Similarity Solutions for Generalized Variable Coefficients Zakharov-Kuznetsov Equation under Some Integrability Conditions

In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov- Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal system seven basic fields are determined, and for every vector field in the optimal system the admissible forms of the coefficients are found and this also leads us to transform the given equation into partial differential equations in two variables. After using some referenced transformations the mentioned partial differential equations eventually reduce to ordinary differential equations. The search for solutions to those equations has yielded many exact solutions in most cases.     

Elastic guided wave propagation in a periodic array of multi-layered piezoelectric plates with finite cross-sections

In this study, we present a model study of guided wave dispersion and resonance behavior of an array of piezoelectric plates with arbitrary cross-sections. The objective of this work is to analyze the influence of the geometry of an element of a 1D-array ultrasound transducer on generating multi-resonance frequency so as to increase the frequency bandwidth of the transducers. A semi-analytical finite-element (SAFE) method is used to model guided wave propagation in multi-layered 1D-array ultrasound transducers. Each element of the array is composed of LiNbO₃ piezoelectric material with rectangular or subdiced cross-section. Four-node bilinear finite-elements have been used to discretize the cross-section of the transducer. Dispersion curves showing the dependence of phase and group velocities on the frequency, and mode shapes of propagating modes were obtained for different geometry consurations. A parametric analysis was carried out to determine the effect of the aspect ratio, subdicing, inversion layer and matching layers on the vibrational behavior of 1D-array ultrasound transducers. It was found that the geometry with subdiced cross-section causes more vibration modes compared with the rectangular section. Modal analysis showed that the additional modes correspond to lateral modes of the piezoelectric subdiced section. In addition, some modes have strong normal displacements, which may influence the bandwidth and the pressure field in front of the transducer. In addition, the dispersion curves reveal strong coupling between waveguide modes due to the anisotropy of the piezoelectric crystal. The effect of the matching layers was to cluster extensional and flexural modes within a certain frequency range. Finally, inversion layer is found to have a minor effect on the dispersion curves. This analysis may provide a means to analyze and understand the dynamic response of 1D-array ultrasound transducers.     

Is-ClusterMPP: clustering algorithm through point processes and influence space towards high-dimensional data

Advances in Data Analysis and Classification - Clustering via marked point processes and influence space, Is-ClusterMPP, is a new unsupervised clustering algorithm through adaptive MCMC sampling of...     

On the class of almost L-weakly and almost M-weakly compact operators

In this paper, we introduce and study new concepts of almost L-weakly and almost M-weakly compact operators.     

Autour de la condition d'engel dans les algèbres de bernstein

We know that, in general, an algebra satisfying an Engel's condition is a nilalgebra. But an Engel's condition don't implies necessarily the nilpotency of the algebra. In this paper we show that every Bernstein algebra satisfying the second or the third Engel's condition is genetic, that is, the kernel of his weight fonction is nilpotent. This is also the case for a Bernstein algebra satisfying the second weak Engel's condition.

On sait que, en général, toute algèbre vérifiant une condition d'Engel est une nilalgèbre. Cependant, une condition d'Engel n'entraîne pas nécessairement la nilpotence de l'algèbre. Nous montrons, dans ce papier, que taute algèbre de Bernstein vérifiant la deuxième ou la troisième condition d'Engel est génétique, c'est-à-dire, le noyau de sa pondération est nilpotent. C'est aussi le cas pour la deuxième condition faible d'Engel.     

Catalytic C1 Alkylation with Methanol and Isotope‐Labeled Methanol

A metal‐catalyzed methylation process has been developed. By employing an air‐ and moisture‐stable manganese catalyst together with isotopically labeled methanol, a series of D‐, CD₃‐, and ¹³C‐labeled products were obtained in good yields under mild reaction conditions with water as the only byproduct.     

Synthesis and characterization of silica-coated Fe3O4 nanoparticle@silylpropyl triethylammonium polyoxometalate as an organic–inorganic hybrid heterogeneous catalyst for the one-pot synthesis of tetrahydrobenzimidazo[2,1-b]quinazolin-1(2H)-ones

In this study, silica-coated Fe₃O₄ nanoparticle@silylpropyl triethylammonium polyoxometalate catalyst was fabricated and characterized using atomic absorption, inductively coupled plasma optical emission spectrometry, elemental analysis, thermogravimetric analysis, Fourier-transform infrared, scanning electron microscopy, energy-dispersive X-ray spectroscopy, and vibrating sample magnetometry analyses. The activity of this catalyst was examined in the synthesis of tetrahydrobenzimidazo[2,1-b]quinazolin-1(2H)-ones. The bonding of the polyoxometalate to the surface of the nanoparticles exhibited excellent catalytic activity in this synthesis. Besides, the catalyst showed good reusability and recovery from the reaction mixture. Tetrahydrobenzimidazo[2,1-b]quinazolin-1(2H)-ones were synthesized in high yields in the presence of inexpensive supported solid acid catalysts under classical heating conditions.     

Regioselective remote CH fluoroalkylselenolation of 8-aminoquinolines

Herein, the direct C-5 fluoroalkylselenolation of 8-aminoquinolines is described. The Pd-catalyzed reaction is performed with the in situ generated fluoroalkylselenyl chloride and various 8-aminoquinoline amides or sulfonamides. The desired products were formed in moderate to excellent yields.     

Can Coordination‐Driven Supramolecular Self‐Assembly Reactions Be Conducted from Fully Aliphatic Linkers?

The reaction between a preassembled Cu^I bimetallic molecular clip with a short intermetallic distance and a series of fully aliphatic cyano‐capped ditopic linkers with increasing lengths was investigated. It is shown that, depending on the length of the ditopic linkers, the rational design of unprecedented supramolecular compact metallacycles containing fully aliphatic walls is possible. The specific preorganized molecular arrangement of the molecular clip used favors stabilizing interlinker London dispersion interactions, which allow, as the length of the linkers increases, the selective formation of discrete compact metallacycles at the expense of 1D coordination polymers. The generalizability of this approach was demonstrated by the reaction of fully aliphatic cyano‐capped linkers with two other types of preassembled Cu^I bimetallic molecular clips that also had short intermetallic distances.     

Supramolecular assemblies based on organometallic quinonoid linkers: a new class of coordination networks

Self-assembly of coordination frameworks exhibiting original architectures is an active area of research. Generally, such assemblies are constructed from organic spacers and transition metals of different geometrical structures. Herein, we report a novel class of supramolecular coordination assemblies with organometallic linkers based on metalated quinonoid and thioquinonoid complexes that serve as spacers. The organometallic ligands are stable and have the general formula [Cp*M(eta(4)-benzoquinone)] (o- and p-benzoquinone, Cp*=C(5)Me(5), M=Rh, Ir) and [Cp*Ir(eta(4)-thiobenzoquinone)] (o- and p-thiobenzoquinone). These units bind through both oxygen or sulfur atoms to metal ions of different coordination geometry, such as Cu(I), Ag(I), and Pt(II), to generate supramolecular coordination networks, with the metalated quinonoid or thioquinonoid linkers acting as backbones and the metal centers as nodes. This novel family of supramolecular assemblies exhibits short pi-pi and MM interactions. These results illustrate successfully the role of the organometallic linkers to produce an impressive range of novel supramolecular architectures that hold promise for the development of functional materials.