Über die Stetigkeit der analytischen Funktionale

Ohne Zusammenfassung     

In Bezug auf die Bestimmung des Stickstoffs

Ohne Zusammenfassung     

Introduction to the Special Issue: Fundamental Problems in Biocomplexity

Nonlinear Dynamics, Psychology, and Life Sciences -     

Femtosecond filament amplification in liquids

We study the femtosecond filamentation in a liquid amplifying medium, sulphorhodamine 640 in a methanol solvent. In the presence of population inversion, the energy of the filament increases while its diameter expands because of peak intensity clamping. PACS 42.25.Bs; 42.65.Jx; 42.65.Re; 42.65.Sf     

Frobenius-type theorems for Lipschitz distributions

We generalize the classical Frobenius Theorem to distributions that are spanned by locally Lipschitz vector fields. The various versions of the involutivity conditions are extended by means of set-valued Lie derivatives—in particular, set-valued Lie brackets—and set-valued exterior derivatives. A PDEs counterpart of these Frobenius-type results is investigated as well.     

Femtosecond filamentation in air at low pressures: Part I: Theory and numerical simulations

We investigate numerically the influence of the pressure on femtosecond filamentation in air. We show that femtosecond filamentation occurs at low pressure and compute the features of the plasma channel generated in the wake of the pulse. We discuss the influence of the pulse duration, chirp and input beam shape on the length of the plasma channels. These calculations constitute a prerequisite for laboratory experiments over short distances as well as for vertical femtosecond filamentation at high altitude on which light detection and ranging techniques or lightning protection rely.     

Structure and high-pressure behavior of 2,5-di-(4-aminophenyl)-1,3,4-oxadiazole

The crystalline structures of two modifications of a compound containing the oxadiazole ring, 2,5-di-(4-aminophenyl)-1,3,4-oxadiazole (DAPO) were determined. One of these modifications contains water molecules in the crystal structure, which is observed for the first time for an oxadiazole crystal. Both crystals show an orthorhombic structure. The water free modification, DAPO I, belongs to the space group Pbca (61) and has the lattice parameters: a=13.461(5), b=7.937(3) and c=22.816(8) Å (CCDC 246608). The water containing pseudo-polymorph, DAPO II, has the space group Cmcm (63) and the lattice parameters: a=16.330(5), b=12.307(2) and c=6.9978(14) Å (CCDC 246609). To gain information on the inter molecular interactions within the crystals, X-ray experiments under compression at ambient temperature and under heating at vacuum conditions were performed. Neither DAPO I nor DAPO II undergo phase transitions in the ressure range up to 5 GPa, as could be concluded from X-ray and Raman experiments. X-ray and calorimetric studies indicate that DAPO II dehydrates into DAPO I under increasing temperature. Structural considerations suggest a two-stage process. The compression behavior of both substances is well described by the Murnaghan equation of state (MEOS) and the values of the bulk modulus and its pressure derivative are determined for these crystals. Additionally, in the case of DAPO I, also the thermal expansion coefficient α₀ was measured.     

Gas-Phase Synthesis of Ethyl tert-Butyl Ether (ETBE) on H-ZSM-5 Catalyst in Continuous Fixed-Bed and Fluidized-Bed Reactors

The gas-phase synthesis of ETBE from ethanol and isobutene has been carried out over a H-ZSM-5 catalyst in two types of continuous-flow catalytic reactors, fixed-bed and fluidized-bed. We have studied the influence of temperature, molar ratio ethanol/isobutene and weight hourly space velocity on the yield of ETBE.