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SPHERICAL MEANS, DISTRIBUTIONS AND CONVOLUTION OPERATORS IN CLIffORD ANALYSIS

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Chinese Annals of Mathematics,Series B 2003年第2期24卷 133-146页

作者： f.brackx R.DELANGHE f.SOMMEN Department of Mathematical Analysis Ghent UniversityB-9000 GentBelgium.Department of Mathematical AnalysisGhent UniversityB-9000 GentBelgium.Department of Mathematical AnalysisGhent UniversityB-9000 GentBelgium.

New higher dimensional distributions are introduced in the framework of Clifford *** complete the picture already established in previous work, offering unity and structuralclarity. Amongst them are the building block... 详细信息

关键词： Spherical means Distributions Convolution operators Clifford analysis

The Mehler formula for the Generalized Clifford-Hermite Polynomials

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Acta Mathematica Sinica,English Series 2007年第4期23卷 697-704页

作者： f.brackx N.DE SCHEPPER K.I.KOU f.SOMMEN Clifford Research Group Ghent UniversityDepartment of Mathematical AnalysisFaculty of EngineeringGalglaan 2B-9000 GentBelgium University of Macao Department of MathematicsFaculty of Science and TechnologyP.O.Box 3001Macao Clifford Research Group Ghent UniversityDepartment of Mathematical AnalysisFaculty of SciencesGalglaan 2B-9000 GentBelgium

The Mehler formula for the Hermite polynomials allows for an integral representation of the one-dimensional fractional fourier transform. In this paper, we introduce a multi-dimensional fractional fourier transform in the framework of Clifford analysis. By showing that it coincides with the classical tensorial approach we are able to prove Mehler＇s formula for the generalized Clifford-Hermite polynomials of Clifford analysis.

关键词： Clifford analysis fractional fourier transform. Hermite Dolvnomials

The Teodorescu Operator in Clifford Analysis

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Chinese Annals of Mathematics,Series B 2012年第4期33卷 625-640页

作者： f.brackx H.De SCHEPPER M.E. LUNA-ELIZARRARS M.SHAPIRO Clifford Research Group Faculty of Engineering and Architecture Ghent University Belgium Instituto Politcnico Nacional Mexico City Mexico

Euclidean Clifford analysis is a higher dimensional function theory centred around monogenic functions, i.e., null solutions to a first order vector valued rotation in- variant differential operator called the Dirac operator. More recently, Hermitian Clifford analysis has emerged as a new branch, offering yet a refinement of the Euclidean case; it focuses on the simultaneous null solutions, called Hermitian monogenic functions, to two Hermitian Dirac operators and which are invariant under the action of the unitary group. In Euclidean Clifford analysis, the Teodorescu operator is the right inverse of the Dirac operator __0. In this paper, Teodorescu operators for the Hermitian Dirac operators c9~_ and 0_~, are constructed. Moreover, the structure of the Euclidean and Hermitian Teodor- escu operators is revealed by analyzing the more subtle behaviour of their components. finally, the obtained inversion relations are still refined for the differential operators is- suing from the Euclidean and Hermitian Dirac operators by splitting the Clifford algebra product into its dot and wedge parts. Their relationship with several complex variables theory is discussed.

关键词： Clifford analysis Teodorescu operator Dirac operator

Rapid post-earthquake safety assessment of low-rise reinforced concrete structures

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Earthquake Engineering and Engineering Vibration 2025年第1期24卷 101-112页

作者： Koji Tsuchimoto Yasutaka Narazaki Billie f.Spencer,Jr. International Design Division Design DepartmentTaisei CorporationTokyo 163-0606Japan Zhejiang University–University of Illinois Urbana-Champaign Institute Zhejiang UniversityHaining 314400China Civil and Environmental Engineering University of Illinois Urbana-ChampaignUrbana 61821USA

Many countries throughout the world have experienced large earthquakes,which cause building damage or *** such earthquakes,structures must be inspected rapidly to judge whether they are safe to *** facilitate the inspection process,the authors previously developed a rapid building safety assessment system using sparse acceleration measurements for steel framed *** proposed system modeled nonlinearity in the measurement data using a calibrated simplified lumped-mass model and convolutional neural networks(CNNs),based on which the buildinglevel damage index was estimated rapidly after *** proposed system was validated for a nonlinear 3D numerical model of a five-story steel building,and later for a large-scale specimen of an 18-story building in Japan tested on the E-Defense shaking ***,the applicability of the safety assessment system for reinforced concrete(RC)structures with complex hysteretic material nonlinearity has yet to be explored;the previous approach based on a simplified lumpedmass model with a Bouc-Wen hysteretic model does not accurately represent the inherent nonlinear behavior and resulting damage states of RC *** study extends the rapid building safety assessment system to low-rise RC moment resisting frame structures representing typical residential apartments in ***,a safety classification for RC structures based on a damage index consistent with the current state of practice is ***,a 3D nonlinear numerical model of a two-story moment frame structure is created.A simplified lumped-mass nonlinear model is developed and calibrated using the 3D model,incorporating the Takeda degradation model for the RC material *** model is used to simulate the seismic response and associated damage sensitive features(DSf)for random ground *** resulting database of responses is used to train a convolutional neural network(CNN)that performs rapid safety ***

