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1.
This paper is devoted to the construction of weak solutions to the singular constant Q-curvature problem. We build on several tools developed in the last years. This is the first construction of singular metrics on closed manifolds of sufficiently large dimension with constant (positive) Q-curvature. 相似文献
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4.
《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
5.
Clemens G. Raab Georg Regensburger Jamal Hossein Poor 《Journal of Pure and Applied Algebra》2021,225(5):106564
A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials. 相似文献
6.
M. Amar D. Andreucci R. Gianni C. Timofte 《Journal of Mathematical Analysis and Applications》2021,493(2):124533
We prove a well-posedness result for two pseudo-parabolic problems, which can be seen as two models for the same electrical conduction phenomenon in heterogeneous media, neglecting the magnetic field. One of the problems is the concentration limit of the other one, when the thickness of the dielectric inclusions goes to zero. The concentrated problem involves a transmission condition through interfaces, which is mediated by a suitable Laplace-Beltrami type equation. 相似文献
7.
旅游文本大数据以其方便、快捷和低门槛的特点为游客情感计算提供了极大便利,已经成为旅游大数据的主要来源之一。基于大数据理论和情感理论,以文本大数据为数据源,在全面梳理国内外情感计算相关成果的基础上,利用人工智能中的逻辑/算法编程方法、机器学习方法、深度学习方法对旅游文本大数据进行挖掘,探索最佳的基于文本大数据的游客情感计算方法。研究发现:(1)基于情感词典的游客情感计算模型,其核心是构建情感词典和设计情感计算规则,方法简单,容易实现,适用语料范围广。(2)机器学习,用统计学方法抽取文本中的特征项,具有非线性特征,可靠性较线性特征的情感词典方法高。(3)基于深度学习技术的游客情感计算,效果良好,准确率在85%以上。训练多领域的文本语料易于移植,实用性强,且泛化能力好,较适合大数据时代游客情感计算研究。 相似文献
8.
本文设计了一种梯形的周期极化掺镁铌酸锂(PPMgLN)波导,并通过在传播方向上引入温度梯度来拓宽其倍频(SHG)过程的泵浦光源可接收带宽。通过有限差分的光束传输法,计算波导的有效折射率,并进行波导尺寸的设计。结果表明,通过改变梯形波导不同位置的温度,使其形成一个温度梯度,可拓宽泵浦光源的波长可接收带宽。本文所设计的PPMgLN波导最大泵浦光源可接收带宽为C波段,即1 530~1 565 nm,该波导可倍频C波段,得到输出波段带宽为765~782.5 nm,温度调谐范围为30~150 ℃。 相似文献
9.
Dong Gun Oh Prof. Hristiyan A. Aleksandrov Haneul Kim Dr. Iskra Z. Koleva Dr. Konstantin Khivantsev Prof. Georgi N. Vayssilov Prof. Ja Hun Kwak 《Chemistry (Weinheim an der Bergstrasse, Germany)》2022,28(49):e202200684
Pd-based catalysts are the most widely used for CO oxidation because of their outstanding catalytic activity and thermal stability. However, fundamental understanding of the detailed catalytic processes occurring on Pd-based catalysts under realistic conditions is still lacking. In this study, we investigated CO oxidation on metallic Pd clusters supported on Al2O3 and SiO2. High-angle annular dark-field scanning transmission electron microscopy revealed the formation of similar-sized Pd clusters on Al2O3 and SiO2. In contrast, CO chemisorption analysis indicated a gradual change in the dispersion of Pd (from 0.79 to 0.2) on Pd/Al2O3 and a marginal change in the dispersion (from 0.4 to 0.24) on Pd/SiO2 as the Pd loading increased from 0.27 to 5.5 wt %; these changes were attributed to differences in the metal-support interactions. Diffuse reflectance infrared Fourier-transform spectroscopy revealed that fewer a-top CO species were present in Pd supported on Al2O3 than those in Pd supported on SiO2, which is related to the morphological differences in the metallic Pd clusters on these two supports. Despite the different dispersion profiles and surface characteristics of Pd, O2 titration demonstrated that linearly bound CO (with an infrared signal at 2090 cm−1) reacted first with oxygen in the case of CO-saturated Pd on Al2O3 and SiO2, which suggests that a-top CO on the terrace site plays an important role in CO oxidation. The experimental observations were corroborated by periodic density functional calculations, which confirmed that CO oxidation on the (111) terrace sites is most plausible, both kinetically and thermodynamically, compared to that on the edge or corner sites. This study will deepen the fundamental understanding of the effect of Pd clusters on CO oxidation under reaction conditions. 相似文献
10.
Hasan Kara Muhammad Aamir Ali Hüseyin Budak 《Mathematical Methods in the Applied Sciences》2021,44(1):104-123
In this paper, we define interval‐valued left‐sided and right‐sided generalized fractional double integrals. We establish inequalities of Hermite‐Hadamard like for coordinated interval‐valued convex functions by applying our newly defined integrals. 相似文献