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Existence and asymptotics of normalized solutions for the logarithmic Schrödinger system

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Science China Mathematics 2024年第9期67卷 2019-2048页

作者： qian Zhang Wenming Zou Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China

This paper is concerned with the following logarithmic Schrodinger system:{-Δu_(1.+ω_(1.u_(1.=u_(1.u_(1.logu_(1.^(2)+2p/p+q|u_(2)|^(q)|u_(1.|^(p-2)u_(1.,-Δu_(2)+ω_(2)u_(2)=u_(2)u_(2)log u_(2)^(2)+2q/p+q|u_(1.|^(p)|u_(2)|^(q-2)u_(2),∫_(Ω)|u_(i)|^(2)dx=ρ_(i),i=1.2,(u_(1.,u_(2))∈H_(0)^(1.(Ω;R^(2)),where Ω=R^(N)or Ω■R^(N)(N≥3)is a bounded smooth domain,andω_(i)R,μ_(i),ρ_(i)>0 for i=1.***,p,q≥1.and 2≤p+q≤2^(*),where 2^(*):=2N/*** using a Gagliardo-Nirenberg inequality and a careful estimation of u log u^(2),firstly,we provide a unified proof of the existence of the normalized ground state solution for all 2≤p+q≤2^(*).Secondly,we consider the stability of normalized ground state ***,we analyze the behavior of solutions for the Sobolev-subcritical case and pass to the limit as the exponent p+q approaches 2^(*).Notably,the uncertainty of the sign of u log u^(2)in(0,+∞)is one of the difficulties of this paper,and also one of the motivations we are interested *** particular,we can establish the existence of positive normalized ground state solutions for the Brézis-Nirenberg type problem with logarithmic perturbations(i.e.,p+q=2^(*)).In addition,our study includes proving the existence of solutions to the logarithmic type Bréis-Nirenberg problem with and without the L^(2)-*** ∫_(Ω)|u_(i)|^(2)dx=ρ_(i)(i=1.2)by two different methods,*** results seem to be the first result of the normalized solution of the coupled nonlinear Schrodinger system with logarithmic perturbations.

关键词： logarithmic Schrodinger system Brézis-Nirenberg problem normalized solution existence and stability behavior of solutions

Special issue:Catenary optics and catenary electromagnetics

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Opto-Electronic Advances 2024年第5期7卷 1-4页

作者： qian Sun Minghui Hong Pen-Tung Sah Institute of Micro-Nano Science and Technology Xiamen UniversityXiamen 361005China Innovation Laboratory for Sciences and Technologies of Energy Materials of Fujian Province(IKKEM) Xiamen 361005China

As a natural mathematical form,a catenary is the curve that a hanging chain or cable adopts under its own weight when supported at its ends in a homogeneous gravitational *** unique shape arises from the balance of forces acting on each segment of the chain,resulting in a curve described by hyperbolic cosine *** functions play pivotal roles in describing the electromagnetic field,intensity distribution,and dispersion of structured light on the sub-wavelength scale^(1..

关键词： functions field optics

Potential role of the protein interactome in translating TCM theory and clinical practice into modern biomedical knowledge

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Chinese Journal of Natural Medicines 2024年第5期22卷 385-386页

作者： CHEN qian FAN Xiaohui Pharmaceutical Informatics Institute College of Pharmaceutical SciencesZhejiang UniversityHangzhou 310058China National Key Laboratory of Chinese Medicine Modernization Innovation Center of Yangtze River DeltaZhejiang UniversityJiaxing 314100China

With the awarding of the 201. Nobel Prize in Physiology or Medicine to Chinese pharmacologist Tu Youyou,and the significant contributions of traditional Chinese medicine(TCM)for coronavirus disease 201.(COVID-1.),TCM has garnered increasing attention and interest *** advanced research progress has been made in the efficacy research,mechanism elucidation and target prediction of TCM in recent years[1..

