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Atexco:With over 30 years of expertise in digital printing,delivering comprehensive digital printing solutions across multiple industries
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《China Textile》 2025年第5期62-62,共1页
For more than 30 years,Hangzhou Honghua Digital Technology Stock Co.,Ltd(hereinafter also referred to as Atexco)has led digital inkjet innovation.From textiles to packaging and publishing,we deliver turnkey solutions ... For more than 30 years,Hangzhou Honghua Digital Technology Stock Co.,Ltd(hereinafter also referred to as Atexco)has led digital inkjet innovation.From textiles to packaging and publishing,we deliver turnkey solutions that unite precision printers,high-performance inks,process know-how and AI-driven design—one ecosystem powering global industry upgrade with Chinese inkjet excellence. 展开更多
关键词 global industry upgrade inkjet excellence digital printing precision printing digital inkjet inkjet technology industrial solutions turnkey solutions
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Colorectal cancer early screening:Dilemmas and solutions 被引量:2
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作者 Di Wu Qi-Ying Song +4 位作者 Bai-Shu Dai Jie Li Xin-Xin Wang Jia-Yu Liu Tian-Yu Xie 《World Journal of Gastroenterology》 2025年第9期154-160,共7页
Colorectal cancer(CRC)is a prevalent malignancy worldwide,posing a significant public health concern.Mounting evidence has confirmed that timely early screening facilitates the detection of incipient CRC,thereby enhan... Colorectal cancer(CRC)is a prevalent malignancy worldwide,posing a significant public health concern.Mounting evidence has confirmed that timely early screening facilitates the detection of incipient CRC,thereby enhancing patient prognosis.Obviously,non-participation of asymptomatic individuals in screening programs hampers early diagnosis and may adversely affect long-term outcomes for CRC patients.In this letter,we provide a comprehensive overview of the current status of early screening practices,while also thoroughly examine the dilemmas and potential solutions associated with early screening for CRC.In response to these issues,we proffer a set of recommendations directed at governmental authorities and the general public,which focus on augmenting financial investment,establishing standardized screening protocols,advancing technological capabilities,and bolstering public awareness campaigns.The importance of collaborative efforts from various stakeholders cannot be overstated in the quest to enhance early detection rates and alleviate the societal burden of CRC. 展开更多
关键词 Colorectal cancer Early screening Asymptomatic candidates DILEMMAS solutions
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Investigation of the formation processes of CO_(2) hydrate films on the interface of liquid carbon dioxide with humic acids solutions 被引量:1
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作者 Aleksey K.Sagidullin Sergey S.Skiba +1 位作者 Tatyana P.Adamova Andrey Y.Manakov 《Chinese Journal of Chemical Engineering》 2025年第3期53-61,共9页
Morphology and growth rate of carbon dioxide hydrate on the interface between liquid carbon dioxide and humic acid solutions were studied in this work.It was found that after the growth of the hydrate film at the inte... Morphology and growth rate of carbon dioxide hydrate on the interface between liquid carbon dioxide and humic acid solutions were studied in this work.It was found that after the growth of the hydrate film at the interface,further growth of hydrate due to the suction of water in the capillary system formed between the wall of the cuvette and the end boundary of the hydrate layer occurs.Most probably,substantial effects on the formation of this capillary system may be caused by variations in reactor wall properties,for example,hydrophobic-hydrophilic balance,roughness,etc.We found,that the rate of CO_(2) hydrate film growth on the surface of the humic acid aqueous solution is 4-fold to lower in comparison with the growth rate on the surface of pure water.We suppose that this is caused by the adsorption of humic acid associates on the surface of hydrate particles and,as a consequence,by the deceleration of the diffusion of dissolved carbon dioxide to the growing hydrate particle. 展开更多
关键词 HYDRATES Carbon dioxide Humic acids solutions Reaction kinetics Liquid liquid reaction Film growth
