NH-bridged and pyrazine-fused metallodiazaporphyrin dimers have been prepared from nickel(II) and copper(II) complexes of 3-amino-5,15-diazaporphyrin by Pd-catalyzed C-N cross-coupling and oxidative dimerization reactions, respectively. The synergistic effects of the nitrogen bridges and meso-nitrogen atoms play major roles in enhancing the light-harvesting properties and delocalization of an electron spin over the entire π-skeletons of the metallodiazaporphyrin dimers.

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We discuss Monge-Ampère equations from the view point of differential geometry. It is known that a Monge-Ampère equation corresponds to a special exterior differential system on a 1-jet space. In this paper, we generalize Monge-Ampère equations and prove that a (k + 1)st order generalized Monge-Ampère equation corresponds to a special exterior differential system on a k-jet space. Then its solution naturally corresponds to an integral manifold of the corresponding exterior differential system. Moreover, we verify that the Korteweg-de Vries (KdV) equation and the Cauchy-Riemann equations are examples of our equation.

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