Response reconstruction is used to obtain accurate replication of vehicle structural responses of field recorded measurements in a laboratory environment, a crucial step in the process of Accelerated Destructive Testing (ADT). Response Reconstruction is cast as an inverse problem whereby the desired input is inferred using the measured outputs of a system. ADT typically involves large shock loadings resulting in a nonlinear response of the structure. A promising linear regression technique known as Spanning Basis Transformation Regression (SBTR) in con- junction with non-overlapping windows casts the low dimensional nonlinear problem as a high dimensional linear problem. However, it is determined that the original implementation of SBTR struggles to invert a broader class of sensor configurations. A new windowing method called AntiDiagonal Averaging (ADA) is developed to overcome the shortcomings of the SBTR im- plementation. ADA introduces overlaps within the predicted time signal windows and averages them. The newly proposed method is tested on a numerical quarter car model and is shown to successfully invert a broader range of sensor configurations as well as being capable of describing nonlinearities in the system. / Dissertation (MEng)--University of Pretoria, 2021. / Mechanical and Aeronautical Engineering / MEng / Unrestricted

This project deals with fingerprint biometrics. Describes the origin and significance of ridges. Project denote the significance and detection of singular points. The way of classication fingerprint to the vlase usány by the singular points. It contains a list of types of minutiae and their detection. There is basic methods for matching fingerprints. The minutae-based matching method is realize in program Matlab.

This thesis describes the anatomical characteristics of fingerprints and their applications in identifying the person. The theoretical part describes the importance of papillary lines on fingerprints, statistical analysis and pre-processing of images in particular. The practical section provides the necessary operations to compare fingerprints. The implementation was done in Matlab.

This thesis deals with product design rotating camera crane with variable length telescopic arm. Proposed maximum arm length is 6 [m] with a maximum weight capacity of the camera 8 [kg]. The work deals with the various structural units associated mainly with the issue of the telescopic arm. In individual sections detail the construction of the camera head developed deformation and stress analysis of a telescopic jib.

Cette thèse est consacrée principalement à l’étude de quelques problèmes elliptiques singuliers dans un domaine Ωɛ*, périodiquement perforé par des trous de taille ɛ. On montre l’existence et l’unicité d’une solution, pour tout ɛ fixé, ainsi que des résultats d’homogénéisation et correcteurs pour le problème singulier suivant :{█(-div (A (x/ɛ,uɛ)∇uɛ)=fζ(uɛ) dans Ωɛ*@uɛ=0 sur Γɛ0@@(A (x/ɛ,uɛ)∇uɛ)υ+ɛγρ (x/ɛ) h(uɛ)= ɛg (x/ɛ) sur Γɛ1@)┤Où l’on prescrit des conditions de Dirichlet homogènes sur la frontière extérieure Γɛ0 et des conditions de Robin non linéaires sur la frontière des trous Γɛ1. Le champ matriciel quasi linéaire A est elliptique, borné, périodique dans la primière variable et de Carathéodory. Le terme singulier non linéaire est le produit d’une fonction continue ζ (singulier en zéro) et de f, dont la sommabilité dépend de la croissance de ζ près de sa singularité. Le terme de bord non linéaire h est une fonction croissante de classe C1, ρ et g sont des fonctions périodiques non négatives avec sommabilité convenables. Pour étudier le comportement asymptotique du problème quand ɛ -> 0, on applique la méthode de l’éclatement périodique due à D. Cioranescu-A. Damlamian-G. Griso (cf. D. Cioranescu-A. Damlamian-P. Donato-G. Griso-R. Zaki pour les domaines perforés). Enfin, on montre l’existence et l’unicité de la solution faible pour la même équation, dans un domaine à deux composants Ω = Ω1 υ Ω2 υ Γ, étant Γ l’interface entre le composant connecté Ω1 et les inclusions Ω2. Plus précisément on considère{█(-div (A(x, u)∇u)+ λu=fζ(u) dans Ω\Γ,@u=0 sur δΩ@(A(x, u1)∇u1)υ1= (A(x, u2)∇u2)υ1 sur Γ,@(A(x, u1)∇u1)υ1= -h(u1-u2) sur Γ@)┤Où λ est un réel non négatif et h représente le coefficient de proportionnalité entre le flux de chaleur et le saut de la solution, et il est supposé être borné et non négatif sur Γ. / This thesis is mainly devoted to the study of some singular elliptic problems posed in perforated domains. Denoting by Ωɛ* e domain perforated by ɛ-periodic holes of ɛ-size, we prove existence and uniqueness of the solution , for fixed ɛ, as well as homogenization and correctors results for the following singular problem :{█(-div (A (x/ɛ,uɛ)∇uɛ)=fζ(uɛ) dans Ωɛ*@uɛ=0 sur Γɛ0@@(A (x/ɛ,uɛ)∇uɛ)υ+ɛγρ (x/ɛ) h(uɛ)= ɛg (x/ɛ) sur Γɛ1@)┤Where homogeneous Dirichlet and nonlinear Robin conditions are prescribed on the exterior boundary Γɛ0 and on the boundary of the holles Γɛ1, respectively. The quasilinear matrix field A is elliptic, bounded, periodic in the first variable and Carathéodory. The nonlinear singular lower order ter mis the product of a continuous function ζ (singular in zero) and f whose summability depends on the growth of ζ near its singularity. The nonlinear boundary term h is a C1 increasing function, ρ and g are periodic nonnegative functions with prescribed summabilities. To investigate the asymptotic behaviour of the problem, as ɛ -> 0, we apply the Periodic Unfolding Method by D. Cioranescu-A. Damlamian-G. Griso, adapted to perforated domains by D. Cioranescu-A. Damlamian-P. Donato-G. Griso-R. Zaki. Finally, we show existence and uniqueness of a weak solution of the same equation in a two-component domain Ω = Ω1 υ Ω2 υ Γ, being Γ the interface between the connected component Ω1 and the inclusions Ω2. More precisely we consider{█(-div (A(x, u)∇u)+ λu=fζ(u) dans Ω\Γ,@u=0 sur δΩ@(A(x, u1)∇u1)υ1= (A(x, u2)∇u2)υ1 sur Γ,@(A(x, u1)∇u1)υ1= -h(u1-u2) sur Γ@)┤Where ν1 is the unit external vector to Ω1 and λ a nonnegative real number. Here h represents the proportionality coefficient between the continuous heat flux and the jump of the solution and it is assumed to be bounded and nonnegative on Γ.