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Navigating the Blockchain Trilemma:A Review of Recent Advances and Emerging Solutions in Decentralization,Security,and Scalability Optimization
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作者 Saha Reno Koushik Roy 《Computers, Materials & Continua》 2025年第8期2061-2119,共59页
The blockchain trilemma—balancing decentralization,security,and scalability—remains a critical challenge in distributed ledger technology.Despite significant advancements,achieving all three attributes simultaneousl... The blockchain trilemma—balancing decentralization,security,and scalability—remains a critical challenge in distributed ledger technology.Despite significant advancements,achieving all three attributes simultaneously continues to elude most blockchain systems,often forcing trade-offs that limit their real-world applicability.This review paper synthesizes current research efforts aimed at resolving the trilemma,focusing on innovative consensus mechanisms,sharding techniques,layer-2 protocols,and hybrid architectural models.We critically analyze recent breakthroughs,including Directed Acyclic Graph(DAG)-based structures,cross-chain interoperability frameworks,and zero-knowledge proof(ZKP)enhancements,which aimto reconcile scalability with robust security and decentralization.Furthermore,we evaluate the trade-offs inherent in these approaches,highlighting their practical implications for enterprise adoption,decentralized finance(DeFi),and Web3 ecosystems.By mapping the evolving landscape of solutions,this review identifies gaps in currentmethodologies and proposes future research directions,such as adaptive consensus algorithms and artificial intelligence-driven(AI-driven)governance models.Our analysis underscores that while no universal solution exists,interdisciplinary innovations are progressively narrowing the trilemma’s constraints,paving the way for next-generation blockchain infrastructures. 展开更多
关键词 Blockchain trilemma SCALABILITY DECENTRALIZATION SECURITY consensus algorithms sharding layer-2 solutions DAG-based architectures cross-chain interoperability blockchain optimization
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MULTIPLE SOLUTIONS FOR A HAMILTONIAN ELLIPTIC SYSTEM WITH SIGN-CHANGING PERTURBATION
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作者 Peng CHEN Longjiang GU Yan WU 《Acta Mathematica Scientia》 2025年第2期602-614,共13页
In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome... In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome the absence of the upper semi-continuity assumption which is crucial in traditional variational methods for strongly indefinite problems.By some new tools and techniques we proved the existence of infinitely many geometrically distinct solutions if parametersλ_(1),λ_(2)>0 small enough.To the best of our knowledge,our result seems to be the first result about infinitely many solutions for Hamiltonian system involving sign-changing nonlinearity. 展开更多
关键词 variational method strongly indefinite elliptic system multiple solutions signchanging nonlinearity
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Deriving focal mechanism solutions of small to moderate earthquakes in Sichuan,China via a deep learning method
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作者 Chen Zhang Ji Zhang Jie Zhang 《Earthquake Research Advances》 2025年第3期36-46,共11页
As one of the most seismically active regions,Sichuan Basin is a key area of seismological studies in China.This study applies a neural network model with attention mechanisms,simultaneously picking the P-wave arrival... As one of the most seismically active regions,Sichuan Basin is a key area of seismological studies in China.This study applies a neural network model with attention mechanisms,simultaneously picking the P-wave arrival times and determining the first-motion polarity.The polarity information is subsequently used to derive source focal mechanisms.The model is trained and tested using small to moderate earthquake data from June to December 2019 in Sichuan.We apply the trained model to predict first-motion polarity directions of earthquake recordings in Sichuan from January to May 2019,and then derive focal mechanism solutions using HASH algorithm with predicted results.Compared with the source mechanism solutions obtained by manual processing,the deep learning method picks more polarities from smaller events,resulting in more focal mechanism solutions.The catalog documents focal mechanism solutions of 22 events(M_(L) 2.6–4.8)from analysts during this period,whereas we obtain focal mechanism solutions of 53 events(M_(L) 1.9–4.8)through the deep learning method.The derived focal mechanism solutions for the same events are consistent with the manual solutions.This method provides an efficient way for the source mechanism inversion of small to moderate earthquakes in Sichuan region,with high stability and reliability. 展开更多
