Human life quality requires both industrial/agricultural fast development and high environmental quality.However,the two aspects are conflicted as some contaminants are accidentally released into the environment,poten...Human life quality requires both industrial/agricultural fast development and high environmental quality.However,the two aspects are conflicted as some contaminants are accidentally released into the environment,potentially harmful to human health even at extra-low concentrations.展开更多
In recent years,with the rapid developme nt of the econo my and society,pollution of valuable metal ions in wastewater has become a major challenge to environmental sustainability.In order to solve the pollution cause...In recent years,with the rapid developme nt of the econo my and society,pollution of valuable metal ions in wastewater has become a major challenge to environmental sustainability.In order to solve the pollution caused by metal ions,researchers have conducted continuous re searches and explored various re mediation methods.Crown ether has attracted great attention because of its ionic radius and cavity size matching well with metal ions,which makes it have the ability to selectively complex metal ions.This unique property enables the directed removal and recovery of metal ions and makes crown ethers increasingly popular in extraction and separation processes.In this paper,the research progress of crown ethers in the extraction and separation of valuable metal ions was reviewed,with emphasis on the principles,extraction systems and the key factors affecting the extraction process.This study can provide some technical support for the application of separation and extraction of valuable metal ions by crown ether.展开更多
Aqueous zinc(Zn)-ion batteries(AZIBs)have gained significant interest in energy storage due to several unique advantages.Utilizing waterbased electrolytes enhances environmental sustainability,while the abundance and ...Aqueous zinc(Zn)-ion batteries(AZIBs)have gained significant interest in energy storage due to several unique advantages.Utilizing waterbased electrolytes enhances environmental sustainability,while the abundance and affordability of Zn offer economic benefits.Manganese(Mn)-based materials,commonly used as cathodes in these batteries,provide high theoretical capacity,high electrical conductivity,and good structural stability.However,these materials suffer from capacity degradation over repeated cycles due to structural collapse and limited conductivity.To address this problem,we synthesized a magnesium(Mg)-and Mn-based composite,Mg^(2+)-Mn_(3)O_(4),using the hydrothermal method with an optimized amount of ammonium hydroxide(NH_(4)OH)solution.This approach effectively stabilizes the structure during cycling,enhancing both capacity retention and conductivity.The Zn^(2+)/H+intercalation/deintercalation process was confirmed by experimental results and ex-situ X-ray diffraction analysis,which demonstrates that Mg^(2+),along with optimized NH_(4)OH amount,prevents structural collapse and improves conductivity.Under optimal process conditions,the composite electrode(Mg^(2+)-Mn_(3)O_(4)–8 ml)achieved a capacity of 173.58 mA h g^(-1) at 0.5 A g^(-1),with excellent rate performance of 71.39 mA h g^(-1) at 10 A g^(-1).Remarkably,even at 5 A g^(-1),the electrode maintained a capacity of 86.87 mA h g^(-1) over 2100 cycles,underscoring the role of Mg^(2+)and NH_(4)OH in enhancing the reversible insertion/extraction stability of Zn^(2+)in Mn-based layered materials.This study presents a novel strategy for metal-ion incorporation in Mn-based AZIBs,offering insights into the optimization of cathode materials and advancing research on associated storage mechanisms.展开更多
Aqueous sodium-ion batteries(ASIBs) offer significant advantages for energy storage on a large scale,attributed to their economical cost,secure operatio n,and eco-friend ly natu re.Among the leading cathode materials ...Aqueous sodium-ion batteries(ASIBs) offer significant advantages for energy storage on a large scale,attributed to their economical cost,secure operatio n,and eco-friend ly natu re.Among the leading cathode materials for ASIBs,Na_(3)V_(2)(PO_(4))_(3)(NVP) exhibits excellent structural stability and a high Na+diffusion coefficient,making it a promising option.However,the high solubility of vanadium-based materials in aqueous electrolytes engenders suboptimal cycling stability for Na_(3)V_(2)(PO_(4))_(3),constraining its application in ASIBs.Herein,the Cr-substituted Na_(3)V_(1.3)Cr_(0.7)(PO_(4))3@C(NV_(1.3)Cr_(0.7)P) cathode material was synthesized via a simple sol-gel method.It is found that Cr substitution reduces the cell parameters of NV_(1.3)Cr_(0.7)P,effectively reinforcing the crystal structure.Furthermore,NV_(1.3)Cr_(0.7)P alters the Na^(+)insertion/extraction mechanism,transforming the typical two-phase reaction between Na_(1)V_(2)(PO_(4))_(3)and Na_(3)V_(2)(PO_(4))3into continuous solid-solution reactions with stable intermediates.The Cr substitution diminishes the sodium-ion diffusion energy barrier in NV_(1.3)Cr_(0.7)P,leading to smoother Na+insertion and extraction processes.Consequently,NV_(1.3)Cr_(0.7)P exhibits impressive cycling stability,retaining 74.8% of its capacity after 5,000 cycles at a current density of 5 A g^(-1),along with an outstanding rate performance of 79,2% at 10 A g^(-1).This work elucidates the stable Na^(+)insertion/extraction processes in Cr-substituted NV_(1.3)Cr_(0.7)P,offering insights into the application of vanadium-based materials in aqueous sodium-ion batteries.展开更多
