Front projection is an economical method to produce large displays. However, the twin problems of occlusions, which create shadows on the screen, and light projected onto users near the screen, potentially blinding them, makes front projection a poor fit for large upright interactive surfaces. Virtual Rear Projection (VRP) uses multiple redundant front projectors to provide the user experience of using a rear projected display. By using a projector-camera system to mitigate shadows and blinding light, a virtual rear projected display significantly improves upon the user experience of a traditional front projected display, allowing it to replace a rear projected display. In this thesis we characterize the problems caused by shadows and occlusions and develop projection technologies that mitigate shadows and blinding light. We also present a laboratory performance evaluation, and a user evaluation of the technology showing that VRP improves the user experience with respect to traditional front projection.

Thesis (M.A.)--University of Delaware, 2008. / Principal faculty advisor: Bernard L. Herman, Dept. of Art History. Includes bibliographical references.

Aus Einleitung und Motivation "Die gegenwärtigen Entwicklungen von Head-Mounted Displays (HMD, hier synonym auch als Brille bezeichnet) für Virtual Reality (VR) und Augmented Reality (AR) schaffen ein nie da gewesenes Potential dieser Technologien als Werkzeuge in der Produktentwicklung. Wenngleich VR- und ARAnwendungen keineswegs neu in der Industrie sind, bringt der Fortschritt der Verbraucher-HMDs völlig neue Möglichkeiten. Immersive VR-Systeme bedeuten künftig keine hunderttausend Euro Anschaffung mehr – AR-Brillen dienen zukünftig nicht nur der Erweiterung der Realität mit zweidimensionalen Informationen. Cave Automatic Virtual Environments (CAVE), 360-Grad-Projektoren und interaktive Planungstische sind in der Fabrikplanung teilweise etabliert (Runde et al. 2015). Im Unterschied zu diesen Techniken können HMDs jedoch eine deutlich höhere Immersion ermöglichen, was auch für die Interaktion mit der virtuellen Umgebung von Vorteil sein kann. Das Gefühl der Immersion ist wichtig, um in bestimmten Entwicklungsphasen entsprechende Kriterien besser beurteilen zu können. Primär ist der VR-Einsatz für Bewertungsmerkmale sinnvoll, welche nur qualitativ und nicht quantitativ bewertbar sind (Pawellek 2014). Des Weiteren spielt auch die Eingabetechnologie eine essenzielle Rolle. Um mit virtuellen Elementen interagieren zu können, sollte das Eingabegerät echtzeitfähig und intuitiv sein. ..."

Yes / Random sets are used to get a continuous partition of the cardinality of the union of many overlapping sets. The formalism uses Möbius transforms and adapts Shapley's methodology in cooperative game theory, into the context of set theory. These ideas are subsequently generalized into the context of finite-dimensional Hilbert spaces. Using random projectors into the subspaces spanned by states from a total set, we construct an infinite number of continuous resolutions of the identity, that involve Hermitian positive semi-definite operators. The simplest one is the diagonal continuous resolution of the identity, and it is used to expand an arbitrary vector in terms of a continuum of components. It is also used to define the function on the 'probabilistic quadrant' , which is analogous to the Wigner function for the harmonic oscillator, on the phase-space plane. Systems with finite-dimensional Hilbert space (which are naturally described with discrete variables) are described here with continuous probabilistic variables. / The full-text of this article will be released for public view at the end of the publisher embargo on 15 Oct 2020. / Research Development Fund Publication Prize Award winner, October 2019.

Aus Einleitung und Motivation "Die gegenwärtigen Entwicklungen von Head-Mounted Displays (HMD, hier synonym auch als Brille bezeichnet) für Virtual Reality (VR) und Augmented Reality (AR) schaffen ein nie da gewesenes Potential dieser Technologien als Werkzeuge in der Produktentwicklung. Wenngleich VR- und ARAnwendungen keineswegs neu in der Industrie sind, bringt der Fortschritt der Verbraucher-HMDs völlig neue Möglichkeiten. Immersive VR-Systeme bedeuten künftig keine hunderttausend Euro Anschaffung mehr – AR-Brillen dienen zukünftig nicht nur der Erweiterung der Realität mit zweidimensionalen Informationen. Cave Automatic Virtual Environments (CAVE), 360-Grad-Projektoren und interaktive Planungstische sind in der Fabrikplanung teilweise etabliert (Runde et al. 2015). Im Unterschied zu diesen Techniken können HMDs jedoch eine deutlich höhere Immersion ermöglichen, was auch für die Interaktion mit der virtuellen Umgebung von Vorteil sein kann. Das Gefühl der Immersion ist wichtig, um in bestimmten Entwicklungsphasen entsprechende Kriterien besser beurteilen zu können. Primär ist der VR-Einsatz für Bewertungsmerkmale sinnvoll, welche nur qualitativ und nicht quantitativ bewertbar sind (Pawellek 2014). Des Weiteren spielt auch die Eingabetechnologie eine essenzielle Rolle. Um mit virtuellen Elementen interagieren zu können, sollte das Eingabegerät echtzeitfähig und intuitiv sein. ..."

