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Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on C^n Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

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Science China Mathematics 2006年第11期49卷 1722-1739页

作者： chang der-chen GRIENER Peter Department of Mathematics Georgetown University Washington DC 20057USA Department of Mathematics University of Toronto TorontoON M5S 3G3Canada

Given a principal value convolution on the Heisenberg group Hn = Cn × R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kerne... 详细信息

关键词： Heisenberg group, Fourier transform, Laguerre expansion, Bessel functions,Poisson sum, Dirichlet kernel.

Ellipticity on spaces with higher singularities

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Science China Mathematics 2017年第11期60卷 2053-2076页

作者： chang der-chen SCHULZE Bert-Wolfgang Department of Mathematics and Statistics Georgetown University Department of Mathematics Fu Jen Catholic University Institute of Mathematics University of Potsdam

We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata.

关键词：空间椭圆奇异伪微分算子椭圆度微积分层相低维

Quaternion H-type group and differential operatorΔ_λ

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Science China Mathematics 2008年第4期51卷 523-540页

作者： chang der-chen Irina MARKINA Department of Mathematics Georgetown University Department of Mathematics University of Bergen

We study the relations between the quaternion H-type group and the boundary of the unit ball on the two-dimensional quaternionic *** orthogonal projection of the space of square integrable functions defined on quaternion H-type group into its subspace of boundary values of q- holomorphic functions is *** precise form of Cauchy-Szeg(?)kernel and the orthogonal projection operator is *** fundamental solution for the operatorΔ_λis found.

关键词： quaternion Siegel half space q-holomorphic function subelliptic operator

Trace of heat kernel,spectral zeta function and isospectral problem for sub-laplacians

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Science China Mathematics 2009年第12期52卷 2570-2589页

作者： chang der-chen YEUNG Sai-Kee Department of Mathematics Georgetown University Department of Mathematics Purdue University

In this article,we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in C n+*** we survey some results on the spectral zeta function which is induced by the trace of the heat ... 详细信息

关键词： sub-Laplacian heat kernel CR-isospectral problem Riemannian zeta function Mellin transform pseudo-hermitian structure

Spin-orbit interaction induced Casimir-Lifshitz torque between two-dimensional electron gases

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Science China(Physics,Mechanics & Astronomy) 2024年第8期67卷 134-142页

作者： Jia-Nan Rong Liang chen Kai chang State Key Laboratory of Superlattices and Microstructures Institute of SemiconductorsChinese Academy of SciencesBeijing 100083China School of Mathematics and Physics North China Electric Power UniversityBeijing 102206China School of Physics Zhejiang UniversityHangzhou 310027China College of Materials Science and Opto-electronic Technology University of Chinese Academy of SciencesBeijing 100049China

We investigate theoretically the Casimir interaction between two parallel two-dimensional electron gases(2DEGs)with Rashba and Dresselhaus spin-orbit interactions(SOIs),based on the quantum field *** derive an analytical expression for the polarization tensor and obtain the solution to the motion equation of the electromagnetic(EM)*** calculate the CasimirLifshitz torque(CLT)between two parallel 2DEGs with Rashba and Dresselhaus SOIs,which can be tuned by changing the relative strength between two *** anisotropic Casimir energy between 2DEGs caused by the interplay between the SOIs of 2DEGs offers a new origin of CLT and a new type of optoelectronic device.

关键词： Casimir torque two-dimensional electron gas spin-orbit interaction

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From ore to MOF:A case of MIL-100(Fe)production from iron ore concentrates

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Atomically Dispersed Ruthenium Catalysts with Open Hollow Structure for Lithium-Oxygen Batteries

Progress in Natural Science:Materials International 2024年第1期34卷 66-73页

作者： Miao chang Chiyao Tang Chong-chen Wang chen Zhao Beijing Key Laboratory of Functional Materials for Building Structure and Environment Remediation School of Environment and Energy EngineeringBeijing University of Civil Engineering and ArchitectureBeijing100044China

Within this work,iron ore concentrates instead of elemental iron Fe^(0)and iron salts like Fe(NO_(3))_(3)and FeCl_(3)were selected as iron source to prepare MIL-100(Fe)(labeled as MIL-100(Fe)-ore).The corresponding synthesis cost is reduced to half of the MIL-100(Fe)produced from elemental iron and iron *** well,the unreacted iron ore concentrates can be easily separated from the as-prepared MIL-100(Fe)-ore by magnetic to facilitate the purification process,free of the strong acids to wash the residual *** as-obtained MIL-100(Fe)-ore with Langmuir surface area up to 2281.6 m^(2)g^(-1)displayed long-term chemical ***,the sorption capacity of MIL-100(Fe)-ore towards malachite green(MG)is up to 522.3 mg g^(-1)at 25℃and initial pH=3.2,higher than that of MIL-100(Fe)yielded by conventional hydrothermal ***,the production cost and life cycle assessment of MIL-100(Fe)-ore were compared with other traditional production *** results revealed that our work greatly reduced the synthesis cost and enhanced the environmental sustainability.