关键词 Deep learning Focal mechanism solutions Small-to-moderate earthquake First-motion polarity Attention mechanism SICHUAN
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Renewable Energy-Based Solutions for Decentralized Electrification:Demand Assessment andMulti-Tier Framework Approach
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作者 Jacob Manyuon Deng Cyrus Wabuge Wekesa +1 位作者 Khan Jean De Dieu Hakizimana Joseph Nzabahimana 《Energy Engineering》 2025年第5期1839-1862,共24页
Energy access remains a critical challenge in rural South Sudan,with communities heavily relying on expensive and unfriendly environmental energy sources such as diesel generators and biomass.This study addresses the ... Energy access remains a critical challenge in rural South Sudan,with communities heavily relying on expensive and unfriendly environmental energy sources such as diesel generators and biomass.This study addresses the predicament by evaluating the feasibility of renewable energy-based decentralized electrification in the selected village ofDoleibHill,UpperNile,South Sudan.Using a demand assessment and theMulti-Tier Framework(MTF)approach,it categorizes households,public facilities,private sector,Non-GovernmentalOrganizations(NGOs)and business energy needs and designs an optimized hybrid energy system incorporating solar Photovoltaic(PV),wind turbines,batteries,and a generator.The proposed system,simulated in Hybrid Optimization Model Electric Renewable(HOMER)Pro,demonstrates strong economic viability,with a present worth of$292,145,an annual worth of$22,854,a return on investment(ROI)of 36.5%,and an internal rate of return(IRR)of 42.1%.The simple payback period is 2.31 years,and the discounted payback period is 2.62 years.The system achieves a levelized cost of energy(LCOE)of$0.276/kWh and significantly reduces dependence on diesel,producing 798,800 kWh annually fromwind energy.This research provides a replicable model for cost-effective,sustainable rural electrification,offering valuable insights for policymakers and energy planners seeking to expand electricity access in off-grid communities. 展开更多
关键词 Decentralized electrification demand assessment multi-tier framework South Sudan off-grid solutions payback period
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Gap-filling products for three GRACE/GRACE-FO mascon solutions
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作者 Pu Xie Shuang Yi 《Geodesy and Geodynamics》 2025年第2期223-229,共7页
The primary mission of the Gravity Recovery and Climate Experiment (GRACE) satellite and its successor,GRACE Follow-On (GRACE-FO), is to provide time-variable gravity fields, and its observations have been widely used... The primary mission of the Gravity Recovery and Climate Experiment (GRACE) satellite and its successor,GRACE Follow-On (GRACE-FO), is to provide time-variable gravity fields, and its observations have been widely used in various studies. However, the nearly one-year gap between GRACE and GRACE-FO has affected our ability to obtain continuous time-variable gravity data. In this study, we use the Singular Spectrum Analysis (SSA) method to fill the nearly one-year gap between the GRACE and GRACE-FO missions, as well as the gaps within the GRACE mission itself, to generate a continuous and complete mascon product from April 2002 to December 2022. These products are evaluated at the basin scale in Greenland, Antarctica, and ten river basins worldwide, as well as across oceans. The results show that our filled data can effectively recover seasonal and interannual signals and exhibit good consistency with previous reconstructions. The products provided in this study will benefit GRACE applications related to oceans, glaciers, and terrestrial water storage. 展开更多
关键词 Singular spectrum analysis GRACE GRACE-FO Mascon solutions Data gap flling
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Viscosity,NMR Diffusometry and Light Scattering Data for Aqueous and Aqueous-Salt Solutions of Poly(1-butyl-3-vinylimidazolium bromide)
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作者 Petr A.Korchak Polina S.Yarchenko +2 位作者 Evgenia A.Safonova Alina S.Koneva Alexey I.Victorov 《Chinese Journal of Polymer Science》 2025年第2期380-391,共12页