Dans cette thèse, nous analysons les propriétés géométriques des surfaces obtenues des solutions classiques des modèles sigma bosoniques et supersymétriques en deux dimensions ayant pour espace cible des variétés grassmanniennes G(m,n). Plus particulièrement, nous considérons la métrique, les formes fondamentales et la courbure gaussienne induites par ces surfaces naturellement plongées dans l'algèbre de Lie su(n). Le premier chapitre présente des outils préliminaires pour comprendre les éléments des chapitres suivants. Nous y présentons les théories de jauge non-abéliennes et les modèles sigma grassmanniens bosoniques ainsi que supersymétriques. Nous nous intéressons aussi à la construction de surfaces dans l'algèbre de Lie su(n) à partir des solutions des modèles sigma bosoniques. Les trois prochains chapitres, formant cette thèse, présentent les contraintes devant être imposées sur les solutions de ces modèles afin d'obtenir des surfaces à courbure gaussienne constante. Ces contraintes permettent d'obtenir une classification des solutions en fonction des valeurs possibles de la courbure. Les chapitres 2 et 3 de cette thèse présentent une analyse de ces surfaces et de leurs solutions classiques pour les modèles sigma grassmanniens bosoniques. Le quatrième consiste en une analyse analogue pour une extension supersymétrique N=2 des modèles sigma bosoniques G(1,n)=CP^(n-1) incluant quelques résultats sur les modèles grassmanniens. Dans le deuxième chapitre, nous étudions les propriétés géométriques des surfaces associées aux solutions holomorphes des modèles sigma grassmanniens bosoniques. Nous donnons une classification complète de ces solutions à courbure gaussienne constante pour les modèles G(2,n) pour n=3,4,5. De plus, nous établissons deux conjectures sur les valeurs constantes possibles de la courbure gaussienne pour G(m,n). Nous donnons aussi des éléments de preuve de ces conjectures en nous appuyant sur les immersions et les coordonnées de Plücker ainsi que la séquence de Veronese. Ces résultats sont publiés dans la revue Journal of Geometry and Physics. Le troisième chapitre présente une analyse des surfaces à courbure gaussienne constante associées aux solutions non-holomorphes des modèles sigma grassmanniens bosoniques. Ce travail généralise les résultats du premier article et donne un algorithme systématique pour l'obtention de telles surfaces issues des solutions connues des modèles. Ces résultats sont publiés dans la revue Journal of Geometry and Physics. Dans le dernier chapitre, nous considérons une extension supersymétrique N=2 du modèle sigma bosonique ayant pour espace cible G(1,n)=CP^(n-1). Ce chapitre décrit la géométrie des surfaces obtenues des solutions du modèle et démontre, dans le cas holomorphe, qu'elles ont une courbure gaussienne constante si et seulement si la solution holomorphe consiste en une généralisation de la séquence de Veronese. De plus, en utilisant une version invariante de jauge du modèle en termes de projecteurs orthogonaux, nous obtenons des solutions non-holomorphes et étudions la géométrie des surfaces associées à ces nouvelles solutions. Ces résultats sont soumis dans la revue Communications in Mathematical Physics. / In this Ph. D. thesis, we analyze the geometric properties of surfaces obtained from the classical solutions of the two-dimensional bosonic and supersymmetric sigma models which has Grassmann manifolds G(m,n) as target space. In particular, we consider the metric, the fundamental forms and the gaussian curvature induced by these surfaces which naturally live in the su(n) Lie algebra. The first chapter presents some preliminary tools to understand the elements of the following chapters. We present non-abelian gauge theories and bosonic grassmannian sigma models as well as its supersymmetric counterpart. Another section presents a construction of surfaces in the Lie algebra su(n) from the solutions of the bosonic sigma models. The three last chapters contained in this thesis presents the constraints that have to be imposed on the solutions of the models in order to generate constant gaussian curvature surfaces. From these constraints, we can give a classification of the solutions depending on the possible values of the curvature. The first two papers presents an investigation of these surfaces and of their associated solutions for the bosonic grassmannian sigma models. In the third paper, we generalize our approach to a supersymmetric extension of the bosonic CP^(n-1)= G(1,n) sigma model including some results for the general Grassmann manifold G(m,n). In chapter 2, we study the geometric properties of surfaces associated to holomorphic solutions of the grassmannian sigma models. We give a complete classification of these constant curvature solutions for the particular models G(2,n) with n=3,4,5. Furthermore, we establish two conjectures on the possible values of the gaussian curvature. We also give some elements of proof for these conjectures in terms of Plücker coordinates and immersions as well as Veronese curves. These results are published in the Journal of Geometry and Physics. The third chapter presents a similar analysis as in the second chapter in the case of non-holomorphic solutions of the bosonic grassmannian sigma models. This work generalizes the results obtained in the first paper and give a systematic algorithm to obtain such surfaces from the known solutions of the models. These results are published in the Journal of Geometry and Physics. In the last chapter of this thesis, we consider a N=2 supersymmetric extension of the bosonic sigma model which has the CP^(n-1)=G(1,n) manifold as target space. This chapter presents a geometric description of the surfaces obtained from the solutions of the model and shows, in the holomorphic case, that they have constant gaussian curvature if and only if the solutions consists of a generalization of the Veronese curve. Furthermore, using a gauge invariant formulation of the model in terms of orthogonal projectors, we obtain explicit non-holomorphic solutions and study the geometry of their associated surfaces. These results are submitted to Communications in Mathematical Physics.

