The Ablowitz–Ladik hierarchy integrability analysis revisited: the vertex operator solution representation structure

A regular gradient-holonomic approach to studying the Lax type integrability of the Ablowitz–Ladik hierarchy of nonlinear Lax type integrable discrete dynamical systems in the vertex operator representation is presented. The relationship to the Lie-algebraic integrability scheme is analyzed and the connection with the τ-function representation is discussed.     

一种一致性排序标度方法

针对层次分析法判断矩阵一致性问题,提出了一种新的排序标度方法,证明了采用新方法形成的判断矩阵具有一致性,最后通过实例运用说明了此方法的可行性和有效性.     

Pd(0)-guanidine@MCM-41: a very effective catalyst for rapid production of bis (pyrazolyl)methanes

In this research, a rapid, green and efficient protocol for synthesis of bis (pyrazolyl)methane derivatives in the presence of Pd(0)-guanidine@MCM-41 catalysts under solvent-free conditions by the following two methods has been reported: (i) via the one-pot pseudo five-component reaction among phenylhydrazine (2 equivalents), ethyl acetoacetate (2 equivalents) and aromatic aldehydes (1 equivalent); and (ii) the one-pot pseudo three-component reaction between 3-methyl-1-phenyl-1H-pyrazol-5(4H)-one (2 equivalents) and aromatic aldehydes (1 equivalent). Some advantages of this protocol include: green conditions, extremely short times, high efficiency, proper one-pot operation, generality of method, easy work-up and recyclability, and reusability of the catalyst up to five times without significant loss in catalytic activity.     

Three-Component Reaction for the Synthesis of Highly Functionalized Propargyl Ethers

Multicomponent reactions provide efficient means to access molecular complexity. Herein, we report a copper-catalyzed three-component reaction of diazo compounds, alcohols and ethynyl benziodoxole (EBX) reagents for the synthesis of propargyl ethers. Extensive variations of the three partners of the reaction is possible, leading to highly functionalized and structurally diverse products under mild conditions. Alkynylation of a copper ylide intermediate is postulated as key step for this transformation.     

Bi-Hamiltonian structure of multi-component Novikov equation

In this paper, we present the multi-component Novikov equation and derive it's bi-Hamiltonian structure.     

The gauge transformation of the q-deformed modified KP hierarchy

In this paper, we mainly study three types of gauge transformation operators for the q-mKP hierarchy. The successive applications of these gauge transformation operators are derived. And the corresponding communities between them are also investigated.     

An efficient ‘on-water’ synthesis of 1,4-dihydropyridines using Fe3O4@SiO2 nanoparticles as a reusable catalyst

An ‘on-water’, efficient, high yielding, expeditious method has been developed for the synthesis of 1,4-dihydropyridine (1,4-DHP) derivatives via an one-pot multi-component condensation of dimedone or 4-hydroxycoumarine, aldehydes, and ammonium acetate using Fe₃O₄@SiO₂ nanoparticles as a recyclable heterogeneous catalyst. This method takes advantage of the fact that water, a green solvent is used in combination with Fe₃O₄@SiO₂ nanoparticles as catalyst which can be easily recovered magnetically and reused for further runs.     

Exact solutions for KdV system equations hierarchy

Exact solutions for KdV system equations hierarchy are obtained by using the inverse scattering transform. Exact solutions of isospectral KdV hierarchy, nonisospectral KdV hierarchies and τ$\tau$-equations related to the KdV spectral problem are obtained by reduction. The interaction of two solitons is investigated.