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1.
研究来源于多元统计分析中的一类矩阵迹函数最小化问题$\min c+ tr(AX)+\sum\limits_{j=1}^{m}tr(B_j X C_jX^{T}),\ \ {\rm s. t.} \ X^TX=I_p,$其中$c$为常数, $A\in R^{p\times n}\ (n\geq p)$, $B_j\in R^{n\times n}, C_j\in R^{p\times p}$为给定系数矩阵. 数值实验表明已有的Majorization算法虽可行, 但收敛速度缓慢且精度不高. 本文从黎曼流形的角度重新研究该问题, 基于Stiefel流形的几何性质, 构造一类黎曼非单调共轭梯度迭代求解算法, 并给出算法收敛性分析.数值实验和数值比较验证所提出的算法对于问题模型是高效可行的.  相似文献   
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Bu  De-liang  Zhang  San-guo  Li  Na 《应用数学学报(英文版)》2022,38(4):843-860
Acta Mathematicae Applicatae Sinica, English Series - Joint analysis of multiple phenotypes can have better interpretation of complex diseases and increase statistical power to detect more...  相似文献   
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Red mud wastes have been converted into mesoporous zeolite socony mobile-5 (ZSM-5) followed by deposited titanium dioxide (TiO2) nanoparticles to generate synergy adsorption-photodegradation for removal of dye removal in waste water. The amount of TiO2 loading was varied to achieve optimum photocatalytic activity while maintaining the mesoporosity and high surface area of ZSM-5. Sol-gel method facilitated the formation of anatase TiO2 on the ZSM-5. The fourier transform infrared spectra clarified the formation of Si–O–Ti at 957 cm?1 by the exchanging the hydrogen ion with titanium ion, which proved by decreasing the absorption band of Si–OH and Si–O interaction at 964 and 944 cm?1, respectively. Sol-gel method also preserved the mesopore diameter of ZSM-5 at 3.5 nm which allow the diffusion of methylene blue (MB) molecules into the pores. However, the surface area and the pore volume were slightly reduced with increasing the TiO2 loading. The adsorption performance of samples showed that the increasing in the TiO2 loading led to the decreasing in the adsorption capacity. All samples showed the suitability towards the pseudo second order kinetic. The Langmuir isotherm was suitable to describe the adsorption mechanism by monolayer adsorption. Mesoporosity of ZSM-5 accelerated the adsorption of dye via the increase of mass transfer in the pore channel which confirmed by the low intercept of intraparticle diffusion model at the first stage. The photocatalytic test showed that 10% TiO2 loading on the ZSM-5 exhibited the highest methylene blue removal followed by 5% and 20% TiO2 loading. Optimization on the amount of photocatalyst and the pH of solution indicated the reaction favoured 1 g L?1 of catalysts and at alkaline pH. 10% TiO2/ZSM-5 also exhibited high stability and reusability up to four reaction cycles. Photocatalytic performance of 10% TiO2/ZSM-5 was further investigated on photodegradation of malachite green and rhodamine B organic dyes, which showed the photocatalytic efficiency of 73 and 88%, respectively. Superoxide radical, hydroxyl radical, and photogenerated electron were identified as the main active species for MB photodegradation based on the reduction of degradation rate following the addition scavenger molecules.  相似文献   
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矩阵平方根在数学的许多应用中起着重要的作用.本文研究M-矩阵平方根的计算问题,提出一种计算正则M-矩阵平方根的迭代方法.首先将这个问题转化为M-矩阵代数Riccati方程,进而提出一种有效的方法来求解这个特殊的MARE.理论分析表明,该方法在一定条件下是收敛的.数值实验表明该方法是可行的,且优于二项式迭代法.  相似文献   
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Yom-Tov  Galit B.  Chan  Carri W. 《Queueing Systems》2021,99(1-2):163-198
Queueing Systems - Consider a population of customers, each of which needs to decide independently when to arrive to a facility that provides a service during a fixed period of time, say a day....  相似文献   
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We investigate a diffusive, stage-structured epidemic model with the maturation delay and freelymoving delay. Choosing delays and diffusive rates as bifurcation parameters, the only possible way to destabilize the endemic equilibrium is through Hopf bifurcation. The normal forms of Hopf bifurcations on the center manifold are calculated, and explicit formulae determining the criticality of bifurcations are derived. There are two different kinds of stable oscillations near the first bifurcation: ...  相似文献   
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Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. Deep neural network architectures and computational issues have been well studied in machine learning. But there lacks a theoretical foundation for understanding the approximation or generalization ability of deep learning methods generated by the network architectures such as deep convolutional neural networks. Here we show that a deep convolutional neural network (CNN) is universal, meaning that it can be used to approximate any continuous function to an arbitrary accuracy when the depth of the neural network is large enough. This answers an open question in learning theory. Our quantitative estimate, given tightly in terms of the number of free parameters to be computed, verifies the efficiency of deep CNNs in dealing with large dimensional data. Our study also demonstrates the role of convolutions in deep CNNs.  相似文献   
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Guo  Xu  Jiang  Xuejun  Zhang  Shumei  Zhu  Lixing 《中国科学 数学(英文版)》2020,63(12):2553-2572
Science China Mathematics - In this study, we propose nonparametric testing for heteroscedasticity in nonlinear regression models based on pairwise distances between points in a sample. The test...  相似文献   
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