Refined inequalities on graded Lie groups

We construct a Littlewood–Paley decomposition associated to a Rockland operator on graded Lie groups, which allows us to deduce refined Gagliardo–Nirenberg, Sobolev and Hardy inequalities.     

Synthesis and evaluation of new phosphonated δ-lactam and glutarimide derivatives as angiotensin converting enzyme inhibitors

An efficient synthesis of new γ,δ-insaturated δ-lactam and glutarimide derivatives bearing a phosphonomethyl group from a common allylphosphonate precursor is described. Our approach is based on a two-step procedure involving the preparation of phosphonated-1,5-ketoester and −1,5-diester followed by an amidation–heterocyclization sequence. The first step proceeds via Michael's addition of ethyl acetoacetate and diethyl malonate on an allylphosphonate starting material. The second step consists of a base-promoted intramolecular amidation-cyclization sequence with primary amines, which accounts for the construction of δ-lactams and glutarimide skeletons. We performed the evaluation of angiotensin I-converting enzyme (ACE) inhibition using an in vitro enzyme assay on six new compounds. Five compounds showed potent ACE inhibitory activity, with IC₅₀ values ranging from 0.02 to 0.27 mg/ml. Compared with Captopril, used as a reference drug, two new glutarimide derivatives exhibited higher efficiency ACE inhibition activity.     

Optical properties of semiconducting iron disilicide thin films

The iron silicides samples were prepared by annealing of iron films evaporated onto silicon wafers and capped with amorphous silicon thin overlayers. Semiconducting FeSi₂ phase is formed by annealing at the temperatures from 550°C to 850°C. The optical properties of the FeSi₂ layers have been deduced from reflectance and transmittance measurements carried out in the temperature range of (77–380) K. The spectral dependence of the absorption coefficient favours direct allowed transitions with forbidden energy gap of 0.87eV at the room temperature. The application of a simple three-parameter semiempirical formula to the temperature dependence of the direct energy gaps leads to the following best fit parameters: the band gap at zero temperature E _g (0) = (0.895 ± 0.004)eV, the dimensionless coupling parameter S = 2.0 ± 0.3, and the average phonon energy <hw> = (46 ± 8)meV. By examining all the reported triplets of parameters for -FeSi₂ fabricated by different techniques and thermal processes, an obvious discrepancy can be found for the lattice coupling parameter and average phonon energy, although the bandgaps at 0 K are very similar. Unlike the theoretical prediction and the earlier reported result, our results do not show any evidence of a particularly strong electron-phonon interaction, which would give the lower carrier mobilities. -FeSi₂ seems to be an intriguing material where states with energies near the band edges permit ambiguous interpretation of the character of transitions. From optical model for the thin film-substrate system we found the index of refraction to be (5–5.9) in the photon energy interval from 0.65 to 1.15eV. There is also indication of an additional higher-energy absorption edge at l.05eV.     

Switching of chirality from racemic to homochiral state in new liquid crystalline monomers with bent-core molecules

The synthesis and physical properties of bent-shaped molecules with ester linkages and methoxy substitution on a non-central ring are presented. Terminal chains of most mesogens contain a group with double bond, which promotes polymerization. In all the compounds studied a B₂ phase just below the isotropic phase has been found. Polarization current profiles indicate that this phase is antiferroelectric, and dielectric spectroscopy data with a pronounced high frequency mode support this fact. For several compound chirality switching from racemic to the homochiral state was seen after application of a low frequency a.c. field. Another phase, which could be assigned to the B₇ family, appears below the B₂ phase on cooling.     

Sur l'ultraconvergence d'une classe de séries de Dirichlet

Sans résumé     

Effect of the chiral chain length on structural and phase properties of ferroelectric liquid crystals

Studies of structural and phase properties obtained on several ferroelectric liquid crystalline materials with 2-alkoxypropionate group used as a chiral centre and without any lateral substitution are presented. In dependence on the chiral chain length these compounds exhibit the cholesteric N* phase, the ferroelectric smectic C* and a low-temperature SmX phase. Values of the spontaneous polarization and spontaneous tilt angle have been determined within the whole range of the SmC* phase. A low-temperature SmX phase has been identified as the orthogonal hexatic SmB* phase. The molecular parameters, namely the layer spacing in the SmC* and SmB* phases and the average intermolecular distances (D) between neighbouring parallel molecules in all investigated phases have been determined using the results of the X-ray diffraction obtained on non-oriented samples. The effect of the chiral chain length on mesomorphic, structural and physical properties of the studied ferroelectric liquid crystalline materials is discussed.     

Nonlinear model predictive control based on Nelder Mead optimization method

In this paper, a model predictive control (MPC) scheme based on Hammerstein model is carried on. The use of such nonlinear models complicates the implementation of the MPC in terms of computational time and burden since a nonlinear and so a nonconvex optimization problem will result. The Nelder Mead (NM) algorithm, as a free derivative method, is used to solve the resulting optimization problem. NM algorithm proves its efficiency in terms of computation time and global optimum seeking that can be successfully exploited especially with fast dynamic systems. A comparative study between the NM algorithm and the gradient-based method (GBM) based on computation time is established. The efficiency of the NM algorithm is illustrated with SISO and MIMO examples compared to GBM algorithm.     

The B2–B7 phase transition in symmetrical bent‐shaped mesogens with methoxy substitution

New mesogens composed of achiral bent molecules with thermally stable ester linkages, and laterally substituted by a methoxy group symmetrically near the central benzene ring, were synthesized. Texture, calorimetric, electro‐optical, X‐ray and dielectric measurements were performed. In most of studied compounds the antiferroelectric B₂ phase was found on cooling from the isotropic phase, followed by the B₇ phase at lower temperatures. Undulation of layers in the B₇ phase was confirmed by precise synchrotron studies.