Bone-ablation mechanism using CO2 lasers of different pulse duration and wavelength

Bone ablation using different pulse parameters and four emission lines of 9.3, 9.6, 10.3, and 10.6 m of the CO₂ laser exhibits effects which are caused by the thermal properties and the absorption spectrum of bone material. The ablation mechanism was investigated with light- and electron-microscopy at short laser-pulse durations of 0.9 and 1.8 s and a long pulse of 250 s. It is shown that different processes are responsible for the ablation mechanism either using the short or the long pulse durations. In the case of short pulse durations it is shown that, although the mineral components are the main absorber for CO₂ radiation, water is the driving force for the ablation process. The destruction of material is based on explosive evaporation of water with an ablation energy of 1.3 kJ/cm³. Histological examination revealed a minimal zone of 10–15 m of thermally altered material at the bottom of the laser drilled hole. Within the investigated spectral range we found that the ablation threshold at 9.3 and 9.6 m is lower than at 10.3 and 10.6 m. In comparison the ablation with a long pulse duration is determined by two processes. On the one side, the heat lost by heat conduction leads to carbonization of a surface layer, and the absorption of the CO₂ radiation in this carbonized layer is the driving force of the ablation process. On the other side, it is shown that up to 60% of the pulse energy is absorbed in the ablation plume. Therefore, a long pulse duration results in an eight-times higher specific ablation energy of 10 kJ/cm³.     

On noise reduction methods for chaotic data

Recently proposed noise reduction methods for nonlinear chaotic time sequences with additive noise are analyzed and generalized. All these methods have in common that they work iteratively, and that in each step of the iteration the noise is suppressed by requiring locally linear relations among the delay coordinates, i.e., by moving the delay vectors towards some smooth manifold. The different methods can be compared unambiguously in the case of strictly hyperbolic systems corrupted by measurement noise of infinitesimally low level. It was found that all proposed methods converge in this ideal case, but not equally fast. Different problems arise if the system is not hyperbolic, and at higher noise levels. A new scheme which seems to avoid most of these problems is proposed and tested, and seems to give the best noise reduction so far. Moreover, large improvements are possible within the new scheme and the previous schemes if their parameters are not kept fixed during the iteration, and if corrections are included which take into account the curvature of the attracting manifold. Finally, the fact that comparison with simple low-pass filters tends to overestimate the relative achievements of these nonlinear noise reduction schemes is stressed, and it is suggested that they should be compared to Wiener-type filters.     

Crystal and molecular structure of the cycloaddition product between maleic anhydride,cyclopentadiene, and 1,2-bis(dibromomethyl)benzene as DMF solvate (1∶2)

Crystal structure determination reveals that the unknown cycloaddition product between maleic anhydride, cyclopentadiene, and 1,2-bis(dibromomethyl)benzene has a nona-cyclic centrosymmetric structure. The compound was studied as DMF solvate (12). There is no significant intermolecular interaction between the title molecule and the DMF. Packing is in layers for both molecular species. A possible mechanism of formation of the title compound is discussed.     

Stochastic dominance with nonadditive probabilities

Choquet expected utility which uses capacities (i.e. nonadditive probability measures) in place of-additive probability measures has been introduced to decision making under uncertainty to cope with observed effects of ambiguity aversion like the Ellsberg paradox. In this paper we present necessary and sufficient conditions for stochastic dominance between capacities (i.e. the expected utility with respect to one capacity exceeds that with respect to the other one for a given class of utility functions). One wide class of conditions refers to probability inequalities on certain families of sets. To yield another general class of conditions we present sufficient conditions for the existence of a probability measureP with f dC= f dP for all increasing functionsf whenC is a given capacity. Examples includen-th degree stochastic dominance on the reals and many cases of so-called set dominance. Finally, applications to decision making are given including anticipated utility with unknown distortion function.