Geometrische Analysis /

Anhang: Versuch einer Wiederherstellung der Bücher des Apollonius von Perga von den Berührungen / von J. P. Grüson. Analytische Auflösung der Aufgabe: Einen Kreis zu Finden, der drei Anderer in einer ebene liegende Kreise berührt / von herrn Gergonnen. Vereinfachung und Erweiterung der Euklidische Geometrie.

Masculinity-femininity as a national characteristic and its relationship with national agoraphobic fear levels: Fodor's sex role hypothesis revitalized

Hofstede's dimension of national culture termed Masculinity-Femininity [Hofstede (1991). Cultures and organizations: software of the mind. London: McGraw-Hill] is proposed to be of relevance for understanding national-level differences in self-assessed agoraphobic fears. This prediction is based on the classical work of Fodor [Fodor (1974). In: V. Franks & V. Burtle (Eds.), Women in therapy: new psychotherapies for a changing society. New York: Brunner/Mazel]. A unique data set comprising 11 countries (total N = 5491 students) provided the opportunity of scrutinizing this issue. It was hypothesized and found that national Masculinity (the degree to which cultures delineate sex roles, with masculine or tough societies making clearer differentiations between the sexes than feminine or modest societies do) would correlate positively with national agoraphobic fear levels (as assessed with the Fear Survey Schedule-III). Following the correction for sex and age differences across national samples, a significant and large effect-sized national-level (ecological) r = +0.67 (P = 0.01) was found. A highly feminine society such as Sweden had the lowest, whereas the champion among the masculine societies, Japan, had the highest national Agoraphobic fear score. (C) 2003 Elsevier Science Ltd. All rights reserved.

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.

Magnification factors for the GTM algorithm

The Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) has been introduced as a principled alternative to the Self-Organizing Map (SOM). As well as avoiding a number of deficiencies in the SOM, the GTM algorithm has the key property that the smoothness properties of the model are decoupled from the reference vectors, and are described by a continuous mapping from a lower-dimensional latent space into the data space. Magnification factors, which are approximated by the difference between code-book vectors in SOMs, can therefore be evaluated for the GTM model as continuous functions of the latent variables using the techniques of differential geometry. They play an important role in data visualization by highlighting the boundaries between data clusters, and are illustrated here for both a toy data set, and a problem involving the identification of crab species from morphological data.

Magnification factors for the SOM and GTM algorithms

Magnification factors specify the extent to which the area of a small patch of the latent (or `feature') space of a topographic mapping is magnified on projection to the data space, and are of considerable interest in both neuro-biological and data analysis contexts. Previous attempts to consider magnification factors for the self-organizing map (SOM) algorithm have been hindered because the mapping is only defined at discrete points (given by the reference vectors). In this paper we consider the batch version of SOM, for which a continuous mapping can be defined, as well as the Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) which has been introduced as a probabilistic formulation of the SOM. We show how the techniques of differential geometry can be used to determine magnification factors as continuous functions of the latent space coordinates. The results are illustrated here using a problem involving the identification of crab species from morphological data.

Modeling geometric rules in object based models:an XML / GML approach

Most object-based approaches to Geographical Information Systems (GIS) have concentrated on the representation of geometric properties of objects in terms of fixed geometry. In our road traffic marking application domain we have a requirement to represent the static locations of the road markings but also enforce the associated regulations, which are typically geometric in nature. For example a give way line of a pedestrian crossing in the UK must be within 1100-3000 mm of the edge of the crossing pattern. In previous studies of the application of spatial rules (often called 'business logic') in GIS emphasis has been placed on the representation of topological constraints and data integrity checks. There is very little GIS literature that describes models for geometric rules, although there are some examples in the Computer Aided Design (CAD) literature. This paper introduces some of the ideas from so called variational CAD models to the GIS application domain, and extends these using a Geography Markup Language (GML) based representation. In our application we have an additional requirement; the geometric rules are often changed and vary from country to country so should be represented in a flexible manner. In this paper we describe an elegant solution to the representation of geometric rules, such as requiring lines to be offset from other objects. The method uses a feature-property model embraced in GML 3.1 and extends the possible relationships in feature collections to permit the application of parameterized geometric constraints to sub features. We show the parametric rule model we have developed and discuss the advantage of using simple parametric expressions in the rule base. We discuss the possibilities and limitations of our approach and relate our data model to GML 3.1. © 2006 Springer-Verlag Berlin Heidelberg.

