Stability criteria for set control differential equations

The existence and comparison results on solutions of set control differential equation were studied in [N.D. Phu, T.T. Tung, Some results on sheaf-solutions of sheaf set control problems, Nonlinear Analysis 67 (2007) 1309–1315]. In this paper, we present the stability criteria for solutions of set control differential equation.     

Topological invariants from quantum group $$\mathcal {U}_{\xi }\mathfrak {sl}(2|1)$$ at roots of unity

In this article we construct link invariants and 3-manifold invariants from the quantum group associated with the Lie superalgebra \(\mathfrak {sl}(2|1)\). The construction is based on nilpotent irreducible finite dimensional representations of quantum group \(\mathcal {U}_{\xi }\mathfrak {sl}(2|1)\) where \(\xi \) is a root of unity of odd order. These constructions use the notion of modified trace and relative \( G \)-modular category of previous authors.     

Picosecond nonlinear absorption and phase conjugation in BSO and BGO crystals

We have observed a very strong nonlinear absorption in BSO and BGO crystals when they are illuminated by picosecond laser pulses with optical intensity on the order of 10⁸ W/cm². In addition, a phase conjugate reflectivity of 2×10^-3 is obtained in a degenerate four-wave mixing (DFWM) experiment using the same optical power. We derive the nonlinear coupled-wave equations to explain the experimental results. We show that the creation of the conjugate wave can be explained by the presence of a strong nonlinear absorption.     

Four wave mixing in the picosecond range: Intensities,durations, wave front reconstruction

Degenerate four wave mixing is produced by the single pulse of a mode locked laser (duration 25 ps). The intensities are measured. The feasibility of image reconstruction is proved, and methods for time measurements (pulse durations, relaxation times) are proposed.     

Bacteriostatic Behavior of PLA-BaTiO3 Composite Fibers Synthesized by Centrifugal Spinning and Subjected to Aging Test

The present work investigated the effect of Polylactic acid (PLA) fibers produced by centrifugal spinning with incorporated BaTiO₃ particles to improve their bacteriostatic behavior. The PLA matrix and three composites, presenting three different amounts of fillers, were subjected to UV/O₃ treatment monitoring the possible modifications that occurred over time. The morphological and physical properties of the surfaces were characterized by different microscopic techniques, contact angle, and surface potential measurements. Subsequently, the samples were tested in vitro with human dermal fibroblasts (HDF) to verify the cytotoxicity of the substrates. No significant differences between the PLA matrix and composites emerged; the high hydrophobicity of the fibers, derived by the polymer structure, represented an obstacle limiting the fibroblast attachment. Samples underwent bacterial exposure (Staphylococcus epidermidis) for 12 and 24 h. Increasing the concentration of BT, the number of living bacteria and their distribution decreased in comparison with the PLA matrix suggesting an effect of the inorganic filler, which generates a neutralization effect leading to reactive oxygen species (ROS) generation and subsequently to bacterial damages. These results suggest that the barium titanate (BT) fillers clearly improve the antibacterial properties of PLA fibers after aging tests made before bacterial exposure, representing a potential candidate in the creation of composites for medical applications.     

Synthesis of methacrylate-containing oligosilsesquioxanes via acidic hydrolytic polycondensation in the medium of methacrylate monomers

Methacrylate-containing oligosilsesquioxanes with a molecular mass of 700–4000 are synthesized via the acidic hydrolytic polycondensation of γ-methacryloxy-propyltrimethoxysilane (A-174) in the medium of methyl methacrylate or in a mixture of bis(methacrylates). The structure of the oligomers is studied by ¹Н and ²⁹Si NMR spectroscopy and MALDI-TOF mass spectrometry.     

A new lactam 28-norlimonoid from the leaves of Azadirachta indica A. Juss. (Meliaceae)

From an EtOAc-soluble fraction of the leaves of Azadirachta indica, one new lactam 28-norlimonoid named nimbandiolactam-21 (1), together with 2 known limonoids (2 and 3) were isolated. Their relative structures were elucidated based on NMR spectroscopic analysis. Nimbandiolactone-23 (2) showed the most potent α-glucosidase inhibitory activity, with an IC₅₀ value of 38.7 μM. Compound 1 represents the first naturally occurring example of a 28-norlimonoid having the lactam moiety. The plausible biosynthetic pathway for the formation of lactam moiety in 1 was proposed.     

Backscattering in the picosecond range: An optical triggered switching effect

In a new picosecond phase conjugation experiment, an optical triggered switching effect has been observed in backscattering. Comparison with an almost similar configuration used in a nanosecond experiment shows significant differences, which can be explained by the small duration of the pulse.     

Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

α-Glucosidase inhibitors from the stem of Mangifera reba

Two new neolignans, named rebaneolignan A (1) and B (2), were isolated from the stem of Mangifera reba (Anacardiaceae), together with six known compounds (3–8). Their structures were elucidated on the basis of NMR spectroscopic analysis and the absolute configurations of 1 and 2 were determined by NOESY and CD data. All isolated compounds were found to possess more potent inhibitory activity, with IC₅₀ values ranging from 28.5 to 162.8 µM, than the positive control acarbose (IC₅₀, 214.5 µM). Plausible biosynthetic pathways for the formation of 1 and 2 were proposed based on the oxidative β-5′ coupling reactions.