Chemoselective palladium-catalyzed deprotonative arylation/[1,2]-Wittig rearrangement of pyridylmethyl ethers

Control of chemoselectivity is one of the most challenging problems facing chemists and is particularly important in the synthesis of bioactive compounds and medications. Herein, the first highly chemoselective tandem C(sp³)–H arylation/[1,2]-Wittig rearrangement of pyridylmethyl ethers is presented. The efficient and operationally simple protocols enable generation of either arylation products or tandem arylation/[1,2]-Wittig rearrangement products with remarkable selectivity and good to excellent yields (60–99%). Choice of base, solvent, and reaction temperature play a pivotal role in tuning the reactivity of intermediates and controlling the relative rates of competing processes. The novel arylation step is catalyzed by a Pd(OAc)₂/NIXANTPHOS-based system via a deprotonative cross-coupling process. The method provides rapid access to skeletally diverse aryl(pyridyl)methanol core structures, which are central components of several medications.     

A high resolution NV/TVD Hermite polynomial upwind scheme for convection‐dominated problems

A high‐order convection‐bounded scheme is constructed by combining the total variational diminishing constraint and convection boundedness criterion condition in the normalized variable formulation. It employs the Hermite polynomial interpolation to design its characteristic line in the normalized variable diagram. Numerical results of the convection‐dominated problems with smooth or discontinuous initial distributions demonstrate the present scheme possesses high resolution and good robustness. Copyright © 2012 John Wiley & Sons, Ltd.     

Chaos in a seasonally and periodically forced phytoplankton–zooplankton system

The effect of seasonality and periodicity on plankton dynamics is investigated. Periodic variations are added to two different parameters of the plankton ecosystem: the growth rate of phytoplankton and the death rate of the zooplankton. The dynamic behaviors of the system is simulated numerically. A variety of complex population dynamics including chaos, quasi-periodicity, and periodic resonance are obtained. Our result reinforces the conjecture that seasonality and periodicity are crucial to plankton dynamics.     

一类二阶多点边值问题正解的存在性

利用锥上不动点定理讨论了二阶常微分方程组多点边值问题正解的存在性，所得结论推广了最近的一些结果．