Embedded below the radome of a missile, existing RF-seekers use a mechanical rotating antenna to steer the radiating beam in the direction of a target. Latest research is looking at replacing the mechanical antenna components of the RF seeker with a novel 3D conformal antenna array that can steer the beam electronically. 3D antennas may oer signicant advantages, such as faster beamsteering and better coverage but, at the same time, introduce new challenges resulting from a much more complex radiation pattern than that of 2D antennas. Thanks to the mechanical system removal, the new RF-seeker has a wider available space for the design of a new 3D conformal antenna. To take best benets of this space, dierent array shapes are studied, hence the impact of the position, orientation and conformation of the elements is assessed on the antenna performance in terms of directivity, ellipticity and polarisation. To facilitate this study of 3D conformal arrays, a Matlab program has been developed to compute the polarisation pattern of a given array in all directions. One of the task of the RF-seeker consists in estimating the position of a given target to correct the missile trajectory accordingly. Thus, the impact of the array shape on the error between the measured direction of arrival of the target echo and its true value is addressed. The Cramer-Rao lower bound is used to evaluate the theoretical minimum error. The model assumes that each element receives independently and allows therefore to analyse the potential of active 3D conformal arrays. Finally, the phase monopulse estimator is studied for 3D conformal arrays whose quadrants do not have the same characteristics. A new estimator more adapted to non-identical quadrants is also proposed.

Every day we recognize a numerous objects and human brain can recognize objects under many conditions. The way in which humans are able to identify an object is remarkably fast even in different size, colours or other factors. Computers or robots need computational tools to identify objects. Shape descriptors are one of the tools commonly used in image processing applications. Shape descriptors are regarded as mathematical functions employed for investigating image shape information. Various shape descriptors have been studied in the literature. The aim of this thesis is to develop new shape descriptors which provides a reasonable alternative to the existing methods or modified to improve them. Generally speaking shape descriptors can be categorized into various taxonomies based on the information they use to compute their measures. However, some descriptors may use a combination of boundary and interior points to compute their measures. A new shape descriptor, which uses both region and contour information, called centeredness measure has been defined. A new alternative ellipticity measure and sensitive family ellipticity measures are introduced. Lastly familiy of ellipticity measures, which can distinguish between ellipses whose ratio between the length of the major and minor axis differs, have been presented. These measures can be combined and applied in different image processing applications such as image retrieval and classification. This simple basis is demonstrated through several examples.

In this work we have studied the relationship between the kinematics and shapes of Early Type Galaxies (ETGs) in rich clusters. In particular we were interested to extend the kinematic morphology density relation to the richest clusters. We obtained data from FLAMES/GIRAFFE to probe the stellar kinematics of a sample of 30 ETGs in the massive cluster Abell 1689 at z = 0.183, to classify them as Slow Rotators (SRs) or Fast Rotators (Frs). To date, this is the highest redshift cluster studied in this way. We simulated FLAMES/GIRAFFE observations of the local SAURON galaxies to account for the bias introduced compared to the ATLAS3D sample, which we used as a local comparison. We find that the luminosity function of SRs in Abell 1689 is the same as that in ATLAS^3D, down to the faintest objects probed (M_K ≈ -23). The number fraction of SRs over the ETG population in Abell 1689 is f_SR = 0.15 +/- 0.03, consistent with the value found in the Virgo Cluster. However, within the cluster, f_SR rises sharply with the projected number density of galaxies, rising from f_SR = 0.01 in the least dense bin to f_SR = 0.58 in the densest bin. We conclude that the fraction of SRs is not determined by the local number density of galaxies, but rather by the physical location within the cluster. This might be due to dynamical processes which cause SRs (on average more massive) to sink in the gravitational potential of the cluster. Next we explore the distribution of projected ellipticity &epsilon; in galaxies belonging to a sample of clusters from SDSS (z </~ 0.1) and the CLASH survey (z ≈ 0.2). We were interested to establish whether the fraction of galaxies flatter than &epsilon; = 0.4 (a proxy for FRs) varies from cluster to cluster. We find some significant variations. We go on to probe the projected shape as a function of projected cluster-centric radius. In both samples we find that on average galaxies have progressively rounder projected shapes at lower cluster-centric projected distance. In the SDSS sample we show that this trend exists above and beyond the trend for brighter galaxies to be more common near the centre of clusters (bright galaxies are on average rounder). In order to disentangle the trend for SRs (which are rounder) to be more common near the centre of clusters, we isolate a subsample of FRs only, by considering only galaxies with &epsilon; > 0.4. We find that even the intrinsically flat FRs are on average rounder at lower projected cluster-centric distance. We conclude that the observed trend is due either to the dynamic heating of the stellar discs being strongest near the centre of clusters, or due to an anti-correlation of the bulge fractions with the cluster-centric distance.

We construct a class of elliptic operators in the edge algebra on a manifold M with an embedded submanifold Y interpreted as an edge. The ellipticity refers to a principal symbolic structure consisting of the standard interior symbol and an operator-valued edge symbol. Given a differential operator A on M for every (sufficiently large) s we construct an associated operator As in the edge calculus. We show that ellipticity of A in the usual sense entails ellipticity of As as an edge operator (up to a discrete set of reals s). Parametrices P of A then correspond to parametrices Ps of As, interpreted as Mellin-edge representations of P.

Edge representations of operators on closed manifolds are known to induce large classes of operators that are elliptic on specific manifolds with edges, cf. [9]. We apply this idea to the case of boundary value problems. We establish a correspondence between standard ellipticity and ellipticity with respect to the principal symbolic hierarchy of the edge algebra of boundary value problems, where an embedded submanifold on the boundary plays the role of an edge. We first consider the case that the weight is equal to the smoothness and calculate the dimensions of kernels and cokernels of the associated principal edge symbols. Then we pass to elliptic edge operators for arbitrary weights and construct the additional edge conditions by applying relative index results for conormal symbols.

The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy σ = (σψ, σ∧), where the second component takes value in operators on the infinite model cone of the local wedges. In general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the elliptcity of the principal edge symbol σ∧ which includes the (in general not explicitly known) number of additional conditions on the edge of trace and potential type. We focus here on these queations and give explicit answers for a wide class of elliptic operators that are connected with the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation and ellipticity for Dirichlet-Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues of the Agranovich-Dynin formula for edge boundary value problems, and we establish relations of elliptic operators for different weights, via the spectral flow of the underlying conormal symbols.

Understanding how global ice volume on the Earth has changed is of significant importance to improving our understanding of the climate system. Fortunately, the geographically unique perturbations in sea level that result from rapid changes in the mass of, otherwise difficult to measure, land-ice reservoirs can be used to infer the sources and magnitude of melt water. We explore the history of land-ice mass changes through the effect that these mass fluxes have had on both global and regional gravity and sea-level fields. / Earth and Planetary Sciences

We develop a new approach to the analysis of pseudodifferential operators with small parameter 'epsilon' in (0,1] on a compact smooth manifold X. The standard approach assumes action of operators in Sobolev spaces whose norms depend on 'epsilon'. Instead we consider the cylinder [0,1] x X over X and study pseudodifferential operators on the cylinder which act, by the very nature, on functions depending on 'epsilon' as well. The action in 'epsilon' reduces to multiplication by functions of this variable and does not include any differentiation. As but one result we mention asymptotic of solutions to singular perturbation problems for small values of 'epsilon'.

The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah-Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point.

The quantization of contact transformations of the cosphere bundle over a manifold with conical singularities is described. The index of Fredholm operators given by this quantization is calculated. The answer is given in terms of the Epstein-Melrose contact degree and the conormal symbol of the corresponding operator.