关键词： Protein interactome Traditional Chinese medicine Therapeutic effectiveness

Toward a rapid and convenient nanoplastic quantification method in laboratory-scale study based on fluorescence intensity

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Frontiers of Environmental Science & Engineering 2024年第5期18卷 117-126页

作者： Ruiqi Yan Sen Lin qian Ding Lei Zhang Xia Yu Wentao Zhao qian Sui State Environmental Protection Key Laboratory of Environmental Risk Assessment and Control on Chemical Process School of Resources and Environmental EngineeringEast China University of Science and TechnologyShanghai200237China State Key Laboratory of Pollution Control and Resource Reuse College of Environmental Science and EngineeringTongji UniversityShanghai200092China Shanghai Institute of Pollution Control and Ecological Security Shanghai200092China

The thorough investigation of nanoplastics(NPs)in aqueous environments requires efficient and expeditious quantitative analytical methods that are sensitive to environmentally relevant NP concentrations and convenient to *** analysis-based quantitative methods have been acknowledged as effective and rapid approaches for quantifying NP concentrations in laboratory-scale ***,we compared three commonly used optical response indicators,namely fluorescence intensity(FI),ultraviolet absorbance,and turbidity,to assess their performance in quantifying ***,orthogonal experiments were conducted to evaluate the influence of various water quality parameters on the preferred indicator-based quantification *** results revealed that FI exhibits the highest correlation coefficient(>0.99)with NP ***,the limit of quantification(LOQ)for various types of NPs is exceptionally low,ranging from 0.0089 to 0.0584 mg/L in ultrapure water,well below environmentally relevant *** variations in water quality parameters such as pH,salinity,suspended solids(SS),and humic acid,a robust relationship between detectable FI and NP concentration was ***,an increased matrix,especially SS in water samples,results in an enhanced LOQ for ***,the quantitative method remains applicable in real water bodies,especially in drinking water,with NP LOQ as low as 0.01.7–0.071. mg/*** exceeds the previously reported detectable concentration for 1.0 nm NPs at 40µg/mL using surface-enhanced Raman *** study confirms the potential of FI as a reliable indicator for the rapid quantification of NPs in aqueous environments,offering substantial advantages in terms of both convenience and cost-effectiveness.

关键词： Nanoplastic quantification Fluorescence intensity Drinking water Limit of quantification(LOQ) Matrix effects

Prescribed-Time Fully Distributed Nash Equilibrium Seeking Strategy in Networked Games

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IEEE/CAA Journal of Automatica Sinica 2024年第1期11卷 261-263页

作者： Cheng qian Lei Ding the Institute of Advanced Technology for Carbon Neutrality College of Automation&the College of Artificial Intelligence Nanjing University of Posts and TelecommunicationsNanjing 210023China IEEE

Dear Editor, This letter is concerned with prescribed-time fully distributed Nash equilibrium seeking for networked games under directed graphs. An adaptive algorithm is proposed to ensure the convergence of all players to the Nash equilibrium without requiring any knowledge of global parameters. Moreover, it is theoretically proved that the convergence time of the proposed seeking strategy can be predefined based on practical requirements. Finally, a numerical example is presented to validate the effectiveness of the proposed method.

关键词： parameters seeking prescribed

Novel Optimal Dispatch Method for Multiple Energy Sources in Regional Integrated Energy Systems Considering Wind Curtailment

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CSEE Journal of Power and Energy Systems 2024年第5期10卷 2166-2173页

作者： Yang Gao qian Ai Key Laboratory of Control of Power Transmission and Conversion Ministry of EducationShanghai Jiao Tong UniversityShanghai 200240China

Power-to-gas technology uses temporary surplus electricity to create either renewable hydrogen or renewable natural gas,which can then be stored in natural-gas pipelines and used when *** a result,P2G transforms conventional one-way coupling of a power/heat/natural-gas system into twoway ***,its operating characteristics makes it possible to more effectively utilize *** paper describes a new optimal dispatch model for integrated electricity/gas/heat energy *** model considers the effective use of surplus wind-energy with electricity-to-gas ***,a multi-energy network model is built,taking into account both equipment and network ***,we apply a novel two-layer optimization method,which uses P2G,to“absorb”wind *** the top-layer model is used for the dayahead dispatch of the natural-gas network containing P2G,the bottom-layer model describes the day-ahead economic dispatch of the electricity/heat system,which includes wind *** on the Karush-Kuhn-Tucher conditions of the bottom-layer model,the two-layer model is transformed into a single-layer model,and we linearize the nonlinear equation to convert the nonlinear model into a mix-integer linear programming problem,which is solvable using the General Algebraic Modeling ***,numerical case-studies are performed to evaluate the accuracy and effectiveness of the proposed method.

