Normkonvergenz von Fourierreihen in rearrangement invarianten Banachräumen

This paper studies rearrangement invariant Banach spaces of 2π-periodic functions with respect to norm convergence of Fourier series. The main result is that norm convergence takes place if and only if the space is an interpolation space of $\text{(}\text{L}{}^{\mathrm{p\prime }}\text{(T),}\text{L}{}^{\mathrm{p}}\text{(T)), 1 < p < 2,}\text{1}\text{p′}\text{+}\text{1}\text{p}\text{= 1}$, and L^p′(T) is dense in it (compare Satz 2.8). Since norm convergence and continuity of the conjugation operator are closely connected (compare Satz 2.2), this is achieved by a careful examination of this operator similar to that of D. W. Boyd for the Hilbert transform on the whole real axis. Finally, there are applications to Orlicz and Lorentz spaces.     

Generalite de l'effet structural d'un motif bitertiaire en rmn 13C: effet gem-6 de 6ème substitution methyle

In di-tertiary groups like (Me₃C)₂¹³C, the sixth methyl substituent $\text{inverts}$ or $\text{attenuates}$ the induced ¹³C chemical shift of sp² or sp³ sites (B_σ and y_π effects).     

Antiferroelectric phase in liquid crystalline compounds containing an azo group in their molecular core

Novel lactic acid derivatives containing an azo group in their molecular core have been synthesised and their mesomorphic properties established. Compounds with a short aliphatic non-chiral chain exhibited the SmA* phase and ferroelectric (FE) SmC* phase. The monotropic antiferroelectric (AF) phase was found in the homologues with a longer terminal chain. Spontaneous polarisation and tilt angle were measured for the FE and AF phases. Dielectric spectroscopy in the frequency range 1 Hz–10 MHz was carried out and dielectric properties established within the temperature range of the smectic phases. Two high frequency modes were detected in the AF phase. Small-angle X-ray measurements were conducted, and the temperature dependence of layer spacing values is established and discussed.     

Anomalous phase sequence in new chiral liquid crystalline materials

We have prepared and studied a series of rod-like liquid crystalline compounds with the molecular core laterally substituted by bromine atom and with the lactate unit in the chiral terminal chain. Microscopic observation under the polarising microscope, x-ray and dielectric spectroscopy results enable us to establish the TGBA–SmA–TGBA_RE–TGBC phase sequence. The presence of the re-entrant TGBA phase below the regular SmA phase, found for three homologues, is quite uncommon. Results are discussed and compared with the previously studied compounds with regular phase sequences.     

New series of chiral ferroelectric liquid crystals with the keto group attached to the molecule core

Two new series of ferroelectric liquid crystals with a keto group attached to the molecular core and a lactate unit as a chiral centre were synthesized and studied. All the compounds exhibit the paraelectric SmA phase and the ferroelectric SmC * phase over very wide temperature ranges and down to room temperature. The main characteristics of the chiral ferroelectric SmC * phase, namely spontaneous polarization, spontaneous tilt angle, and dielectric constant, have been measured to establish their relationship to the length of the terminal chains. The influence of the chiral and non-chiral chain lengths on the helix pitch length is also discussed.     

Reactivity of cyclohexene epoxides toward intramolecular acid-catalyzed cyclizations for the synthesis of naturally occurring cage architectures

This account compiles our results on the reactivity of cyclohexene epoxides toward the synthesis of naturally occurring cage architectures, in particular, the one found in harringtonolide. Bicyclic and branched monocyclic functional triads (hydroxy-epoxy-esters) were synthesized with the aim of undertaking cascade processes toward the formation of lactone and/or cycloether bridges, through a central epoxide opening. This work successfully culminated in the cascade cyclization of the fully oxygenated bridge-structure of harringtonolide, by using a dual Brønsted-Lewis acid complex.     

A Laccase/Chitosan‐Lambda‐Carrageenan Based Voltammetric Biosensor for Phenolic Compound Detection

In this contribution, a new concept of voltammetric catechol biosensor, based on the encapsulation of laccase (LAC) in a chitosan+lambda‐carrageenan (CHIT+CAR) polyelectrolyte complex (PEC) employing a simple coacervation process is presented. Chitosan (CHIT) was prepared from α‐chitin extracted from shrimp shells and lambda‐carrageenan (CAR) was extracted from red algae, both polysaccharides and PEC being characterized using FTIR spectrometry and electrochemistry. Cyclic voltammetry was utilized to determine the analytical features of the laccase (LAC) biosensor for catechol detection. The linear range was from 10^?20 M to 10^?14 M with a sensitivity of 1.55 mA/p[catechol] and a limit of detection of 3×10^?21 M.The laccase biosensor exhibits good repeatability (RSD 2.38 %) and stability (four weeks). The developed biosensor was tested by applying it to the evaluation of the total polyphenolic content in natural oil samples.