A Stochastic Subgradient Method for Distributionally Robust Non-convex and Non-smooth Learning

Journal of Optimization Theory and Applications - We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with...     

Space-Time Directional Lyapunov Exponents for Cellular Automata

Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as function of the velocity and an inequality relating them to the directional entropy is proved.     

Spectral decomposition of an elementary 3-fermion 2-body operator

The eigenvalues and eigenfunctions of an elementary 3-fermion 2-body operator 3P²_g∧I¹A³∑_{1≤i≤j≤3}P²_g(i, j)A³ acting on a 3-particle antisymmetric finite-dimensional Hilbert space have been found. Here P_g² denotes the projection operator onto a 2-particle antisymmetric function g², while A³ denotes the 3-particle antisymmetrizing operator.     

On Non-Continuous Dirichlet Processes

We introduce here some Itô calculus for non-continuous Dirichlet processes. Such calculus extends what was known for continuous Dirichlet processes or for semimartingales. In particular we prove that non-continuous Dirichlet processes are stable under C ¹ transformation.     

Analysis of Glycosides and Aglycones of Flavonoid Compounds by Double-Development Thin-Layer Chromatography

JPC – Journal of Planar Chromatography – Modern TLC - Flavonoid glycosides are much more polar than their aglycones and the two groups of compounds are difficult to separate by planar...     

Tablet disintegration monitored by magnetic resonance imaging

The disintegration of bromhexin tablets was monitored by magnetic resonance imaging. The fast imaging method FLASH with spoiling gradients was used to obtain images of the tablets in short time intervals. The rate of the disintegration depends on the preparation method, kind and percentage of the carrier (polyethylene glycol, lactose). Solid dispersion with slow evaporation of solvent yields materials with decreased dissolution rate. Increasing molecular mass of polyethylene glycol and its percentage content also hampers disintegration.     

The capacity of parabolic julia sets

Supported by SFB 170 “Geometrie und Analysis” at the University of G?ttingen