关键词： Multi-enery coupling power-to-gas two-layer optimization wind-power consumption

The homogenous growth of Co-based coordination compound on graphene nanosheet for high-performance K-organic battery and its reaction mechanism

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Rare Metals 2024年第4期43卷 1622-1634页

作者： qian-qian Peng Yi-Ting Wang Shuo Qi Yao Xiao Yong Wang Shuang-qiang Chen School of Environmental and Chemical Engineering Shanghai UniversityShanghai200444China School of Chemistry and Materials Engineering Wenzhou UniversityWenzhou325035China

Metal coordination compounds(MCCs)are gaining popularity for potassium-ion batteries(PIBs)owing to their tuneable structure,multiple reaction sites,low cost and unique ***,they are generally subjected to intrinsic features of the sluggish ionic diffusion coefficient,low electronic conductivity and slow ***,a new MCC material of cobalt-1.3,5-trioxy-2,4,6-triamino-benzo(Co-TB)coordination compound was synthesized and homogenously grown on the surface of graphene nanosheets(GNS),forming a Co-TB@GNS composite with enhanced electronic conductivity and flexible *** from the overall enhanced conductivity,high surface area and abundant activated K-storage sites,Co-TB@GNS electrodes have exhibited superior cycling performance with high reversible capacities(31. mAh·g^(-1.after 1.0 cycles at 1.0 mA·g^(-1.,224 mAh·g^(-1.after 500 cycles at 1.A·g^(-1.)and better rate performances compared with the pure Co-TB compound when served as PIB's ***,multiple in-situ measurement techniques have jointly confirmed that the organic functional groups(C=O,C=N and C=C of benzene rings)and Co^(2+)in Co-TB are the main reversible K-storage sites,including in-situ Fourier transform infrared spectroscopy(FTIR)and X-ray diffraction(XRD),and partial capacity contribution is originated from GNS by the apparent K-storage behavior in the in-situ XRD pattern,proving the possibility of K-storage for metal-organic materials.

关键词： Metal coordination compounds Potassiumion battery Cobalt coordination compound K-storage mechanism

Learning physically based material and lighting decompositions for face editing

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Computational Visual Media 2024年第2期10卷 295-308页

作者： qian Zhang Vikas Thamizharasan James Tompkin Brown University ProvidenceRhode Island 02906USA

Lighting is crucial for portrait photography,yet the complex interactions between the skin and incident light are expensive to model computationally in graphics and difficult to reconstruct analytically via computer ***,to allow fast and controllable reflectance and lighting editing,we developed a physically based decomposition through deep learned priors from path-traced portrait *** approaches that used simplified material models or low-frequency or low-dynamic-range lighting struggled to model specular reflections or relight directly without intermediate ***,we estimate the surface normal,skin albedo and roughness,and high-frequency HDRI maps,and propose an architecture to estimate both diffuse and specular reflectance *** our experiments,we show that this approach can represent the true appearance function more effectively than simpler baseline methods,leading to better generalization and higher-quality editing.

关键词： intrinsic decomposition portrait relighting inverse rendering deep learning

Emerging Bio-relevant Applications of Polymer Mechanochemistry

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Chinese Journal of Chemistry 2024年第17期42卷 2066-2070页

作者： Wenjie Liu Hai qian State Key Laboratory of Molecular Engineering of Polymers Department of Macromolecular ScienceFudan UniversityShanghai 200438China

Polymer mechanochemistry has rapidly evolved since the *** advancements highlight the development of mechanophore platforms for the controlled release of bioactive payloads and the exploration of biocompatible activation *** platforms,ranging from furan-maleimide Diels-Alder adducts to disulfide motifs withβ-carbonate linkages,demonstrate promising prospects in targeted drug ***,supramolecular assemblies and free radical-generating mechanophores present innovative avenues for potential therapeutic *** activation methods,notably high-intensity and/or low-intensity focused ultrasound,hold potential for in vivo ***,challenges persist in comprehending the fundamental physics of ultrasound and its utilization for activation.

关键词： Polymer mechanochemistry Mechanophores Bio-relevant applications Ultrasound Drug delivery