Manganese dioxide(MnO_(2)),based on a two-electron-transfer deposition/dissolution chemistry,features an ultrahigh theoretical capacity(616 mAh·g^(−1)),a favorable redox potential(1.23 V vs.the standard hydrogen ...Manganese dioxide(MnO_(2)),based on a two-electron-transfer deposition/dissolution chemistry,features an ultrahigh theoretical capacity(616 mAh·g^(−1)),a favorable redox potential(1.23 V vs.the standard hydrogen electrode),inherent nontoxicity,and low cost,making it a promising cathode candidate for high-energy aqueous batteries.However,its practical application is hindered by limited electrochemical reversibility and cycling stability,primarily attributed to the formation and accumulation of electrochemically inactive Mn species commonly known as“dead Mn”.This perspective provides an in-depth analysis of the“dead Mn”dilemma inherent in Mn^(2+)/MnO_(2) chemistry.First,the fundamental causes of“dead Mn”—insufficient electron supply and imbalanced(insufficient or excessive)proton supply,are systematically analyzed,as they detract from active material utilization,cycle life,and energy density.Then,mitigation strategies are examined from three aspects:preventing“dead Mn”formation caused by insufficient electron supply,mitigating“dead Mn”formation related to imbalanced proton supply,and activating and regenerating existing“dead Mn”.Finally,future research directions are visualized to enhance the practical viability of Mn^(2+)/MnO_(2) deposition/dissolution chemistry,aiming to catalyze advancements in high-energy aqueous battery systems.展开更多
Microemulsions are usually used to prepare nanomaterials.The fo rmation behavior of microemulsions is crucial to the preparation of nanomaterials.Water in the internal phase is usually replaced by electrolyte solution...Microemulsions are usually used to prepare nanomaterials.The fo rmation behavior of microemulsions is crucial to the preparation of nanomaterials.Water in the internal phase is usually replaced by electrolyte solutions to prepare nanomaterials.Knowing the effects of electrolyte solution on the phase behavior of microemulsion is significant to the nanomaterial preparation.Microemulsion systems were studied by a conductivity method with cyclohexane as oil,Triton X-100 as surfactant,hexanol as cosurfactant,and deionized water or the electrolyte solutions of Cu(Ac)_(2)and Zn(Ac)_(2)as aqueous phases.The results showed that the replacement of water with electrolyte solution had a strong effect on the phase behavior of microemulsion system.The O/W microemulsion zone in water system was not observed in the studied electrolyte system.The shape and area of the corresponding phase zone in electrolyte system were different from that in water system.The microemulsion regions of electrolyte solution systems were always larger than that of water system.Zn(Ac)_(2)showed a larger microemulsion region than Cu(Ac)_(2)at 0.1 mol·L^(-1).The microemulsion phase region formed by 0.1 mol·L^(-1)Zn(Ac)_(2)+0.1 mol·L^(-1)Cu(Ac)_(2)was smaller than that formed by 0.1 mol·L^(-1)Zn(Ac)_(2)or 0.1 mol·L^(-1)Cu(Ac)_(2)lonely.With the increase of electrolyte concentration in the electrolyte solution and the rise of temperature,the microemulsion region shrank gradually.The changes of interactions between different components in the system should be responsible to the variation of phase behavior.The results provide important information for the microemulsion system with electrolyte solution as aqueous phase.展开更多
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
The low specific capacitances(SCs)of traditional carbonaceous negative electrodes significantly limit the enhancement in energy density of aqueous hybrid supercapacitors(AHCs).It is still hugely challengeable to explo...The low specific capacitances(SCs)of traditional carbonaceous negative electrodes significantly limit the enhancement in energy density of aqueous hybrid supercapacitors(AHCs).It is still hugely challengeable to explore a candidate with large SCs,which can stably operate in the negative potential region mean-while.For this propose,we design and fabricate solid-solution Ru_(x)Cu_(1-x)O_(2) nanocrystals(NCs),which exhibit competitive SCs and electrochemical stability within the potential range from-0.9 V to 0.0 V in the aqueous KOH electrolyte.The incorporation of Cu enhances the electrochemical utilization of RuO_(2),reaction kinetics,electronic conductivity,and hydrogen evolution overpotentials,which are all highly dependent upon the added contents of Cu species.The optimized Ru_(0.8)Cu_(0.2)O_(2)(RuCu82)electrode of a high mass loading of 5 mg cm^(-2) reveals the best electrochemical capacitances in terms of reversible SCs and capacitance degradation at room temperature and-20℃.Furthermore,the reversible K^(+)-(de)intercalation induced pseudocapacitance is proposed for electrochemical charge storage process of RuCu82.In particu-lar,remarkable specific energy of 59.1 Wh kg-1 at 400 W kg-1 and excellent cycling stability are achieved in the assembled NiCoO_(2)//RuCu82 AHCs.Our contribution here presents a new promising negative elec-trode platform with high SCs and electrochemical stability for next-generation AHCs.展开更多