A singularly perturbed reaction diffusion problem is considered. The small diffusion coefficient generically leads to solutions with boundary layers. The problem is discretized by a vertex-centered finite volume method. The anisotropy of the solution is reflected by using \emph{anisotropic meshes} which can improve the accuracy of the discretization considerably. The main focus is on \emph{a posteriori} error estimation. A residual type error estimator is proposed and rigorously analysed. It is shown to be robust with respect to the small perturbation parameter. The estimator is also robust with respect to the mesh anisotropy as long as the anisotropic mesh sufficiently reflects the anisotropy of the solution (which is almost always the case for sensible discretizations). Altogether, reliable and efficient \emph{a posteriori} error estimation is achieved for the finite volume method on anisotropic meshes.

Die Arbeit untersucht planare optische Mikrokavitäten, welche aus einer beidseitig von Multischichtspiegeln umgebenen Kavitätsschicht bestehen. Im Rahmen einer Transfermatrixbeschreibung für ebene Wellen wird ein genereller Ansatz zur Berechnung von optischen Kavitätsmoden von planaren Mikrokavitäten entwickelt, welche aus optisch beliebig anisotropen Medien bestehen. Die zugrunde liegende Modenbedingung kommt ohne vorherige Einschränkungen bezüglich der betrachteten Lichtpolarisation aus. Basierend auf diesem Ansatz werden numerische Modenberechnungen von Mikrokavitäten mit optisch uniaxialen Kavitätsschichten vorgenommen. Generell sind die Moden in einem solchen System elliptisch polarisiert, und zudem i.A. nicht orthogonal. Ein besonderes Phänomen stellen sogenannte exzeptionelle Punkte dar. Dies sind Richtungen, für welche Energie und Verbreiterung der zwei Kavitätsphotonmoden zugleich entarten. Die Moden werden an solchen Punkten zirkular ko-polarisiert, die Orientierung der linearen Modenpolarisation windet sich im Impulsraum um diese Punkte herum. Die Eigenschaften der anisotropen Mikrokavitäten und exzeptionellen Punkte sind charakteristisch für singuläre, biaxiale Optik. So entsprechen die exzeptionellen Punkte Richtungen sogenannter singulärer optischer Achsen der effektiv biaxialen Strukturen, und können als Entartung nicht-Hermitescher Operatoren beschrieben werden. Die experimentelle Realisierung wird am Beispiel ZnO-basierter Mikrokavitäten gezeigt und bestätigt die theoretischen Vorhersagen im Wesentlichen, wenngleich im Experiment keine komplett zirkular polarisierten Zustände an den Entartungspunkten beobachtet wurden.:0 Introduction 1 Theory I: Linear optics principles 1.1 Maxwell theory 1.1.1 Plane-wave ansatz 1.1.2 Light polarization 1.1.3 Crystal optics 1.1.4 The polariton concept 1.2 Matrix formalisms for planar structures 1.2.1 Transfer-matrix approach 1.2.2 Scattering, Jones and Müller matrices 2 Theory II: Planar optical microcavities 2.1 Fabry-Pérot resonators and photonic modes 2.2 Practical mode computation 2.3 Quasi-particle approach 3 Computation: Exceptional points in anisotropic microcavities 3.1 Numerical methods 3.2 Model and findings for anisotropic, dielectric microcavities 3.3 Classification and discussion 3.3.1 General characteristics of exceptional points in anisotropic microcavities 3.3.2 Polarization vortices and singular optics 3.3.3 Net topology of the system 3.3.4 Effective-medium approaches 3.3.5 Quasi-particle approaches 3.3.6 Other familiar systems and phenomena 3.4 Anisotropic exciton-polaritons 4 Experiment: ZnO-based planar microcavities 4.1 Microcavity samples 4.2 Experimental methods 4.3 Experimental results vs. theoretical computations 4.4 Summary and discussion 5 Conclusion A Appendix A.1 Determining optic axes A.2 Exceptional points A.3 Expressions in Gaußian CGS units A.4 Polarization patterns of isotropic microcavities Bibliography Symbols and Abbreviations Authored and co-authored publications directly related to this thesis Acknowledgments Curriculum Vitae / In this thesis, planar optical cavities are investigated. They consist of a cavity layer which is surrounded by multi-layer mirrors. Using a transfer matrix technique for planar structures, a general mode condition is developed, which allows computation of cavity-photon modes for planar microcavities, which consist of optically arbitrarily anisotropic media. With this approach, no prior restriction of the considered light polarization is required. Based on this formalism, numerical computations of planar microcavities with optically uniaxial cavity layers are performed. Generally, the cavity-photon modes in such systems obtain elliptic