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A New Method for Solving Nonlinear Partial Differential Equations Based on Liquid Time-Constant Networks

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Journal of Systems Science & Complexity 2024年第2期37卷 480-493页

作者： SUN Jiuyun DONG Huanhe fang Yong College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China

In this paper,physics-informed liquid networks(PILNs)are proposed based on liquid time-constant networks(LTC)for solving nonlinear partial differential equations(PDEs).In this approach,the network state is controlled via ordinary differential equations(ODEs).The significant advantage is that neurons controlled by ODEs are more expressive compared to simple activation *** addition,the PILNs use difference schemes instead of automatic differentiation to construct the residuals of PDEs,which avoid information loss in the neighborhood of sampling *** this method draws on both the traveling wave method and physics-informed neural networks(PINNs),it has a better physical ***,the KdV equation and the nonlinear Schr¨odinger equation are solved to test the generalization ability of the *** the best of the authors’knowledge,this is the first deep learning method that uses ODEs to simulate the numerical solutions of PDEs.

关键词： Nonlinear partial differential equations numerical solutions physics-informed liquid networks physics-informed neural networks

Adaptive Algorithms on Maximizing Monotone Nonsubmodular Functions

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Journal of the Operations Research Society of China 2024年第2期12卷 428-445页

作者： Bin Liu Hui Su Shu-fang Gong Qi-Zhi fang School of Mathematical Sciences Ocean Universityof ChinaQingdao266100ShandongChina

Submodular optimization is widely used in large *** order to speed up the problems solving,it is essential to design low-adaptive algorithms to achieve acceleration in *** general,the function values are given by a value oracle,but in practice,the oracle queries may consume a lot of ***,how to strike a balance between optimizing them is *** this paper,we focus on maximizing a normalized and strictly monotone set function with the diminishing-return ratio under a cardinality constraint,and propose two algorithms to deal with *** apply the adaptive sequencing technique to devise the first algorithm,whose approximation ratio is arbitrarily close to 1-e^(-γ)in O(logn·log(log k/γ)) adaptive rounds,and requires O(logn^(2)·log(log k/γ)) *** by adding preprocessing and parameter estimation steps to the first algorithm,we get the second *** second algorithm trades a small sacrifice in adaptive complexity for a significant improvement in query *** the same approximation and adaptive complexity,the query complexity is improved *** the best of our knowledge,this is the first paper of designing adaptive algorithms for maximizing a monotone function using the diminishing-return ratio.

关键词： Approximation algorithm Adaptivity Nonsubmodular maximization Cardinality constraint

Concept, configuration, and application of on-board nanogrids for use in electric vehicles

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Science China(Technological Sciences) 2024年第7期67卷 2053-2073页

作者： ZHAO Bing LI Yong WU fang WAN JiangHu CAI JiuQing YANG HaiTao LIU fang College of Electrical and Information Engineering Hunan UniversityChangsha 410082China Wuhan Second Ship Design and Research Institute Wuhan 430000China School of Automation Central South UniversityChangsha 410083China

Against the backdrop of increasingly serious climate change, researchers are attempting to extend macroscale carbon reduction research to smaller scales. With the rapid development and widespread application of electric vehicles(EVs), an effective approach for carbon reduction based on EVs has the potential to be developed. To coordinate and manage the EV platform in diverse application scenarios, the concept of an on-board nanogrid(OBNG), in which a nanogrid is combined with the EV, is proposed and defined, and the characteristics summarized. A configuration that includes a physical layer with the on-board hardware system;an information layer for logical control, energy management, and communication coordination;and an application layer that can cope with different working environments is proposed. A detailed introduction to the basic architecture and management mode of each layer is provided along with information concerning the relevant technologies for coordinated operation. New ideas and approaches to improve the existing performance are proposed, and finally, combined with a background of smart and low-carbon cities, major application scenarios are envisioned.