关键词： rapid post-earthquake safety assessment acceleration interstory drift angle damage sensitive feature convolutional neural network RC structure simplified non-linear analysis model Takeda degradation model

Energy Meteorology for the Evaluation of Solar farm Thermal Impacts on Desert Habitats

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ADVANCES IN ATMOSPHERIC SCIENCES 2025年第2期42卷 313-326页

作者： Coimbra, Carlos f. M. Univ Calif San Diego Ctr Excellence Renewable Resource Integrat Jacobs Sch Engn Dept Mech & Aerosp Engn La Jolla CA 92093 USA Univ Calif San Diego Ctr Energy Res La Jolla CA 92093 USA

This work addresses challenges and opportunities in the evaluation of solar power plant impacts, with a particular focus on thermal effects of solar plants on the environment and vice-versa. Large-scale solar power plants are often sited in arid or desert habitats, which tend to include fauna and flora that are highly sensitive to changes in temperature and humidity. Our understanding of both shortwave (solar) and longwave (terrestrial) radiation processes in solar power plants is complete enough to render the modeling of radiation fluxes with high confidence for most applications. In contrast to radiation, the convective environment in large-scale solar power plants is much more difficult to characterize. Wind direction, wind speed, turbulence intensity, dust concentration, ground condition, panel configuration density, orientation and distribution throughout the solar field, all affect the local environment, the balance between radiation and convection, and in turn, the performance and thermal impact of solar power plants. Because the temperatures of the two sides of photovoltaic (PV) panels depend on detailed convection-radiation balances, the uncertainty associated with convection affects the heat and mass transfer balances as well. Those balances are critically important in estimating the thermal impact of large-scale solar farms on local habitats. Here we discuss outstanding issues related with these transfer processes for utility-scale solar generation and highlight potential pathways to gain useful knowledge about the convective environment directly from solar farms under operating conditions. (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic), (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic). (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic), (sic)

关键词： environmental impact solar farms thermal balances shortwave and longwave radiation convection (sic)(sic)(sic)(sic) (sic)(sic)(sic)(sic)(sic)(sic) (sic)(sic)(sic) (sic)(sic)(sic)(sic)(sic)(sic)(sic) (sic)(sic)

Magnitude, spatial patterns and drivers of methane fluxes from coastal salt marshes and mangrove forests in China

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Science China Earth Sciences 2025年第3期68卷 850-866页

作者： Yixuan YU Derrick Y.f.LAI Minjie HU Chuan TONG Key Laboratory of Humid Subtropical Eco-geographical Process of Ministry of Education Fujian Normal University School of Geographical Sciences Fujian Normal University Department of Geography and Resource Management The Chinese University of Hong Kong

Methane（CH4） is a highly potent greenhouse gas due to its high radiative forcing and global warming *** the magnitude, spatial patterns, and drivers of CH4emission from wetlands at the regional scale is crucial for formulating suitable strategies to mitigate future climate change. In this study, we synthesized the CH4flux data reported for major plant communities in the coastal salt marshes and mangrove forests in China and produced a spatial map of CH4fluxes from the mangrove sediments and salt marshes in China based on the results of machine learning models. Moreover, we examined the main drivers of CH4flux from these coastal wetlands and estimated the annual CH4emissions from the salt marshes and mangrove forests in different coastal provinces of China using a bottom-up approach. Our results showed that the mean CH4fluxes from the salt marsh and mangrove ecosystems in China were 2.22±0.29 and 2.26±0.55 mg m-2h-1, respectively. Across China, the total annual CH4emission from salt marshes was 31,179.75 Mg CH4a-1, while that from mangroves was 5,533.97 Mg CH4a-1with the sediments contributing to 12.7%(701.64 Mg CH4a-1) of the total efflux. The salt marshes and mangroves in China accounted for 2.75% and 0.14%–0.15% of the global annual CH4emissions from these two ecosystems,respectively. Moreover, we found that CH4emissions from the salt marshes and mangroves could offset the cooling impact arising from net carbon dioxide uptake by 88% and 53%, respectively, over a 100-year time scale. Mean annual temperature, soil moisture, and soil organic carbon content were the main factors controlling CH4emissions from these coastal ***, we found that CH4fluxes from the salt marshes in China decreased with latitude, which implied a possible increase in marsh CH4emission in response to global warming that should be considered carefully when developing nature-based climate solutions to achieve national goals for carbon neutrality.

