Heterotrimetallic Mixed‐Valent Molecular Precursors Containing Periodic Table Neighbors: Assignment of Metal Positions and Oxidation States

A known trinuclear structure was used to design the heterobimetallic mixed‐valent, mixed‐ligand molecule [Co^II(hfac)₃?Na?Co^III(acac)₃] ( 1 ). This was used as a template structure to develop heterotrimetallic molecules [Co^II(hfac)₃?Na?Fe^III(acac)₃] ( 2 ) and [Ni^II(hfac)₃?Na?Co^III(acac)₃] ( 3 ) via isovalent site‐specific substitution at either of the cobalt positions. Diffraction methods, synchrotron resonant diffraction, and multiple‐wavelength anomalous diffraction were applied beyond simple structural investigation to provide an unambiguous assignment of the positions and oxidation states for the periodic table neighbors in the heterometallic assemblies. Molecules of 2 and 3 are true heterotrimetallic rather than a statistical mixture of two heterobimetallic counterparts. Trinuclear platform 1 exhibits flexibility in accommodating a variety of di‐ and trivalent metals, which can be further utilized in the design of molecular precursors for the NaMM′O₄ functional oxide materials.     

Henstock-Kurzweil delta and nabla integrals

We will study the Henstock-Kurzweil delta and nabla integrals, which generalize the Henstock-Kurzweil integral. Many properties of these integrals will be obtained. These results will enable time scale researchers to study more general dynamic equations. The Henstock-Kurzweil delta (nabla) integral contains the Riemann delta (nabla) and Lebesque delta (nabla) integrals as special cases.     

Preface in dedication to Professors Yong Jin and Zhiqing Yu

This special issue of China PARTICUOLOGY is dedicated to Professors Yong Jin and Zhiqing Yu of Tsinghua University, China, to celebrate over five decades of their careers in chemical engineering research and education.……     

Diffusion

Ohne Zusammenfassung     

A construction of codimension three arithmetically Gorenstein subschemes of projective space

This paper presents a construction method for a class of codimension three arithmetically Gorenstein subschemes of projective space. These schemes are obtained from degeneracy loci of sections of certain specially constructed rank three reflexive sheaves. In contrast to the structure theorem of Buchsbaum and Eisenbud, we cannot obtain every arithmetically Gorenstein codimension three subscheme by our method. However, certain geometric applications are facilitated by the geometric aspect of this construction, and we discuss several examples of this in the final section.

     

On the notion of relative property (T) for inclusions of von Neumann algebras

We prove that the notion of rigidity (or relative property (T)) for inclusions of finite von Neumann algebras recently defined by the second author is equivalent to a weaker property, in which no “continuity constants” are required. The proof is by contradiction and uses infinite products of completely positive maps, regarded as correspondences.