On a mechanical lens

In this paper, we consider the dynamics of a heavy homogeneous ball moving under the influence of dry friction on a fixed horizontal plane. We assume the ball to slide without rolling. We demonstrate that the plane may be divided into two regions, each characterized by a distinct coefficient of friction, so that balls with equal initial linear and angular velocity will converge upon the same point from different initial locations along a certain segment. We construct the boundary between the two regions explicitly and discuss possible applications to real physical systems.     

Synthese de Nouveaux Derives Phosphones a Chaine Perfluoree et Leurs Proprietes Adhesives Sur Acier

Ce mémoire décrit la synthèse de phosphonates comportant une chaîne perfluorée. Ces composés sont obtenus par la télomérisation d'allylphosphonates de dialkyle en présence d'un agent de transfert fluoré de type mercaptan. Ensuite, nous employons deux méthodes de déalkylation menant sélectivement soit au monoacide soit au diacide phosphonique. Tous ces produits comprenant une extrémité de chaîne phosphonée, sous forme acide ou ester, ont été caractérisés et leur adhésion respective sur des plaques d'acier est étudiée. Ces tests montrent que le monoacide phosphonique est un excellent promoteur d'adhésion et qu'il est aussi efficace que le diacide. This article describes the synthesis of phosphonic derivatives bearing a perfluorinated chain. These compounds have been synthetized by telomerization of dialkyl allylphosphonate with a fluorinated transfer agent type mercaptan. Then two methods of dealkylation leading selectively were used to mono or to diacid phosphonic moieties. All the products bearing phosphonic end-groups, more or less acidic, have been characterized and their own adhesion on steel plates is studied. These tests show that phosphonic monoacid is an excellent adhesion promoter on steel, as efficient as the diacid compound.     

Golf ball-assisted electrospray ionization of mass spectrometry for the determination of trace amino acids in complex samples

During the electrospray ionization (ESI) process, ions move through a heated capillary aperture to be detected on arrival at a mass analyzer. However, the ESI process creates an ion plume, which expands into an ion cloud with an area larger than that of the heated capillary aperture, significantly contributing to an ion loss of 50% due to coulombic repulsion. The use of DC and RF fields to focus ions from the ion source into the vacuum chamber has been proposed in the literature, but the improvement of ion transmission efficiency is limited. To improve ion transmission, in this study we propose a novel method using a home-made golf ball positioned between the ion source and the inlet of the mass analyzer to hydrodynamically focus the ions passing through the golf ball. The ion plume produced by the ESI process passes through the golf ball will reduce the size of the ion cloud then be focused and most of them flowed into the mass analyzer. Therefore, the sensitivity will be improved, the aim of this investigation is to study the enhancing of the signal using golf ball-assisted electrospray ionization liquid chromatography tandem mass spectrometry (LC-MS/MS) to determine 20 trace amino acids in complex samples, including tea, urine and serum. The results showed that the analytical performance of the determination of the 20 amino acids in tea, urine and serum samples using the home-made golf ball-assisted ESI source is better than that of a commercial ESI source. The signal intensities of the 20 amino acids were enhanced by factors of 2–2700, 11–2525, and 31–342680 in oolong tea, urine and serum analyses, respectively. The precision of the proposed method ranged from 1–9%, 0.4–9% and 0.4–8% at low, medium and high concentration levels of amino acids, respectively. The home-made golf ball-assisted ESI source effectively increased the signal intensity and enhanced the ion transmission efficiency and is also an easy, convenient and economical device. This technique can be applied to the analysis of trace compounds in complex matrices.     

Synergetic catalytic effect of rGO,Pd, Fe3O4 and PPy as a magnetically separable and recyclable nanocomposite for coupling reactions in green media

In this paper, rGO/Pd–Fe₃O₄@PPy as an efficient stable nanocomposite was synthesized. To understand the synergetic effects of rGO, Pd, Fe₃O₄ and PolyPyrrole, the performance of rGO/Pd–Fe₃O₄@PPy as a heterogeneous recyclable nanocatalyst in the green synthesis of C‐C and C‐O coupling products, as well as different conditions are studied. Synthesized rGO/Pd–Fe₃O₄@PPy was characterized by FT‐IR, XRD, FE‐SEM, EDS, TGA and AFM analysis. Best results are obtained under sonication in H₂O for C‐C coupling and by ball‐milling for C‐O coupling. The benefits of this method include: green solvents and conditions, absence of external base, low reaction times with high yield and easy work‐up method.     

On the complexity of extending the convergence ball of Wang’s method for finding a zero of a derivative

Ball convergence results are very important, since they demonstrate the complexity in choosing initial points for iterative methods. One of the most important problems in the study of iterative methods is to determine the convergence ball. This ball is small in general restricting the choice of initial points. We address this problem in the case of Wang’s method utilized to determine a zero of a derivative. Finding such a zero has many applications in computational fields, especially in function optimization. In particular, we find the convergence ball of Wang’s method using hypotheses up to the second derivative in contrast to earlier studies using hypotheses up to the fourth derivative. This way, we also extend the applicability of Wang’s method. Numerical experiments used to test the convergence criteria complete this study.     

On weighted spectral radius of unraveled balls and normalized Laplacian eigenvalues

For a graph G, the unraveled ball of radius r centered at a vertex v is the ball of radius r centered at v in the universal cover of G. We obtain a lower bound on the weighted spectral radius of unraveled balls of fixed radius in a graph with positive weights on edges, which is used to present an upper bound on the $s^{\text{th}}$ (where $s\ge 2$) smallest normalized Laplacian eigenvalue of irregular graphs under minor assumptions. Moreover, when $s=2$, the result may be regarded as an Alon–Boppana type bound for a class of irregular graphs.     

有界平均振幅空间上的乘法算子

有界平均振幅空间的研究在算子理论及全纯空间的研究中具有重要的作用.主要研究了有界平均振幅空间上乘法算子的性质,并且得到了托普里兹算子有界性及紧性的条件.     

多重调和Bergman空间上径向Toeplitz算子的交换性

In this paper, we study the commutativity of Toeplitz operators with radial symbols on the pluriharmonic Bergman space. We obtain the necessary and sufficient conditions for the commutativity of bounded Toeplitz operator and Toeplitz operator with radial symbol on the pluriharmonic Bergman space.     

Solvent-Free Mechanochemical Synthesis of Aryl Glycosides[ 1 ]

Aryl glycosides have been prepared from a range of readily available glycosyl halides by a solvent-free mechanochemical procedure employing a planetary ball mill in excellent yields. Besides being a solvent-free reaction, the procedure has been successful in eliminating the need for employing any phase-transfer catalyst in the reaction.