1,355,098 research outputs found
Dependently Sorted Theorem Proving for Mathematical Foundations
No full textWe describe a new meta-logical system for mechanising foundations of mathematics. Using dependent sorts and first order logic, our system (implemented as an LCF-style theorem-prover) improves on the state-of-the-art by providing efficient type-checking, convenient automatic rewriting and interactive proof support. We assess our implementation by axiomatising Lawvere’s Elementary Theory of the Category of Sets (ETCS) [F. William Lawvere, 1964], and Shulman’s Sets, Elements and Relations (SEAR) [Michael Shulman, 2022]. We then demonstrate our system’s ability to perform some basic mathematical constructions such as quotienting, induction and coinduction by constructing integers, lists and colists. We also compare with some existing work on modal model theory done in HOL4 [Yiming Xu and Michael Norrish, 2020]. Using the analogue of type-quantification, we are able to prove a theorem that this earlier work could not. Finally, we show that SEAR can construct sets that are larger than any finite iteration of the power set operation. This shows that SEAR, unlike HOL, can construct sets beyond V_{ω+ω}
Norrish Type II Reactions of Acyl Azolium Salts
No full textThe photochemical reactivity of acyl azolium salts derived from aliphatic carboxylic acids has been investigated. These species, which serve as models for intermediates generated in N-heterocyclic carbene (NHC) organocatalysis, undergo Norrish type II elimination reactions under irradiation with UVA light in analogy to structurally related aromatic ketones. Moreover, efficient Norrish-Yang cyclization was observed from an adamantyl-substituted derivative. These results further demonstrate the ability of NHCs to influence the absorption properties and photochemical reactivity of carbonyl groups during a catalytic cycle
Frank Norrish Farm
No full textThe Frank Norrish Farm is located in Morrison, Illinois. The typical buildings of a Corn Belt stock farm are shown in the background. Included in this grouping is a barn, windmill, and silos, a vital element of the feed lot. In the foreground are Mr. Norrish\u27s herd of calves, bred by West Love of Marfa, Texas. He purchased the cattle at the Highland Hereford Show at Marfa, Texas last fall, where he was a judge. Published in the Fort Worth Star-Telegram morning edition, January 26, 1941.https://mavmatrix.uta.edu/specialcollections_startelegram1940s/1009/thumbnail.jp
Frank Norrish Farm
No full textThe Frank Norrish Farm is located in Morrison, Illinois. The typical buildings of a Corn Belt stock farm are shown in the background. Included in this grouping is a barn, windmill, and silos, a vital element of the feed lot. In the foreground feedlot are Mr. Norrish\u27s herd of calves, bred by West Love of Marfa, Texas. He purchased the cattle at the Highland Hereford Show at Marfa, Texas last fall, where he was a judge. Published in the Fort Worth Star-Telegram morning edition, January 26, 1941.https://mavmatrix.uta.edu/specialcollections_startelegram1940s/1008/thumbnail.jp
Jennifer Norrish, circa 1981
No full textJennifer Norrish, engineering student at Swinburne, who came with a high HSC score of 348.
