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Journal of Geographical Sciences 2025年第1期 39-64页

作者： HE Chenyang WANG Yanjiao YAN Feng lu qi School of Ecological and Environmental Science East China Normal University Institute of Ecological Conservation and Restoration Chinese Academy of Forestry National Climate Center China Meteorological Administration

Water use efficiency （WUE）,as a pivotal indicator of the coupling degree within the carbon–water cycle of ecosystems,holds considerable importance in assessment of the carbon–water balance within terrestrial ***,in the context of global warming,WUE evolution and its primary drivers on the Tibetan Plateau remain *** study employed the ensemble empirical mode decomposition method and the random forest algorithm to decipher the nonlinear trends and drivers of WUE on the Tibetan Plateau in 2001–*** indicated an annual mean WUE of 0.8088 gC/mm·m2across the plateau,with a spatial gradient reflecting decrease from the southeast toward the *** manifesting monotonous trends of increase or decrease in WUE accounted for 23.64%and 9.69%of the total,***,66.67%of the region exhibited trend reversals,i.e.,39.94%of the area of the Tibetan Plateau showed transition from a trend of increase to a trend of decrease,and 26.73%of the area demonstrated a shift from a trend of decrease to a trend of *** factors accounted for 70.79%of the variability in *** leaf area index and temperature served as the major driving forces of WUE variation.

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Bang-Bang Principle of Time Optimal Controls and Null Controllability of Fractional Order Parabolic Equations

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Acta Mathematica Sinica,English Series 2010年第12期26卷 2377-2386页

作者： qi lu School of Mathematics Sichuan University Chengdu 610064 P. R. China

In this paper, we establish a bang-bang principle of time optimal controls for a controlled parabolic equation of fractional order evolved in a bounded domain Ω of R^n, with a controller w to be any given nonempty open subset of Ω. The problem is reduced to a new controllability property for this equation, i.e. the null controllability of the system at any given time T 〉 0 when the control is restricted to be active in ω× E, where E is any given subset of [0, T] with positive （Legesgue） measure. The desired controllability result is established by means of a sharp observability estimate on the eigenfunctions of the Dirichlet Laplacian due to Lebeau and Robbiano, and a delicate result in the measure theory due to Lions.

关键词： Bang-bang principle time optimal control null controllability fractional order parabolicequation

Nonreciprocal Head-on Collision Between Two Nonlinear Solitary Waves in Granular Metamaterials with an Interface

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Acta Mechanica Solida Sinica 2022年第1期35卷 139-151页

作者： qi lu Yi-Ze Wang Department of Mechanics Tianjin UniversityTianjin 300350China

In this work,the head-on collision and transmission with nonreciprocal properties of opposite propagating solitary waves are studied,in which the interface between different granular chains is *** to the discontinuity of two periodic granular systems,the transmitted and reflected solitary waves are *** head-on collision appears at the interface and the reductive perturbation method is applied to derive the generated solitary *** to the derivation and numerical simulation,we can find that the transmitted and reflected solitary waves can propagate with the same speed when they locate at the same ***,the influences of both the arrangement and prestress are *** is found that the amplitude and velocity of solitary waves become larger because of a bigger prestress,which result in the nonreciprocal collision and transmission in the granular mechanical *** study is expected to be helpful for the design and application of elastic wave metamaterials and mechanical diodes with nonlinear solitary waves.

关键词： Granular metamaterial Nonlinear solitary waves Head-on collision Interface Nonreciprocal properties

On the lower bounds of the curvatures in a bounded domain

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Science China Mathematics 2015年第1期58卷 1-10页

作者： lu qi Keng Institute of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences

Let KD（z, z） be the Bergman kernel of a bounded domain 7P in Cn and Sect （z, ） and Ricci （z, ） be the holomorphic sectional curvature and Ricci curvature of the Bergman metric ds2 = T T：）（z,N）dzCdz respectively at the point z E T with tangent vector . It is proved by constructing suitable minimal functions that where z ∈D1 D D2, D1 is a ball contained in D and D2 is a ball containing D.