In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar perce...In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar percentage of Na_(2)Ni_(2)Ti_(6)O_(16)(NNTO)within Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)(NMTO),with x values of 10,20,30,40,and 50.Both XPS(X-ray Photoelectron Spectroscopy)and EDX(Energy Dispersive X-ray Spectroscopy)analyses unequivocally validated the formation of the NNMTO-x solid solutions.It was observed that when x is below 40,the NNMTO-x solid solution retains the structural characteristics of the original NMTO.However,beyond this threshold,significant alterations in crystal morphology were noted,accompanied by a noticeable decline in photocatalytic activity.Notably,the absorption edge of NNMTO-x(x<40)exhibited a shift towards the visible-light spectrum,thereby substantially broadening the absorption range.The findings highlight that NNMTO-30 possesses the most pronounced photocatalytic activity for the reduction of CO_(2).Specifically,after a 6 h irradiation period,the production rates of CO and CH_(4)were recorded at 42.38 and 1.47μmol/g,respectively.This investigation provides pivotal insights that are instrumental in the advancement of highly efficient and stable photocatalysts tailored for CO_(2)reduction processes.展开更多
Aqueous sodium-ion batteries(ASIBs)have attracted great attention in aqueous batteries due to their merit of high safety.However,the constrained work potential and insufficient chemical stability of anode materials in...Aqueous sodium-ion batteries(ASIBs)have attracted great attention in aqueous batteries due to their merit of high safety.However,the constrained work potential and insufficient chemical stability of anode materials in aqueous electro-lytes hinder the large-scale application of ASIBs.Sodium titanium phosphate,NaTi_(2)(PO_(4))_(3)(NTP),is considered one of the most promising anode materials for ASIBs due to its excellent electrochemical performance and tunable structure.Recently,great achievements have been made in the development of NTP,however,a comprehensive review of existing studies is still lacking.This article firstly introduces the basic properties of NTP and analyzes the existing challenges.Subsequently,it will provide a comprehensive overview of the key strategies related to the design and modification of NTP materials with optimized electrochemical performance.Finally,based on the current research status and practical needs,suggestions,and future perspectives for advancing NTP in practical applications of ASIBs are presented.This review aims to guide the future research trajectory from basic material innovation to industrial applications,thus promoting the large-scale commercializa-tion of ASIBs.展开更多
Aqueous zinc metal batteries(AZMBs)are promising candidates for next-generation energy storage,but their commercialization is hindered by zinc anode challenges,notably parasitic reactions and dendrite growth.Herein,we...Aqueous zinc metal batteries(AZMBs)are promising candidates for next-generation energy storage,but their commercialization is hindered by zinc anode challenges,notably parasitic reactions and dendrite growth.Herein,we present a biodegradable biomass-derived protective layer,primarily composed of curcumin,as a zincophilic interface for AZMBs.The curcumin-based layer,fabricated via a homogeneous solution process,exhibits strong adhesion,uniform coverage,and robust mechanical integrity.Rich polar functional groups in curcumin facilitate homogeneous Zn~(2+)flux and suppress side reactions.The curcumin-based layer shows a favorable affinity for zinc trifluoromethanesulfonate(Zn(OTf)_(2))electrolyte,which is the representative of organic zinc salts,enabling optimal thickness for both protection and ion transport.The protected Zn anodes demonstrate an extended lifespan of 2500 h in symmetrical cells and a high Coulombic efficiency of 99.15%.Furthermore,Zn(OTf)_(2)-based system typically exhibits poor stability at high current densities.Fortunately,the lifespan of symmetrical cells was extended by 40-fold at the high current density.When paired with an Na V_(3)O_(8)·1.5H_(2)O(NVO)cathode,the system achieves 86.5%capacity retention after 3000 cycles at a large specific current density of 10 A g^(-1).These results underscore the efficacy of the curcumin-based protective layer in enhancing the reversibility and stability of metal electrodes,specifically relieving the instability of Zn(OTf)_(2)-based systems at high current densities,advancing its commercial viability.展开更多