Mild wear in dry and lubricated sliding systems

A vertical pin on horizontal disc machine has been used to conduct a series of experiments in air under dry and lubricating sliding conditions. For dry sliding low load and speed combinations were chosen to correspond to the mild wear region below the Welsh T1 transition. Lubricated tests were conducted under flooded conditions using Esso Technical White Oil alone and with a 0.1% stearic acid additive, for load and speed ranges that produced substantial amounts of asperity contact and thus a boundary lubricated regime of wear. The test material in all cases was AISI 52100 steel, for unlubricated sliding subjected to loads from 5 to 50 N and a range of speeds from 10-3 to 1.0 ms-1, and for lubricated sliding loads of 50 to 123 N and for speeds of 10-2 to 1.0 ms-1. Unlubricated wear debris was found to be a mixture of -Fe_2O_3 and -Fe. Unlubricated wear was found to occur via a thin film logarithmic oxide growth followed by agglomeration into thicker oxide plateaux 2 to 10 m in thickness. Lubricated wear occurred via thick film diffusion controlled oxide growth producing homogeneous oxide plateaux 0.1 to 0.2 m in thickness. X-ray photoelectron spectroscopy identified the presence of a surface film on pins worn in White Oil with stearic acid, which is thought to be iron stearate. A model has been developed for unlubricated wear based upon the postulated growth of thin film oxides by a logarithmic rate law. The importance of sliding geometry and environment to the dominant wear mechanism has been illustrated.

Investigating viscous fluid flow in an internal mixer using computational fluid dynamics

This thesis presents an effective methodology for the generation of a simulation which can be used to increase the understanding of viscous fluid processing equipment and aid in their development, design and optimisation. The Hampden RAPRA Torque Rheometer internal batch twin rotor mixer has been simulated with a view to establishing model accuracies, limitations, practicalities and uses. As this research progressed, via the analyses several 'snap-shot' analysis of several rotor configurations using the commercial code Polyflow, it was evident that the model was of some worth and its predictions are in good agreement with the validation experiments, however, several major restrictions were identified. These included poor element form, high man-hour requirements for the construction of each geometry and the absence of the transient term in these models. All, or at least some, of these limitations apply to the numerous attempts to model internal mixes by other researchers and it was clear that there was no generally accepted methodology to provide a practical three-dimensional model which has been adequately validated. This research, unlike others, presents a full complex three-dimensional, transient, non-isothermal, generalised non-Newtonian simulation with wall slip which overcomes these limitations using unmatched ridding and sliding mesh technology adapted from CFX codes. This method yields good element form and, since only one geometry has to be constructed to represent the entire rotor cycle, is extremely beneficial for detailed flow field analysis when used in conjunction with user defined programmes and automatic geometry parameterisation (AGP), and improves accuracy for investigating equipment design and operation conditions. Model validation has been identified as an area which has been neglected by other researchers in this field, especially for time dependent geometries, and has been rigorously pursued in terms of qualitative and quantitative velocity vector analysis of the isothermal, full fill mixing of generalised non-Newtonian fluids, as well as torque comparison, with a relatively high degree of success. This indicates that CFD models of this type can be accurate and perhaps have not been validated to this extent previously because of the inherent difficulties arising from most real processes.

