Thermally stimulated current (TSC) study of the Tg and Tll transitions in anionic polystyrenes

The thermally stimulated current (TSC) technique has been used to investigate three anionic polystyrenes of M?_n 17,000, 71,700, and 1.55 × 10⁶, i.e., M < M_c, M > M_c, and M ? M_c, where M_c is the entanglement molecular weight. A current maximum near T_g designated T_Mg, has relaxation times which follow an Arrhenius equation. A second current maximum at T > T_g appears to be the T_ll process and is designated T_Mll. Relaxation times for it follow a Vogel equation. T_Mg and T_Mll vary with molecular weight, increasing below M_c and leveling off above M_c at a temperature of about 170°C. Values of T_Mg and T_Mll are compared with values of T_g and T_ll obtained from torsional braid analysis, which involves melt flow; and with differential-scanning-calorimetric values on fused films, where there is no transport of polymer. It is concluded from such cross-comparisons that TSC, at least for polystyrene, is a quasistatic test which may involve microscopic viscosity. Macroscopic viscosity does not play a role. The ratio T_Mll/T_Mg is in the range 1.10–1.16, similar to T_ll/T_g values by other methods. A few comments about T_ll in atactic poly(methyl methacrylate) by the TSC method are given.     

Proprietes des α-phenylselenoaldehydes reactions de wittig conduisant a des α-hydroxyesters et cetones β,γ-ethyleniques et a des aldehydes α,β-ethyleniques

Wittig and Wittig-Horner reactions with α-phenylselenoaldehydes lead to allylic selenides. The corresponding selenoxides undergo 2,3-sigmatropic rearrangement providing a route to α-hydroxy β,γ-ethylenic esters and ketones in good yields. In a same way, we prepare, also enals with an additionnal carbon.     

A novel femtosecond-laser formation of CdS nanocrystallites in zirconia matrices

A novel method for direct laser writing of two-dimensional cadmium sulfide (CdS) semiconductor nanoparticle microstructures is reported. A two photon or a higher-order multiphoton absorption process, originating from femtosecond laser pulses, was used to decompose CdS precursors dispersed in a zirconia thin film previously dip-coated on a glass substrate. The kinetics of nanoparticle formation as a function of laser power were monitored in situ by photoluminescence spectroscopy. Raman spectroscopy was also performed to characterize the structural changes of the zirconia matrix under irradiation and to verify the formation of CdS nanoparticles. Results show that CdS nanoparticles were formed by two-photon absorption (TPA) with or without the help of an additional carbazole photoinitiator.     

Study of tryptophan assisted synthesis of gold nanoparticles by combining UV–Vis, fluorescence, and SERS spectroscopy

We developed a rapid and non-toxic method for the preparation of colloidal gold nanoparticles (GNPs) by using tryptophan (Trp) as reducing/stabilizing agent. We show that the temperature has a major influence on the kinetics of gold ion reduction and the crystal growth, higher temperatures favoring the synthesis of anisotropic nanoparticles (triangles and hexagons). The as-synthesized nanostructures were characterized by UV–Vis absorption spectroscopy, transmission electron microscopy (TEM), X-ray diffraction (XRD), fluorescence, and surface-enhanced Raman scattering (SERS) spectroscopy. The UV–Vis measurements confirmed that temperature is a critical factor in the synthesis process, having a major effect on the shape of the synthesized GNPs. Moreover, fluorescence spectroscopy was able to monitor the quenching of the Trp fluorescence during the in situ synthesis of GNPs. Using Trp as molecular analyte to evaluate the SERS efficiency of as-prepared GNPs at different temperatures, we demonstrated that the Raman enhancement of the synthesized gold nanoplates is higher than that of the gold spherical nanoparticles.     

Design of the spatial filter window for digital holographic convolution reconstruction of object beam field

In the convolution reconstruction process of digital holographic object beam field, the object beam fields with different magnifications can be obtained when the reconstructing beams are spherical waves with different wave curvature radii. This paper presents a theoretical and experimental discussion on the useful spatial frequency spectrum of the hologram numerically illuminated by the spherical wave. The result shows that there would be an image in the spatial frequency spectrum of digital hologram, which is completely the same as the object, if the wave surface radius of the spherical wave is equal to the distance from the object to the CCD sensor. Taking this image as a reference and designing a filter, the position of the reconstructed images with different magnifications can be predicted correctly in the reconstructed plane. Additionally, since the spectrum distribution of zero-order diffraction can be forecasted accurately in theory, its contribution can be effectively eliminated through changing the spatial filter shape; then a reconstructed object field containing more high-frequency information can be obtained.     

An abelian analogue of Schanuel’s conjecture and applications

The Ramanujan Journal - In this article we study an abelian analogue of Schanuel’s conjecture. This conjecture falls in the realm of the generalised period conjecture of André. As shown...     

A reliable algorithm to solve 3D frictional multi-contact problems: Application to granular media

We present in this paper an improved non-smooth Discrete Element Method (DEM) in 3D based on the Non-Smooth Contact Dynamics (NSCD) method. We consider a three-dimensional collection of rigid particles (spheres) during the motion of which contacts can occur or break. The dry friction is modeled by Coulomb’s law which is typically non-associated. The non-associativity of the constitutive law poses numerical challenges. By adopting the use of the bi-potential concept in the framework of the NSCD DEM, a faster and more robust time stepping algorithm with only one predictor-corrector step where the contact and the friction are coupled can be devised. This contrasts with the classical method where contact and friction are treated separately leading to a time stepping algorithm that involves two predictor-corrector steps. The algorithm has been introduced in a 3D version of the NSCD DEM software MULTICOR. Numerical applications will show the robustness of the algorithm and the possibilities of the MULTICOR software for solving three-dimensional problems.     

Smoothing Windows for the Synthesis of Gaussian Stationary Random Fields Using Circulant Matrix Embedding

When generating Gaussian stationary random fields, a standard method based on circulant matrix embedding usually fails because some of the associated eigenvalues are negative. The eigenvalues can be shown to be nonnegative in the limit of increasing sample size. Computationally feasible large sample sizes, however, rarely lead to nonnegative eigenvalues. Another solution is to extend suitably the covariance function of interest so that the eigenvalues of the embedded circulant matrix become nonnegative in theory. Though such extensions have been found for a number of examples of stationary fields, the method depends on nontrivial constructions in specific cases.

In this work, the embedded circulant matrix is smoothed at the boundary by using a cutoff window or overlapping windows over a transition region. The windows are not specific to particular examples of stationary fields. The resulting method modifies the standard circulant embedding, and is easy to use. It is shown that this straightforward approach works for many examples of interest, with the overlapping windows performing consistently better. The method even outperforms in the cases where extending the covariance leads to nonnegative eigenvalues in theory, in the sense that the transition region is considerably smaller. The Matlab code implementing the method is included in the online supplementary materials and also publicly available at www.hermir.org.     

Affine Slice for the Coadjoint Action of a Class of Biparabolic Subalgebras of a Semisimple Lie Algebra

In this article, we give a simple explicit construction of an affine slice for the coadjoint action of a certain class of biparabolic (also called seaweed) subalgebras of a semisimple Lie algebra over an algebraically closed field of characteristic zero. In particular, this class includes all Borel subalgebras.