Abstract:
The stereoscopic reconstruction of air showers viewed by multiple imaging atmospheric Cherenkov telescopes (IACTs) allows a more precise reconstruction of shower energies and hence an improved determination of energy spectra. Reconstruction techniques and in particular new systematic checks are discussed on the basis of the large sample of gamma-rays from Mkn 501 detected with the HEGRA IACT system. (Talk presented at the Workshop ``Towards a Major Atmospheric Cherenkov Detector V'', Kruger Park, South Africa, 1997)

Abstract:
Based on data and Monte-Carlo simulations of the HEGRA IACT system, improved analysis techniques were developed for the determination of the shower geometry and shower energy from the multiple Cherenkov images. These techniques allow, e.g., to select subsamples of events with better than 3' angular resolution, which are used to limit the rms radius of the VHE emission region of the Crab Nebula to less than 1.5'. For gamma-rays of the Mrk 501 data sample, the energy can be determined to typically 10% and the core location to 2-3 m.

Abstract:
The infrared problem of the effective action in 2D is discussed in the framework of the Covariant Perturbation Theory. The divergences are regularised by a mass and the leading term is evaluated up to the third order of perturbation theory. A summation scheme is proposed which isolates the divergences from the finite part of the series and results in a single term. The latter turns out to be equivalent to the coupling to a certain classical external field. This suggests a renormalisation by factorisation.

Abstract:
The computation of the radiation flux related to the Hawking temperature of a Schwarzschild Black Hole or another geometric background is still well-known to be fraught with a number of delicate problems. In spherical reduction, as shown by one of the present authors (W. K.) with D.V. Vassilevich, the correct black body radiation follows when two ``basic components'' (conformal anomaly and a ``dilaton'' anomaly) are used as input in the integrated energy-momentum conservation equation. The main new element in the present work is the use of a quite different method, the covariant perturbation theory of Barvinsky and Vilkovisky, to establish directly the full effective action which determines these basic components. In the derivation of W. K. and D.V. Vassilevich the computation of the dilaton anomaly implied one potentially doubtful intermediate step which can be avoided here. Moreover, the present approach also is sensitive to IR (renormalisation) effects. We realize that the effective action naturally leads to expectation values in the Boulware vacuum which, making use of the conservation equation, suffice for the computation of the Hawking flux in other quantum states, in particular for the relevant Unruh state. Thus, a rather comprehensive discussion of the effects of (UV and IR) renormalisation upon radiation flux and energy density is possible.

Abstract:
We investigate the class of root systems R obtained by extending an irreducible root system by a torsion-free group G. In this context there is a Weyl group W and a group U with the presentation by conjugation. We show under additional hypotheses that the kernel of the natural homomorphism from U to W is isomorphic to the kernel of the homomorphism from the abelianization of U to that of W. For this we introduce the concept of a symmetric system, a discrete version of the concept of a symmetric space. Mathematics Subject Classification 2000: 20F55, 17B65, 17B67, 22E65, 22E40. Key Words and Phrases: Weyl group, root system, presentation by conjugation, extended affine Weyl group (EAWeG), extended affine root system (EARS), irreducible root system extended by an abelian group.

Abstract:
We investigate the class of root systems $R$ obtained by extending an $A_1$-type irreducible root system by a free abelian group $G$. In this context there is a Weyl group $W$ and a group $U$ with the presentation by conjugation. Both groups are reflection groups with respect to a discrete symmetric space $T$ associated to $R$. We show that the natural homomorphism $U\to W$ is an isomorphism if and only if an associated subset $T^{ab}\setminus\{0\}$ of $G_2=G/2G$ is 2-independent, i.e. its image under the map $G_2\to G_2\otimes G_2, g\mapsto g\otimes g$ is linearly independent over the Galois field $F_2$.

Abstract:
Ground-based gamma-ray astronomy, which provides access to the TeV energy range, is a young and rapidly developing discipline. Recent discoveries in this waveband have important consequences for a wide range of topics in astrophysics and astroparticle physics. This article is an attempt to review the experimental status of this field and to provide the basic formulae and concepts required to begin the interpretation of TeV observations.

Abstract:
An outdoor study was conducted to examine relationships between plant productivity and stress-protective phenolic plant metabolites. Twenty-two populations of the pasture legume white clover were grown for 4？ months during spring and summer in Palmerston North, New Zealand. The major phenolic compounds identified and quantified by HPLC analysis were glycosides of the flavonoids quercetin and kaempferol. Multivariate analysis revealed a trade-off between flavonoid accumulation and plant productivity attributes. White clover populations with high biomass production, large leaves and thick tap roots showed low levels of quercetin glycoside accumulation and low quercetin:kaempferol ratios, while the opposite was true for less productive populations. The latter included stress-resistant ecotypes from Turkey and China, and the analysis also identified highly significant positive relationships of quercetin glycoside accumulation with plant morphology (root:shoot ratio). Importantly, a high degree of genetic variation was detected for most of the measured traits. These findings suggest merit for considering flavonoids such as quercetin as potential selection criteria in the genetic improvement of white clover and other crops.

Abstract:
Dimensional reduction of generalized gravity theories or string theories generically yields dilaton fields in the lower-dimensional effective theory. Thus at the level of D=4 theories, and cosmology many models contain more than just one scalar field (e.g. inflaton, Higgs, quintessence). Our present work is restricted to two-dimensional gravity theories with only two dilatons which nevertheless allow a large class of physical applications. The notions of factorizability, simplicity and conformal simplicity, Einstein form and Jordan form are the basis of an adequate classification. We show that practically all physically motivated models belong either to the class of factorizable simple theories (e.g. dimensionally reduced gravity, bosonic string) or to factorizable conformally simple theories (e.g. spherically reduced Scalar-Tensor theories). For these theories a first order formulation is constructed straightforwardly. As a consequence an absolute conservation law can be established.