Dans cette thèse, nous considérons la dernière génération du radar. Il s’agit d’un radar MIMO bistatique qui est composé de plusieurs antennes d’émission et de réception. Pour ce système, les antennes émettrices transmettent des signaux linéairement indépendants afin qu’ils puissent être identifiés à l’aide d’un banc de filtres adaptés au niveau des antennes de réception. Les signaux filtrés sont alors traités pour extraire les paramètres des cibles, tels que les DOA, DOD, vitesse, etc. Un radar MIMO bistatique offre une grande diversité spatiale et une excellente identifiabilité des paramètres, etc., ce qui nous a incités à l’utiliser dans ce travail. La situation en champ lointain d’un radar MIMO bistatique est largement traitée dans la littérature. Mais, peu de travaux existe sur la situation en champ proche, c’est ce qui a motivé le travail de cette thèse. La localisation de cibles en champ proche est importante en raison de nombreuses applications à l’intérieur des constructions. A ce sujet, la plupart des méthodes actuelles utilisent l’approximation de Fresnel dans laquelle le front d’onde sphérique des signaux reçus est supposé quadrique plutôt que planaire comme en champ lointain. Dans ce travail de thèse, nous avons proposé une nouvelle méthode de localisation des cibles en champ proche qui utilise l’approximation de Fresnel. Celle-ci conduit à une estimation biaisée des paramètres de localisation car en réalité le front d’onde est sphérique. Nous avons proposé alors deux méthodes de correction pour réduire les effets de l’approximation de Fresnel et deux autres méthodes qui utilisent directement le modèle exacte basé sur le front d’onde sphérique. / Sources localization is used in radar, sonar, and telecommunication. Radar has numerous civilian and military applications. Radar system has gone through many developments over the last few decades and reached the latest version known as MIMO radar. A MIMO radar is composed of multiple transmitting and receiving antennas like a conventional phased array radar. However, its transmitting antennas transmit linearly independent signals so that they can be easily identified by the matched filters bank at its receiving end. The matched filtered signals are then processed to extract the ranges, DOAs, DODs, velocities, etc. of the targets. A bistatic MIMO radar system provides high resolution, spatial diversity, parameter identifiability, etc. which inspired us to use it in this work. There are many existing methods to deal with the far field region of MIMO radar system. However, little work can be found on the near field region of a bistatic MIMO radar which motivated the work in this thesis. Near field targets localization is also important because of many indoor applications. Most of the existing near field sources localization techniques use Fresnel approximation in which the real spherical wavefront is assumed quadric unlike planar in far field situation. In this work we have proposed a novel near field targets localization method using Fresnel approximation. The Fresnel approximation leads to a biased estimation of the location parameters because the true wavefront is spherical. Consequently, we have proposed two correction methods to reduce the effects of Fresnel approximation and other two methods which directly use the exact signal model based on spherical wavefront.

A new viscous-inviscid semi-inverse (VISI) interaction method has been developed for predicting the flow field arising from a combination of inviscid potential flow and viscous flow. The technique involves matching the bounding velocities for each region by iteratively solving for the displacement thickness, δ*(x). The formula used to update δ*(x) after each iteration is generated by linearly perturbing the governing equations. Application of the VISI procedure to predict the unseparated flow past a flat plate gives excellent results, producing numerical solutions essentially indistinguishable from the appropriate analytical solution in less than 0.5 seconds of CPU time on an Amdahl 5850 computer. Application of the technique to external flow over a backward facing step (BFS) indicates that the region of strong interaction between the viscous and inviscid flows is much larger than reported for internal flow. Calculated reattachment lengths, LR, are clearly influenced by the thickness of the boundary layer upstream of the step, thicker boundary layers producing longer reattachment lengths. Good accuracy is achieved for a relatively coarse distribution of control points, and rapid convergence (< 2 seconds on the Amdahl 5850) usually occurs. Finite-difference predictions using an elliptic code (TEACH-T), modified at the outer boundary to simulate external flow, have also been made for the BFS, largely as a basis of comparison for the VISI results. Comparison of results for the two models (VISI and TEACH) gives similar trends in LR as a function of Rh and x₈, (a measure of the displacement thickness at the step). The values of LR obtained with the VISI method, however, are 15-80% longer than those from TEACH. Direct comparison with experiments is difficult because the experimental data does not clearly identify the effects of x₈, in the resulting values of LR. Trends appear to be the same for all computed and observed cases however. Disagreement between the VISI and TEACH results is thought to be due to a combination of neglecting velocities in the recirculation region in the VISI model, and numerical error and inaccurate boundary conditions in the TEACH code. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The use of spline basis functions in solving least squares approximation problems is investigated. The question as to which are appropriate basis functions to use is discussed along with the reasons why the final choice was made. The Householder transformation method for solving the fixed knot spline approximation problem is examined. Descriptions of both an automatic procedure using function minimization and an interactive procedure using a graphics terminal for solving the variable knot spline approximation problem are given. In conclusion, numerical results using the interactive system are presented and analyzed. / Science, Faculty of / Computer Science, Department of / Graduate