Aqueous zinc-ion batteries(AZIBs)hold great promise for next-generation energy storage but face challenges such as Zn dendrite growth,side reactions,and limited performance at low temperatures.Here,we propose an elect...Aqueous zinc-ion batteries(AZIBs)hold great promise for next-generation energy storage but face challenges such as Zn dendrite growth,side reactions,and limited performance at low temperatures.Here,we propose an electrolyte design strategy that reconstructs the hydrogenbond network through the synergistic effect of glycerol(GL)and methylsulfonamide(MSA),enabling the formation of a(100)-oriented Zn anode.This design significantly broadens the operating current and temperature windows of AZIBs.As a result,Zn||Zn symmetric cells exhibit remarkable cycling stability,achieving 4,000 h at 1 mA cm^(-2)and 600 h at 40 mA cm^(-2)(both at 1 mAh cm^(-2)capacity);even at-20℃,Zn||Zn symmetric cells deliver ultra-stable cycling for over 5,400 h.Furthermore,Zn||VO_(2)full cells retain 77.3%of their capacity after 2,000 cycles at 30°C with a current density of 0.5 A g^(-1)and 85.4%capacity retention after 2,000 cycles at-20°C and 0.25 A g^(-1).These results demonstrate a robust pathway for enhancing the practicality and low-temperature adaptability of AZIBs.展开更多
Aqueous alkali metal-ion batteries(AAMIBs)have been recognized as emerging electrochemical energy storage technologies for grid-scale applications owning to their intrinsic safety,cost-effectiveness,and environmental ...Aqueous alkali metal-ion batteries(AAMIBs)have been recognized as emerging electrochemical energy storage technologies for grid-scale applications owning to their intrinsic safety,cost-effectiveness,and environmental sustainability.However,the practical application of AAMIBs is still severely constrained by the tendency of aqueous electrolytes to freeze at low temperatures and decompose at high temperatures,limiting their operational temperature range.Considering the urgent need for energy systems with higher adaptability and resilience at various application scenarios,designing novel electrolytes via structure modulation has increasingly emerged as a feasible and economical strategy for the performance optimization of wide-temperature AAMIBs.In this review,the latest advancement of wide-temperature electrolytes for AAMIBs is systematically and comprehensively summarized.Specifically,the key challenges,failure mechanisms,correlations between hydrogen bond behaviors and physicochemical properties,and thermodynamic and kinetic interpretations in aqueous electrolytes are discussed firstly.Additionally,we offer forward-looking insights and innovative design principles for developing aqueous electrolytes capable of operating across a broad temperature range.This review is expected to provide some guidance and reference for the rational design and regulation of widetemperature electrolytes for AAMIBs and promote their future development.展开更多
Aqueous zinc-ion batteries(AZIBs)are currently confronted with the challenge of achieving long-term cyclic stability under high current densities.This issue is primarily attributed to the excessive growth of dendrites...Aqueous zinc-ion batteries(AZIBs)are currently confronted with the challenge of achieving long-term cyclic stability under high current densities.This issue is primarily attributed to the excessive growth of dendrites and the occurrence of significant side reactions.Herein,sucralose(SCL),as an electrolyte additive,has been used to promote the exposure of the Zn(002)texture.The introduction of SCL can adjust the Zn~(2+)nucleation and diffusion along different crystal facets,promoting the exposure of the Zn(002)texture.By substituting water molecules in the[Zn(H_(2)O)_(6)]~(2+),SCL reconfigures the hydrogen bond network in the electrolyte,reconstructing the solvation structure and suppressing the hydrogen evolution reaction.Consequently,the Zn//Zn symmetric battery exhibits long-term cycling stability of over 4900 h at 1 mA cm^(-2)-1 mAh cm^(-2).Even at a harsh condition of 30 mA cm^(-2)-30 mAh cm^(-2)(DOD=73.3%),it can stably cycle for 171 h.The CE of the Zn//Cu half battery reaches 99.61% at 0.2 mA cm^(-2)with 0.2 mAh cm^(-2).Employing the optimized electrolyte,after 500 cycles,a high specific capacity of 420 mAh g^(-1)can be retained for the NH_4V_4O_(10)//Zn full battery at 500 mA g^(-1),corresponding to a capacity retention of 90.7%.展开更多