Poly(1-butyl-3-vinylimidazolium bromide)is a polymerized ionic liquid(PILs),a relatively new class of materials that combines the attractive properties of ionic liquids(ILs)and polyelectrolytes and finds wide applicat... Poly(1-butyl-3-vinylimidazolium bromide)is a polymerized ionic liquid(PILs),a relatively new class of materials that combines the attractive properties of ionic liquids(ILs)and polyelectrolytes and finds wide applications.The backbone of this PIL is composed of quaternary imidazolium salts,which are among the most promising and popular ILs.However,little is known about the physicochemical characteristics of the aqueous solutions of this PIL.In this study,we synthesized and characterized samples of this PIL and obtained experimental data on the viscosity,static and dynamic light scattering,and nuclear magnetic resonance diffusometry for aqueous and aqueous KBr solutions with varying polymer contents at T=298.15 K.We discuss the effects of the polymer concentration and salinity on the behavior of the solution. 展开更多
关键词 Polymerized ionic liquid Polyelectrolyte solutions VISCOSITY Light scattering NMR diffusometry
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N-soliton solutions and asymptotic analysis for the massive Thirring model in laboratory coordinates via the Riemann-Hilbert approach
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作者 Yuan Li Min Li +2 位作者 Tao Xu Ye-Hui Huang Chuan-Xin Xu 《Communications in Theoretical Physics》 2025年第6期30-50,共21页
In this paper,the N-soliton solutions for the massive Thirring model(MTM)in laboratory coordinates are analyzed via the Riemann-Hilbert(RH)approach.The direct scattering including the analyticity,symmetries,and asympt... In this paper,the N-soliton solutions for the massive Thirring model(MTM)in laboratory coordinates are analyzed via the Riemann-Hilbert(RH)approach.The direct scattering including the analyticity,symmetries,and asymptotic behaviors of the Jost solutions as|λ|→∞andλ→0 are given.Considering that the scattering coefficients have simple zeros,the matrix RH problem,reconstruction formulas and corresponding trace formulas are also derived.Further,the N-soliton solutions in the reflectionless case are obtained explicitly in the form of determinants.The propagation characteristics of one-soliton solutions and interaction properties of two-soliton solutions are discussed.In particular,the asymptotic expressions of two-soliton solutions as|t|→∞are obtained,which show that the velocities and amplitudes of the asymptotic solitons do not change before and after interaction except the position shifts.In addition,three types of bounded states for two-soliton solutions are presented with certain parametric conditions. 展开更多
关键词 massive thirring model Riemann-Hilbert approach N-soliton solutions asymptotic analysis bounded states
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GLOBAL CLASSICAL SOLUTIONS OF 3D COMPRESSIBLE MICROPOLAR FLUIDS WITH FAR-FIELD VACUUM
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作者 Mingyu ZHANG 《Acta Mathematica Scientia》 2025年第3期919-936,共18页
This paper concerns the Cauchy problem of 3D compressible micropolar fluids in the whole space R^(3). For regular initial data with m0E0 is suitable small, where m0 and E0 represent the upper bound of initial density ... This paper concerns the Cauchy problem of 3D compressible micropolar fluids in the whole space R^(3). For regular initial data with m0E0 is suitable small, where m0 and E0 represent the upper bound of initial density and initial energy, we prove that if ρ0 ∈ Lγ ∩ H3 with γ ∈ (1, 6), then the problem possesses a unique global classical solution on R^(3) × [0, T] with any T ∈ (0, ∞). It’s worth noting that both the vacuum states and possible random largeness of initial energy are allowed. 展开更多
关键词 compressible micropolar fluids Cauchy problem global classical solutions s-mall density VACUUM
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MULTIPLE NON-RADIAL SOLUTIONS TO A MIXED DISPERSION NONLINEAR SCHRODINGER EQUATION
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作者 HE Ju-hua 《数学杂志》 2025年第4期307-321,共15页
In this thesis,we consider the existence of solutions for the following mixed dispersion nonlinear Schrödinger equation■where is a continuous function,,.We shall prove that(1)has multiple non-radial solutions by... In this thesis,we consider the existence of solutions for the following mixed dispersion nonlinear Schrödinger equation■where is a continuous function,,.We shall prove that(1)has multiple non-radial solutions by variational method.This paper provides a method to prove compactness for the study of the mixed dispersion nonlinear Schrödinger equation with quasilinear terms. 展开更多