Non-linear hierarchical visualisation

This thesis applies a hierarchical latent trait model system to a large quantity of data. The motivation for it was lack of viable approaches to analyse High Throughput Screening datasets which maybe include thousands of data points with high dimensions. High Throughput Screening (HTS) is an important tool in the pharmaceutical industry for discovering leads which can be optimised and further developed into candidate drugs. Since the development of new robotic technologies, the ability to test the activities of compounds has considerably increased in recent years. Traditional methods, looking at tables and graphical plots for analysing relationships between measured activities and the structure of compounds, have not been feasible when facing a large HTS dataset. Instead, data visualisation provides a method for analysing such large datasets, especially with high dimensions. So far, a few visualisation techniques for drug design have been developed, but most of them just cope with several properties of compounds at one time. We believe that a latent variable model (LTM) with a non-linear mapping from the latent space to the data space is a preferred choice for visualising a complex high-dimensional data set. As a type of latent variable model, the latent trait model can deal with either continuous data or discrete data, which makes it particularly useful in this domain. In addition, with the aid of differential geometry, we can imagine the distribution of data from magnification factor and curvature plots. Rather than obtaining the useful information just from a single plot, a hierarchical LTM arranges a set of LTMs and their corresponding plots in a tree structure. We model the whole data set with a LTM at the top level, which is broken down into clusters at deeper levels of t.he hierarchy. In this manner, the refined visualisation plots can be displayed in deeper levels and sub-clusters may be found. Hierarchy of LTMs is trained using expectation-maximisation (EM) algorithm to maximise its likelihood with respect to the data sample. Training proceeds interactively in a recursive fashion (top-down). The user subjectively identifies interesting regions on the visualisation plot that they would like to model in a greater detail. At each stage of hierarchical LTM construction, the EM algorithm alternates between the E- and M-step. Another problem that can occur when visualising a large data set is that there may be significant overlaps of data clusters. It is very difficult for the user to judge where centres of regions of interest should be put. We address this problem by employing the minimum message length technique, which can help the user to decide the optimal structure of the model. In this thesis we also demonstrate the applicability of the hierarchy of latent trait models in the field of document data mining.

Engineering liposomal systems to develop solubility enhancing technology

This research primarily focused on identifying the formulation parameters which control the efficacy of liposomes as delivery systems to enhance the delivery of poorly soluble drugs. Preliminary studies focused on the drug loading of ibuprofen within vesicle systems. Initially both liposomal and niosomal formulations were screened for their drug-loading capacity: liposomal systems were shown to offer significantly higher ibuprofen loading and thereafter lipid based systems were further investigated. Given the key role cholesterol is known to play within the stability of bilayer vesicles. the optimum cholesterol content in terms of drug loading and release of poorly soluble drugs was then investigated. From these studies a concentration of 11 total molar % of cholesterol was used as a benchmark for all further formulations. Investigating the effect of liposomc composition on several low solubility drugs, drug loading was shown to be enhanced by adopting longer chain length lipids. cationic lipids and. decreasing drug molecular weight. Drug release was increased by using cationic lipids and lower molecular weight of drug; conversely, a reduction was noted when employing longer chain lipids thus supporting the rational of longer chain lipids producing more stable liposomes, a theory also supported by results obtained via Langmuir studies· although it was revealed that stability is also dependent on geometric features associated with the lipid chain moiety. Interestingly, reduction in drug loading appeared to be induced when symmetrical phospholipids were substituted for lipids constituting asymmetrical alkyl chain groups thus further highlighting the importance of lipid geometry. Combining a symmetrical lipid with an asymmetrical derivative enhanced encapsulation of a hydrophobic drug while reducing that of another suggesting the importance of drug characteristics. Phosphatidylcholine liposornes could successfully be prepared (and visualised using transmission electron microscopy) from fatty alcohols therefore offering an alternative liposomal stabiliser to cholesterol. Results obtained revealed that liposomes containing tetradecanol within their formulation shares similar vesicle size, drug encapsulation, surface charge. and toxicity profiles as liposomes formulated with cholesterol, however the tetradecanol preparation appeared to release considerably more drug during stability studies. Langmuir monolayer studies revealed that the condensing influence by tetradecanol is less than compared with cholesterol suggesting that this reduced intercalation by the former could explain why the tetradecanol formulation released more drug compared with cholesterol formulations. Environmental scanning electron microscopy (ESEM) was used to analyse the morphology and stability of liposomes. These investigations indicated that the presence of drugs within the liposomal bilayer were able to enhance the stability of the bilayers against collapse under reduced hydration conditions. In addition the presence of charged lipids within the formulation under reduced hydration conditions compared with its neutral counterpart. However the applicability of using ESEM as a new method to investigate liposome stability appears less valid than first hoped since the results are often open to varied interpretation and do not provide a robust set of data to support conclusions in some cases.