Aqueous zinc-ion batteries(AZIBs)have garnered considerable attention as promising post-lithium energy storage technologies owing to their intrinsic safety,cost-effectiveness,and competitive gravimetric energy density...Aqueous zinc-ion batteries(AZIBs)have garnered considerable attention as promising post-lithium energy storage technologies owing to their intrinsic safety,cost-effectiveness,and competitive gravimetric energy density.However,their practical commercialization is hindered by critical challenges on the anode side,including dendrite growth and parasitic reactions at the anode/electrolyte interface.Recent studies highlight that rational electrolyte structure engineering offers an effective route to mitigate these issues and strengthen the electrochemical performance of the zinc metal anode.In this review,we systematically summarize state-of-the-art strategies for electrolyte optimization,with a particular focus on the zinc salts regulation,electrolyte additives,and the construction of novel electrolytes,while elucidating the underlying design principles.We further discuss the key structure–property relationships governing electrolyte behavior to provide guidance for the development of next-generation electrolytes.Finally,future perspectives on advanced electrolyte design are proposed.This review aims to serve as a comprehensive reference for researchers exploring high-performance electrolyte engineering in AZIBs.展开更多
Aqueous zinc metal batteries(AZMBs)face significant challenges in achieving reversibility and cycling stability,primarily due to hydrogen evolution reactions(HER)and zinc dendrite growth.In this study,by employing car...Aqueous zinc metal batteries(AZMBs)face significant challenges in achieving reversibility and cycling stability,primarily due to hydrogen evolution reactions(HER)and zinc dendrite growth.In this study,by employing carefully designed cells that approximate the structural characteristics of practical batteries,we revisit this widely held view through in-operando X-ray radiography to examine zinc dendrite formation and HER under nearpractical operating conditions.While conventional understanding emphasizes the severity of these processes,our findings suggest that zinc dendrites and HER are noticeably less pronounced in dense,real-operation configurations compared to modified cells,possibly due to a more uniform electric field and the suppression of triple-phase boundaries.This study indicates that other components,such as degradation at the cathode current collector interface and configuration mismatches within the full cell,may also represent important barriers to the practical application of AZMBs,particularly during the early stages of electrodeposition.展开更多
MnO_(2) stands out among cathode materials for aqueous zinc-ion batteries(AZIBs)high capacity and voltage,it has poor stability and slow Zn^(2+) kinetics.Herein,we propose a dual-regulation strategy integrating copper...MnO_(2) stands out among cathode materials for aqueous zinc-ion batteries(AZIBs)high capacity and voltage,it has poor stability and slow Zn^(2+) kinetics.Herein,we propose a dual-regulation strategy integrating copper doping and carbon-based confinement.Residual carbon(RC),derived from acid-washed coal gasification fine slag(CGFS),serves as a conductive and porous framework for the directional growth of Cu-doped MnO_(2) nanowires(CMO@RC).The synergistic modulation of Cu-induced electronic structure tuning and carbon confinement induced mechanical/electrical stabilization significantly enhances Zn^(2+) transport and electrochemical performance.CMO@RC achieves a high capacity of 563 mA·h·g^(−1) at 0.1 A·g^(−1) and maintains 106%after 1000 cycles at 1 A·g^(−1).Kinetic analyses confirm the dual-path Zn^(2+) diffusion and accelerated reaction kinetics,while DFT calculations reveal that Cu doping enhances Mn 3d orbital hybridization and electron interaction with carbon,elevating the density of states near the Fermi level and reducing charge transfer barriers.Furthermore,pouch cell testing demonstrates outstanding flexibility and mechanical resilience.This study provides a cost-effective and scalable strategy for high-performance AZIBs,leveraging both experimental and theoretical validations.展开更多
Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challeng...Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challenging.By utilizing classification techniques,we establish all solutions of the Yang-Baxter-like matrix equation in this paper when the coefficient matrix A is similar to non-diagonalizable matrix diag(λ,J_(2)(λ))withλ̸=0.More specifically,we divide the non-diagonal elements of the solution into 10 different cases.By discussing each situation,we establish all solutions of the Yang-Baxter-like matrix equation.The results of this work enrich the existing ones.展开更多
This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic fie...This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic field is assumed to satisfy the Neumann boundary condition,which was first investigated by Kazhikhov in 1987.We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data.More precisely,our result can be regarded as a natural generalization of Kazhikov’s result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.展开更多
In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→...In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.展开更多
基金supported by National Natural Science Foundation of China(No.U21A20290)。
文摘Human life quality requires both industrial/agricultural fast development and high environmental quality.However,the two aspects are conflicted as some contaminants are accidentally released into the environment,potentially harmful to human health even at extra-low concentrations.