Soient k, n des entiers avec 1 ≤ k ≤ n − 2. On cherche le suprémum ω(n, k) des nombres ω avec la propriété suivante. Pour tout point u ∈ ℝ^n u à coordonnées linéairement indépendantes sur ℚ, tout sous-espace E de ℝ^n orthogonal à u de dimension k et tout δ > 0, il existe une infinité de points non nuls x ∈ ℤ^n formant un angle au plus δ avec E tels que |x·u| ≤ ∥x∥^−ω. Ici, x·u désigne le produit scalaire de x avec u et ∥x∥ désigne la norme de x. En posant ν(m) = (m − 1 +√(m² + 2m − 3))/2, Schmidt (1976) a démontré que ω(3, 1) ≥ ν(2), puis Thurnheer (1990) a obtenu ω(n, n − 2) ≥ ν(n−1) en général. En 2014, Roy a établi que ω(3, 1) = ν(2). Dans ce mémoire, on montre que ω(n, 1) = ν(2) quel que soit n, on simplifie l’argument de Thurnheer et on montre que ω(n, k) ≥ ν(k+1) en général. On répond également à une question connexe de Badziahin et Bugeaud.

We give a 2-approximation algorithm for Cluster Vertex Deletion. This tight result matches the hardness lower bound. We obtain a new deterministic 7/3-approximation algorithm for Feedback Vertex Set in Tournaments. This result is based on the LP given by just one round of Sherali-Adams. We find a new, simpler deterministic (2 + epsilon)-approximation algorithm for Split Vertex Deletion. We give a 2-approximation algorithm for Claw-Free Vertex Deletion in triangle-free graphs. In the case of general graphs we prove that it is UGC-hard to obtain an approximation ratio lower than 3. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

A thesis submitted to the Faculty of science, University of Witwatersrand, Johannesburg in fulfilment of the requirements of the degree of Doctor of Philosophy. Johannesburg 1995. / We investigate Mean Convergence of Lagrange Interpolation and Rates of Approximation for Erdo's Weights on the Real line. An Erdos Weight is of the form, W = exp[-Q], where typically Q is even, continous and is of faster than polynomial growth at infinity. Concerning Lagrange Interpolation, we first investigate the problem of formulating and proving the correct Jackson Theorems for Erdos Weights. [ Abbreviated abstract : Open document to view full version] / GR2017

A research report submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in partial fulfilment of the degree of Master of Science / The importance of Pade approximation has been increasingly recognized in ' recent years. The first convergence result of Pade approximants valid for general meromorphic functions was obtained by de Montessus de Ballore in 1902. He proved that when a function f has precisely n poles in I z 1< R, then the (n+ 1)th column in thePade table of f converges to f in I z J< R. (Abbreviation abstract) / Andrew Chakane 2019

Thesis submitted 1970; degree awarded 1971. / In this dissertation we consider the minimax approximation of functions f(x) E"C[O, l] rotated about the origin, and the characterization of the optimal rotation, a*, of f in the sense of least minimax error over all possible rotations. The paper divides naturally into two sections: a) Existence, uniqueness, and characterization for unisolvent minimax approximation for each rotation a of f. These results are applications of Dunham (1967). b) Existence, non-uniqueness, and com.putation of a*; derivation of necessary conditions for the minimax [TRUNCATED]

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