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.     

Compatible relations on filters and stability of local topological properties under supremum and product

An abstract scheme using particular types of relations on filters leads to general unifying results on stability under supremum and product of local topological properties. We present applications for Fréchetness, strong Fréchetness, countable tightness and countable fan-tightness, some of which recover or refine classical results, some of which are new. The reader may find other applications as well.     

The semi‐iterative method applied to the hyper‐power iteration

The semi‐iterative method (SIM) is applied to the hyper‐power (HP) iteration, and necessary and sufficient conditions are given for the convergence of the semi‐iterative–hyper‐power (SIM–HP) iteration. The root convergence rate is computed for both the HP and SIM–HP methods, and the quotient convergence rate is given for the HP iteration. Copyright © 2005 John Wiley & Sons, Ltd.     

Globally Linked Pairs of Vertices in Equivalent Realizations of Graphs

A two-dimensional framework (G,p) is a graph G = (V,E) together with a map p: V → ℝ². We view (G,p) as a straight line realization of G in ℝ². Two realizations of G are equivalent if the corresponding edges in the two frameworks have the same length. A pair of vertices {u,v} is globally linked in G if %and for all equivalent frameworks (G,q), the distance between the points corresponding to u and v is the same in all pairs of equivalent generic realizations of G. The graph G is globally rigid if all of its pairs of vertices are globally linked. We extend the characterization of globally rigid graphs given by the first two authors [13] by characterizing globally linked pairs in M-connected graphs, an important family of rigid graphs. As a byproduct we simplify the proof of a result of Connelly [6] which is a key step in the characterization of globally rigid graphs. We also determine the number of distinct realizations of an M-connected graph, each of which is equivalent to a given generic realization. Bounds on this number for minimally rigid graphs were obtained by Borcea and Streinu in [3].     

The tetrahedron algebra and its finite-dimensional irreducible modules

Recently Terwilliger and the present author found a presentation for the three-point sl₂ loop algebra via generators and relations. To obtain this presentation we defined a Lie algebra ? by generators and relations and displayed an isomorphism from ? to the three-point sl₂ loop algebra. In this paper we classify the finite-dimensional irreducible ?-modules.