基金financially supported by the National Natural Science Foundation of China (52174336)the Natural Science Foundation of Shandong Province (ZR2021MB051)。
文摘In recent years,with the rapid developme nt of the econo my and society,pollution of valuable metal ions in wastewater has become a major challenge to environmental sustainability.In order to solve the pollution caused by metal ions,researchers have conducted continuous re searches and explored various re mediation methods.Crown ether has attracted great attention because of its ionic radius and cavity size matching well with metal ions,which makes it have the ability to selectively complex metal ions.This unique property enables the directed removal and recovery of metal ions and makes crown ethers increasingly popular in extraction and separation processes.In this paper,the research progress of crown ethers in the extraction and separation of valuable metal ions was reviewed,with emphasis on the principles,extraction systems and the key factors affecting the extraction process.This study can provide some technical support for the application of separation and extraction of valuable metal ions by crown ether.
基金supported by a National Research Foundation of Korea(NRF)grant funded by the Korean government(MSIT)(No.2018R1A6A1A03025708).
文摘Aqueous zinc(Zn)-ion batteries(AZIBs)have gained significant interest in energy storage due to several unique advantages.Utilizing waterbased electrolytes enhances environmental sustainability,while the abundance and affordability of Zn offer economic benefits.Manganese(Mn)-based materials,commonly used as cathodes in these batteries,provide high theoretical capacity,high electrical conductivity,and good structural stability.However,these materials suffer from capacity degradation over repeated cycles due to structural collapse and limited conductivity.To address this problem,we synthesized a magnesium(Mg)-and Mn-based composite,Mg^(2+)-Mn_(3)O_(4),using the hydrothermal method with an optimized amount of ammonium hydroxide(NH_(4)OH)solution.This approach effectively stabilizes the structure during cycling,enhancing both capacity retention and conductivity.The Zn^(2+)/H+intercalation/deintercalation process was confirmed by experimental results and ex-situ X-ray diffraction analysis,which demonstrates that Mg^(2+),along with optimized NH_(4)OH amount,prevents structural collapse and improves conductivity.Under optimal process conditions,the composite electrode(Mg^(2+)-Mn_(3)O_(4)–8 ml)achieved a capacity of 173.58 mA h g^(-1) at 0.5 A g^(-1),with excellent rate performance of 71.39 mA h g^(-1) at 10 A g^(-1).Remarkably,even at 5 A g^(-1),the electrode maintained a capacity of 86.87 mA h g^(-1) over 2100 cycles,underscoring the role of Mg^(2+)and NH_(4)OH in enhancing the reversible insertion/extraction stability of Zn^(2+)in Mn-based layered materials.This study presents a novel strategy for metal-ion incorporation in Mn-based AZIBs,offering insights into the optimization of cathode materials and advancing research on associated storage mechanisms.
基金financially supported by the Scientific and Technological Plan Project of Guizhou Province ([2024]054)Additional support came from the Industry and Education Combination Innovation Platform of Intelligent Manufacturing and Graduate Joint Training Base at Guizhou University (2020-520000-83-01324061)the Guizhou Engineering Research Center for Smart Services (2203-520102-04-04-298868)。
文摘Aqueous sodium-ion batteries(ASIBs) offer significant advantages for energy storage on a large scale,attributed to their economical cost,secure operatio n,and eco-friend ly natu re.Among the leading cathode materials for ASIBs,Na_(3)V_(2)(PO_(4))_(3)(NVP) exhibits excellent structural stability and a high Na+diffusion coefficient,making it a promising option.However,the high solubility of vanadium-based materials in aqueous electrolytes engenders suboptimal cycling stability for Na_(3)V_(2)(PO_(4))_(3),constraining its application in ASIBs.Herein,the Cr-substituted Na_(3)V_(1.3)Cr_(0.7)(PO_(4))3@C(NV_(1.3)Cr_(0.7)P) cathode material was synthesized via a simple sol-gel method.It is found that Cr substitution reduces the cell parameters of NV_(1.3)Cr_(0.7)P,effectively reinforcing the crystal structure.Furthermore,NV_(1.3)Cr_(0.7)P alters the Na^(+)insertion/extraction mechanism,transforming the typical two-phase reaction between Na_(1)V_(2)(PO_(4))_(3)and Na_(3)V_(2)(PO_(4))3into continuous solid-solution reactions with stable intermediates.The Cr substitution diminishes the sodium-ion diffusion energy barrier in NV_(1.3)Cr_(0.7)P,leading to smoother Na+insertion and extraction processes.Consequently,NV_(1.3)Cr_(0.7)P exhibits impressive cycling stability,retaining 74.8% of its capacity after 5,000 cycles at a current density of 5 A g^(-1),along with an outstanding rate performance of 79,2% at 10 A g^(-1).This work elucidates the stable Na^(+)insertion/extraction processes in Cr-substituted NV_(1.3)Cr_(0.7)P,offering insights into the application of vanadium-based materials in aqueous sodium-ion batteries.
