A new method for estimating derivatives based on a distribution approach

In many applications, the estimation of derivatives has to be done from noisy measured signal. In this paper, an original method based on a distribution approach is presented. Its interest is to report the derivatives on infinitely differentiable functions. Thus, the estimation of the derivatives is done only from the signal. Besides, this method gives some explicit formulae leading to fast calculus. For all these reasons, it is an efficient method in the case of noisy signals as it will be confirmed in several examples.     

Interaction of the general volatile anesthetic Enflurane with bacteriorhodopsin-DPPC proteoliposomes

Thermal decomposition of dried crystalline powder obtained from titanium(IV) bis(acetylacetonate) diisopropoxide (75% solution in 2-propanol) (1) was monitored by simultaneous TG/DTA, EGA-FTIR and EGA-MS measurements and the results were compared with those of amorphous powder obtained by gelling of acetylacetonate-modified titanium(IV) tetra-isopropoxide at molar ratio of 1:2 in boiling 2-methoxyethanol (2). Thermal degradation of 1 in the temperature range of 25–700°C consists of 5 steps with a total mass loss of 62.5%. EGA by FTIR and MS revealed the release of H₂O below 120°C; followed by an intensive evolution of acetylacetone around 245°C. The release of acetone and acetic acid occurs up to 270°C and that of CO and CO₂ up to 530°C.     

Regioselective intramolecular N1-C3 cyclizations on pyrrole-proline to ABC tricycles of dibromophakellin and ugibohlin

Pyrrole N1-C and C3-C regioselective linkage to the fused tricycle ABC system present in the marine metabolites ugibohlin and dibromoisophakellin is described. The cyclization is closely dependent on the electrophilic function, bromination degree of the pyrrole moiety and pH conditions. The mechanism of the functionalization of the ABC olefin by oxidative agents was found to occur through an N-acyliminium intermediate as showed by the natural chemical connection between ugibohlin and dibromoisophakellin.     

Dynkin's isomorphism theorem and the Ray-Knight theorems

Summary In the case of diffusions, we show that the isomorphism theorem of Dynkin and the Ray-Knight theorems can be derived from each other. Our proof uses additivity properties of squared Bessel processes and an absolute continuity relation between squared Bessel processes of dimensions one and three.Research supported in part by Air Force Office of Scientific Research (USAFOSR 89-0261)This work was carried out while visiting the Technion     

Femtosecond laser Fourier transform absorption spectroscopy

A femtosecond mode-locked laser is used for what is believed to be the first time as a broadband infrared source for high-resolution Fourier transform absorption spectroscopy. A demonstration is made with a Cr(4+):YAG laser. The entire nu(1)+nu(3) vibration-rotation band region of acetylene, observed after passing through a single-pass 80-cm-long cell, is simultaneously recorded between 1480 and 1600 nm, in 7.9 s with a signal-to-noise ratio equal to 1000. Two hot bands of the most abundant acetylene isotopologue and the nu(1)+nu(3) band of the (13)C(12)CH(2) are also present. Replacement of the usual conventional tungsten lamp by the bright laser source reduces by about a factor of 150 the recording time needed to get similar results. The noise equivalent absorption coefficient at 1 s averaging is equal to 7x10(-7) cm(-1)Hz(-1/2) per spectral element.