Many metals or their complexes can catalyze the cyclotrimerization of alkynes to give benzene derivatives.1-9 Among these catalysts, palladium chloride10 and its bis(benzonitrile) complex11 are the most convenient. In these reactions, the yields of benzene derivatives generally depend on the substituents of alkynes. In the past 50 years, the regioand chemoselectivity for the cyclotrimerization ...

The derivation of Boussinesq's type of equations is revisited for the shallow uid layers and nonlinear atomic chains. It is shown that the linearly stable equation with purely spatial derivatives representing dispersion must be of sixth order. The corresponding conservation and balance laws are derived. The shapes of solitary stationary waves are calculated numerically for diierent signs of the...

Stable spatially localized structures occur in many systems of physical interest. Examples can be found in the fields of optics, chemistry, fluid mechanics, and neuroscience to name a few. The models used to describe these systems have much in common. They are typically of at least fourth order in spatial derivatives, invariant under spatial translations and reflections, and exhibit bistability...

A discontinuous Galerkin finite element method has been developed to treat the high-order spatial derivatives appearing in the Cahn–Hilliard equation. The Cahn–Hilliard equation is a fourth-order nonlinear parabolic partial differential equation, originally proposed to model phase segregation of binary alloys. The developed discontinuous Galerkin approach avoids the need for mixed finite elemen...

We propose to measure the weak cosmic shear using the spatial derivatives of the galaxy surface brightness field. The measurement should be carried out in Fourier space, in which the point spread function (PSF) can be transformed to a desired form with multiplications, and the spatial derivatives can be easily measured. This method is mathematically well defined regardless of the galaxy morphol...

Abstract An efficient direct domain decomposition method is developed coupled with Poly-Sinc approximation over complex geometry. We solve 2D Poisson equations in L-Shaped geometry. The spatial domains of interest are decomposed into several non-overlapping rectangular subdomains. In each sub-domain, a Poly-Sinc collocation scheme is used to approximate the solution of the governing equation. S...