Photograph originally appeared in the 'Swinburne Newsletter', 19 February 1981
Adiabatic and Nonadiabatic Bond Cleavages in Norrish Type I Reaction
No full textOne of the fundamental photoreactions for ketones is Norrish type I reaction, which has been extensively studied both experimentally and theoretically. Its a bond-cleavage mechanisms are usually explained in an adiabatic picture based on the involved excited-state potential energy surfaces, but scarcely investigated in terms of a non-adiabatic picture. In this work, the S-1 alpha bond-cleavage reactions of CH3OC(O)Cl have been investigated by using the CASSCF and MRCI-SD calculations, and the ab initio based time-dependent quantum wave-packet simulation. The numerical results indicate that the photoinduced dissociation dynamics of CH3OC(O)Cl could exhibit strong nonadiabatic bond-fission characteristics for the S-1 alpha C-Cl bond cleavage, while the dynamics of the S-1 alpha C-O bond cleavage is mainly of adiabatic characteristics. This nonadiabatic mechanism for Norrish type I reaction of CH3OC(O)Cl is uncovered for the first time. The quantum wavepacket dynamics, based on the reduced-dimensional coupled potential energy surfaces, to some extent illustrates the significance of the nonadiabatic effect in the transition-state region on the dynamics of Norrish type I reaction
Photochemistry of α-Diketones in carbohydrates : anomalous Norrish typeII photoelimination and Norrish-Yang photocyclization promoted the internal carbonyl group
No full textA series of four α-diketones placed as 1α-pyruvoyl tethers on D-glucopyranose and D-glucopyranosiduronic acid skeletons was prepared in order to determine the influence of captodative and stereoelectronic effects on the regioselectivity of the hydrogen atom transfer (HAT) in Norrish typeII photochemical processes. We observed that the 1,5-HAT regioselectivity can be switched between the two potentially abstractable syn-1,3-diaxial hydrogens at H6 and H8. Highly unusual photoproducts from Norrish typeII photoelimination and Norrish-Yang photocyclization initiated by the excited internal carbonyl group were obtained, in some cases in excellent synthetic yield. The 1,5-HAT transition state in the Norrish typeII photoelimination was investigated by photochemical experiments in the crystalline state
Frank Norrish feedlots
No full textCattle bred by W. E. Love and W. E. Moore, of Marfa, Texas, in the feedlots of Frank Norrish at Morrison, Illinois. There is a farmhouse in the background, at right.https://mavmatrix.uta.edu/specialcollections_startelegram1940s/1052/thumbnail.jp
Dynamics of Triplet-State Photochemistry of Pentanal: Mechanisms of Norrish I, Norrish II, and H Abstraction Reactions
No full text ABSTRACT: The photochemistry of aldehydes in the gas phase has been the topic of extensive studies over the years. However, for all but the smallest aldehydes the dynamics of the processes is largely unknown, and key issues of the mechanisms are open. In this article, the photochemistry of pentanal<br />
is studied by dynamics simulation using a semiempirical MRCI code for the singlet and triplet potential energy surfaces involved. The simulations explore the processes on the triplet state following intersystem crossing from the initially excited singlet. Test simulations show that the photochemistry takes place on the adiabatic triplet surface only and that no nonadiabatic transitions occur to the other triplets. The main findings include the following: (1) Norrish type I and type II reactions and H detachment have been observed. (2) The time scales of Norrish type I and Norrish type II reactions are determined: Norrish type I reaction tends to occur in the time scale below 10 ps, whereas the Norrish type II reaction is mostly pronounced after 20 ps. The factors affecting the time scales are analyzed. (3) The relative yield for Norrish type I and type II reactions is 34% and 66%, which is close to the experimental observed ones. Bond orders and Mulliken partial charges are computed along the trajectories and provide mechanistic insights. The results throw light on the time scales and mechanisms and competition between different channels in aldehyde photochemistry. It is suggested that direct dynamics simulations using semiempirical potentials can be a very useful tool for exploring the photochemistry of large aldehydes, ketones, and related species.<br />
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<br />The photochemistry of aldehydes in the gas phase has been the topic of extensive studies over the years. However, for all but the smallest aldehydes the dynamics of the processes is largely unknown, and key issues of the mechanisms are open. In this article, the photochemistry of pentanal is studied by dynamics simulation using a semiempirical MRCI code for the singlet and triplet potential energy surfaces involved. The simulations explore the processes on the triplet state following intersystem crossing from the initially excited singlet. Test simulations show that the photochemistry takes place on the adiabatic triplet surface only and that no nonadiabatic transitions occur to the other triplets. The main findings include the following: (1) Norrish type I and type II reactions and H detachment have been observed. (2) The time scales of Norrish type I and Norrish type II reactions are determined: Norrish type I reaction tends to occur in the time scale below 10 ps, whereas the Norrish type II reaction is mostly pronounced after 20 ps. The factors affecting the time scales are analyzed. (3) The relative yield for Norrish type I and type II reactions is 34% and 66%, which is close to the experimental observed ones. Bond orders and Mulliken partial charges are computed along the trajectories and provide mechanistic insights. The results throw light on the time scales and mechanisms and competition between different channels in aldehyde photochemistry. It is suggested that direct dynamics simulations using semiempirical potentials can be a very useful tool for exploring the photochemistry of large aldehydes, ketones, and related species
Tony Norrish and Bruce Sandie, 1981
No full textTony Norrish (right) is a fourth year civil engineering student who has just returned to study after a 6 month Cooperative Education placement in Scotland.
Photograph originally appeared in the 'Swinburne Newsletter', 19 March 1981
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