关键词： electric vehicle nanogrid energy management hybrid energy storage power electronics converter

On Hamiltonian Property of Cayley Digraphs

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 547-556页

作者： fang DUAN Qiong-xiang HUANG School of Mathematics Science Xinjiang Normal UniversityUrumqi 830017China College of Mathematics and Systems Science Xinjiang UniversityUrumqi 830017China

Let G be a finite group generated by S and C(G,S) the Cayley digraphs of G with connection set *** this paper,we give some sufficient conditions for the existence of hamiltonian circuit in C(G,S),where G=Zm×H is a semiproduct of Zmby a subgroup H of *** particular,if m is a prime,then the Cayley digraph of G has a hamiltonian circuit unless G=Zm×*** addition,we introduce a new digraph operation,called φ-semiproduct of Γ1by Γ2and denoted by Γ1×Γ_φΓ2,in terms of mapping φ:V(Γ2)→{1,-1}.Furthermore we prove that C(Zm,{a})×_φ C(H,S) is also a Cayley digraph if φ is a homomorphism from H to{1,-1} ≤ Zm~*,which produces some classes of Cayley digraphs that have hamiltonian circuits.

关键词： Cayley digraphs hamiltonian circuit external semidirect product

Trudinger–Moser Inequalities on a Closed Riemann Surface with a Symmetric Conical Metric

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Acta Mathematica Sinica,English Series 2024年第9期40卷 2263-2284页

作者： Yu fang Yun Yan YANG College of Teacher Education Quzhou UniversityQuzhou 324003P.R.China Department of Mathematics Renmin University of ChinaBeijing 100872P.R.China

This is a continuation of our previous work(*** ***.,20,1295–1324,2020).Let(Σ,g)be a closed Riemann surface,where the metric g has conical singularities at finite *** G is a group whose elements are isometries acting on(Σ,g).Trudinger–Moser inequalities involving G are established via the method of blow-up analysis,and the corresponding extremals are also *** extends previous results of Chen(***.,1990),Iula–Manicini(Nonlinear Anal.,2017),and the authors(2020).

关键词： Trudinger-Moser inequality blow-up analysis conical singularity

Life forms affect beta-diversity patterns of larch forests in China

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Plant Diversity 2024年第1期46卷 49-58页

作者： Wenjing fang Qiong Cai Chengjun Ji Jiangling Zhu Zhiyao Tang Jingyun fang School of Ecology and Environmental Science Yunnan UniversityKunming 650091China Department of Ecology College of Urban and Environmental Sciencesand Key Laboratory for Earth Surface Processes of the Ministry of EducationPeking UniversityBeijing 100871China

Beta-diversity reflects the spatial changes in community species composition which helps to understand how communities are assembled and biodiversity is formed and maintained. Larch(Larix) forests, which are coniferous forests widely distributed in the mountainous and plateau areas in North and Southwest China, are critical for maintaining the environmental conditions and species diversity. Few studies of larch forests have examined the beta-diversity and its constituent components(species turnover and nestedness-resultant components). Here, we used 483 larch forest plots to determine the total betadiversity and its components in different life forms(i.e., tree, shrub, and herb) of larch forests in China and to evaluate the main drivers that underlie this beta-diversity. We found that total betadiversity of larch forests was mainly dependent on the species turnover component. In all life forms,total beta-diversity and the species turnover component increased with increasing geographic, elevational, current climatic, and paleoclimatic distances. In contrast, the nestedness-resultant component decreased across these same distances. Geographic and environmental factors explained 20%-25% of total beta-diversity, 18%-27% of species turnover component, and 4%-16% of nestedness-resultant component. Larch forest types significantly affected total beta-diversity and species turnover component. Taken together, our results indicate that life forms affect beta-diversity patterns of larch forests in China, and that beta-diversity is driven by both niche differentiation and dispersal limitation. Our findings help to greatly understand the mechanisms of community assemblies of larch forests in China.

