Mean first passage time for a class of non-Markovian processes

We determine the probability distribution of the first passage time for a class of non-Markovian processes. This class contains, amongst others, the well-known continuous time random walk (CTRW), which is able to account for many properties of anomalous diffusion processes. In particular, we obtain the mean first passage time for CTRW processes with truncated power-law transition time distribution. Our treatment is based on the fact that the solutions of the non-Markovian master equation can be obtained via an integral transform from a Markovian Langevin process.     

Schnitt- und Zykelgeometrien

Ohne ZusammenfassungHabilitationsschrift Darmstadt 1975.     

Eine Charakteristische Spiegelungseigenschaft hermitescher Quadriken

If is a projective space of dimension 3 and characteristic 2 and a semi ovoid of, then is a non degenerate semi quadric and is of finite dimension, if and only if there exists a perspectivity of order 2 and axish stabilizing, for every hyperplaneh meeting in at least 2 points.     

Verallgemeinerte Vierecke in projektiven Räumen

Ohne Zusammenfassung Wolfgang Gaschütz zum 60. Geburtstag gewidmet     

On a Problem of Schoenberg and Wills in Diophantine Approximation

Let n be a fixed natural number. Wills has shown that there exist irrational numbers α₁,..., α_n and real numbers β₁,..., β₁ with max_1≤i≤n ‖qα_i-β_i‖ > 1/2 – 1/2n for all integers q (‖·‖ denotes the distance to the nearest integer). His example is α_i = α and β_i = i/n + δ, δ suitably chosen. Beyond that, he asked if α_i can be found with pairwise different ‖α_i‖. We prove that this does not hold for n ≤ 5, thereby revealing the close relation to Schoenberg's billiard ball problem for cubes and classifying its critical lines in these dimensions.     

Zu Sekanten symmetrische Halbovoide

Ohne Zusammenfassung