An official website of the United States government
Abstract Neutral three‐coordinate iron alkylidenes of the form PN−Fe=CHR have been proposed as viable candidates for alkene metathesis. Indeed, during the final stages of preparing this current study, a separate report disclosed that dearomatized PN−Fe‐alkyl complexes are active precatalysts for ring‐opening metathesis polymerization (ROMP) of norbornene implicating PN−Fe=CHR species as possible intermediates. In yet another separate report, we prepared Zn analogues of PN−Fe‐alkyl complexes and herein provide an account for the synthesis, characterization, and reactivity of some new iron complexes with the sametBu substituted PN platform.
more »
« less
This content will become publicly available on March 1, 2026
Central limit theorem for Rényi divergence of infinite order
For normalized sums Zn of i.i.d. random variables, we explore necessary and sufficient conditions, which guarantee the normal approximation with respect to the Rényi divergence of infinite order. In terms of densities pn of Zn, this is a strengthened variant of the local limit theorem taking the form sup (pn(x)− ϕ(x))/ϕ(x)→0 as n→∞.
more »
« less
- Award ID(s):
- 2154001
- PAR ID:
- 10613517
- Publisher / Repository:
- Inst. Math. Statist.
- Date Published:
- Journal Name:
- The Annals of Probability
- Volume:
- 53
- Issue:
- 2
- ISSN:
- 0091-1798
- Subject(s) / Keyword(s):
- Central limit theorem, Rényi divergence.
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)Redox-active multimetallic platforms with synthetically addressable and hemilabile active sites are attractive synthetic targets for mimicking the reactivity of enzymatic co-factors toward multielectron transformations. To this end, a family of ternary clusters featuring three edge metal sites anchored on a [Co 6 Se 8 ] multimetallic support via amidophosphine ligands are a promising platform. In this report, we explore how small changes in the stereoelectronic properties of these ligands alter [Co 6 Se 8 ] metalloligand formation, but also substrate binding affinity and strength of the edge/support interaction in two new ternary clusters, M 3 Co 6 Se 8 L 6 (M = Zn, Fe; L (−) = Ph 2 PN (−)i Pr). These clusters are characterized extensively using a range of methods, including single crystal X-ray diffraction, electronic absorption spectroscopy and cyclic voltammetry. Substrate binding studies reveal that Fe 3 Co 6 Se 8 L 6 resists coordination of larger ligands like pyridine or tetrahydrofuran, but binds the smaller ligand CN t Bu. Additionally, investigations into the synthesis of new [Co 6 Se 8 ] metalloligands using two aminophosphines, Ph 2 PN(H) i Pr (L H ) and i Pr 2 PN(H) i Pr, led to the synthesis and characterization of Co 6 Se 8 L H 6 , as well as the smaller clusters Co 4 Se 2 (CO) 6 L H 4 , Co 3 Se(μ 2 -PPh 2 )(CO) 4 L H 3 , and [Co(CO) 3 ( i Pr 2 PN(H) i Pr)] 2 . Cumulatively, this study expands our understanding on the effect of the stereoelectronic properties of aminophosphine ligands in the synthesis of cobalt chalcogenide clusters, and, importantly on modulating the push–pull dynamic between the [Co 6 Se 8 ] support, the edge metals and incoming coordinating ligands in ternary M 3 Co 6 Se 8 L 6 clusters.more » « less
-
Macrophage (Mϕ)-lineage cells are integral to the immune defences of all vertebrates, including amphibians. Across vertebrates, Mϕdifferentiation and functionality depend on activation of the colony stimulating factor-1 (CSF1) receptor by CSF1 and interluekin-34 (IL34) cytokines. Our findings to date indicate that amphibian (Xenopus laevis) Mϕs differentiated with CSF1 and IL34 are morphologically, transcriptionally and functionally distinct. Notably, mammalian Mϕs share common progenitor population(s) with dendritic cells (DCs), which rely on fms-like tyrosine kinase 3 ligand (FLT3L) for differentiation whileX. laevisIL34-Mϕs exhibit many features attributed to mammalian DCs. Presently, we comparedX. laevisCSF1- and IL34-Mϕs with FLT3L-derivedX. laevisDCs. Our transcriptional and functional analyses indicated that indeed the frog IL34-Mϕs and FLT3L-DCs possessed many commonalities over CSF1-Mϕs, including transcriptional profiles and functional capacities. Compared toX. laevisCSF1-Mϕs, the IL34-Mϕs and FLT3L-DCs possess greater surface major histocompatibility complex (MHC) class I, but not MHC class II expression, were better at eliciting mixed leucocyte responsesin vitroand generatingin vivore-exposure immune responses againstMycobacterium marinum. Further analyses of non-mammalian myelopoiesis akin to those described here, will grant unique perspectives into the evolutionarily retained and diverged pathways of Mϕand DC functional differentiation. This article is part of the theme issue ‘Amphibian immunity: stress, disease and ecoimmunology’.more » « less
-
Graphene and graphene oxide have shown good antibacterial activity against different bacterial species due to their unique physicochemical properties. Graphene oxide (GO) has been widely used to load metallic and metal oxide nanoparticles (NPs) to minimize their surface energy during processing and preparation, hence reducing their aggregation. In this work, GO was effectively synthesized and coated with different concentrations of zinc hydroxide Zn (OH)x using the precipitation method to prepare a GO/Zn (OH)x hybrid composite. The Zn (OH)x NPs and GO/Zn (OH)x nanocomposites were synthesized and characterized using various methods such as scanning electron microscopy (SEM), X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS). Coating GO with Zn (OH)x NPs resulted in improved aggregation of Zn (OH)x NPs as well as enhanced antibacterial activity of GO against Gram-positive and Gram-negative bacteria. Additionally, the effect of Zn (OH)x coating on the antibacterial properties of the GO/Zn (OH)x composite was systematically investigated. The synergistic effects of GO and Zn (OH)x NPs resulted in enhanced antibacterial properties of the composites compared to the pristine GO material. In addition, increasing the Zn (OH)x wt. % concentration led to an increased inhibition zone of the GO/Zn (H)x composite against Bacillus megaterium and E. coli bacteria.more » « less
-
Abstract Consider an ergodic measure preserving dynamical system ( T , X , μ ), and an observable ϕ : X → R . For the time series X n ( x ) = ϕ ( T n ( x )), we establish limit laws for the maximum process M n = max k ⩽ n X k in the case where ϕ is an observable maximized on a line segment, and ( T , X , μ ) is a hyperbolic dynamical system. Such observables arise naturally in weather and climate applications. We consider the extreme value laws and extremal indices for these observables on hyperbolic toral automorphisms, Sinai dispersing billiards and coupled expanding maps. In particular we obtain clustering and nontrivial extremal indices due to self intersection of submanifolds under iteration by the dynamics, not arising from any periodicity.more » « less