polarization. Furthermore, they are in general not orthogonal to each other. A particular phenomenon is the occurrence of so called exceptional points. Here, the two cavity-photon modes degenerate in energy and broadening simultaneously, and the modes become circularly co-polarized. In addition, the exceptional points are vortex centers in momentum space for the orientation of the linear polarization of the modes. With this, anisotropic planar microcavities show typical characteristics of singular as well as biaxial optics. The exceptional points can be regarded as singular optic axes of the effectively biaxial structures. They can be described by the degeneracy of non-Hermitian operators. Experimental implementation is demonstrated by ZnO-based microcavities. In general, experimental findings prove the theoretical predictions, albeit the degree of circular polarization does not approach 100% at the exceptional points.:0 Introduction 1 Theory I: Linear optics principles 1.1 Maxwell theory 1.1.1 Plane-wave ansatz 1.1.2 Light polarization 1.1.3 Crystal optics 1.1.4 The polariton concept 1.2 Matrix formalisms for planar structures 1.2.1 Transfer-matrix approach 1.2.2 Scattering, Jones and Müller matrices 2 Theory II: Planar optical microcavities 2.1 Fabry-Pérot resonators and photonic modes 2.2 Practical mode computation 2.3 Quasi-particle approach 3 Computation: Exceptional points in anisotropic microcavities 3.1 Numerical methods 3.2 Model and findings for anisotropic, dielectric microcavities 3.3 Classification and discussion 3.3.1 General characteristics of exceptional points in anisotropic microcavities 3.3.2 Polarization vortices and singular optics 3.3.3 Net topology of the system 3.3.4 Effective-medium approaches 3.3.5 Quasi-particle approaches 3.3.6 Other familiar systems and phenomena 3.4 Anisotropic exciton-polaritons 4 Experiment: ZnO-based planar microcavities 4.1 Microcavity samples 4.2 Experimental methods 4.3 Experimental results vs. theoretical computations 4.4 Summary and discussion 5 Conclusion A Appendix A.1 Determining optic axes A.2 Exceptional points A.3 Expressions in Gaußian CGS units A.4 Polarization patterns of isotropic microcavities Bibliography Symbols and Abbreviations Authored and co-authored publications directly related to this thesis Acknowledgments Curriculum Vitae

This thesis is split into two parts, the first one is concerned with some problems in stochastic homogenization and the second addresses a problem in singular SPDEs. In the part on stochastic homogenization we are interested in developing large-scale regularity theories for random linear elliptic operators by using estimates for the homogenization error to transfer regularity from the homogenized operator to the heterogeneous one at large scales. In the whole-space case this has been done by Gloria, Neukamm, and Otto through means of a homogenization-inspired Campanato iteration. Here we are specifically interested in boundary regularity and as a model setting we consider random linear elliptic operators on the half-space with either homogeneous Dirichlet or Neumann boundary data. In each case we obtain a large-scale regularity theory and the main technical difficulty turns out to be the construction of a sublinear homogenization corrector that is adapted to the boundary data. The case of Dirichlet boundary data is taken from a joint work with Julian Fischer. In an attempt to head towards a percolation setting, we have also included a chapter concerned with the large-scale behaviour of harmonic functions on a domain with random holes assuming that these are 'well-spaced'. In the second part of this thesis we would like to provide a pathwise solution theory for a singular quasilinear parabolic initial value problem with a periodic forcing. The difficulty here is that the roughness of the data limits the regularity the solution such that it is not possible to define the nonlinear terms in the equation. A well-posedness result, therefore, comes with two steps: 1) Giving meaning to the nonlinear terms and 2) Showing that with this meaning the equation has a solution operator with some continuity properties. The solution theory that we develop in this contribution is a perturbative result in the sense that we think of the solution of the initial value problem as a perturbation of the solution of an associated periodic problem, which has already been handled in a work by Otto and Weber. The analysis in this part relies entirely on estimates for the heat semigroup. The results in the second part of this thesis will be in an upcoming joint work with Felix Otto and Jonas Sauer.