关键词： Salt marsh Mangrove Methane flux Spatial pattern Driving factors China

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Energy Meteorology for the Evaluation of Solar farm Thermal Impacts on Desert Habitats

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Advances in Atmospheric Sciences 2025年第02期 313-326页

作者： Carlos f.M.COIMBRA Department of Mechanical and Aerospace Engineering Jacobs School of Engineering Center of Excellence in Renewable Resource Integration and Center for Energy Research University of California San Diego

This work addresses challenges and opportunities in the evaluation of solar power plant impacts, with a particular focus on thermal effects of solar plants on the environment and vice-versa. Large-scale solar power plants are often sited in arid or desert habitats, which tend to include fauna and flora that are highly sensitive to changes in temperature and humidity. Our understanding of both shortwave(solar) and longwave(terrestrial) radiation processes in solar power plants is complete enough to render the modeling of radiation fluxes with high confidence for most applications. In contrast to radiation, the convective environment in large-scale solar power plants is much more difficult to characterize. Wind direction, wind speed, turbulence intensity, dust concentration, ground condition, panel configuration density, orientation and distribution throughout the solar field, all affect the local environment, the balance between radiation and convection,and in turn, the performance and thermal impact of solar power plants. Because the temperatures of the two sides of photovoltaic(PV) panels depend on detailed convection–radiation balances, the uncertainty associated with convection affects the heat and mass transfer balances as well. Those balances are critically important in estimating the thermal impact of large-scale solar farms on local habitats. Here we discuss outstanding issues related with these transfer processes for utility-scale solar generation and highlight potential pathways to gain useful knowledge about the convective environment directly from solar farms under operating conditions.

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Anomalous open orbits in Hofstadter spectrum of Chern insulator

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Science China(Physics,Mechanics & Astronomy) 2025年第3期Mechanics & Astronomy) .卷 143-148页

作者： Haijiao Ji Peng Zhou Noah f.Q.Yuan Hua Jiang Haiwen Liu X.C.Xie Center for Advanced Quantum Studies Department of Physics Beijing Normal University Tsung-Dao Lee Institute Shanghai Jiao Tong University Department of Mathematics UC Berkeley Institute for Nanoelectronic Devices and Quantum Computing Fudan University International Center for Quantum Materials School of Physics Peking University Hefei National Laboratory

The nontrivial band topology of Chern insulator can enrich the content of its Hofstadter butterfly spectra, which is closely related to recent experiments in twisted bilayer graphene and cold atom systems. We investigate the Hofstadter spectrum for various models of Chern insulators under a rational flux φ0/q, here φ0=h/e and q being an integer. We find the number of splitting subbands is |q-C| with C denoting the Chern number of parent band. Importantly, anomalous open-orbital subbands with Chern numbers q-1 and-q-1 emerge unexpectedly, which are beyond the parameter window（-q/2, q/2） of the Diophantine equation studied by Thouless-Kohmoto-Nightingale-den Nijs [Phys. Rev. Lett. 49, 405（1982）]. The emergence of anomalous open orbits can be traced by analyzing the evolution of the Hofstadter spectrum, identifying as a new type of topological phase transition. These novel findings not only pinpoint the peculiar Hofstadter spectrum of Chern insulator, but also provide routes to study exotic characteristics beyond the Landau level physics.

关键词： Hofstadter spectrum topological phase transition open orbit

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Hlder Norm Estimate for a Hilbert Transform in Hermitean Clifford Analysis

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Acta Mathematica Sinica,English Series 2012年第11期28卷 2289-2300页

作者： Ricardo ABREU-BLAYA Juan BORY-REYES fred brackx Hennie DE SCHEPPER frank SOMMEN facultad de Informática y Matemática Universidad de Holguín Departamento de Matemática Universidad de Oriente Clifford Research Group Faculty of Engineering Ghent University Clifford Research Group Faculty of Sciences Ghent University

A Hilbert transform for H61der continuous circulant （2 × 2） matrix functions, on the d- summable （or fractal） boundary f of a Jordan domain Ω in R2n, has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the HSlder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the HSlder exponents, the diameter of f and a specific d-sum （d 〉 d） of the Whitney decomposition of Ω. The result is shown to include the case of a more standard Hilbert transform for domains with left Ahlfors-David regular boundary.

关键词： Hermitean Clifford analysis Hilbert transform fractal geometry