Die spontane Brechung der chiralen Symmetrie ist ein faszinierendes Phenomän der QCD mit fundamentalen phänomenologischen Implikationen. Die Brechung der chiral Symmetrie ist beispielsweise verantwortlich für die niedrige Masse der Pionen, welche die effektiven Goldstone Boson der spontan gebrochene Symmetrie sind. Die spontane Brechung der chiral Symmetrie und die chirale Anomalie sind niedrig Energie-Phenomäne der QCD, weshalb nichtperturbative Methoden nötig sind um sie zu studieren. In der vorliegenden Arbeit verwenden wir die Gitterregularisierung der QCD, um das chirale Kondensat, den Ordnungsparameter der spontanen Brechung der chiralen Symmetrie zu bestimen. Dazu wendeten wir die Definition der in dieser Arbeit studierten Observablen über Dichteketten an, die eine theoretisch wohldefinierte Bahndlung der Observablen zulässt. Für die praktische Berechnung wurde die kürzlich entwickelte Methode der spektralen Projektoren angewandt. In dieser Weise berchnen wir den Kontinuumlimes des chiralen Kondensates, das im chiralen Limes gewonnen, sowohl für N_f=2 als auch für N_f=2+1+1 Flavour von so genannten twisted mass Fermionen. Des Weiteren untersuchen wir das chirale Verhalten der topologischen Suszeptibilität. Wir verwenden hier wieder die Methode der spektralen Projektoren, anstelle aufwendigerer Verfahren, die chirale Symmetrie erhalten, aber zu numerisch sehr aufwändigen Simulationen führen. Schließ lich kommentieren wir die sich aus den starken Autokorrelationen ergebenden Schwierigkeiten dieser Rechnung. Abschließ end stellen wir die Kontinuumlimes-Ergebnisse der topologischen Suszeptibilität in der rein gluonischen Theorie vor, die es uns erlauben, die Witten-Veneziano-Formel zu testen. Unseren Untersuchung zufolge ist diese Formel gut erfüllt. Diese Tatsache stützt die Gültigkeit der Formel, die die topologischen Fluktuationen der Eichfelder mit der unerwartet groß en Masse des eta'' Mesons in Verbindung setzt. / The spontaneous breaking of chiral symmetry is a fascinating phenomenon of QCD whose mechanism is still not well understood and it has fundamental phenomenological implications. It is, for instance, responsible for the low mass of the pions which are effectively Goldstone bosons of the spontaneously broken symmetry. Since these phenomena belong to the low energy regime of QCD, non-perturbative techniques have to be applied in order to study them. In this work we use the twisted mass lattice QCD regularization to compute the chiral condensate, the order parameter of spontaneous chiral symmetry breaking. To this end we apply the recently introduced method of spectral projectors which allows us to perform calculations in large volumes due to its inherently low computational cost. This approach, moreover, enables a direct calculation of the chiral condensate based on a theoretically clean definition of the observable via density chains. We thus present a continuum limit determination of the chirally extrapolated condensate for N_f=2 and N_f=2+1+1 flavours of twisted mass fermions at maximal twist. In addition we study the chiral behavior of the topological susceptibility, a measure of the topological fluctuations of the gauge fields. We again apply the spectral projector method for this calculation. We comment on the difficulties which appear in the calculation of this observable due to the large autocorrelations involved. Finally we present the continuum limit result of the topological susceptibility in the pure gluonic theory which allows us to perform a test of the Witten-Veneziano relation. We found that this relation is well satisfied. Our results support the validity of the Witten-Veneziano formula which relates the topological fluctuations of the gauge fields with the unexpectedly large value of the eta''

