The harsh conditions of space, the stringent requirements for orbiting devices, and the increasing precision pointing requirements of many space applications demand an actuator that can provide necessary force while using less space and power than its predecessors. Ideally, this actuator would be able to isolate vibrations and never fail due to mechanical wear, while pointing with unprecedented accuracy. This actuator has many space applications from satellite optical communications and satellite appendage positioning to orbiting telescopes. This thesis presents the method of design of such an actuator a self-bearing motor. The actuator uses Lorentz forces to generate both torque and bearing forces. It has a slotless winding configuration with four sets of three-phase currents. A stand-alone software application, LFMD, was written to automatically optimize and configure such a motor according to a designers application requirements. The optimization is done on the bases of minimum powerloss, minimum motor outer diameter, minimum motor mass, and minimum length. Using that program, two sample space applications are analyzed and applicable motor configurations are presented.

Neste trabalho apresentamos uma classificação das hipersuperfícies regradas e de Weingarten no espaço hiperbólico. / In this work we provide a classification for ruled and Weingarten hypersurfaces in hyperbolic space.

The measure of non-compactness is defined for any continuous mapping T : X Y between two Banach spaces X and Y as β(T) := inf { r > 0: T(BX) can be covered by finitely many open balls with radius r } . It can easily be shown that 0 ≤ β(T) ≤ ∥T∥ and that β(T) = 0, if and only if the mapping T is compact. My supervisor prof. Stanislav Hencl has proved in his paper that the measure of non-compactness of the known embedding W k,p 0 (Ω) → Lp∗ (Ω), where kp is smaller than the dimension, is equal to its norm. In this thesis we prove that the measure of non-compactness of the embedding between function spaces is under certain general assumptions equal to the norm of that embedding. We apply this theorem to the case of Lorentz spaces to obtain that the measure of non-compactness of the embedding Wk 0 Lp,q (Ω) → Lp∗,q (Ω) is for suitable p and q equal to its norm. 1

Neste trabalho apresentamos uma classificação das hipersuperfícies regradas e de Weingarten no espaço hiperbólico. / In this work we provide a classification for ruled and Weingarten hypersurfaces in hyperbolic space.

We study the behaviour of logarithmically convex combinations of operators given by Tf = |S1f| 1 θ |S2f|1− 1 θ , where S1, S2 are some (usually quasi-linear) operators acting on spaces of measurable functions and θ ∈ (1, ∞) is a parameter. We develop two, quite different in nature, interpolation theories, each of which enables us to obtain a rather com- prehensive information about the behavior of such operators on function spaces. The first one is completely general and is based on abstract interpolation and Calderón spaces. We illustrate the theoretical results by a wide variety of examples of pairs of spaces X, Y such that T: X → Y is bounded, these in particular include the so-called Calderón-Lozanovskiı̌ construction. The second theory departs from pointwise estimates by Calderón operators and is particularly tailored for obtaining boundedness results between Orlicz spaces given weak-type estimates that arise in applications. A common feature of both theories is an approach, apparently new, involving interpolation of four spaces. The input data in each case consists of two reasonable separate endpoint estimates for the operators S1 and S2. 1

The presented work contains a survey of the so far known results about the operator inequalities of the type "good λ", "better good λ" and "rearranged good λ" on the function spaces over the Euclidean space with the Lebesgue measure and their corollaries in the form of more complex operator inequal- ities and norm estimates. However, the main aim is to build similar theory for the Riesz potential operator on the function spaces over the quasi-metric space with the so-called "doubling" measure. Combining the corollaries of this theory with the known norm estimates we obtain the boundedness for the Riesz potential operator on the Lebesgue and Lorentz spaces.