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1.
《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2021,38(5):1337-1371
In this paper we consider minimizers of the functional where is a bounded open set and where are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets have finite perimeter and that their free boundary is composed of a regular part, which is locally the graph of a -regular function, and a singular part, which is empty if , discrete if and of Hausdorff dimension at most if , for some . 相似文献
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乳腺癌是当前最常见的恶性肿瘤之一,其电子病历数据可用于挖掘隐含规律,对治疗与预后分析有重要意义。通过与乳腺科医生合作,选择合适的预测模型和可视化方法,搭建了一个基于电子病历的乳腺癌群组和治疗方案可视分析系统。首先,对具有高维属性的病人进行降维和聚类处理,形成病人群组,并采用南丁格尔图、词云和时间轴可视化方法,直观展示病人群组间特征的差异;然后,用支持向量机(support vector machine,SVM)模型预测治疗方案,用平行坐标、矩阵热力图和分类图分别展示属性相关性、训练后的特征权重和预测结果;最后,用真实案例验证了系统在群组分析、治疗方案及病人属性关联分析中的有效性,从而较好地帮助医生选择合适的治疗方案。 相似文献
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Natalia L. Calvo Sebastian O. SimonettiRubén M. Maggio Teodoro S. Kaufman 《Analytica chimica acta》2015
Exposure of cimetidine (CIM) to dry heat (160–180 °C) afforded, upon cooling, a glassy solid containing new and hitherto unknown products. The kinetics of this process was studied by a second order chemometrics-assisted multi-spectroscopic approach. Proton and carbon-13 nuclear magnetic resonance (NMR), as well as ultraviolet and infrared spectroscopic data were jointly used, whereas multivariate curve resolution with alternating least squares (MCR-ALS) was employed as the chemometrics method to extract process information. It was established that drug degradation follows a first order kinetics. 相似文献
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设R■A是环的Frobenius扩张,其中A是右凝聚环,M是任意左A-模.首先证明了_AM是Gorenstein平坦模当且仅当M作为左R-模也是Gorenstein平坦模.其次,证明了Nakayama和Tsuzuku关于平坦维数沿着Frobenius扩张的传递性定理的"Gorenstein版本":若_AM具有有限Gorenstein平坦维数,则Gfd_A(M)=Gfd_R(M).此外,证明了若R■S是可分Frobenius扩张,则任意A-模(不一定具有有限Gorenstein平坦维数),其Gorenstein平坦维数沿着该环扩张是不变的. 相似文献
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We show that the Smith normal form of a skew‐symmetric D ‐optimal design of order is determined by its order. Furthermore, we show that the Smith normal form of such a design can be written explicitly in terms of the order , thereby proving a recent conjecture of Armario. We apply our result to show that certain D ‐optimal designs of order are not equivalent to any skew‐symmetric D ‐optimal design. We also provide a correction to a result in the literature on the Smith normal form of D ‐optimal designs. 相似文献
10.
Nejal M. Bhatt Vijay D. Chavada Mallika Sanyal Pranav S. Shrivastav 《Biomedical chromatography : BMC》2019,33(10)
The present work describes novel methods using densitometry and indirect or off‐line high performance thin‐layer chromatography–mass spectrometry (HPTLC–MS) for the simultaneous detection and quantification of asenapine, propranolol and telmisartan and their phase II glucuronide metabolites. After chromatographic separation of the drugs and their metabolites the analytes were scraped, extracted in methanol and concentrated prior to mass spectrometric analysis. Different combinations of toluene and methanol–ethanol–n‐butanol–iso‐propanol were tested for analyte separation and the best results were obtained using toluene–methanol–ammonia (6.9:3.0:0.1, v/v/v) as the elution solvent. All of the drug–metabolite pairs were separated with a homologous retardation factor difference of ≥22. The conventional densitometric approach was also studied and the method performances were compared. Both of the approaches were validated following the International Conference on Harmonization guidelines, and applied to spiked human plasma samples. The major advantage of the TLC–MS approach is that it can provide much lower limits of detection (1.98–5.83 pg/band) and limit of quantitation (5.97–17.63 pg/band) with good precision (?3.0% coefficient of variation) compared with TLC–densitometry. The proposed indirect HPTLC–MS method is simple yet effective and has tremendous potential in the separation and quantitation of drugs and their metabolites from biological samples, especially for clinical studies. 相似文献