ABSTRACT(­^ ¤å ºK ­n) The mother of the industrial machinery industry, often regarded as a national benchmark assessment of industrial competitiveness, the traditional concept of the cutting and forming machine tools for the spindle, including optoelectronics, semiconductors, automobiles, 3C electronics and aerospace industries, the relevant production or processing equipment, all belong to this category. With the evolution of technology, increasingly stringent product quality requirements, such as the appearance of the size of the high precision requirements and the material surface, gradually the importance of testing equipment and manufacturing go hand in hand, on behalf of the state's technology industry is expected in the near The future will be an important assessment of industrial competitiveness indicators. On the other hand, the mainland market after ten years of cross-strait exchange, itself played a significant change, from the early to the extreme dependence on imported equipment to produce the world-famous cottage products, no matter how the people of Taiwan to the mainland products exclusion, in the free under the natural law of market competition, the consumer market in Taiwan has long been filled with many mainland-made products. Their number and variety of the broad, deep penetration, simply makes hard to detect, and many exclusive products in the mainland business executives, the factory uses a lot of their own system of equipment are still unaware of the mainland, and even know, but also not find to alternative products. Indeed, many products have to meet the continent needs, these needs is not only reflected in the consumer goods market, is also rapidly spreading to the industrial market. Most of the countries with advanced manufacturing technology in the world, more or less with metrology industry. Taiwan alone will not only have no metrology manufacturing base, and even the Taiwan metrology companies in , mainland China, the increasing decline in ability to survive, the market that introduced by the Taiwan factories in the past swallowed gradually and easily by the local vendors. Worry about the future of Taiwan metrology industry. If Taiwan metrology industry can not get a good position in the world, can we be famous just by create a brand? Case is a company with more than 30 years of metrology sales background, in southern Taiwan. Because the relatively small market, it is difficult to obtain the dominant position of advantage. However, with the rise in the mainland market, the case company is full of many opportunities. This paper will research the sale strategy during these changeable situations. Bisides, metrology includes wide range products, this paper choose Coordinate Measuring Machines (CMM) as the basis of the primary products, mainly because of higher prices, the level of broader considerations in business, relatively high barriers to entry, in addition, it also has many features quite representative of the industry's products. Key words: Metrology, Coordinate Measuring Machines, CMM, hardness, surface roughness measuring instrument, roundness measuring instrument, the contour profile instrument, caliper, height gauge, optical flatness gauge, indicating scale, micrometer , microscopes , projectors , block gauge

Ce mémoire étudie la théorie de la représentation des algèbres de Temperley-Lieb à couture Bn,k (β) et plus particulièrement la famille exceptionnelle des algèbres à couture Bn,l (β). Les algèbres à couture sont paramétrées par deux entiers positifs et un paramètre complexe q ∈ ℂˣ tel que β = q + q⁻¹. La famille Bn,l (β) fait intervenir un entier positif l satisfaisant q²ˡ = 1. Les algèbres à couture ont été introduites par Morin-Duchesne, Rasmussen et Ridout et elles ont été étudiés par Langlois-Rémillard et Saint-Aubin lorsqu'elles ne font pas partie d'une certaine famille dite exceptionnelle. Il a été souligné par Morin-Duchesne, Rasmussen et Ridout que la famille manquante nécessiterait probablement une analyse particulière. Ce mémoire a comme objectif d'introduire des outils servant au traitement de la famille manquante. Plus particulièrement, en réinterprétant les relations définissant les algèbres à couture, l'algèbre Bn,l (β) est identifiée à un quotient de l'algèbre à une frontière par un idéal nilpotent engendré par un élément généralisant les projecteurs de Wenzl-Jones. / This thesis studies the representation theory of the Temperley-Lieb seam algebras Bn,k (β), more specifically the exceptionnal family of seam algebras Bn,l (β). The seam algebras are parametrized by two positive integers and one complex parameter q ∈ ℂˣ such that β = q + q⁻¹. The family Bn,l (β) involves a positive integer l satisfying q²ˡ = 1. The seam algebras were introduced by Morin-Duchesne, Rasmussen and Ridout and they were studied by Langlois-Rémillard and Saint-Aubin when they are not part of a particular case which is called exceptionnal. It was highlighted by Morin-Duchesne, Rasmussen and Ridout that the missing cases would probably need a separate analysis. This thesis has the objective of introducing tools which render the study of those missing cases possible. More specifically, by reinterpreting the defining relations of the seam algebras, the algebras Bn,l (β) are redefined as a quotient of the one boundary algebras by a nilpotent ideal generated by an element which generalises the Wenzl-Jones projectors.