Reduction of underdetermined systems of ordinary differential equations: I

We consider the equivalence problem for underdetermined systems of ordinary differential equations. We present canonical forms for some types of autonomous systems linear in the derivatives. It is shown that, among three-dimensional autonomous systems linear in the derivatives, there are infinitely many locally nonequivalent systems.     

Evidence of a Uranium-Paddlewheel Node in a Catecholate-Based Metal–Organic Framework

The interactions between uranium and non-innocent organic species are an essential component of fundamental uranium redox chemistry. However, they have seldom been explored in the context of multidimensional, porous materials. Uranium-based metal–organic frameworks (MOFs) offer a new angle to study these interactions, as these self-assembled species stabilize uranium species through immobilization by organic linkers within a crystalline framework, while potentially providing a method for adjusting metal oxidation state through coordination of non-innocent linkers. We report the synthesis of the MOF NU-1700 , assembled from U⁴⁺-paddlewheel nodes and catecholate-based linkers. We propose this highly unusual structure, which contains two U⁴⁺ ions in a paddlewheel built from four linkers—a first among uranium materials—as a result of extensive characterization via powder X-ray diffraction (PXRD), sorption, transmission electron microscopy (TEM), and thermogravimetric analysis (TGA), in addition to density functional theory (DFT) calculations.