关键词 MULTIPLICITY non-radial solutions Quasilinar problem fourth-order operator
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Fabrication of Superoleophobic Aluminum Alloy with Hierarchical Micro/Nano Structures for Long-Term Corrosion Protection in Ethylene Glycol-Water Solutions
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作者 Xiaoguang Li Zhongxu Lian +2 位作者 Jinkai Xu Yanling Tian Huadong Yu 《Journal of Bionic Engineering》 2025年第4期1834-1849,共16页
Aluminum(Al)alloys are widely used in aerospace,automotive,and electronics industries due to their light weight and durability.However,their poor corrosion resistance has hindered further development,especially when i... Aluminum(Al)alloys are widely used in aerospace,automotive,and electronics industries due to their light weight and durability.However,their poor corrosion resistance has hindered further development,especially when in contact with oily solutions.In this work,a simple method was adopted to superoleophobic Al alloys with hierarchical micro/nano structures,including plasma electrolytic oxidation,hydrothermal treatment,and fluorination modification.The Contact Angle(CA)and Sliding Angle(SA)of water on the surface were measured to be 164.1°and 0.6°,and those of ethylene glycol-water solutions were 157.1°and 0.7°,respectively.The surface exhibited excellent low adhesion and self-cleaning properties.The electrochemical test results showed that compared with bare Al alloy,the corrosion current density of the superoleophobic surface decreased by 2 orders of magnitude,the charge transfer resistance(R_(ct))increased by 3 orders of magnitude,and the corrosion inhibition efficiency reached 98.11%.Additionally,the superoleophobic surface still exhibited good corrosion resistance after 45 days of immersion.We believe that this work provides a novel perspective and theoretical support for the long-term durability of Al alloys in the ethylene glycol-water solution environment. 展开更多
关键词 Superoleophobic Corrosion resistance SELF-CLEANING Ethylene glycol-water solutions
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Low-Altitude Aerial Information Network:Challenges and Solutions
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作者 Niu Zhisheng Wei Zhang Cao Lei 《China Communications》 2025年第9期I0002-I0004,共3页
Low-altitude economy opens up a completely new aerial space for economic growth by enabling brand new services such as fast logistics delivery,timely emergency rescue,and wide-area,high-definition environmental monito... Low-altitude economy opens up a completely new aerial space for economic growth by enabling brand new services such as fast logistics delivery,timely emergency rescue,and wide-area,high-definition environmental monitoring.This new space has many distinct features and therefore faces many new challenges compared with ground-and high-altitude-based information infrastructures.As a result,the rapid and mass development of unmanned aerial vehicles(UAVs)in low-altitude space will inevitably necessitate research on providing ultra-reliable,low-latency,high-capacity. 展开更多
关键词 unmanned aerial vehicles low latency challenges economic growth solutions unmanned aerial vehicles uavs ultra reliable low altitude economy
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Chirped solutions and dynamical properties of the resonant Schr?dinger equation with quadratic-cubic nonlinearity
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作者 TANG Jia-xuan 《Applied Mathematics(A Journal of Chinese Universities)》 2025年第1期223-237,共15页
In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensa... In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems. 展开更多
关键词 chirped solutions bifurcation theory trial equation method quadratic-cubic nonlinearity non-linear waves
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Progress in study of spray pyrolysis technology for chloride salt solutions in rare earth extraction and separation processes
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作者 Ziyi Cheng Xiaowei Huang +5 位作者 Zongyu Feng Jianping Long Hai Yu Meng Wang Juanyu Yang Haiqing Hao 《Journal of Rare Earths》 2025年第10期2053-2064,I0001,共13页
