Projections in a normed linear space and a generalization of the pseudo-inverse

The concept of a "projection function" in a finite-dimensional real or complex normed linear space H (the function P_M which carries every element into the closest element of a given subspace M) is set forth and examined.

If dim M = dim H - 1, then P_M is linear. If P_N is linear for all k-dimensional subspaces N, where 1 ≤ k < dim M, then P_M is linear.

The projective bound Q, defined to be the supremum of the operator norm of P_M for all subspaces, is in the range 1 ≤ Q < 2, and these limits are the best possible. For norms with Q = 1, P_M is always linear, and a characterization of those norms is given.

If H also has an inner product (defined independently of the norm), so that a dual norm can be defined, then when P_M is linear its adjoint P_M^H is the projection on (kernel P_M)^⊥ by the dual norm. The projective bounds of a norm and its dual are equal.

The notion of a pseudo-inverse F⁺ of a linear transformation F is extended to non-Euclidean norms. The distance from F to the set of linear transformations G of lower rank (in the sense of the operator norm ∥F - G∥) is c/∥F⁺∥, where c = 1 if the range of F fills its space, and 1 ≤ c < Q otherwise. The norms on both domain and range spaces have Q = 1 if and only if (F⁺)⁺ = F for every F. This condition is also sufficient to prove that we have (F⁺)^H = (F^H)⁺, where the latter pseudo-inverse is taken using dual norms.

In all results, the real and complex cases are handled in a completely parallel fashion.

Pick and Place Aplikazioaren Garapena ABBko IRB120 Errobotarekin

[ES]El origen de este proyecto se encuentra dentro de la línea de investigación del equipo CompMech del Departamento de Ingeniería Mecánica de la Escuela, el cual financia tanto la inversión como el mantenimiento del prototipo utilizado en este proyecto. Partiendo de esta base, el objetivo principal de esta línea de estudio es profundizar en el control del robot para poder después llegar a desarrollar una aplicación práctica. Para lograr este objetivo se trabajará con el software RobotStudio, mediante el cual se llevarán a cabo diferentes tareas tales como la generación de trayectorias, optimización de las mismas y la implementación de aplicaciones prácticas. En este trabajo se dan los primeros pasos hacia el control del robot, siendo una base de partida para estudios más complejos y profundos. De modo que el objetivo principal es dar los primeros pasos en el campo de estudio de la robótica, para proporcionar una base sólida y útil que sea válida para el desarrollo de posteriores aplicaciones prácticas más complejas.

General-domain compressible Navier-Stokes solvers exhibiting quasi-unconditional stability and high-order accuracy in space and time

This thesis presents a new class of solvers for the subsonic compressible Navier-Stokes equations in general two- and three-dimensional spatial domains. The proposed methodology incorporates: 1) A novel linear-cost implicit solver based on use of higher-order backward differentiation formulae (BDF) and the alternating direction implicit approach (ADI); 2) A fast explicit solver; 3) Dispersionless spectral spatial discretizations; and 4) A domain decomposition strategy that negotiates the interactions between the implicit and explicit domains. In particular, the implicit methodology is quasi-unconditionally stable (it does not suffer from CFL constraints for adequately resolved flows), and it can deliver orders of time accuracy between two and six in the presence of general boundary conditions. In fact this thesis presents, for the first time in the literature, high-order time-convergence curves for Navier-Stokes solvers based on the ADI strategy---previous ADI solvers for the Navier-Stokes equations have not demonstrated orders of temporal accuracy higher than one. An extended discussion is presented in this thesis which places on a solid theoretical basis the observed quasi-unconditional stability of the methods of orders two through six. The performance of the proposed solvers is favorable. For example, a two-dimensional rough-surface configuration including boundary layer effects at Reynolds number equal to one million and Mach number 0.85 (with a well-resolved boundary layer, run up to a sufficiently long time that single vortices travel the entire spatial extent of the domain, and with spatial mesh sizes near the wall of the order of one hundred-thousandth the length of the domain) was successfully tackled in a relatively short (approximately thirty-hour) single-core run; for such discretizations an explicit solver would require truly prohibitive computing times. As demonstrated via a variety of numerical experiments in two- and three-dimensions, further, the proposed multi-domain parallel implicit-explicit implementations exhibit high-order convergence in space and time, useful stability properties, limited dispersion, and high parallel efficiency.

Iris recognition algorithm based on point covering of high-dimensional space and neural network

In this paper, we constructed a Iris recognition algorithm based on point covering of high-dimensional space and Multi-weighted neuron of point covering of high-dimensional space, and proposed a new method for iris recognition based on point covering theory of high-dimensional space. In this method, irises are trained as "cognition" one class by one class, and it doesn't influence the original recognition knowledge for samples of the new added class. The results of experiments show the rejection rate is 98.9%, the correct cognition rate and the error rate are 95.71% and 3.5% respectively. The experimental results demonstrate that the rejection rate of test samples excluded in the training samples class is very high. It proves the proposed method for iris recognition is effective.

