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Heat kernel estimates on effective resistance metric spaces

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Progress in Natural Science:Materials International 2007年第7期17卷 775-783页

作者： Hu Jiaxin Ji Yuan wen zhiying (department of Mathematical Sciences,tsinghua university,beijing 100084,china) [a]department of Mathematical Sciences Tsinghua University Beijing China

We obtain two-sided estimates of heat kernels on effective-resistance metric spaces by using an analytic *** applications,such as on post-critically finite self-similar sets and on products of effective resistance spa... 详细信息

关键词： Heat kernel effective resistance Dirichlet form Green’s function

Some Boundary Fractal Properties of the Convolution Transform of Measures by an Approximate Identity

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Acta Mathematica Sinica,English Series 1999年第2期15卷 207-214页

作者： zhiying wen, department of mathematics, Wuhan university, Wuhan 430072, P. R. china department of Applied mathematics, tsinghua university, beijing 100084, P. R. chinaE-mail: wenzy@tsinghua.edu.cnYiping Zhang, department of mathematics, Wuhan university, Wuhan 430072, P. R. chinaE-mail: ypzhang@*** department of mathematics Wuhan University Wuhan P. R. China department of Applied mathematics Tsinghua University Beijing P. R. China

We consider the convolution transforms of measures on Rd defined by some approximate identity. We shall establish some relations between the irregular boundary properties of the convolution function and the local Lipschitz exponent of the measure. In particular, the results can be applied to the Poisson and Gauss-Weierstrass kernels. We can then obtain some singular boundary behavior of positive harmonic or parabolic functions on R+d+1 by multifractal analysis of measures.

关键词： Approximate identity Multifractal Logarithmic density

Mitigating the Reconstruction of Metal Sulfides for Ultrastable Oxygen Evolution at High Current Density

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CCS Chemistry 2024年第1期6卷 137-148页

作者： Shuai Niu Tang Tang Yuanju qu Yuyun Chen Hao Luo Hui Pan wen-Jie Jiang Jianan Zhang Jin-Song Hu beijing National Laboratory for Molecular Sciences CAS Key Laboratory of Molecular Nanostructure and NanotechnologyInstitute of ChemistryChinese Academy of SciencesBeijing 100190 Joint Key Laboratory of the Ministry of Education Institute of Applied Physics and Materials EngineeringUniversity of MacaoMacao SAR 999078 department of Chemical Engineering University of MelbourneParkvilleVictoria 3010 College of Materials Science and Engineering Zhengzhou UniversityZhengzhou 450001 School of Chemical Sciences University of Chinese Academy of SciencesBeijing 100049 Dalian National Laboratory for Clean Energy Dalian 116023

Metal sulfides are emerging highly active electrocatalysts for the oxygen evolution reaction(OER),but still suffer from the instability caused by their inevitable reconstruction,especially at industrial-level current ***,it is discovered that Fe-incorporated Ni3S2 nanowires can deliver extraordinary durability with an ultralow potential degradation rate of 0.006 mV/h in alkaline electrolytes made with fresh water and seawater at a benchmark of 500 mA cm^(-2) while meeting the industrial activity requirement for overpotential less than 300 mV(290 mV).Systematic experiments and theoretical simulations suggest that after forming the S-doped NiFeOOH shell to boost intrinsic activity,Fe incorporation effectivelymitigates the reconstruction of the Ni_(3)S_(2) nanowire core by restraining Ni oxidation and S dissolution,justifying the *** work highlights the significance of circumventing reconstruction and provides a strategy to explore practical chalcogenides-based OER electrocatalysts.

关键词： oxygen evolution reaction sulfur-doped NiFeOOH NiFe sulfides nanowire ultrastable high current density

Relations among gauge functions, metrics and Hausdorff measures

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Progress in Natural Science:Materials International 2003年第4期 16-20页

作者： wen shengyou and wen zhiying (1. Nonlinear Scicntific Center, Wuhan university, Wuhan 430072, china 2 . department of mathematics, tsinghua university, Bei-jing 100084, china) Nonlinear Scientific Center Wuhan University Wuhan 430072 China department of mathematics Tsinghua University Beijing 100084 China

In this paper we discuss the relations among the doubling condition, equivalence of the Hausdorff measures and equiva-lence of metries. We will show that (?)ρ·g1 and (?)ρ·g2 are equivalent for any cornpact metric space (X, ρ) if and only if g1 and g2 are equiva-lent gauge functions. Then, we prove that for given c ∈ (0,∞) \ {1} , (?)ρ·g and (?)ρ·g are equivalent for any compact metric space (X, ρ) if and only if the gauge function g satisfies the doubling condition, where (?)ρ·g is the Hausdorff measure with respect to the metric ρ and gauge function g.

关键词： Hausdorff measure metrics gauge function doubling condition.

