Corrole-based applications

Despite of the many similarities between corroles and porphyrins, the chemistry of the former remained undeveloped for decades because of severe synthetic obstacles. The recent discoveries of facile methodologies for the synthesis of triarylcorroles and the corresponding metal complexes allowed for their utilization in various fields. This survey reveals many examples where corroles were used as the key components in catalysis, sensing of gaseous molecules and medicine-oriented research. The focus in all these cases was on the special features of corroles: stabilization of high valent transition metal ions, unique photophysical properties, large NH acidity, facile synthetic manipulation and distinct catalytic properties. The latter aspect includes several examples of reactions that are not catalyzed by any non-corrole metal complex, such as the iron-based aziridination by Chloramine-T, the clean disproportionation of peroxynitrite, and the very facile N-H activation of amines.     

Oxidation reactivity channels for 2-(pyridin-2-yl)-N,N-diphenylacetamides

Synthetic routes to 2-(pyridin-2-yl)-N,N-diphenylacetamide and 2-(6-methylpyridin-2-yl)-N,N-diphenyl-acetamide are described along with results from the chemical oxidation of these compounds with peracetic acid, m-chloroperbenzoic acid, and OXONE. In each case, oxidations generate four products in varying amounts depending on the oxidant and reaction conditions. Each product has been characterized by spectroscopic methods and the molecular structures of several of the new compounds have been confirmed by X-ray crystallography.     

Stabilization of periodic Stokesian Hele–Shaw flows of ferrofluids

We consider an incompressible ferrofluid in a vertical Hele–Shaw cell and develop a proper analytic framework for the free interface and the velocity potential of the fluid in a periodic geometry. The flow is assumed to obey a non-Newtonian Darcy law. The forces influencing the fluid are gravity, surface tension and the response to a magnetic field induced by a current. In addition, the flow is stabilized at the lower boundary component by an external source b. We prove a well-posedness result for the flow near flat solutions. Moreover, we find conditions on the parameters and on the slope of b for the exponential stability and instability of flat interfaces. Furthermore, we identify values for the current's intensity ι where critical bifurcation of nontrivial finger-shaped solutions from the branch of trivial (flat) solutions takes place.     

Symmetric identities on Bernoulli polynomials

In this paper, we obtain a generalization of an identity due to Carlitz on Bernoulli polynomials. Then we use this generalized formula to derive two symmetric identities which reduce to some known identities on Bernoulli polynomials and Bernoulli numbers, including the Miki identity.