基金National Key Research and Development Program of China(Grant No.2022YFB2404500)the National Natural Science Foundation of China(Grant Nos.22479110,22109116 and 22121004)+3 种基金the Energy Revolution S&T Program of Yulin Innovation Institute of Clean Energy(Grant No.E411050316)the Natural Science Foundation of Tianjin(Grant No.23JCQNJC01750)the“Pandeng Plan”Project in Tianjin University(Grant No.2024XPD-0002)the Fundamental Research Funds for the Central Universities,and the Haihe Laboratory of Sustainable Chemical Transformations.
文摘Manganese dioxide(MnO_(2)),based on a two-electron-transfer deposition/dissolution chemistry,features an ultrahigh theoretical capacity(616 mAh·g^(−1)),a favorable redox potential(1.23 V vs.the standard hydrogen electrode),inherent nontoxicity,and low cost,making it a promising cathode candidate for high-energy aqueous batteries.However,its practical application is hindered by limited electrochemical reversibility and cycling stability,primarily attributed to the formation and accumulation of electrochemically inactive Mn species commonly known as“dead Mn”.This perspective provides an in-depth analysis of the“dead Mn”dilemma inherent in Mn^(2+)/MnO_(2) chemistry.First,the fundamental causes of“dead Mn”—insufficient electron supply and imbalanced(insufficient or excessive)proton supply,are systematically analyzed,as they detract from active material utilization,cycle life,and energy density.Then,mitigation strategies are examined from three aspects:preventing“dead Mn”formation caused by insufficient electron supply,mitigating“dead Mn”formation related to imbalanced proton supply,and activating and regenerating existing“dead Mn”.Finally,future research directions are visualized to enhance the practical viability of Mn^(2+)/MnO_(2) deposition/dissolution chemistry,aiming to catalyze advancements in high-energy aqueous battery systems.
基金funded by the National Natural Science Foundation of China(22078203)fundamental research funds for the central universities(2022SCUH0041)。
文摘Microemulsions are usually used to prepare nanomaterials.The fo rmation behavior of microemulsions is crucial to the preparation of nanomaterials.Water in the internal phase is usually replaced by electrolyte solutions to prepare nanomaterials.Knowing the effects of electrolyte solution on the phase behavior of microemulsion is significant to the nanomaterial preparation.Microemulsion systems were studied by a conductivity method with cyclohexane as oil,Triton X-100 as surfactant,hexanol as cosurfactant,and deionized water or the electrolyte solutions of Cu(Ac)_(2)and Zn(Ac)_(2)as aqueous phases.The results showed that the replacement of water with electrolyte solution had a strong effect on the phase behavior of microemulsion system.The O/W microemulsion zone in water system was not observed in the studied electrolyte system.The shape and area of the corresponding phase zone in electrolyte system were different from that in water system.The microemulsion regions of electrolyte solution systems were always larger than that of water system.Zn(Ac)_(2)showed a larger microemulsion region than Cu(Ac)_(2)at 0.1 mol·L^(-1).The microemulsion phase region formed by 0.1 mol·L^(-1)Zn(Ac)_(2)+0.1 mol·L^(-1)Cu(Ac)_(2)was smaller than that formed by 0.1 mol·L^(-1)Zn(Ac)_(2)or 0.1 mol·L^(-1)Cu(Ac)_(2)lonely.With the increase of electrolyte concentration in the electrolyte solution and the rise of temperature,the microemulsion region shrank gradually.The changes of interactions between different components in the system should be responsible to the variation of phase behavior.The results provide important information for the microemulsion system with electrolyte solution as aqueous phase.
基金financially supported by the Russian Science Foundation(No.20-13-00038).
文摘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.
基金supported by the National Natural Science Foundation of China(Nos.U22A20145,51904115,52072151,52171211,and 52271218)Jinan Independent Innovative Team(No.2020GXRC015)the Major Program of Shandong Province Natural Science Foundation(Nos.ZR2023ZD43 and ZR2021ZD05).
