Coupling of the GB set property for ergodic averages

Let (Y,,,T) be an ergodic dynamical system. LetA be an nonempty subset ofL ²() such that , whereA=sup{||sȒt||₂ ,s, tA} andN(A, u) is the smallest number ofL ²()-open balls of radiusu, centered inA, enough to coverA. Let . We prove as a consequence of a more general result, thatC(A) is aGB subset ofL ²().     

Threshold conditions for 800 nm pumping of 2 μm Tm : Ho lasers

Pumping requirements of pulsed and continuous wave (CW) 2 m Tm : Ho lasers are investigated experimentally and theoretically for excitation at 800 nm. The influence of the pulse duration on threshold is measured using a chopped Ti : Al₂O₃ laser. Based on the experimental and simulated results the spatial and temporal pump requirements in future quasi-CW high-power diode-pumped 2 m Tm : Ho lasers are determined. The experiments and the model allow the evaluation of different loss mechanisms and indicate significant 540 nm emitting loss mechanisms.     

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.     

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.