关键词： Metal-organic framework Iron ore concentrates Adsorption Life cycle assessment

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Nano-Micro Letters 2024年第2期16卷 154-164页

作者： Xin chen Yu Zhang chang chen Huinan Li Yuran Lin Ke Yu Caiyun Nan chen chen Beijing Advanced Innovation Center for Materials Genome Engineering Institute of Solid State ChemistryUniversity of Science and Technology BeijingBeijing 100083People’s Republic of China Engineering Research Center of Advanced Rare Earth Materials Department of ChemistryTsinghua UniversityBeijing 100084People’s Republic of China Beijing Key Laboratory of Energy Conversion and Storage Materials Institution College of ChemistryBeijing Normal UniversityBeijing 100875People’s Republic of China

Lithium–oxygen battery with ultrahigh theoretical energy density is considered a highly competitive next-generation energy storage device,but its practical application is severely hindered by issues such as difficult decomposition of discharge products at ***,we have developed N-doped carbon anchored atomically dispersed Ru sites cathode catalyst with open hollow structure(h-RuNC)for Lithium–oxygen *** one hand,the abundance of atomically dispersed Ru sites can effectively catalyze the formation and decomposition of discharge products,thereby greatly enhancing the redox *** the other hand,the open hollow structure not only enhances the mass activity of atomically dispersed Ru sites but also improves the diffusion efficiency of catalytic ***,the excellent activity from atomically dispersed Ru sites and the enhanced diffusion from open hollow structure respectively improve the redox kinetics and cycling stability,ultimately achieving a high-performance lithium–oxygen battery.

关键词： Atomically dispersed Open hollow structure Discharge product Lithium Oxygen battery

Musielak–Orlicz–Lorentz Hardy Spaces: Maximal Function, Finite Atomic, and Littlewood–Paley Characterizations with Applications to Dual Spaces and Summability of Fourier Transforms

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Acta Mathematica Sinica,English Series 2024年

作者： Hong Chao JIA der-chen chang Ferenc WEISZ Da Chun YANG Wen YUAN Department of Numerical Analysis E?tv?s L.University Laboratory of Mathematics and Complex Systems (Ministry of Education of China) School of Mathematical Sciences Beijing Normal University Department of Mathematics and Statistics Georgetown University Washington Institute of Business Administration College of Management Fu Jen Catholic University

Let q ∈(0, ∞] and φ be a Musielak–Orlicz function with uniformly lower type pφ-∈(0, ∞) and uniformly upper type pφ+∈(0, ∞). In this article, the authors establish various realvariable characterizations of the Musielak–Orlicz–Lorentz Hardy space Hφ,q(Rn), respectively, in terms of various maximal functions, finite atoms, and various Littlewood–Paley functions. As applications, the authors obtain the dual space of Hφ,q(Rn) and the summability of Fourier transforms from Hφ,q(Rn)to the Musielak–Orlicz–Lorentz space Lφ,q(Rn) when q ∈(0, ∞) or from the Musielak–Orlicz Hardy space Hφ(Rn) to Lφ,∞(Rn) in the critical case. These results are new when q ∈(0, ∞) and also essentially improve the existing corresponding results(if any) in the case q = ∞ via removing the original assumption that φ is concave. To overcome the essential obstacles caused by both that φmay not be concave and that the boundedness of the powered Hardy–Littlewood maximal operator on associated spaces of Musielak–Orlicz spaces is still unknown, the authors make full use of the obtained atomic characterization of Hφ,q(Rn), the corresponding results related to weighted Lebesgue spaces,and the subtle relation between Musielak–Orlicz spaces and weighted Lebesgue spaces.

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Generalized load graphical forecasting method based on modal decomposition

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Global Energy Interconnection 2024年第2期7卷 166-178页

作者： Lizhen Wu Peixin chang Wei chen Tingting Pei College of Electrical and Information Engineering Lanzhou University of TechnologyLanzhou 730050P.R.China School of Electrical Data Engineering University of Technology SydneyNSW2007Australia

In a“low-carbon”context,the power load is affected by the coupling of multiple factors,which gradually evolves from the traditional“pure load”to the generalized load with the dual characteristics of“load+power supply.”Traditional time-series forecasting methods are no longer suitable owing to the complexity and uncertainty associated with generalized *** the perspective of image processing,this study proposes a graphical short-term prediction method for generalized loads based on modal ***,the datasets are normalized and feature-filtered by comparing the results of Xtreme gradient boosting,gradient boosted decision tree,and random forest ***,the generalized load data are decomposed into three sets of modalities by modal decomposition,and red,green,and blue(RGB)images are generated using them as the pixel values of the R,G,and B *** generated images are diversified,and an optimized DenseNet neural network was used for training and ***,the base load,wind power,and photovoltaic power generation data are selected,and the characteristic curves of the generalized load scenarios under different permeabilities of wind power and photovoltaic power generation are obtained using the density-based spatial clustering of applications with noise *** on the proposed graphical forecasting method,the feasibility of the generalized load graphical forecasting method is verified by comparing it with the traditional time-series forecasting method.

关键词： Load forecasting Generalized load Image processing DenseNet Modal decomposition