关键词： minimal function minimal integral lower bound

On the Quaternion Ball and the Quaternion Projective Space

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Acta Mathematica Sinica,English Series 2005年第3期21卷 449-456页

作者： qi Keng lu Institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 P. R. China

Since the quaternion ball was used to study the AdS/CFT problems tor spinor fields, it is worthwhile to study further the geometry （in sense of Klein） and analysis on it and on its extended space （in the sense of B... 详细信息

关键词： Discontinuous solutions Heat kernel

On the Curvature Conjecture of Hua Loo-Keng

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Acta Mathematica Sinica,English Series 2012年第2期28卷 295-298页

作者： qi Keng lu Institute of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190 P.R.China

It is proved that both the holomorphic sectional and the bisectional curvatures of the conformal Bergman metric

关键词： Conformal metric curvature

Heisenberg Group and Energy-Momentum Conservative Law in de-Sitter Spaces—— In Memory of the 100th Anniversary of Einstein＇s Special Relativity and the 70th Anniversary of Dirac＇s de-Sitter Spaces

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Communications in Theoretical Physics 2005年第3X期44卷 389-392页

作者： lu qi-Keng Institute of Mathematics Academy of Mathematics and System Sciences the Chinese Academy of Sciences Beijing 100080 China

In 1935 Dirac established the physical wave equations in the de-Sitter spaces but neither energy-momentum operators nor their conservative laws were given. In this article it is proved that in the de-Sitter group there is a subgroup group isomorphic to the Heisenberg group and the generators of this groups are the energy-momentum operators which obey a conservative law.

关键词： energy-momentum conservation Heisenberg grup de-Sitter space

CO2-mediated bicarbonate conversion to concentrated formate in a CEM-based electrolyzer

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Journal of Energy Chemistry 2025年第1期 605-611页

作者： Haocheng Xiong Donghuan Wu Haonan Li Andrew Li qikun Hu Siyao Song Bingjun Xu qi lu State Key Laboratory of Chemical Engineering Department of Chemical Engineering Tsinghua University College of Chemistry and Molecular Engineering Peking University Ordos Laboratory

Renewable energy-driven bicarbonate conversion to valuable chemicals presents an attractive strategy for mitigating CO2emissions,as bicarbonate can be efficiently generated from the capture of atmospheric CO2using alkaline solutions with reactive *** this work,we present a CO2-mediated bicarbonate conversion to pure formate using a cation exchange membrane-based electrolyzer with a 25 cm2electrode *** electrolysis achieved selectivities exceeding 75%for formate at a total current of 2.5 A,achieving formate concentrations up to 1.2 M and yields as high as 95%over extended *** techno-economic assessment confirmed the economic viability of the process,highlighting the potential for bicarbonate electrolysis as a sustainable method for producing valuable chemicals.

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Exponential Attractor of the 3D Derivative Ginzburg-Landau Equation

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Acta Mathematica Sinica,English Series 2008年第5期24卷 809-828页

作者： Shu Juan lu qi Shao lu Department of Mathematics & LMIB Beijing University of Aeronautics and Astronautics Beijing 100083 P. R. China

In this paper, we consider a derivative Ginzburg-Landau-type equation with periodic initial-value condition in three-dimensional spaces. Sufficient conditions for existence and uniqueness of a global solution are obtained by uniform a priori estimates of the solution. Furthermore, the existence of a global attractor and an exponential attractor with finite dimensions are proved.

关键词： derivative Ginzburg-Landau equation global attractor exponential attractor Hausdorff dimension fractal dimension

A Representation of the Lorentz Spin Group and Its Application

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Acta Mathematica Sinica,English Series 2007年第4期23卷 577-598页

作者： qi Keng lu Ke WU Institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 P. R. China School of Mathematical Science Capital Normal University Beijing 100037 P. R. China

For an integer m ≥ 4, we define a set of 2[m/2] × 2[m/2] matrices γj （m）, （j = 0, 1,..., m - 1） which satisfy γj （m）γk （m）＋γk （m）γj （m） = 2ηjk （m）I[m/2], where （ηjk （m）） 0≤j,k≤m-1 is a d... 详细信息

For an integer m ≥ 4, we define a set of 2[m/2] × 2[m/2] matrices γj （m）, （j = 0, 1,..., m - 1） which satisfy γj （m）γk （m）＋γk （m）γj （m） = 2ηjk （m）I[m/2], where （ηjk （m）） 0≤j,k≤m-1 is a diagonal matrix, the first diagonal element of which is 1 and the others are -1, I[m/2] is a 2[m/1] × 2[m/2] identity matrix with [m/2] being the integer part of m/2. For m = 4 and 5, the representation （m） of the Lorentz Spin group is known. For m≥ 6, we prove that （i） when m = 2n, （n ≥ 3）, （m） is the group generated by the set of matrices {T｜T=1/√ξ（（I＋k） 0 ＋ 0 I-K）（ U 0 0 U）, （ii） when m = 2n ＋ 1 （n≥ 3）, （m） is generated by the set of matrices {T｜T=1/√ξ（I -k^- k I）U,U∈ （m-1）,ξ=1-m-2 ∑k,j=0 ηkja^k a^j〉0, K=i[m-3 ∑j=0 a^j γj（m-2）＋a^（m-2） In],K^-=i[m-3∑j=0 a^j γj（m-2）-a^（m-2） In]}

关键词： Lorentz spin group representation Yang-Mills equation