Improving the Fundamental Theorem of Algebra

Theorems 2 and 3 establish the minimum algebraic conditions necessary for a field to be algebraically closed, and they can therefore be said to “optimize” the Fundamental Theorem of Algebra. But each specific“degree implication” is a first-order consequence of the axioms for fields, and could have been discovered two centuries ago; the existence of these finitary relationships appears to have been unsuspected by practically everyone, with one important exception.     

含R_2dtc配体Mo-Cu化合物的动态~(95)Mo NMR

本实验利用动态~(95)Mo NMR监测Mo-Cu系列化合物的形成过程,对反应CuCl+NaR_2dtc+MoO_nS,摩尔比3:3:1,溶剂为DMF;R=Et,n=0(Ⅰ);R=Me,n=0(Ⅱ);R=Et,n=2(Ⅲ)进行了研究,观察到具有不同簇骼的多种中间产物的存在及随反应进程相互转化等现象。     

Ab initio calculations on large molecules using molecular fragments. Characterization of the zwitterion of glycine

The ab initio molecular fragment approach is applied to a characterization study of the ground state of the zwitterion of glycine. Included among the properties studied are the — conformational energy surface, the electronic structure, and the magnitude and direction of the dipole moment. The results of the present study are compared to the results of other theoretical and experimental studies.This work was supported in part by the National Science Foundation, the University of Kansas, and the Upjohn Company, Kalamazoo, Michigan 49001.NSF Trainee (1969-1972).Alfred P. Sloan Research Fellow (1971–1973).     

Monomer, dimer, tetramer, polymer: structural diversity in zinc and cadmium complexes of chelate-tethered nucleobases

A series of ZnII and CdII complexes of adenine and guanine derivatives containing a diamine tether have been isolated from aqueous solutions and characterised by single crystal X-ray analysis. These studies reveal a wide range of structural types including monomeric, dimeric, tetrameric and polymeric architectures. The extended structures arise from the ability of the ligands to bridge metal ions using the chelating tether in conjunction with N7 of the nucleobase. Additional metal-nucleobase co-ordination is generally observed at the N3-site of the adenine derivatives. With CdII, ethylenediamine-N9-ethylguanine forms an inverted G-tetrad type structure.     

Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. The paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.     

Stereoelectronic properties of photosynthetic and related systems: Ab initio configuration interaction calculations on the ground and lower excited singlet and triplet states of magnesium chlorin and chlorin

Ab initio configuration interaction wavefunctions and energies are reported for the ground state and many low-lying singlet and triplet states of magnesium chlorin and chlorin, and are employed in an analysis of the electronic absorption spectra of these systems.In chlorin, the calculated visible spectrum consists of two ${}^1\text{(π, π}{}^1\text{)}$ states, the lower energy, y-polarized state exhibiting moderate absorption intensity in contrast to the very weak absorption of the higher energy x-polarized state. The configurational composition of both states is well described by the four-orbital model. Five ${}^1\text{(π, π}{}^1\text{)}$ states are responsible for the Soret band envelope. A moderately intense y-state lies under the low energy edge of the band envelope, while two x-polarized states of moderate and strong intensity, respectively, are responsible for the band maximum. The final two ${}^1\text{(π, π}{}^1\text{)}$ states lie at the high energy edge of the Soret band and introduce a measure of asymmetry into the band envelope. Two ${}^1\text{(n, π}{}^1\text{)}$ states of very weak oscillator strength are also found in this region of the spectrum. All the Soret states are of complex configurational composition, and several of the higher lying states contain contributions from doubly excited configurations.The calculated visible spectrum of magnesium chlorin also consists of two ${}^1\text{(π, π}{}^1\text{)}$ states, with the weakly absorbing x-polarized state lying approximately 200 cm^?1 lower in energy than the moderately intense y-polarized state. The configurational composition of both states is well described by the four-orbital model. Four ${}^1\text{(π, π}{}^1\text{)}$ states constitute the bulk of the intensity in the Soret band envelope. In distinction to chlorin, the moderately intense ${}^1\text{(π, π}{}^1\text{)}$ state at the low energy edge of the band envelope is x-polarized. Two intense ${}^1\text{(π, π}{}^1\text{)}$ states of y- and x-polarization, respectively, constitute the band maximum region, and a single x-polarized state of moderately strong intensity can be assigned to the high energy shoulder of the band envelope. Two other weakly absorbing ${}^1\text{(π, π}{}^1\text{)}$ states are also found in this region, along with another weakly absorbing state of mixed in-plane and out-of-plane polarization. No clearly defined ${}^1\text{(n, π}{}^1\text{)}$ states are observed. As was the case for chlorin, all the Soret states are of complex configurational composition, and some of the higher energy states contain significant contributions from doubly excited configurations.Chlorin and magnesium chlorin both possess three ${}^3\text{(π, π}{}^1\text{)}$ states which lie below S₁ and a single ${}^3\text{(π, π}{}^1\text{)}$ which lies slightly above S₂. All four of the low-lying ${}^3\text{(π, π}{}^1\text{)}$ states in each molecule are well described by the four-orbital model, with T₁ being essentially a single configuration in each case. The remainder of the ${}^3\text{(π, π}{}^1\text{)}$ states are clustered in the same energetic region as the comparable ${}^1\text{(π, π}{}^1\text{)}$ Soret states, with comparably complex configurational compositions.Dipole moments and charge distributions for low-lying singlet and triplet states are also reported, and are used to rationalize chemical reactivity characteristics.     

Solid-phase, multicomponent reactions of methyleneaziridines: synthesis of 1,3-disubstituted propanones

[reaction: see text] Polymer-supported methyleneaziridines undergo ring opening by Grignard reagents under copper catalysis to yield metalloenamines which are alkylated in situ to yield ketimines. Filtration and washing of these Merrifield resin-bound intermediates prior to hydrolysis provides the corresponding 1,3-disubstituted propanones in a high state of purity without recourse to column chromatography.     

Asymmetric synthesis of 2-substituted piperidines using a multi-component coupling reaction: rapid assembly of (S)-coniine from (S)-1-(1-phenylethyl)-2-methyleneaziridine

(S)-Coniine is made using a reaction which assembles the piperidine ring by the sequential formation of four new chemical bonds and installs the C-2 stereogenic centre with high levels of diastereocontrol (90% de).