Classification and Characterization of rationally elliptic manifolds in low dimensions

We give a characterization of closed, simply connected, rationally elliptic 6-manifolds in terms of their rational cohomology rings and a partial classification of their real cohomology rings. We classify rational, real and complex homotopy types of closed, simply connected, rationally elliptic 7-manifolds. We give partial results in dimensions 8 and 9.Comment: 23 pages; extended Section 2, revised Section 5 and several minor revision

Single Jump Processes and Strict Local Martingales

Many results in stochastic analysis and mathematical finance involve local martingales. However, specific examples of strict local martingales are rare and analytically often rather unhandy. We study local martingales that follow a given deterministic function up to a random time $\gamma$ at which they jump and stay constant afterwards. The (local) martingale properties of these single jump local martingales are characterised in terms of conditions on the input parameters. This classification allows an easy construction of strict local martingales, uniformly integrable martingales that are not in $H^1$, etc. As an application, we provide a construction of a (uniformly integrable) martingale $M$ and a bounded (deterministic) integrand $H$ such that the stochastic integral $H\bullet M$ is a strict local martingale.Comment: 21 pages; forthcoming in 'Stochastic Processes and their Applications

Minimal Conditions for Implications of Gronwall-Bellman Type

Gronwall-Bellman type inequalities entail the following implication: if a sufficiently integrable function satisfies a certain homogeneous linear integral inequality, then it is nonpositive. We present a minimal (necessary and sufficient) condition on the Borel measure underlying the integrals for this implication to hold. The condition is also a necessary prerequisite for any nontrivial bound on solutions to inhomogeneous linear integral inequalities of Gronwall-Bellman type.Comment: 11 pages; forthcoming in 'Journal of Mathematical Analysis and Applications

Satisfiability of cross product terms is complete for real nondeterministic polytime Blum-Shub-Smale machines

Nondeterministic polynomial-time Blum-Shub-Smale Machines over the reals give rise to a discrete complexity class between NP and PSPACE. Several problems, mostly from real algebraic geometry / polynomial systems, have been shown complete (under many-one reduction by polynomial-time Turing machines) for this class. We exhibit a new one based on questions about expressions built from cross products only.Comment: In Proceedings MCU 2013, arXiv:1309.104

Time-resolved Microwave Conductivity. Part 2.-Quantum-sized TiO_2 and the Effect of Adsorbates and Light Intensity on Charge-carrier Dynamics

Charge-carrier recombination dynamics after a pulsed laser excitation are investigated by time-resolved microwave conductivity (TRMC) for quantum-sized (Q-) TiO_2 and P25, a bulk-phase TiO_2. Adsorbed scavengers such as HNO_3, HC, HCIO_4, isopropyl alcohol, trans-decalin, tetranitromethane, and methyl viologen dichloride result in different charge-carrier recombination dynamics for Q-TiO_2 and P25. The differences include a current doubling with isopropyl alcohol for which electron injection into Q-TiO_2 is much slower than into P25 and relaxation of the selection rules of an indirect-bandgap semiconductor due to size quantization. However, the faster interfacial charge transfer predicted for Q-TiO_2 due to a 0. 2 eV gain in redox overpotentials is not observed. The effect of light intensity is also investigated. Above a critical injection level, fast recombination channels are opened, which may be a major factor resulting in the dependence of the steady-state photolysis quantum yields on l^(–1/2). The fast recombination channels are opened at lower injection levels for P25 than for Q-TiO_2, and a model incorporating the heterogeneity of surface-hole traps is presented

Homogeneous spaces, curvature and cohomology

We give new counterexamples to a question of Karsten Grove, whether there are only finitely many rational homotopy types among simply connected manifolds satisfying the assumptions of Gromov's Betti number theorem. Our counterexamples are homogeneous Riemannian manifolds, in contrast to previous ones. They consist of two families in dimensions 13 and 22. Both families are nonnegatively curved with an additional upper curvature bound and differ already by the ring structure of their cohomology rings with complex coefficients. The 22-dimensional examples also admit almost nonnegative curvature operator with respect to homogeneous metrics.Comment: 11 pages; minor changes, accepted versio