Observation of some elastic networks

We consider a network of vibrating elastic strings. Using a generalized Poisson formula and some Tauberian theorem, we give a Weyl formula with optimal remainder estimate. As a consequence we prove some observability and stabilization results. To cite this article: K. Ammari, M. Dimassi, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Improvement of photoluminescence and electrical properties of porous silicon layer treated with lanthanum

The influence of surface treatment of porous silicon (PS) in lanthanum (La) containing solution during different times on its photoluminescence and electrical properties has been investigated. For this purpose, chemical composition, structural, vibrational, photoluminescence and electrical characteristics of the porous silicon layer with and without lanthanum were examined using X-ray diffractometry (XRD), energy dispersive X-ray (EDX) spectroscopy, Fourier transmission infrared (FTIR) spectroscopy, photoluminescence (PL) spectroscopy and current–voltage (I–V) measurements. The results indicate that porous silicon layers treated with lanthanum exhibit an enhancement of photoluminescence intensity and show an improvement current intensity compared to untreated porous silicon layer.     

A local trace formula for resonances of perturbed periodic Schrödinger operators

We give a local trace formula for the pair (P₁(h)=P₀+W(hy),P₀), where P₀ is a periodic Schrödinger operator, W is a decreasing perturbation and h is a small positive parameter. We apply this result to establish the existence of ∼h⁻ⁿ resonances near some energy λ of σ(P₀).     

Multi-component analysis (sterols, tocopherols and triterpenic dialcohols) of the unsaponifiable fraction of vegetable oils by liquid chromatography-atmospheric pressure chemical ionization-ion trap mass spectrometry

A simple and sensitive method for the analysis of sterols, tocopherols and triterpenic dialcohols from the unsaponifiable fraction from oil samples in a single analytical run using liquid chromatography coupled to mass spectrometry was developed. With this method, the compounds could be detected directly after dissolving the unsaponifiable fraction in acetonitrile without necessity of time-consuming sample pre-treatment or derivatization. Separation of the analytes was carried out at room temperature, by using a C18 column (5 μm i.d. 3.0 mm × 250 mm) with a linear gradient of acetonitrile/water (0.01% acetic acid) at a flow rate of 1.5 mL/min. The full scan mass spectra of the investigated compounds were measured by an ion trap mass spectrometer equipped with an APCI ion source. The optimized methodology was suitable for the identification of 23 compounds belonging to different families present in olive oil and other kinds of oils, as well as for the quantification of 15 analytes (vs. their commercial standards).     

Hom-Lie quadratic and Pinczon Algebras

Presenting the structure equation of a hom-Lie algebra 𝔤, as the vanishing of the self commutator of a coderivation of some associative comultiplication, we define up to homotopy hom-Lie algebras, which yields the general hom-Lie algebra cohomology with value in a module. If the hom-Lie algebra is quadratic, using the Pinczon bracket on skew symmetric multilinear forms on 𝔤, we express this theory in the space of forms. If the hom-Lie algebra is symmetric, it is possible to associate to each module a quadratic hom-Lie algebra and describe the cohomology with value in the module.     

Anti-lipid peroxidation and induction of apoptosis in the erythroleukaemic cell line K562 by extracts from (Tunisian) Rhamnus alaternus L. (Rhamnaceae)

Total oligomer flavonoids (TOF) enriched and ethyl acetate (EA) extracts from Rhamnus alaternus induce apoptotic death in human chronic myelogenous leukaemia K562 cell line, as demonstrated by gel electrophoresis, which demonstrates the characteristic ladder patterns of DNA fragmentation and the proteolytic cleavage of poly(ADP ribose) polymerase (PARP). The effect of R. alaternus extract in reducing oxidative stress was evaluated by anti-lipid peroxidation which was monitored by measuring malondialdehyde level in K562 cultured cells. The TOF and EA extracts were found to be effective to protect against lipid peroxidation. Their IC?? values were 196 and 273?μg?mL?1, respectively. These findings suggest that R. alaternus extracts exhibit potential antioxidant and proapoptotic properties.     

Low loss broadband polarization independent fishnet negative index metamaterial at 40 GHz

We present a polarization independent fishnet negative index metamaterial at 40 GHz. The structure is investigated theoretically using finite element method simulations and experimentally by measuring the amplitude and phase of the S-parameters. The experimental setup for free space measurements of both transmission and reflection is hereby introduced. The internal properties are thereafter retrieved and show the double-negative behavior of the structure. This negative index metamaterial exhibits very high transmission (?0.13 dB), low reflection (?33.1 dB) and a high figure of merit (FOM = |Re(n)/Im(n)| = 42), where the real part of the refractive index is nearly ?1 (Re(n) = ?0.93) at 40 GHz.     

Extended arithmetic functions

The Ramanujan Journal - In this paper, we give an attempt to extend some arithmetic properties such as multiplicativity and convolution products to the setting of operator theory and we provide...