Abstract:
There are presented the morpho-physiological and ornamental characteristics of two new varieties of roses, as follows: "Simfonia" (Th) has vigorous bushes, up-right stems, good resistance to mildew, well-shaped and large shining-white petalled buds. Suitable for cut flowers. Introduced 1978; "Rosabunda" (Fl.) has vigorous bushes, good resistance to mildew, early and very abundant bloom, with shining-pink coloured and fragrant petals. Suitable to bedding. Introduced 1979.

Abstract:
A (smooth) dynamical system with transformation group $\mathbb{T}^n$ is a triple $(A,\mathbb{T}^n,\alpha)$, consisting of a unital locally convex algebra $A$, the $n$-torus $\mathbb{T}^n$ and a group homomorphism $\alpha:\mathbb{T}^n\rightarrow\Aut(A)$, which induces a (smooth) continuous action of $\mathbb{T}^n$ on $A$. In this paper we present a new, geometrically oriented approach to the noncommutative geometry of principal torus bundles based on such dynamical systems. Our approach is inspired by the classical setting: In fact, after recalling the definition of a trivial noncommutative principal torus bundle, we introduce a convenient (smooth) localization method for noncommutative algebras and say that a dynamical system $(A,\mathbb{T}^n,\alpha)$ is called a noncommutative principal $\mathbb{T}^n$-bundle, if localization leads to a trivial noncommutative principal $\mathbb{T}^n$-bundle. We prove that this approach extends the classical theory of principal torus bundles and present a bunch of (non-trivial) noncommutative examples.

Abstract:
From a geometrical point of view it is, so far, not sufficiently well understood what should be a "noncommutative principal bundle". Still, there is a well-developed abstract algebraic approach using the theory of Hopf algebras. An important handicap of this approach is the ignorance of topological and geometrical aspects. The aim of this thesis is to develop a geometrically oriented approach to the noncommutative geometry of principal bundles based on dynamical systems and the representation theory of the corresponding transformation group.

Abstract:
A dynamical system is a triple $(A,G,\alpha)$, consisting of a unital locally convex algebra $A$, a topological group $G$ and a group homomorphism $\alpha:G\rightarrow\Aut(A)$, which induces a continuous action of $G$ on $A$. Further, a unital locally convex algebra $A$ is called continuous inverse algebra, or CIA for short, if its group of units $A^{\times}$ is open in $A$ and the inversion $\iota:A^{\times}\rightarrow A^{\times},\,\,\,a\mapsto a^{-1}$ is continuous at $1_A$. For a compact manifold $M$, the Fr\'echet algebra of smooth functions $C^{\infty}(M)$ is the prototype of such a continuous inverse algebra. We show that if $A$ is a complete commutative CIA, $G$ a compact group and $(A,G,\alpha)$ a dynamical system, then each character of $B:=A^G$ can be extended to a character of $A$. In particular, the natural map on the level of the corresponding spectra $\Gamma_A\rightarrow\Gamma_B$, $\chi\mapsto\chi_{\mid B}$ is surjective.

Abstract:
In this paper we present a new characterization of free group actions (in classical differential geometry), involving dynamical systems and representations of the corresponding transformation groups. In fact, given a dynamical system, we provide conditions including the existence of "sufficiently many" representations of the transformation group which ensure that the corresponding action of that group on the spectrum of the algebra is free. In particular, the case of compact abelian groups is discussed very carefully. We further present an application to the structure theory of C*-algebras and an application to the noncommutative geometry of principal bundles.

Abstract:
Let $\Lambda$ be a finite abelian group. A dynamical system with transformation group $\Lambda$ is a triple $(A,\Lambda,\alpha)$, consisting of a unital locally convex algebra $A$, the finite abelian group $\Lambda$ and a group homomorphism $\alpha:\Lambda\rightarrow\Aut(A)$, which induces an action of $\Lambda$ on $A$. In this paper we present a new, geometrically oriented approach to the noncommutative geometry of principal bundles with finite abelian structure group based on such dynamical systems.

Abstract:
We analyse the decay $\tau\to\pi\pi\pi\nu$ based on the recently developed techniques to generate axial-vector resonances dynamically. Under the assumption that the a1 is a coupled-channel meson-molecule, the spectral function is described surprisingly well by adjusting only one free parameter. Including, in addition, an elementary a1 corrupts the results.

Abstract:
The isovector--vector and the isovector--axial-vector current are related by a chiral transformation. These currents can be called chiral partners at the fundamental level. In a world where chiral symmetry was not broken, the corresponding current-current correlators would show the same spectral information. In the real world chiral symmetry is spontaneously broken. A prominent peak -- the rho-meson -- shows up in the vector spectrum (measured in (e^+ e^-)-collisions and tau-decays). On the other hand, in the axial-vector spectrum a broad bump appears -- the a_1-meson (also accessible in tau-decays). It is tempting to call rho and a_1 chiral partners at the hadronic level. Strong indications are brought forward that these ``chiral partners'' do not only differ in mass but even in their nature: The rho-meson appears dominantly as a quark-antiquark state with small modifications from an attractive pion-pion interaction. The a_1-meson, on the other hand, can be understood as a meson-molecule state mainly formed by the attractive interaction between pion and rho-meson. A key issue here is that the meson-meson interactions are fixed by chiral symmetry breaking. It is demonstrated that one can understand the vector and the axial-vector spectrum very well within this interpretation. It is also shown that the opposite cases, namely rho as a pion-pion molecule or a_1 as a quark-antiquark state lead to less satisfying results. Finally speculations on possible in-medium changes of hadron properties are presented.

Abstract:
The decay $\tau\to \pi\pi\pi\nu$ is analysed using different methods to account for the resonance structure, which is usually ascribed to the a1. One scenario is based on the recently developed techniques to generate axial-vector resonances dynamically, whereas in a second calculation the a1 is introduced as an explicit resonance. We investigate the influence of different assumptions on the result. In the molecule scenario the spectral function is described surprisingly well by adjusting only one free parameter. This result can be systematically improved by adding higher order corrections to the iterated Weinberg-Tomozawa interaction. Treating the a1 as an explicit resonance on the other hand leads to peculiar properties.

Abstract:
We study free and compact group actions on unital C*-algebras. In particular, we provide a complete classification theory of these actions for compact abelian groups and explain its relation to the classical classification theory of principal bundles.