Nickel-Catalyzed Cross-Coupling of Aryl 2-Pyridyl Ethers with Organozinc Reagents: Removal of the Directing Group via Cleavage of the Carbon-Oxygen Bonds.

Reaction of aryl 2-pyridyl ethers with arylzinc reagents under catalysis of NiCl(PCy) affords aryl-aryl cross-coupling products via selective cleavage of C-OPy bonds. The reaction features a wide substrate range and good compatibility of functional groups. β-H-free alkylzinc reagents are also applicable as the nucleophiles in the transformation, whereas β-H-containing alkylzinc reagents lead to a mixture of cross-coupling and hydrogenation products.

Qualitative analysis of a time-delayed free boundary problem for tumor growth with angiogenesis and Gibbs-Thomson relation.

In this paper we consider a time-delayed mathematical model describing tumor growth with angiogenesis and Gibbs-Thomson relation. In the model there are two unknown functions: One is $\sigma(r,t)$ which is the nutrient concentration at time $t$ and radius $r$, and the other one is $R(t)$ which is the outer tumor radius at time $t$. Since $R(t)$ is unknown and varies with time, this problem has a free boundary.