New ferroelectric and antiferroelectric liquid crystalline materials containing differing numbers of lactate units

A new series of chiral liquid crystalline materials having the same rigid core containing a keto group, and various numbers of ( S )-lactate groups in the chiral segment, has been synthesized and studied. All the compounds contain a branched terminal alkyl chain derived from ( S )-2-methylbutanol. The influence of the number of lactate units on mesogenic behaviour has been studied. All the compounds show the paraelectric SmA phase and the ferroelectric SmC * phase over rather wide temperature ranges. The antiferroelectric SmC * A phase was observed for the compound possessing two lactate groups.     

Cyclisation par amination intramoléculaire dans la série de la pyrazine.

An original one-pot ayntheais of 4,7-diazaindoles is achieved by metalation of methylpyrazines or methylquinoxaline wich are then condensed with an aromatic nitrile: an intermediate imine-enamine is formed which leads, by intramolecular cyclization, to diazaindoles.     

Réactions chimiques oscillantes III. Effets de la température et de la composition chimique sur la «période d'induction» des systèmes BrO/Ce4+/Cyclohexanone et BrO/Ce4+/Cyclopentanone

Oscillating Chemical Reactions. III. Effects of the Temperature and Chemical Composition on the ‘Induction Period’ of the BrO /Ce⁴⁺/Cyclohexanon and BrO /Ce⁴⁺/Cyclopentanon Systems A study of the influence of the temperature and composition of the BrO/Ce⁴⁺/cyclohexanon (S1) and BrO/Ce⁴⁺/cyclopentanon (S2) systems has shown a very particular behaviour for τ_ind. for a given ratio α of concentrations: Moreover, for 0.27 ? α ? 0.32, log¹/τ_ind. is no longer a linear function of the inverse of the temperature: a break in the line log¹/τ_ind. = f(1/T) occurs.     

New antiferroelectric liquid crystalline materials containing a keto group and two lactate groups

New chiral liquid crystalline materials containing a keto group and two lactate units attached to the mesogenic core have been synthesized and studied. All the new compounds show the paraelectric SmA, ferroelectric SmC* and antiferroelectric SmC*_A phases each over rather broad temperature ranges. The properties of the phases were characterized by DSC, electro-optical and dielectric studies. The spontaneous polarization, tilt angle, helical pitch, and switching times were determined for the polar phases.     

Photoinduced phase transitions and helix untwisting in the SmC* phase of a novel cinnamoyl-based liquid crystal

A photoinduced phase transition and helix untwisting in a new liquid crystal forming the SmC* phase were studied in detail. The compound consists of a cinnamoyl photosensitive fragment with C?=?C double bond capable of photoisomerisation and photocycloaddition. It was shown that ultraviolet (UV) irradiation (365 nm) induces an extreme decrease in phase transitions temperatures (SmC*–SmA*, SmA*–N*, N*–I). Vertically aligned samples in the SmC* phase cause selective light reflection in the visible spectral range. The light action results in a noticeable helix untwisting that causes a shift in the selective light reflection peak to the long-wavelength spectral region. The temperature dependence of spontaneous polarisation P _s was measured and it was found that UV irradiation induces a decrease in the values of P _s. Photo-optical phenomena taking place in the liquid crystal are attributed to the formation of photoproducts having low anisometry, which disrupts mesophases.     

New chlorine-substituted ferroelectric liquid crystals with four aromatic rings in the mesogenic core

New series of liquid crystals with an alkyl-lactate chiral chain and four aromatic rings in the mesogenic core and chloro-substitution were synthesized. For all the compounds studied, SmA and SmC* phases, existing over very broad temperature ranges, were detected and characterized. Mesomorphic properties were analysed with respect to the lengths of the chiral and/or non-chiral chains.     

Phenomenological models of elastic nucleon scattering and predictions for LHC

The hitherto analyses of elastic collisions of charged nucleons involving common influence of Coulomb and hadronic scattering have been based practically on West and Yennie formula. However, this approach has been shown recently to be inadequate from experimental as well as theoretical points of view. The eikonal model enabling to determine physical characteristics in impact parameter space seems to be more pertinent. The contemporary phenomenological models admit, of course, different distributions of collision processes in the impact parameter space and cannot give any definite answer. Nevertheless, some predictions for the planned LHC energy that have been given on their basis may be useful, as well as the possibility of determining the luminosity from elastic scattering.     

Local Dispersive and Strichartz Estimates for the Schrödinger Operator on the Heisenberg Group

It was proved by Bahouri et al. [9] that the Schrödinger equation on the Heisenberg group $\mathbb{H}^d,$ involving the sublaplacian, is an example of a totally non-dispersive evolution equation: for this reason global dispersive estimates cannot hold. This paper aims at establishing local dispersive estimates on $\mathbb{H}^d$ for the linear Schrödinger equation, by a refined study of the Schrödinger kernel $S_t$ on $\mathbb{H}^d.$ The sharpness of these estimates is discussed through several examples. Our approach, based on the explicit formula of the heat kernel on $\mathbb{H}^d$ derived by Gaveau [19], is achieved by combining complex analysis and Fourier-Heisenberg tools. As a by-product of our results we establish local Strichartz estimates and prove that the kernel $S_t$ concentrates on quantized horizontal hyperplanes of $\mathbb{H}^d.$     

Fixed point results on a metric space endowed with a finite number of graphs and applications

In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings.