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Semistability of Frobenius Direct Image of Representations of Cotangent Bundles

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Acta Mathematica Sinica,English Series 2018年第11期34卷 1677-1691页

作者： ling Guang li School of Mathematical Sciences Tongji University

Let k be an algebraically closed field of characteristic p 〉 0, X a smooth projective variety over k with a fixed ample divisor H, FX：X → X the absolute Frobenius morphism on X. Let E be a rational GLn（k）-bundle on X, and ρ：GLn（k） → GLm（k） a rational GLn（k）-representation of degree at most d such that ρ maps the radical R（GLn（k）） of GLn（k） into the radical R（GLm（k）） of GLm（k）. We show that if FXN＊（E） is semistable for some integer N ≥ max0 〈 r 〈 m （rm） · logp（dr）, then the induced rational GLm（k）-bundle E（GLm（k）） is semistable. As an application, if dim X=n, we get a sufficient condition for the semistability of Frobenius direct image FX＊（ρ＊（ΩX1））, where ρ＊（ΩX1） is the vector bundle obtained from ΩX1 via the rational representation ρ.

关键词： Semistability principal bundle Probenius morphism cotangent bundle

Basic functions and unramified local L-factors for split groups

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Science China Mathematics 2017年第5期60卷 777-812页

作者： li Wen-Wei Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 China

According to a program of Braverman, Kazhdan and NgS, for a large class of split unramified reductive groups G and representations p of the dual group G, the unramified local L-factor L（s, π, ρ） can be expressed as the trace of π（fρ,s） for a function fρ,s with non-compact support whenever Re（s） ≥ 0. Such a function should have useful interpretations in terms of geometry or eombinatories, and it can be plugged into the trace formula to study certain sums of automorphic L-functions. It also fits into the conjectural framework of Schwartz spaces for reductive monoids due to Sakellaridis, who coined the term basic functions; this is supposed to lead to a generalized Tamagawa-Godement-Jaequet theory for （G, ρ）. In this paper, we derive some basic properties for the basic functions fρ,s and interpret them via invariant theory. In particular, their coefficients are interpreted as certain generalized Kostka-Foulkes polynomials defined by Panyushev. These coefficients can be encoded into a rational generating function.

关键词： L-function Satake isomorphism generalized Kostka-Foulkes polynomial

Microstructures, mechanical properties and in vitro corrosion behavior of biodegradable Zn alloys microalloyed with Al, Mn, Cu, Ag and li elements

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Journal of Materials Science & Technology 2022年第8期103卷 244-260页

作者： Lei li Huanzheng Jiao Congfu liu lin Yang Yusong Suo Ruixue Zhang Tie liu Jianzhong Cui Key Laboratory of Electromagnetic Processing of Materials Ministry of EducationNortheastern UniversityShenyang 110819China School of Materials Science and Engineering Northeastern UniversityShenyang 110819China

In this work,Zn microalloyed with Al,Mn,Cu,Ag and li was cast,annealed and *** results showed that addition of multiple trace elements causes significant change in the microstructures,mechanical properties and corrosion behavior of Zn-0.1Al-0.1Mn-0.1Cu-0.1Ag(^(1)ZM),Zn-0.1Al-0.1Mn-0.1Cu0.1Ag-0.1li(^(2)ZM-0.1li)and Zn-0.1Al-0.1Mn-0.1Cu-0.1Ag-0.35li(^(3)ZM-0.35li)*** ternary phases with the approximate compositions of Al_(13)Mn_(3)Zn_(34) and Al_(10)MnZn_(89) phases are formed in the casting and annealing processes of these alloys,***β-liZn_(4) lamellae that have not been extensively reported are precipitated from the primary Zn dendrites in the casting process of ZM-0.35li ***,Zn laths are precipitated from the eutecticβ-liZn_(4) phase in the annealing process of ZM-0.35li *** above-mentioned phases are crushed or elongated in the as-extruded alloys,which play an important role in improving the strength of the *** the as-extruded alloys have typical(0001)basal texture,accompanied with relatively low{0001}slip and high{1012}twinning Schmid factors,which are advantageous and disadvantageous to the strength enhancement of the alloys,*** the as-cast alloys exhibit poor mechanical properties,especially low *** as-extruded ZM alloy exhibits ultrahigh ductility,with an elongation of up to 82.2%±2.94%.The as-extruded ZM0.35li alloy shows the best comprehensive mechanical properties,with yield strength,ultimate tensile strength,elongation and hardness of 380±1.6 MPa,449±7.4 MPa,62.3%±4.63%and 98±1.4 HV,*** corrosion rates of the ZM,ZM-0.1li and ZM-0.35li alloys are 0.241±0.004,0.206±0.006 and 0.189±0.008 mm/year,*** vitro immersion corrosion rates(after 26 d in SBF solution)of them are 0.134±0.005,0.125±0.004 and 0.121±0.003 mm/year,*** as-extruded ZM-0.35li alloy exhibits the best corrosion resistance.

