On derivatives of planar mappings and their connections to complete mappings

Given are necessary conditions for a permutation polynomial to be the derivative of a planar mapping. These conditions are not sufficient and there might exist permutation polynomials which are not derivatives of some planar mapping satisfying these conditions. For the first time we show that there is a close connection between two seemingly unrelated structures, namely planar and complete mappings. It is shown that any planar mapping induces a sequence of complete mappings having some additional interesting properties. Furthermore, a class of almost planar mappings over extension fields is introduced having the property that its derivatives are permutations in most of the cases. This class of functions then induces many infinite classes of complete mappings (permutations) as well

Controlling the Polymorphism and Topology Transformation in Porphyrinic Zirconium Metal-Organic Frameworks via Mechanochemistry

The mechanochemical approach has been used here for preparation and polymorph resolution in porphyrinic MOF-525/PCN-223 zirconium metal-organic frameworks system, achieving pure target MOF phases in 30-60 minutes milling. In specific reaction condition, MOF-525 forms rapidly by milling but transforms into PCN-223, confirming it to be the kinetic phase in this polymorphic system. ESR measurements showed a strong effect of internal MOF structure on the spin structure of paramagnetic cations coordinated into porphyrin linkers, which show potential for these polymorphic MOFs in spintronics application

Controlling the Polymorphism and Topology Transformation in Porphyrinic Zirconium Metal–Organic Frameworks via Mechanochemistry

Tetratopic porphyrin-based metal−organicframeworks (MOFs) represent a particularly interestingsubclass of zirconium MOFs due to the occurrence ofseveral divergent topologies. Control over the targettopology is a demanding task, and reports often showproducts containing phase contamination. We demonstratehow mechanochemistry can be exploited forcontrolling the polymorphism in 12-coordinated porphyriniczirconium MOFs, obtaining pure hexagonal PCN-223and cubic MOF-525 phases in 20−60 min of milling. Thereactions are mainly governed by the milling additives andthe zirconium precursor. In situ monitoring by synchrotronpowder X-ray diffraction revealed that specificreaction conditions resulted in the formation of MOF-525 as an intermediate, which rapidly converted to PCN-223 upon milling. Electron spin resonance measurementsrevealed significant differences between the spectra ofparamagnetic centers in two polymorphs, showing apotential of polymorphic Zr-MOFs as tunable supports inspintronics applications

Physical mapping of 5S and 18S-5.8S-26S RNA gene families in polyploid series of Cenchrus ciliaris Linnaeus,\ua01771 (Poaceae)

Volume: 6Start Page: 273End Page: 28