A control-theoretic perspective on optimal high-order optimization

Mathematical Programming - We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a convex function in a finite-dimensional Euclidean space. Given a function...     

Catalytic Nitrene Transfer by an FeIV-Imido Complex Generated by a Comproportionation Process

Nitrene transfer reactions have emerged as one of the most powerful and versatile ways to insert an amine function to various kinds of hydrocarbon substrates. However, the mechanisms of nitrene generation have not been studied in depth albeit their formation is taken for granted in most cases without definitive evidence of their occurrence. In the present work, we compare the generation of tosylimido iron species and NTs transfer from Fe^II and Fe^III precursors where the metal is embedded in a tetracarbene macrocycle. Catalytic nitrene transfer to reference substrates (thioanisole, styrene, ethylbenzene and cyclohexane) revealed that the same active species was at play, irrespective of the ferrous versus ferric nature of the precursor. Through combination of spectroscopic (UV-visible, Mössbauer), ESI-MS and DFT studies, an Fe^IV tosylimido species was identified as the catalytically active species and was characterized spectroscopically and computationally. Whereas its formation from the Fe^II precursor was expected by a two-electron oxidative addition, its formation from an Fe^III precursor was unprecedented. Thanks to a combination of spectroscopic (UV-visible, EPR, Hyscore and Mössbauer), ESI-MS and DFT studies, we found that, when starting from the Fe^III precursor, an Fe^III tosyliodinane adduct was formed and decomposed into an Fe^V tosylimido species which generated the catalytically active Fe^IV tosylimide through a comproportionation process with the Fe^III precursor.     

Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

Mesoscopic Modeling of Capillarity-Induced Two-Phase Transport in a Microfluidic Porous Structure

Mesoscopic modeling at the pore scale offers great promise in exploring the underlying structure transport performance of flow through porous media. The present work studies the fluid flow subjected to capillarity-induced resonance in porous media characterized by different porous structure and wettability. The effects of porosity and wettability on the displacement behavior of the fluid flow through porous media are discussed. The results are presented in the form of temporal evolution of percentage saturation and displacement of the fluid front through porous media. The present study reveals that the vibration in the form of acoustic excitation could be significant in the mobilization of fluid through the porous media. The dependence of displacement of the fluid on physicochemical parameters like wettability of the surface, frequency along with the porosity is analyzed. It was observed that the mean displacement of the fluid is more in the case of invading fluid with wetting phase where the driving force strength is not so dominant.     

Three-term polynomial progressions in subsets of finite fields

We prove that the group of diffeomorphisms of the interval [0, 1] contains surface groups whose action on (0, 1) has no global fix point and such that only countably many points of the interval (0, 1) have non-trivial stabiliser.