Influence of Anthropogenic Climate Change on the Ecophysiology of the Cold Water Coral Lophelia pertusa = Einfluss des anthropogenen Klimawandels auf die Ökophysiologie der Kaltwasserkoralle Lophelia pertusa

Monographic work describing the cultivation of cold-water coral Lophelia pertusa in closed recirculating systems and climate change related short- and long-term experiments

Rank 3 permutation characters and maximal subgroups

In this paper we classify all maximal subgroups M of a nearly simple primitive rank 3 group G of type L=Omega_{2m+1}(3), m > 3; acting on an L-orbit E of non-singular points of the natural module for L such that 1_P^G <=1_M^G where P is a stabilizer of a point in E. This result has an application to the study of minimal genera of algebraic curves which admit group actions.Comment: 41 pages, to appear in Forum Mathematicu

Feller semigroups, Lp-sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols

The question of extending L-p-sub-Markovian semigroups to the spaces L-q, q &gt; P, and the interpolation of LP-sub-Markovian semigroups with Feller semigroups is investigated. The structure of generators of L-p-sub-Markovian semigroups is studied. Subordination in the sense of Bochner is used to discuss the construction of refinements of L-p-sub-Markovian semigroups. The role played by some function spaces which are domains of definition for L-p-generators is pointed out. The problem of regularising powers of generators as well as some perturbation results are discussed

Loop homology of spheres and complex projective spaces

In his Inventiones paper, Ziller (Invent. Math: 1-22, 1977) computed the integral homology as a graded abelian group of the free loop space of compact, globally symmetric spaces of rank 1. Chas and Sullivan (String Topology, 1999)showed that the homology of the free loop space of a compact closed orientable manifold can be equipped with a loop product and a BV-operator making it a Batalin-Vilkovisky algebra. Cohen, Jones and Yan (The loop homology algebra of spheres and projective spaces, 2004) developed a spectral sequence which converges to the loop homology as a spectral sequence of algebras. They computed the algebra structure of the loop homology of spheres and complex projective spaces by using Ziller's results and the method of Brown-Shih (Ann. of Math. 69:223-246, 1959, Publ. Math. Inst. Hautes \'Etudes Sci. 3: 93-176, 1962). In this note we compute the loop homology algebra by using only spectral sequences and the technique of universal examples. We therefore not only obtain Zillers' and Brown-Shihs' results in an elementary way, we also replace the roundabout computations of Cohen, Jones and Yan (The loop homology algebra of spheres and projective spaces, 2004) making them independent of Ziller's and Brown-Shihs' work. Moreover we offer an elementary technique which we expect can easily be generalized and applied to a wider family of spaces, not only the globally symmetric ones.Comment: 10 pages, 8 figure

Ree geometries

We introduce a rank 3 geometry for any Ree group over a not necessarily perfect field and show that its full collineation group is the automorphism group of the corresponding Ree group. A similar result holds for two rank 2 geometries obtained as a truncation of this rank 3 geometry. As an application, we show that a polarity in any Moufang generalized hexagon is unambiguously determined by its set of absolute points, or equivalently, its set of absolute lines

Manifolds associated with (Z2)n(Z_2)^n-colored regular graphs

In this article we describe a canonical way to expand a certain kind of $(\mathbb Z_2)^{n+1}$-colored regular graphs into closed $n$-manifolds by adding cells determined by the edge-colorings inductively. We show that every closed combinatorial $n$-manifold can be obtained in this way. When $n\leq 3$, we give simple equivalent conditions for a colored graph to admit an expansion. In addition, we show that if a $(\mathbb Z_2)^{n+1}$-colored regular graph admits an $n$-skeletal expansion, then it is realizable as the moment graph of an $(n+1)$-dimensional closed $(\mathbb Z_2)^{n+1}$-manifold.Comment: 20 pages with 9 figures, in AMS-LaTex, v4 added a new section on reconstructing a space with a $(Z_2)^n$-action for which its moment graph is a given colored grap

Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms

Let E be an unbounded open (or closed) domain in Euclidean space of dimension greater or equal to two. We present conservativeness criteria for (possibly reflected) diffusions with state space E that are associated to fairly general perturbed divergence form operators. Our main tool is a recently extended forward and backward martingale decomposition, which reduces to the well-known Lyons-Zheng decomposition in the symmetric case.Comment: Corrected typos, minor modification