Spectrality of planar self-affine measures with two-element digit set

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Science china mathematics 2012年第3期55卷 593-605页

作者： LI JianLin wen zhiying College of mathematics and Information Science Shaanxi Normal University Xi＇an 710062 China department of Mathematical Sciences Tsinghua University Beijing 100084 China

The iterated function system with two element digit set is the simplest case and the most important case in the study of self affine *** one dimensional case corresponds to the Bernoulli convolution whose spectral property is *** higher dimensional analogue is not known,for which two conjectures about the spectrality and the non spectrality remain *** the present paper,we consider the spectrality and non spectrality of planar self affine measures with two element digit *** give a method to deal with the two dimensional case,and clarify the spectrality and non spectrality of a class of planar self affine *** result here provides some supportive evidence to the two related conjectures.

关键词： self-affine measure orthogonal exponentials spectrality Bernoulli convolution compatible pair

DERIVED SEquENCES AND THE FACTOR SPECTRUM OF THE PERIOD-DOUBLING SEquENCE

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Acta Mathematica Scientia 2021年第6期41卷 1921-1937页

作者： Yuke HUANG zhiying wen School of Science Beijing University of Posts and TelecommunicationsBeijing100876China department of Mathematical Sciences Tsinghua UniversityBeijing100084China

Factor properties and their structures are important themes in combinatorics on *** D be the infinite one-sided sequence over the alphabet{a,b}generated by the period-doubling substitutionσ(a)=ab andσ(b)=*** this paper,we determine the derived sequence D_(ω)(D)for any factorω■D,and study some factor spectra using the structures of derived *** also prove the reflexivity property of derived sequences.

关键词： combinatorics on words envelope word derived sequence factor spectrum reflexivity of derived sequence

The Factor Spectrum and Derived Sequence

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Journal of Mathematical Research with Applications 2019年第6期39卷 718-732页

作者： Yuke HUANG zhiying wen School of Science Beijing University of Posts and Telecommunications department of Mathematical Sciences Tsinghua University

Given a sequence ρ over a finite alphabet A, an important topic in combinatorics on words is to find out all factors ω of ρ and positive integers p such that ωp(the p-th occurrence of ω) fulfills property P. This problem is equivalent to determining a notion called the factor spectrum. Determining the factor spectrum is a difficult problem. To this aim, we introduce several notions, such as: kernel word, envelope word, return word and derived sequence of each factor ω. Using the factor spectrum and derived sequence, we can solve some enumerations of factors, such as the numbers of palindromes, fractional powers, etc. We will show some results for several sequences, such as the Fibonacci sequence, the Tribonacci sequence, the Period-doubling sequence, etc. And we think that these notions and methods are suitable for all recurrent sequences.

关键词： kernel word envelope word return word derived sequence the factor spectrum

Decomposition of L^P( Da) Space and Boundary Value of Holomorphic Functions

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Chinese Annals of mathematics,Series B 2017年第5期38卷 1093-1110页

作者： Zhihong wen Guantie DENG Cuiqiao WANG Feifei qu department of mathematics and Statistics Jiangsu Normal University Xuzhou 221116 Jiangsu China School of Mathematical Sciences Key Laboratory of Mathematics and Complex Systems of Ministry of Education Beijing Normal University Beijing 100875 China

This paper deals with two topics mentioned in the title. First, it is proved that function f in L^P（ Da） can be decomposed into a sum g ＋ h, where Da is an angular domain in the complex plane, g and h are the non-tangential limits of functions in H^P（Da） and H^P（aD^c） in the sense of LP（Da）, respectively. Second, the sufficient and necessary conditions between boundary values of holomorphic functions and distributions in n-dimensional complex space are obtained.

关键词： Hardy space Rational function Holomorphic function Distribution

TiO2 sensitized by red-, green-, blue-emissive carbon dots for enhanced H2 production

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Rare Metals 2019年第5期38卷 404-412页

作者： Dong-Xue Yang Dan qu Xiang Miao wen-Shuai Jiang Li An Yuan-Jing wen Dan-Dan Wu Zai-Cheng Sun beijing Key Laboratory for Green Catalysis and Separation Department of Chemistry and Chemical Engineering School of Environmental and Energy Beijing University of Technology

Carbon dots(Cdots)with a broad light absorption range could be a potential stable sensitizer for TiO2,which is an excellent ultraviolet(UV)response ***,we systematically investigated the different color emissive Cdots-sensitized TiO2 for H2 ***,all kinds of Cdots enhanced the photocatalytic properties of *** the Cdots-sensitized TiO2 exhibits visible light H2 production due to their absorption in the visible light *** photocurrent and H2 production amount display strong dependence on the light absorption range of *** blue-emissive Cdots endow the weak H2 production rate due to its weak absorption in the visible *** enhanced photocatalytic activities are mainly contributed to the strong light absorbance and high-efficient charge *** light absorption of green-and red-emissive Cdots is another main factor for the high catalytic activities besides charge separation.

关键词： TiO2 Carbon dots Visible light absorption Sensitizer H2 production