Information geometry theory of high-dimension space and application for speaker independent continuous digit speech recognition

In the light of descriptive geometry and notions in set theory, this paper re-defines the basic elements in space such as curve and surface and so on, presents some fundamental notions with respect to the point cover based on the High-dimension space (HDS) point covering theory, finally takes points from mapping part of speech signals to HDS, so as to analyze distribution information of these speech points in HDS, and various geometric covering objects for speech points and their relationship. Besides, this paper also proposes a new algorithm for speaker independent continuous digit speech recognition based on the HDS point dynamic searching theory without end-points detection and segmentation. First from the different digit syllables in real continuous digit speech, we establish the covering area in feature space for continuous speech. During recognition, we make use of the point covering dynamic searching theory in HDS to do recognition, and then get the satisfying recognized results. At last, compared to HMM (Hidden Markov models)-based method, from the development trend of the comparing results, as sample amount increasing, the difference of recognition rate between two methods will decrease slowly, while sample amount approaching to be very large, two recognition rates all close to 100% little by little. As seen from the results, the recognition rate of HDS point covering method is higher than that of in HMM (Hidden Markov models) based method, because, the point covering describes the morphological distribution for speech in HDS, whereas HMM-based method is only a probability distribution, whose accuracy is certainly inferior to point covering.

Comparison of space- and ground-grown Ce: Bi12SiO20 single crystals

Ce doped Bi12SiO20 single crystals were grown either on board of the Chinese Spacecraft-Shenzhou No.3 (SZ-3) or on the ground at the same conditions with the exception of microgravity. The surface morphology of crystals clearly showed significant differences between the space- and ground-grown portions. The space- and ground-grown crystals have been measured by X-ray rocking curve, Cc concentration distribution in growth direction, dislocation density, absorption spectrums. These results show that the compositional homogeneity and structural perfection of Ce doped crystal grown in space are obviously improved.

Peripheries of molecular projection in three-dimensional space and studies of quantitative structure-activity relationships

A new index, i.e., the periphery representation of the projection of a molecule from 3D space to a 2D plane is described. The results, correlation with toxicity of substituted nitrobenzenes, obtained by using periphery descriptors are much better than that obtained by using the areas (i.e., shadows) of projections of the compounds. Even better results were achieved by using the combination of periphery descriptors and the projections areas as well as the indicated variable K reflecting the action of group NO position on the benzene ring.

New Approaches to Social History. Myth, Memory and Place: Monmouth and Bath 1750-1900

Borsay, Peter, 'New Approaches to Social History. Myth, Memory and Place: Monmouth and Bath 1750-1900', Journal of Social History (2006) 39(3) pp.867-889 RAE2008

People and place in the new frontier: an examination of Han and Uyghur ethnic identities

This thesis demonstrates how Han and Uyghur ethnic identities are constructed in urban Xinjiang, how they have evolved over time and how both identities gain their meaning largely from a process of interaction with the ‘other’. It shows that the boundaries that exist between Uyghur and Han hugely influence the identity content of both. Based on over 120 interviews carried out over 3 years, it brings a clear analytical framework and conceptual clarity to the questions of how ethnic identities are constructed and maintained in Xinjiang

Preserving patent policy space and securing access to medicines in developing countries: the role of states and pharmaceutical corporations

This thesis examines the tension between patent rights and the right to health and it recognizes patent rights on pharmaceutical products as one of the factors responsible for the problem of lack of access to affordable medicines in developing countries. The thesis contends that, in order to preserve their patent policy space and secure access to affordable medicines for their citizens, developing countries should incorporate a model of human rights into the design, implementation, interpretation, and enforcement of their national patent laws. The thesis provides a systematic analysis of court decisions from four key developing countries (Brazil, India, Kenya, and South Africa) and it assesses how the national courts in these countries resolve the tension between patent rights and the right to health. Essentially, this thesis demonstrates how a model of human rights can be incorporated into the adjudication of disputes involving patent rights in national courts. Focusing specifically on Brazil, the thesis equally demonstrates how policy makers and law makers at the national level can incorporate a model of human rights into the design or amendment of their national patent law. This thesis also contributes to the ongoing debate in the field of business and human rights with regard to the mechanisms that can be used to hold corporate actors accountable for their human rights responsibilities. This thesis recognizes that, while states bear the primary responsibility to respect, protect, and fulfil the right to health, corporate actors such as pharmaceutical companies also have a baseline responsibility to respect the right to health. This thesis therefore contends that pharmaceutical companies that own patent rights on pharmaceutical products can be held accountable for their right to health responsibilities at the national level through the incorporation of a model of civic participation into a country’s patent law system.