关键词： Biodegradable Zn alloy Multi-microalloying Microstructure Mechanical properties Corrosion behavior

Convergence of the Solution to General Viscoelastic Koiter Shell Equations

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Acta Mathematica Sinica,English Series 2007年第9期23卷 1683-1688页

作者： Fu Shan li School of Mathematical Sciences Qufu Normal University Qufu 273165 P. R. China and Institute of Mathematics Fudan University Shanghai 200433 P. R. China

By applying the inequality of Korn＇s type without boundary conditions on a general surface, we prove that the scaled displacement of the two-dimensional linearly viscoelastic Koiter＇s shell converges to the solution... 详细信息

关键词： Koiter's shells Korn's inequality membrane shells

Machine learning aided design of perovskite oxide materials for photocatalytic water splitting

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Journal of Energy Chemistry 2021年第9期30卷 351-359页

作者： Qiuling Tao Tian Lu Ye Sheng Long li Wencong Lu Minjie li Department of Chemistry College of SciencesShanghai UniversityShanghai 200444China Materials Genome Institute Shanghai UniversityShanghai 200444China

Suffering from the inefficient traditional trial-and-error methods and the huge searching space filled by millions of candidates, discovering new perovskite visible photocatalysts with higher hydrogen production rate(RH_(2)) still remains a challenge in the field of photocatalytic water splitting(PWS). Herein, we established structural-property models targeted to RH_(2) and the proper bandgap(Eg) via machine learning(ML) technology to accelerate the discovery of efficient perovskite photocatalysts for PWS. The Pearson correlation coefficients(R) of leave-one-out cross validation(LOOCV) were adopted to compare the performances of different algorithms including gradient boosting regression(GBR), support vector regression(SVR), backpropagation artificial neural network(BPANN), and random forest(RF). It was found that the BPANN model showed the highest R values from LOOCV and testing data of 0.9897 and 0.9740 for RH_(2),while the GBR model had the best values of 0.9290 and 0.9207 for Eg. Furtherly, 14 potential PWS perovskite candidates were screened out from 30,000 ABO3-type perovskite structures under the criteria of structural stability, Eg, conduction band energy, valence band energy and RH_(2). The average RH_(2) of these14 perovskites is 6.4% higher than the highest value in the training data set. Moreover, the online web servers were developed to share our prediction models, which could be accessible in http://***/ocpmdm/material_api/ahfga3d9puqlknig(E_g prediction) and http://***/ocpmdm/material_api/i0 ucuyn3 wsd14940(RH_(2) prediction).

关键词： Perovskite Machine learning Online web service Photocatalytic water splitting Bandgap Hydrogen production rate

Transport of Asian surface pollutants to the global stratosphere from the Tibetan Plateau region during the Asian summer monsoon

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National Science Review 2020年第3期7卷 516-533页

作者： Jianchun Bian Dan li Zhixuan Bai Qian li Daren Lyu Xiuji Zhou Key Laboratory of Middle Atmosphere and Global Environment Observation Institute of Atmospheric Physics Chinese Academy of Sciences College of Earth and Planetary Sciences University of Chinese Academy of Sciences State Key Laboratory of Severe Weather Chinese Academy of Meteorological Sciences China Meteorological Administration

