Deformation monitoring on ancient terracotta warriors by microscopic TV-holography

In order to investigate deterioration processes on the famous 2000-yr-old Chinese Terracotta warriors, deformation measurements were performed with TV-holography. The aim of the investigations is to estimate the suitability of several conservation agents and procedures, which are developed to preserve the extremely endangered paint layers of the figures. Due to the occurrence of small-scale deformation areas the field of view had to be reduced. A microscopic system was constructed and typical object deformations due to shrinkage and swelling are presented. To investigate the individual layers of the multilayered objects a short-coherent superluminescence diode instead of a laser diode is used in a further modification. By changing the path length of one of the interfering beams it is possible to select a region limited in depth where deformations are measured even if it is located below the surface. Results on an artificial test object and on original terracotta fragments demonstrate the capabilities of this new short-coherence TV-holography system.     

Logarithmic Terms in Trace Expansions of Atiyah–Patodi–Singer Problems

For Dirac-type operator D on a manifold X with a spectral boundarycondition (defined by a pseudodifferential projection), the associated heatoperator trace has an expansion in integer and half-integer powers and log-powersof t; the interest in the expansion coefficients goes back to the work of Atiyah,Patodi and Singer. In the product case considered by APS, it is known that allthe log-coefficients vanish when dim X is odd, whereas the log-coefficients atinteger powers vanish when dim X is even. We investigate here whether this partialvanishing of logarithms holds more generally. One type of result, shown forgeneral D with well-posed boundary conditions, is that a perturbation of Dby a tangential differential operator vanishing to order k on the boundaryleaves the first k log-power terms invariant (and the nonlocal power termsof the same degree are only locally perturbed). Another type of result is thatfor perturbations of the APS product case by tangential operators commuting withthe tangential part of D, all the logarithmic terms vanish when dim X is odd(whereas they can all be expected to be nonzero when dim X is even). The treatmentis based on earlier joint work with R. Seeley and a recent systematic parameter-dependentpseudodifferential boundary operator calculus, applied to the resolvent.     

Cubic form Geometry for Immersions in Centro-Affine and Graph Hypersurfaces

We study hypersurfaces whose traceless cubic form vanishes.     

On Lipschitz conditions for ordinary differential equations in Fréchet spaces

We will give an existence and uniqueness theorem for ordinary differential equations in Fréchet spaces using Lipschitz conditions formulated with a generalized distance and row-finite matrices.     

Numerical Investigation of the Effects of the Injection Current on the SHB-Effects of VCSEL''s

A spatially independent model of vertical-cavity surface-emitting lasers (VCSEL's) is built up in this paper by integrating the spatially dependent rate equations over the cross section of the active reigon of VCSEL's. The LP cosine modes in a weakly guiding cylindrical waveguide are used to represent the transverse modes in the VCSEL's cavity. This model is performed numerically with the 4^th order Runge-Kutta method in a self-consistent way. The dynamic and steady state characteristics of the multi-transverse mode competitions are investigated in detail. Different kinds of injection currents such as a disk-contact and ring-contact injection current are employed in these numerically implementations. Some interesting results are obtained and analyzed detailedly.