells experiencing growth-limiting nutrient depletion have larger coccosphere sizes and greater numbers of coccoliths per cell. Although the exact numbers are species-specific, these growth-phase shifts in coccosphere geometry are common to four different coccolithophore families (Calcidiscaceae, Coccolithaceae, Isochrysidaceae, Helicosphaeraceae), demonstrating that this is a core physiological response to nutrient depletion across a representative diversity of this phytoplankton group. Polarised light microscopy was used for all coccosphere geometry measurements.

Discovery of relict subglacial lakes and their geometry and mechanism of drainage

Recent proxy measurements reveal that subglacial lakes beneath modern ice sheets periodically store and release large volumes of water, providing an important but poorly understood influence on contemporary ice dynamics and mass balance. This is because direct observations of how lake drainage initiates and proceeds are lacking. Here we present physical evidence of the mechanism and geometry of lake drainage from the discovery of relict subglacial lakes formed during the last glaciation in Canada. These palaeo-subglacial lakes comprised shallow (<10 m) lenses of water perched behind ridges orientated transverse to ice flow. We show that lakes periodically drained through channels incised into bed substrate (canals). Canals sometimes trend into eskers that represent the depositional imprint of the last high-magnitude lake outburst. The subglacial lakes and channels are preserved on top of glacial lineations, indicating long-term re-organization of the subglacial drainage system and coupling to ice flow.