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Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients
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Hongjie Dong 《分析论及其应用》2020,36(2):161-199
In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $\rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations. 相似文献
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Ieva
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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Savita Verma Deepak M. Maher Samadhan S. Nagane Bhausaheb V. Tawade Prakash P. Wadgaonkar 《Journal of polymer science. Part A, Polymer chemistry》2019,57(5):588-597
New aromatic (co)polyesters containing pendant propargyloxy groups were synthesized by phase transfer‐catalyzed interfacial polycondensation of 5‐(propargyloxy)isophthaloyl chloride (P‐IPC) and various compositions of P‐IPC and isophthaloyl chloride with bisphenol A. FTIR and NMR spectroscopic data, respectively, revealed successful incorporation of pendant propargyloxy groups into (co)polyesters and formation of (co)polyesters with desired compositions. (Co)polyesters exhibited good solubility in common organic solvents such as chloroform, dichloromethane, and tetrahydrofuran and could be cast into transparent, flexible, and tough films from chloroform solution. Inherent viscosities and number average molecular weights of (co)polyesters were in the range 0.77–1.33 dL/g and 43,600–118,000 g/mol, respectively, indicating the achievement of reasonably high‐molecular weights. The 10% weight loss temperatures of (co)polyesters were in the range 390–420 °C, demonstrating their good thermal stability. (Co)polyesters exhibited Tg in the range 146–170 °C and Tg values decreased with increase in mol % incorporation of P‐IPC. The study of non‐isothermal curing by DSC indicated thermal crosslinking of (co)polyesters via propargyloxy groups. The utility of pendant propargyloxy group was demonstrated by post‐modification of the selected copolyester with 1‐(4‐azidobutyl)pyrene, 9‐(azidomethyl)anthracene, and azido‐terminated poly(ethyleneglycol) monomethyl ether via copper(I)‐catalyzed Huisgen 1,3‐dipolar cycloaddition reaction. FTIR and 1H NMR spectra confirmed that click reaction was quantitative. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 588–597 相似文献
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在摄像机进行航拍的图像处理系统中,由摄像机运动所引起的视频运动,背景变化是主要特点。在进行图像采集时,每个像素都在变化,采用传统的图像编码方式进行图像压缩,压缩效果比较差。提出了基于块分割的精确运动估计算法,它是一种很好的图像压缩方法。 相似文献
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This paper reports that the growth of RuOx(110) thin layer growth on Ru(0001)
has been investigated by means of scanning tunnelling microscope (STM). The STM
images showed a domain structure with three rotational domains of RuOx(110)
rotated by an angle of 120℃.
The as-grown RuOx(110) thin layer is expanded from the bulk-truncated
RuOx(110) due to the large mismatch between RuOx(110) and the
Ru(0001) substrate. The results also indicate that growth of RuOx(110)
thin layer on the Ru(0001) substrate by oxidation tends first to formation
of the Ru-O (oxygen) chains in the [001] direction of RuOx(110). 相似文献
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用分子动力学方法对5%负失配条件下面心立方晶体铝薄膜的原子沉积外延生长进行了三维模拟.铝原子间的相互作用采用嵌入原子法(EAM)多体势计算.模拟结果再现了失配位错的形成现象.分析表明,失配位错在形成之初即呈现为Shockley扩展位错,即由两个伯格斯矢量为〈211〉/6的部分位错和其间的堆垛层错组成,两个部分位错的间距、即层错宽度为1.8 nm,与理论计算结果一致;外延晶体薄膜沉积生长中,位错对会发生滑移,但其间距保持稳定.进一步观察发现,该扩展位错产生于一种类似于“局部熔融-重结晶”的表层局部无序紊乱-
关键词:
失配位错
外延生长
薄膜
分子动力学
铝 相似文献