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利用已知的代数的同调满同态来构造其张量积代数的同调满同态.设A,B,C,D是域k上的有限维代数,如果环同态f:A→C和g:B→D是环的同调满同态,则fg:AB→CD也是环的同调满同态. 相似文献
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张量的鲁棒主成分分析是将未知的一个低秩张量与一个稀疏张量从已知的它们的和中分离出来.因为在计算机视觉与模式识别中有着广阔的应用前景,该问题在近期成为学者们的研究热点.本文提出了一种针对张量鲁棒主成分分析的新的模型,并给出交替方向极小化的求解算法,在求解过程中给出了两种秩的调整策略.针对低秩分量本文对其全部各阶展开矩阵进行低秩矩阵分解,针对稀疏分量采用软阈值收缩的策略.无论目标低秩张量为精确低秩或近似低秩,本文所提方法均可适用.本文对算法给出了一定程度上的收敛性分析,即算法迭代过程中产生的任意收敛点均满足KKT条件.如果目标低秩张量为精确低秩,当迭代终止时可对输出结果进行基于高阶奇异值分解的修正.针对人工数据和真实视频数据的数值实验表明,与同类型算法相比,本文所提方法可以得到更好的结果. 相似文献
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本研究旨在分析脑胶质瘤患者的磁共振弥散张量成像(DTI)参数与病变组织血管内皮生长因子(VEGF)和基质金属蛋白酶-9(MMP-9)表达的相关性,以及DTI参数对脑胶质瘤进行分级诊断的价值。根据病理分级将102例脑胶质瘤患者分为低级别组(47例)和高级别组(55例),均行MRI和DTI检查,定量测定表观弥散系数(ADC)、各向异性分数(FA)、相对ADC(rADC)、相对FA(rFA)值及相对轴向扩散系数(rAD)值;用免疫组化法检测VEGF和MMP-9表达情况。结果显示,高级别组患者的rADC、ADC、rAD、FA、rFA均低于低级别组(P<0.05);高级别组患者的VEGF和MMP-9阳性表达均高于低级别组(P<0.05)。rADC、ADC、rAD、FA、rFA与VEGF和MMP-9表达均呈负相关(P<0.05);rADC、ADC、rAD、FA、rFA对脑胶质瘤分级诊断的AUC均具有一定诊断价值(P<0.05)。本研究结果提示DTI定量参数与脑胶质瘤VEGF和MMP-9表达具有相关性,且有助于脑胶质瘤的分级诊断。 相似文献
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The topology of the Ehrenfest force density revisited. A different perspective based on Slater‐type orbitals 下载免费PDF全文
Jan Dillen 《Journal of computational chemistry》2015,36(12):883-890
The topology of the Ehrenfest force density was studied with Slater‐type orbitals (STO). At larger distances from the nuclei, STOs generate similar artefacts as noticed before with Gaussian‐type orbitals. The topology of the Ehrenfest force density was found to be mainly homeomorphic with the topology of the electron density. For the first time, reliable integrations of several properties over force density atomic basins were performed successfully. Integration of the electron density of a number of hydrides, fluorides, and chlorides of first row elements over force density basins indicate substantial differences between the partial charges of the atoms as compared with those obtained from electron density basins. Calculations on saturated hydrocarbons confirm that the electronegativity of carbon atoms increases with increasing geometrical strain. Atomic interaction lines are observed to exist in the Ehrenfest force density between the hydrogen atoms of several so‐called “congested” molecules, and also in some inclusion complexes of alkanes with helium. However, interaction lines are lacking in several other controversial cases. © 2015 Wiley Periodicals, Inc. 相似文献
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Nikolaus Bck Gerhard A. Holzapfel 《International Journal of Solids and Structures》2004,41(26):7459-7469
Starting from the issue of what is the correct form for a Legendre transformation of the strain energy in terms of Eulerian and two-point tensor variables we introduce a new two-point deformation tensor, namely H=(F−F−T)/2, as a possible deformation measure involving points in two distinct configurations. The Lie derivative of H is work conjugate to the first Piola–Kirchhoff stress tensor P. The deformation measure H leads to straightforward manipulations within a two-point setting such as the derivation of the virtual work equation and its linearization required for finite element implementation. The manipulations are analogous to those used for the Lagrangian and Eulerian frameworks. It is also shown that the Legendre transformation in terms of two-point tensors and spatial tensors require Lie derivatives. As an illustrative example we propose a simple Saint Venant–Kirchhoff type of a strain-energy function in terms of H. The constitutive model leads to physically meaningful results also for the large compressive strain domain, which is not the case for the classical Saint Venant–Kirchhoff material. 相似文献
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Poro-micromechanics allows for the quantification of poroelastic properties such as the Biot and Skempton coefficients, once a continuum micromechanics model for the material under consideration has been developed and validated. Employing such a model for the transversely isotropic elasticity of cortical and trabecular bone, we determine the tensors of Biot and Skempton coefficients as functions of the volume fractions of mineral, collagen, and the micropore space (Haversian and Volkmann canals, and the inter-trabecular space). Increase of microporosity, as experienced in osteoporosis, as well as decrease of mineral content, as experienced in osteomalacia, lead to an increase of Biot and Skempton coefficients, i. e. to magnification of the mechanical role of the marrow filling the micropore space. For quantification of the marrow pressure rise upon downfall, undrained conditions are appropriate, as can be shown by model predictions of non-destructive impact experiments. 相似文献