ix, 99 p. / We characterize the diagonals of four classes of self-adjoint operators on infinite dimensional Hilbert spaces. These results are motivated by the classical Schur-Horn theorem, which characterizes the diagonals of self-adjoint matrices on finite dimensional Hilbert spaces. In Chapters II and III we present some known results. First, we generalize the Schur-Horn theorem to finite rank operators. Next, we state Kadison's theorem, which gives a simple necessary and sufficient condition for a sequence to be the diagonal of a projection. We present a new constructive proof of the sufficiency direction of Kadison's theorem, which is referred to as the Carpenter's Theorem. Our first original Schur-Horn type theorem is presented in Chapter IV. We look at operators with three points in the spectrum and obtain a characterization of the diagonals analogous to Kadison's result. In the final two chapters we investigate a Schur-Horn type problem motivated by a problem in frame theory. In Chapter V we look at the connection between frames and diagonals of locally invertible operators. Finally, in Chapter VI we give a characterization of the diagonals of locally invertible operators, which in turn gives a characterization of the sequences which arise as the norms of frames with specified frame bounds. This dissertation includes previously published co-authored material. / Committee in charge: Marcin Bownik, Chair; N. Christopher Phillips, Member; Yuan Xu, Member; David Levin, Member; Dietrich Belitz, Outside Member

La combinatoire analytique étudie le comportement asymptotique des suites à travers les propriétés analytiques de leurs fonctions génératrices. Ce domaine a conduit au développement d’outils profonds et puissants avec de nombreuses applications. Au delà de la théorie univariée désormais classique, des travaux récents en combinatoire analytique en plusieurs variables (ACSV) ont montré comment calculer le comportement asymptotique d’une grande classe de fonctions différentiellement finies:les diagonales de fractions rationnelles. Cette thèse examine les méthodes de l’ACSV du point de vue du calcul formel, développe des algorithmes rigoureux et donne les premiers résultats de complexité dans ce domaine sous des hypothèses très faibles. En outre, cette thèse donne plusieurs nouvelles applications de l’ACSV à l’énumération des marches sur des réseaux restreintes à certaines régions: elle apporte la preuve de plusieurs conjectures ouvertes sur les comportements asymptotiques de telles marches,et une étude détaillée de modèles de marche sur des réseaux avec des étapes pondérées. / The field of analytic combinatorics, which studies the asymptotic behaviour ofsequences through analytic properties of their generating functions, has led to thedevelopment of deep and powerful tools with applications across mathematics and thenatural sciences. In addition to the now classical univariate theory, recent work in thestudy of analytic combinatorics in several variables (ACSV) has shown how to deriveasymptotics for the coefficients of certain D-finite functions represented by diagonals ofmultivariate rational functions. This thesis examines the methods of ACSV from acomputer algebra viewpoint, developing rigorous algorithms and giving the firstcomplexity results in this area under conditions which are broadly satisfied.Furthermore, this thesis gives several new applications of ACSV to the enumeration oflattice walks restricted to certain regions. In addition to proving several openconjectures on the asymptotics of such walks, a detailed study of lattice walk modelswith weighted steps is undertaken.

Master thesis is focused to design the timber pedestrian bridge over the track. The load-bearing construction is composed from the truss girder and cross laminated tiber plates. Bridge is coveder. Layout dimensions of the bridge are 49.0 m x 4.8 m

This master's thesis deals with the designing of the appropriate supporting steel structure footbridge for pedestrians. The footbridge is used to connect two separate buildings (buildings D and Z at the Faculty of Civil Engineering Brno University of Technology). Four variants have been designed about solutions supporting steel structure. The final variant was prepared in detail and was carried out static assessment of the individual elements and selected details. The main supporting structure of this variant are two trusses. Diagonals of these trusses are designed linkage system of Macalloy 460. Bridge deck is designed of composite steel a concrete board with crossbars. The footbridge is designed as simple beam with an overhanging end. Length span is 34.8 m, length overhanging ends is 5.8 meters. The total length of the footbridge is 40.6 meters. Width of footbridge is 2.8 meters. Free width is 2 meters. In the cross point with the axis of local road is height of footbridge above ground 4.43 meters. Next to the building Z, there is a footbridge stored on a concrete support, near the building D, the footbridge is stored on a steel frame of support. The footbridge is deposited on elastomeric bearings. The footbridge is being protected from the weather. The sheating of the building is designed by Wictec 60 system. The master's thesis also contains drawing documentation of the proposed solution.