PC Points and their Application to Vector Optimization

AMS subject classification: 90C29, 90C48

Robust and high current cold electron source based on carbon nanotube field emitters and electron multiplier microchannel plate

The aim of this research was to demonstrate a high current and stable field emission (FE) source based on carbon nanotubes (CNTs) and electron multiplier microchannel plate (MCP) and design efficient field emitters. In recent years various CNT based FE devices have been demonstrated including field emission displays, x-ray source and many more. However to use CNTs as source in high powered microwave (HPM) devices higher and stable current in the range of few milli-amperes to amperes is required. To achieve such high current we developed a novel technique of introducing a MCP between CNT cathode and anode. MCP is an array of electron multipliers; it operates by avalanche multiplication of secondary electrons, which are generated when electrons strike channel walls of MCP. FE current from CNTs is enhanced due to avalanche multiplication of secondary electrons and in addition MCP also protects CNTs from irreversible damage during vacuum arcing. Conventional MCP is not suitable for this purpose due to the lower secondary emission properties of their materials. To achieve higher and stable currents we have designed and fabricated a unique ceramic MCP consisting of high SEY materials. The MCP was fabricated utilizing optimum design parameters, which include channel dimensions and material properties obtained from charged particle optics (CPO) simulation. Child Langmuir law, which gives the optimum current density from an electron source, was taken into account during the system design and experiments. Each MCP channel consisted of MgO coated CNTs which was chosen from various material systems due to its very high SEY. With MCP inserted between CNT cathode and anode stable and higher emission current was achieved. It was ∼25 times higher than without MCP. A brighter emission image was also evidenced due to enhanced emission current. The obtained results are a significant technological advance and this research holds promise for electron source in new generation lightweight, efficient and compact microwave devices for telecommunications in satellites or space applications. As part of this work novel emitters consisting of multistage geometry with improved FE properties were was also developed.

Engineering Analysis in Imprecise Geometric Models

Engineering analysis in geometric models has been the main if not the only credible/reasonable tool used by engineers and scientists to resolve physical boundaries problems. New high speed computers have facilitated the accuracy and validation of the expected results. In practice, an engineering analysis is composed of two parts; the design of the model and the analysis of the geometry with the boundary conditions and constraints imposed on it. Numerical methods are used to resolve a large number of physical boundary problems independent of the model geometry. The time expended due to the computational process are related to the imposed boundary conditions and the well conformed geometry. Any geometric model that contains gaps or open lines is considered an imperfect geometry model and major commercial solver packages are incapable of handling such inputs. Others packages apply different kinds of methods to resolve this problems like patching or zippering; but the final resolved geometry may be different from the original geometry, and the changes may be unacceptable. The study proposed in this dissertation is based on a new technique to process models with geometrical imperfection without the necessity to repair or change the original geometry. An algorithm is presented that is able to analyze the imperfect geometric model with the imposed boundary conditions using a meshfree method and a distance field approximation to the boundaries. Experiments are proposed to analyze the convergence of the algorithm in imperfect models geometries and will be compared with the same models but with perfect geometries. Plotting results will be presented for further analysis and conclusions of the algorithm convergence

Positive Ricci Curvature on Highly Connected Manifolds

Peer reviewed

Positive Ricci Curvature on Highly Connected Manifolds

Peer reviewed