Due to its surrounding strong and deep Asian summer monsoon(ASM) circulation and active surface pollutant emissions, surface pollutants are transported to the stratosphere from the Tibetan Plateau region,which may have critical impacts on global climate through chemical, microphysical and radiative *** article reviews major recent advances in research regarding troposphere–stratosphere transport from the region of the Tibetan Plateau. Since the discovery of the total ozone valley over the Tibetan Plateau in summer from satellite observations in the early 1990 s, new satellite-borne instruments have become operational and have provided significant new information on atmospheric composition. In addition, in situ measurements and model simulations are used to investigate deep convection and the ASM anticyclone,surface sources and pathways, atmospheric chemical transformations and the impact on global climate. Also challenges are discussed for further understanding critical questions on microphysics and microchemistry in clouds during the pathway to the global stratosphere over the Tibetan Plateau.

关键词： Tibetan Plateau atmospheric composition troposphere–stratosphere transport deep convection Asian summer monsoon

Controllability of Nonlinear Discrete Systems with Degeneracy

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Acta Mathematicae Applicatae Sinica 2023年第2期39卷 293-305页

作者： Yue LYU Xue-li TAN Xue YANG Yong li School of Mathematics Jilin UniversityChangchun130012China Center for Mathematics and Interdisciplinary Sciences Northeast Normal UniversityChangchun 130024China

This paper concerns the controllability of autonomous and nonautonomous nonlinear discrete systems,in which linear parts might admit certain *** introducing Fredholm operators and coincidence degree theory,sufficient conditions for nonlinear discrete systems to be controllable are *** addition,applications are given to illustrate main results.

关键词： nonlinear discrete systems controllability degeneracy Fredholm operators coincidence degree theory

Pd cluster decorated free standing flexible cathode for high performance li-oxygen batteries

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Nano Research 2024年第4期17卷 2678-2686页

作者： liang Guo Guoliang Zhang Ruonan Yang Dongmei Zhang Xiuqi Zhang Han Yu Xia li Feng Dang Key Laboratory for liquid-Solid Structure Evolution and Processing of Materials Ministry of EducationShandong UniversityJinan 250061China

As a promising candidate for the next generation energy storage system,rechargeable lithium-oxygen batteries(LOBs)still face substantial challenges caused by insulating discharge products that preclude their practical *** highly efficient cathode catalysts capable of facilitating formation/decomposition of discharge products is considered as an essential approach towards high performance ***,Pd decorated Te nanowires(Pd@Te NWs)were synthesized as advanced catalyst in LOBs to maximize Pd utilization and achieve synergistic effect,in which Pd clusters were uniformly grown on Te substrate though regulating the Pd:Te ***,Pd@Te nanowires assembled into an interpenetrating network-like structure by vacuum filtration and employed as flexible cathode,enabling LOBs achieved an ultralong 190 cycles stability and a superior specific capacity of 3.35 mAh·cm^(-2).Experimental studies and density functional theory(DFT)calculations reveal the excellent catalytic ability of Pd@Te and synergistic catalytic mechanism of Pd and Te,in which uniform electron distribution,extensive electron exchange,and large adsorption distance between Pd cluster and discharge products promote homogeneous adsorption/desorption of discharge products,while the high adsorption energy of Te substrate for li species reduces the initial dynamical energy barrier during discharging *** current work provides viable strategy to design composite catalysts for flexible cathode of LOBs with synergistic catalytic effects.

关键词： flexible lithium-oxygen batteries Pd@Te synergistic catalysis cathode catalysts density functional theory(DFT)calculation

Regularity of the Density for the Total Weighted Occupation Measure of Super-Brownain Motion

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Acta Mathematica Sinica,English Series 2011年第8期27卷 1557-1572页

作者： Rong li liU Department of Mathematics Nanjing University Nanjing 210093 P. R. China

Let （Xt） be a super-Brownian motion in a bounded domain D in R^d. The random measure Y^D（.） = ∫o^∞ Xt（.）dt is called the total weighted occupation time of （Xt）. We consider the regularity properties for the densities of a class of yD. When d = 1, the densities have continuous modifications. When d ≥ 2, the densities are locally unbounded on any open subset of D with positive y D （dx）-measure.

关键词： Superprocesses Poisson point processes regularity total weighted occupation time