Description of pulse propagation in a dispersive medium by use of a pulse quality factor

We investigated how the duration of short laser pulses evolves in a dispersive material, using rms widths and a propagation law based on a pulse quality factor. Experiments were carried out with femtosecond pulses (10 to 25fs at the temporal waist) propagating in bulk fused silica. Excellent agreement was found between theory and experiment. This approach does not require complete characterization of laser pulses and eliminates the need for any assumption regarding the interpretation of autocorrelation traces. The method is of general validity, and it can be applied to pulses of arbitrary shape.     

Spherical functions and conformal densities on spherically symmetric -spaces

Let be a -space which is spherically symmetric around some point and whose boundary has finite positive dimensional Hausdorff measure. Let be a conformal density of dimension on . We prove that is a weak limit of measures supported on spheres centered at . These measures are expressed in terms of the total mass function of and of the dimensional spherical function on . In particular, this result proves that is entirely determined by its dimension and its total mass function. The results of this paper apply in particular for symmetric spaces of rank one and semi-homogeneous trees.

     

Synthesis, characterization and crystal structure of mesogenic compounds with an alkyloxy and a semi-perfluorinated chain. Influence of the alkyloxy chain length on molecular arrangement and molecular interactions

This paper describes the synthesis and study of the mesomorphic properties (by DSC, microscopic observation and X-ray diffraction) of three new series of semi-perfluorinated liquid crystals: 4-(2,2,3,3,4,4,4-heptafluorobutyloxycarbonyl)phenyl, 4-(2,2,3,3,4,4,5,5-octafluoropentyloxycarbonyl)phenyl, and 4-(3,3,4,4,5,5,6,6,7,7,8,8,8-tridecafluoro-octyloxy-carbonyl)phenyl 4-(n-alkyloxy)benzoates. One compound of the second family crystallizes in the P1 space group with Z ' 2. The molecule adopts a slightly bent conformation with a fully extended alkyloxy and semi-perfluorinated chain in a smectic C-like structure. The comparison of the present structure is made with that of a similar compound of the first family with a longer alkyloxy chain (this latter crystallizes in the P1 space group with two independent molecules in the unit cell). Comparison of the molecular packing shows the importance of the chain lengths in the molecular arrangement and molecular interactions in both structures.     

Group rings over Dedekind rings

Seghal posed the following question: IfA andB are rings, doesA[X,X ⁻¹] ℞B[X,X ⁻¹] implyA ℞B. In general the answer to this question is no. In this note we give an affirmative answer in the case thatA andB are Dedekind rings. The author is research assistant at the NFWO.     

Tetraacylation of isobutene: first synthesis of 1,3,6,8-tetramethyl-2,7-naphthyridine

The tetxaacetylation of isobutene has been perfomed in AlCl₃/AcCl. Treatment of the crude reaction medium with liquid ammonia yields the title compound.     

Multiple points of trajectories of multiparameter fractional Brownian motion

Consider 0<α<1 and the Gaussian process Y(t) on ℝ ^N with covariance E(Y(s)Y(t))=|t|^2α+|s|^2α−|t−s|^2α, where |t| is the Euclidean norm of t. Consider independent copies X ¹,…,X ^d of Y and␣the process X(t)=(X ¹(t),…,X ^d (t)) valued in ℝ ^d . When kN≤␣(k−1)αd, we show that the trajectories of X do not have k-multiple points. If N<αd and kN>(k−1)αd, the set of k-multiple points of the trajectories X is a countable union of sets of finite Hausdorff measure associated with the function ϕ(ɛ)=ɛ ^{k N /α−( k −1) d} (loglog(1/ɛ)) ^k . If N=αd, we show that the set of k-multiple points of the trajectories of X is a countable union of sets of finite Hausdorff measure associated with the function ϕ(ɛ)=ɛ ^d (log(1/ɛ) logloglog 1/ɛ) ^k . (This includes the case k=1.) Received: 20 May 1997 / Revised version: 15 May 1998     

Atmospheric pressure chemical ionization negative mass spectra of the dinitrotoluene isomers

The atmospheric pressure chemical ionization of the dinitrotoluene isomers in ambient air was studied with a quadrupole mass spectrometer operating in the negative mode. The isomers can be grouped on the basis of the product ions: 2,5-, and 2,6- and 3,5-dinitrotoluene give the molecular anion with little fragmentation; 2,3- and the 3,4-dinitrotoluene behave similarly but with more extensive fragmentation; 2,4-dinitrotoluene gives the quasimolecular [DNT ? H]^? ion with little fragmentation. The results are discussed in terms of the molecular structure of the isomers.