关键词： Beta-diversity Species turnover Nestedness-resultant Geographic distance Climatic distance Larch forest

Spatial-temporal patterns and evolution of carbon storage in China's terrestrial ecosystems from 1980 to 2020

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Science China Earth Sciences 2024年第10期67卷 3270-3287页

作者： Shaojian WANG Shijie ZHOU Chuanglin fang School of Geography and Planning Sun Yat-sen UniversityGuangzhou 510006China Institute of Geographic Sciences and Natural Resources Research Chinese Academy of SciencesBeijing 100101China

Analyzing the changes in carbon storage in terrestrial ecosystems caused by land use changes is a crucial part of exploring the carbon cycle. In addition, enhancing carbon storage in terrestrial ecosystems is an effective and environmentally friendly measure to sequester anthropogenic carbon emissions, which is significant for achieving carbon neutrality and curbing global climate change. This paper uses land use data and carbon density tables with the In VEST model to obtain a carbon storage distribution map of China. It further applies land use response elasticity coefficients, Theil index multi-stage nested decomposition, and spatial autocorrelation analysis to examine the spatial-temporal patterns, causes of changes, and evolution characteristics of carbon storage in terrestrial ecosystems from 1980 to 2020. The results show that the temporal changes in China's carbon storage generally present an inverted S-curve, with an initial rapid decline followed by a slower decrease. Spatially, it features high levels in the northeast, low levels in the northwest, and a uniform distribution in the central and southern *** disturbance of land use type changes on terrestrial ecosystem carbon storage has been effectively mitigated. The significant reduction in grassland area in the Southwest region is the main source of carbon storage loss during the study period, and the encroachment of construction land on arable land in large urban agglomerations is one of the important causes of carbon storage loss. The Theil index multi-stage nested decomposition results indicate that the overall difference in carbon storage in China has decreased, while differences among cities within provinces and among counties within cities have increased. The influence of natural factors on the distribution of carbon storage is weakening, whereas the impact of human activities is becoming more profound, enhancing its influence on the spatial distribution of carbon storage in China. From 198

关键词： Terrestrial ecosystem carbon storage Carbon density Land use change InVEST model Spatiotemporal pattern

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Ultrafast optical investigation of carrier and spin dynamics in low-dimensional perovskites

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Science China(Technological Sciences) 2024年第1期67卷 2-18页

作者： FU JinYue JIANG Ying fang HongHua Key Laboratory for Micro-Nano Physics and Technology of Hunan Province School of Physics and ElectronicsHunan UniversityChangsha 410012China State Key Laboratory of Precision Measurement Technology and Instruments Department of Precision InstrumentTsinghua UniversityBeijing 100084China

Low-dimensional perovskite(PVK)materials have attracted significant research interest,because of their quantum-confined effect,tunable band gap structures,and higher stability than that of three-dimensional(3D)*** semiconductor optoelectronic devices,high speed and small size are closely *** development of high-speed devices requires researchers to fully understand the properties of materials,especially the dynamic processes such as carrier recombination,separation,and transport,which often play a crucial role in the performance of *** an indispensable part of dynamic research,spin relaxation is also of great significance in studying the properties of materials and explore possible *** halide PVK materials have strong spin-orbit coupling(SOC),which provides a basis for information storage and processing by using spin degrees of ***,studying the carrier and spin dynamics of low-dimensional PVKs is an effective way to understand the internal properties of low-dimensional PVKs *** paper summarizes the latest research progress on the ultrafast carrier and spin dynamics in low-dimensional PVKs,to comprehensively understand their carrier and spin behaviors and present an outlook for relevant studies in this area.

关键词： low-dimensional perovskites carrier dynamics spin dynamics optoelectronic devices

Low-thermal-budget synthesis of monolayer MoS2

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Science China Materials 2024年第1期67卷 372-374页

作者： Zongmeng Yang Shibo fang Jing Lu State Key Laboratory for Mesoscopic Physics and School of Physics Peking University Collaborative Innovation Center of Quantum Matter Beijing Key Laboratory for Magnetoelectric Materials and Devices (BKL-MEMD) Peking University Peking University Yangtze Delta Institute of Optoelectronics Key Laboratory for the Physics and Chemistry of Nanodevices Peking University Beijing Key Laboratory of Quantum Devices Peking University

Two-dimensional (2D) materials, such as MoS2, have been considered as a competitive coordinate for future electronics due to their excellent electrostatics and high mobility [1–3]. Moreover, the potential integration of 2D materials with silicon circuits can present increased density and multifunction in future heterogeneously integrated circuits [4,5]. However, the high thermal-budget during Mo S2 synthesis exceeds the temperature requirement of direct integration with Si in the back-end-of-line (BEOL) fabrication process [6–8].

关键词： FILMS