A representation theorem for weak automorphisms of a universal algebra

Given a group G and a descending chainG ₀,G ₁,...,G _n, of normal subgroups ofG, we prove that there exists a universal algebra , such that the chain ...W_n( )...W₁( }) W₀( )W( ) is isomorphic to the chain ...G _n ...G ₁G ₀G, where W( ) is the group of weak automorphisms of , and W_n( ) is the group of weak automorphisms of that leaves alln-ary operations fixed.We also prove that there are an infinite number of non-isomorphic algebras that satisfy the above.These results are a generalization of those proved by J. Sichler, in the special case when G=G₀, and G₁=G₂=...=G_n=....Presented by J. Mycielski.This paper comprises part of the author's doctoral dissertation at the University of Notre Dame in 1983. The author wishes to express her deep gratitude to Professor Abraham Goetz for suggesting this problem, for being extremely generous with his time and experience, and for giving her his constant encouragement. The author also thanks the reviewer for his helpful comments.     

A particle growth theory for heterogeneous Ziegler polymerization

Samples of “as produced” polypropylene particles at progressively higher yield levels (grams polymer/gram catalyst) were sliced and examined by electron microscopy. In the polymerization of propylene with the TiCl₃–(C₂H₅)₂AlCl catalyst system the catalyst breaks up immediately into basic 100–1000 Å particles. As the yield increases, the catalyst particles gradually disappear and finally become completely dispersed in the polymer particle. These results are compatible with a theory which views the catalyst as a porous crystal containing a single species of active sites uniformly distributed. As polymerization progresses, all sites should eventually initiate a polymer chain whose length should be inversely proportional to the depth of the site below the surface of the particle. Two apparently equivalent statistical models were developed on the basis of this concept. Both models predict a slow increase in the X?_w/X?_n ration (Q) with increasing molecular weight, after an initial rapid increase. The most useful of these models states that Q is equal to the sum of X?_w terms of the simple harmonic series, and that a complete spectrum of x-mers should be present in the product. This agrees satisfactorily with analytically determined values.     

Preparation of 3-azetidinols with non-bulky 1-alkyl substituents

Cyclization of either the tetrahydropyranyl or trimethylsilyl ether of 1-(alkylamino)-3-chloro-2-propanols 1 followed by cleavage of the azetidinyl ether provides a general method for the preparation of 1-alkyl-3-azetidinols. Unhindered amines provide a more facile preparation of derivatives of 1 , or its ethers, than do hindered amines, while hindered derivatives of 1 undergo more facile ring closure.     

Polybenzodipyrroloquinoxalines

Three polymers have been prepared by the condensation of benzo[1,2-b;5,4-b ′]-dipyrrolo-2,3,4,5-tetraone (I) with 1,2,4,5-tetraaminobenzene (II), 3,3 ′-diaminobenzidine (III), and 3,3 ′,4,4 ′-tetraaminodiphenyl ether (IV) in polyphosphoric acid (PPA) solution. The polymer structures were substantiated by comparison of their infrared and ultraviolet spectra with spectra of the model compounds and elemental analysis. The polymers had inherent viscosities of 0.86-0.90 (H₂SO₄) and thermal stabilities of 460°C and up to 700°C in air and nitrogen atmospheres, respectively.     

Evaluating the impact of functional groups on membrane-mediated CO2/N2 gas separations using a common polymer backbone

Polymeric membranes have shown tremendous promise for the separation of CO₂ from flue gas streams. However, few systematic studies have been conducted to better understand the impact that chemical functionalities have on membrane-based gas separation performance. To address this gap, we herein describe the synthesis and gas separation performance of a series of vinyl-addition polynorbornenes bearing various CO₂-philic functional groups. To facilitate direct comparison between functional groups, each material was designed to maintain a common polymer backbone. Though the incorporation of CO₂-philic moieties within a dense polymeric membrane is frequently hypothesized to enhance CO₂ solubility, and thereby increase CO₂/N₂ selectivity, our results demonstrate that the incorporation of CO₂-philic groups onto a common polymer backbone do not necessarily result in increased gas separation performance. Experimental and computational results demonstrate that the incorporation of amidoxime groups onto a polynorbornene backbone increase CO₂/N₂ selectivity, whereas commonly employed ethereal side chains only increased permeability.     

Understanding the Origin of Highly Selective CO2 Electroreduction to CO on Ni,N-doped Carbon Catalysts

Ni,N-doped carbon catalysts have shown promising catalytic performance for CO₂ electroreduction (CO₂R) to CO; this activity has often been attributed to the presence of nitrogen-coordinated, single Ni atom active sites. However, experimentally confirming Ni−N bonding and correlating CO₂ reduction (CO₂R) activity to these species has remained a fundamental challenge. We synthesized polyacrylonitrile-derived Ni,N-doped carbon electrocatalysts (Ni-PACN) with a range of pyrolysis temperatures and Ni loadings and correlated their electrochemical activity with extensive physiochemical characterization to rigorously address the origin of activity in these materials. We found that the CO₂R to CO partial current density increased with increased Ni content before plateauing at 2 wt % which suggests a dispersed Ni active site. These dispersed active sites were investigated by hard and soft X-ray spectroscopy, which revealed that pyrrolic nitrogen ligands selectively bind Ni atoms in a distorted square-planar geometry that strongly resembles the active sites of molecular metal–porphyrin catalysts.     

An asynchronous high‐speed synchrotron shutter

A high‐repetition‐rate mechanical shutter with asynchronous control and sub‐millisecond operation has been developed and tested for specialist X‐ray systems in the field of medical diagnostics and radiation therapy. Capacitor‐coupled linear voice coil actuators are utilized to achieve opening and closing speeds as fast as 700 µs for an aperture height of 4 mm. The design allows for asynchronous control, permitting slave operation of the shutter, a feature that is distinctly suitable for a number of applications including particle image velocimetry, where high‐frame‐rate operation must be accurately synchronized and triggered by the image acquisition sequence of the detector or timing device. The design and construction of the shutter also makes it ideal, with simple and limited modifications, for applications requiring larger apertures, in particular wide beams as found in many synchrotron beamlines.     

Understanding the Origin of Highly Selective CO2 Electroreduction to CO on Ni,N‐doped Carbon Catalysts

Ni,N‐doped carbon catalysts have shown promising catalytic performance for CO₂ electroreduction (CO₂R) to CO; this activity has often been attributed to the presence of nitrogen‐coordinated, single Ni atom active sites. However, experimentally confirming Ni?N bonding and correlating CO₂ reduction (CO₂R) activity to these species has remained a fundamental challenge. We synthesized polyacrylonitrile‐derived Ni,N‐doped carbon electrocatalysts (Ni‐PACN) with a range of pyrolysis temperatures and Ni loadings and correlated their electrochemical activity with extensive physiochemical characterization to rigorously address the origin of activity in these materials. We found that the CO₂R to CO partial current density increased with increased Ni content before plateauing at 2 wt % which suggests a dispersed Ni active site. These dispersed active sites were investigated by hard and soft X‐ray spectroscopy, which revealed that pyrrolic nitrogen ligands selectively bind Ni atoms in a distorted square‐planar geometry that strongly resembles the active sites of molecular metal–porphyrin catalysts.