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《Journal of Pure and Applied Algebra》2022,226(8):107024
We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation. 相似文献
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《Indagationes Mathematicae》2022,33(1):218-237
We define the notion of basic set data for finite groups (building on the notion of basic set, but including an order on the irreducible characters as part of the structure), and we prove that the Springer correspondence provides basic set data for Weyl groups. Then we use this to determine explicitly the modular Springer correspondence for classical types (defined over a base field of odd characteristic , and with coefficients in a field of odd characteristic ): the modular case is obtained as a restriction of the ordinary case to a basic set. In order to do so, we compare the order on bipartitions introduced by Dipper and James with the order induced by the Springer correspondence. We provide a quick proof, by sorting characters according to the dimension of the corresponding Springer fibre, an invariant which is directly computable from symbols. 相似文献
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近年来,机器学习等人工智能技术被应用于蛋白质工程,其在蛋白质结构、功能预测、催化活性等研究中具有独特优势。在未知蛋白质结构的情况下,将蛋白质序列和功能特性与机器学习相结合,基于序列-活性关系(innovative sequence-activity relationship,ISAR)算法,将蛋白质氨基酸序列数字化,用快速傅里叶变换(fast four transform,FFT)进行预处理,再进行偏最小二乘回归建模,可在数据集较少情况下拟合得到最佳模型。通过机器学习对紫色球杆菌视紫红质(gloeobacter violaceus rhodopsin,GR)的突变体蛋白质氨基酸序列与光谱最大吸收波长进行建模,获得了最佳模型。用最佳索引LEVM760106建模得到的确定系数R2 为0.944,均方误差E为11.64。用小波变换进行的预处理,其R2 虽也约为0.944,但E大于11.64,不及FFT进行的预处理。方法较好地解决了蛋白质序列与功能特性之间的数学建模问题,在蛋白质工程中可为预测更优的突变体提供支持。 相似文献
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Pu Duan Bo Zhi Luke Coburn Christy L. Haynes Klaus Schmidt-Rohr 《Magnetic resonance in chemistry : MRC》2020,58(11):1130-1138
The composition of fluorescent polymer nanoparticles, commonly referred to as carbon dots, synthesized by microwave-assisted reaction of citric acid and ethylenediamine was investigated by 13C, 13C{1H}, 1H─13C, 13C{14N}, and 15N solid-state nuclear magnetic resonance (NMR) experiments. 13C NMR with spectral editing provided no evidence for significant condensed aromatic or diamondoid carbon phases. 15N NMR showed that the nanoparticle matrix has been polymerized by amide and some imide formation. Five small, resolved 13C NMR peaks, including an unusual ═CH signal at 84 ppm (1H chemical shift of 5.8 ppm) and ═CN2 at 155 ppm, and two distinctive 15N NMR resonances near 80 and 160 ppm proved the presence of 5-oxo-1,2,3,5-tetrahydroimidazo[1,2-a]pyridine-7-carboxylic acid (IPCA) or its derivatives. This molecular fluorophore with conjugated double bonds, formed by a double cyclization reaction of citric acid and ethylenediamine as first shown by Y. Song, B. Yang, and coworkers in 2015, accounts for the fluorescence of the carbon dots. Cross-peaks in a 1H─13C HETCOR spectrum with brief 1H spin diffusion proved that IPCA is finely dispersed in the polyamide matrix. From quantitative 13C and 15N NMR spectra, a high concentration (18 ± 2 wt%) of IPCA in the carbon dots was determined. A pronounced gradient in 13C chemical-shift perturbations and peak widths, with the broadest lines near the COO group of IPCA, indicated at least partial transformation of the carboxylic acid of IPCA by amide or ester formation. 相似文献
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Dauickait Amos S. Lawless Jennifer A. Scott Peter Jan van Leeuwen 《Numerical Linear Algebra with Applications》2020,27(5)
We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds. 相似文献
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The finiteness is proved of the set of isomorphism classes of potentially abelian geometric Galois representations with a given set of data. This is a special case of the finiteness conjecture of Fontaine and Mazur. 相似文献
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本文是文[1-7]的继续,研究变权综合问题,从确定变权的经验公式入手引出了变权原理,给出了变权的公理化定义,讨论了与之有关的均衡函数及其梯度向量。 相似文献