<div>Philosophers who affirm the existence of propositions contend that the contents of declarative sentences, beliefs, doubts, and so on are entities (the things picked out by the term “propositions”), and that these entities have truth-values. Unsurprisingly, there’s rampant disagreement among those philosophers about sorts of things are called “propositions”. Propositions have been identified with sui generis abstract objects, interpreted facts, properties, and types of cognitive acts (this is not an exhaustive list). Despite this debate, most agree that propositions are representations (this is how they come to have truth-values), and that propositions are not to be identified with token mental representations. I agree that propositions are representations, but argue that propositions are mental representation tokens. The view I defend has sparse contemporary support, but has an impressive pedigree—ancestral views were widely popular in the late medieval, and early modern periods. In this dissertation I argue at length against contemporary criticisms that this view is still credible.</div><div>In chapter one, I defend a mentalist semantics; that is, I argue that linguistic representation is parasitic on mental representation: for a sentence to mean that p is for it to express (or be conventionally used to express) the thought that p. Once this is established, I argue in chapter two that mental representations (as opposed to non-mental ones) are ideal candidates to serve as the contents of sentences and propositional attitudes. I compare my preferred view, that propositions are token mental representations, against rival views (sorted into two groups) and show that a cost benefit analysis of each favors my position. In chapter three, I start exploring what these mental representations might be like. I argue that they’re structured entities whose constituents are modes of presentation of the things represented. I decline to analyze the relation which unites these modes of presentation, but argue (contra some contemporary philosophers) that this relation is not predication. Finally, in chapter four, I argue against the widely popular view that propositions have the things they’re about as constituents. I show that such a view cannot accommodate thoughts about nonexistent entities. I propose that the modes of presentation which are constituents of propositions are non-descriptive, but criticize the mental file conception of non-descriptive modes of presentation.</div>

The Polar Decomposition (PD) of a dense matrix is an important operation in linear algebra, while being a building block for solving the Symmetric Eigenvalue Problem (SEP) and computing the Singular Value Decomposition (SVD). It can be directly calculated through the SVD itself, or iteratively using the QR Dynamically-Weighted Halley (QDWH) algorithm. The former is difficult to parallelize due to the preponderant number of memory-bound operations during the bidiagonal reduction. The latter is an iterative method, which performs more floating-point operations than the SVD approach, but exposes at the same time more parallelism. Looking at the roadmap of the hardware technology scaling, algorithms perform- ing floating-point operations on locally cached data should be favored over those requiring expensive horizontal data movement. In this context, this thesis investigates new high-performance algorithmic designs of QDWH algorithm to compute the PD. Originally introduced by Nakatsukasa et al. [1, 2], our algorithmic contributions include mixed precision techniques, task-based formulations, and parallel asynchronous executions. Moreover, by making the PD competitive, its application to the SEP and the SVD becomes practical. In particular, we introduce for the first time new algorithms for partial SVD decomposition using QDWH. By the same token, we extend the QDWH to support partial eigen decomposition for SEP. We present new high-performance implementations of the QDWH-based algorithms relying on fine-grained computations, which allows exploiting the sparsity of the underlying data structure. To demonstrate performance efficiency, portability and scalability, we conduct benchmarking campaigns on some of the latest shared/distributed-memory systems. Our QDWH-based algorithm implementations outperform the state-of-the-art numerical libraries by up to 2.8x and 12x on shared and distributed-memory, respectively. The task-based QDWH has been integrated into the Chameleon library (https://gitlab.inria.fr/solverstack/chameleon) for support on shared-memory systems with hardware accelerators. It is also currently being used by astronomers from the Subaru telescope located at the summit of Mauna Kea, Hawaii, USA. The distributed-memory software library of QDWH and its SVD extension are freely available under modified-BSD license at https: //github.com/ecrc/qdwh.git and https://github.com/ecrc/ksvd.git, respectively. Both software libraries have been integrated into the Cray Scientific numerical library LibSci v17.11.1 and v19.02.1.