This paper focuses on the preparation of rare earth oxide products from rare earth chloride solutions during the rare earth extraction and separation processes,as well as the recycling of magnesium chloride solutions.... This paper focuses on the preparation of rare earth oxide products from rare earth chloride solutions during the rare earth extraction and separation processes,as well as the recycling of magnesium chloride solutions.It proposes the idea of introducing spray pyrolysis technology into the rare earth extraction and separation processes.This paper briefly describes the development history of chloride spray pyrolysis technology,focusing on the research status and application progress of rare earth chloride solution and magnesium chloride solution spray pyrolysis technology,as well as spray pyrolysis equipment.The paper also analyzes the challenges and technical intricacies associated with applying spray pyrolysis technology to chloride solutions in the rare earth extraction and separation processes.Additionally,it explores future trends and proposes strategies to facilitate the full recycling of acids and bases,streamline the process flow,and enhance the prospects for green and low-carbon rare earth metallurgy. 展开更多
关键词 Rare earths Separation processes Spray pyrolysis technology Chloride salt solutions Green recycling
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∑-Shaped Connected Component of Positive Solutions for One- Dimensional Prescribed Mean Curvature Equation in Minkowski Space
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作者 QI Tiaoyan LU Yanqiong 《Wuhan University Journal of Natural Sciences》 2025年第3期241-252,共12页
In this work,we demonstrate that the existence of an Z-shaped connected component within the set of positive solutions for the one-dimensional prescribed mean curvature equation in Minkowski space■with boundary condi... In this work,we demonstrate that the existence of an Z-shaped connected component within the set of positive solutions for the one-dimensional prescribed mean curvature equation in Minkowski space■with boundary conditions having parameter in two cases f(O)=0 and f(0)>0 by using upper and lower solution method,where λ>0 is a parameter,f∈C^(2)([0,∞),R)is monotonically increasing and lim_(μ→1)^(f(u)/1-u=0,h∈C^(1)([0,1],(0,∞))is a nonincreasing function and h(t)>1. 展开更多
关键词 boundary conditions with parameters positive solutions the upper and lower solution method asymptotic property
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Conservation Laws and Particular Solutions for a Keller-Segel Model
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作者 Luyun Chen Jie Lou 《Advances in Pure Mathematics》 2025年第2期107-118,共12页
This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that... This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that are related and unrelated to symmetric information. In addition, some exact solutions with particular forms are obtained according to the method of conservation laws. These particular solutions are different from the group-invariant solutions. 展开更多
关键词 Keller-Segel Model Conservation Laws Mixed Method Exact solutions
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Peaked traveling wave solutions of the modified highly nonlinear Novikov equation
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作者 LI Hui-jun WEN Zhen-shu LI Shao-yong 《Applied Mathematics(A Journal of Chinese Universities)》 2025年第2期375-394,共20页
In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system w... In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results. 展开更多
关键词 modified highly nonlinear Novikov equation bifurcation dynamics peakons periodic cusp wave solutions
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High Energy Normalized Solutions for the Schrodinger Equations with Exponential Critical Growth
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作者 ZHANG Xiao-cang XULi-ping 《Chinese Quarterly Journal of Mathematics》 2025年第1期1-19,共19页
In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 rep... In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 represents a trapping potential,and f has an exponential critical growth.Under the appropriate assumptions of f,we have obtained the existence of normalized solutions to the above Schr?dinger equation by introducing a variational method.And these solutions are also high energy solutions with positive energy. 展开更多
关键词 High energy normalized solutions Schrodinger equation Trapping potential Exponential critical growth Variational method
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