文摘The low specific capacitances(SCs)of traditional carbonaceous negative electrodes significantly limit the enhancement in energy density of aqueous hybrid supercapacitors(AHCs).It is still hugely challengeable to explore a candidate with large SCs,which can stably operate in the negative potential region mean-while.For this propose,we design and fabricate solid-solution Ru_(x)Cu_(1-x)O_(2) nanocrystals(NCs),which exhibit competitive SCs and electrochemical stability within the potential range from-0.9 V to 0.0 V in the aqueous KOH electrolyte.The incorporation of Cu enhances the electrochemical utilization of RuO_(2),reaction kinetics,electronic conductivity,and hydrogen evolution overpotentials,which are all highly dependent upon the added contents of Cu species.The optimized Ru_(0.8)Cu_(0.2)O_(2)(RuCu82)electrode of a high mass loading of 5 mg cm^(-2) reveals the best electrochemical capacitances in terms of reversible SCs and capacitance degradation at room temperature and-20℃.Furthermore,the reversible K^(+)-(de)intercalation induced pseudocapacitance is proposed for electrochemical charge storage process of RuCu82.In particu-lar,remarkable specific energy of 59.1 Wh kg-1 at 400 W kg-1 and excellent cycling stability are achieved in the assembled NiCoO_(2)//RuCu82 AHCs.Our contribution here presents a new promising negative elec-trode platform with high SCs and electrochemical stability for next-generation AHCs.
基金Supported by the Doctoral Research Start-up Project of Yuncheng University(YQ-2023067)Project of Shanxi Natural Science Foundation(202303021211189)+1 种基金Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Provinces(20220036)Shanxi ProvinceIntelligent Optoelectronic Sensing Application Technology Innovation Center and Shanxi Province Optoelectronic Information Science and TechnologyLaboratory,Yuncheng University.
文摘In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar percentage of Na_(2)Ni_(2)Ti_(6)O_(16)(NNTO)within Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)(NMTO),with x values of 10,20,30,40,and 50.Both XPS(X-ray Photoelectron Spectroscopy)and EDX(Energy Dispersive X-ray Spectroscopy)analyses unequivocally validated the formation of the NNMTO-x solid solutions.It was observed that when x is below 40,the NNMTO-x solid solution retains the structural characteristics of the original NMTO.However,beyond this threshold,significant alterations in crystal morphology were noted,accompanied by a noticeable decline in photocatalytic activity.Notably,the absorption edge of NNMTO-x(x<40)exhibited a shift towards the visible-light spectrum,thereby substantially broadening the absorption range.The findings highlight that NNMTO-30 possesses the most pronounced photocatalytic activity for the reduction of CO_(2).Specifically,after a 6 h irradiation period,the production rates of CO and CH_(4)were recorded at 42.38 and 1.47μmol/g,respectively.This investigation provides pivotal insights that are instrumental in the advancement of highly efficient and stable photocatalysts tailored for CO_(2)reduction processes.
基金supported by the Natural Sci-ence Foundation of Fujian Province (No.2024J011210)the High-Level Talent Start-Up Foundation of Xiamen Institute of Technology (No.YKJ23017R)。
文摘Aqueous sodium-ion batteries(ASIBs)have attracted great attention in aqueous batteries due to their merit of high safety.However,the constrained work potential and insufficient chemical stability of anode materials in aqueous electro-lytes hinder the large-scale application of ASIBs.Sodium titanium phosphate,NaTi_(2)(PO_(4))_(3)(NTP),is considered one of the most promising anode materials for ASIBs due to its excellent electrochemical performance and tunable structure.Recently,great achievements have been made in the development of NTP,however,a comprehensive review of existing studies is still lacking.This article firstly introduces the basic properties of NTP and analyzes the existing challenges.Subsequently,it will provide a comprehensive overview of the key strategies related to the design and modification of NTP materials with optimized electrochemical performance.Finally,based on the current research status and practical needs,suggestions,and future perspectives for advancing NTP in practical applications of ASIBs are presented.This review aims to guide the future research trajectory from basic material innovation to industrial applications,thus promoting the large-scale commercializa-tion of ASIBs.
基金the financial support from Research Institute for Smart Energy at the Hong Kong Polytechnic University(Grant No.CDB2)the support of the Hong Kong PhD Fellowship Scheme(Grant No.PF21-65328)。
文摘Aqueous zinc metal batteries(AZMBs)are promising candidates for next-generation energy storage,but their commercialization is hindered by zinc anode challenges,notably parasitic reactions and dendrite growth.Herein,we present a biodegradable biomass-derived protective layer,primarily composed of curcumin,as a zincophilic interface for AZMBs.The curcumin-based layer,fabricated via a homogeneous solution process,exhibits strong adhesion,uniform coverage,and robust mechanical integrity.Rich polar functional groups in curcumin facilitate homogeneous Zn~(2+)flux and suppress side reactions.The curcumin-based layer shows a favorable affinity for zinc trifluoromethanesulfonate(Zn(OTf)_(2))electrolyte,which is the representative of organic zinc salts,enabling optimal thickness for both protection and ion transport.The protected Zn anodes demonstrate an extended lifespan of 2500 h in symmetrical cells and a high Coulombic efficiency of 99.15%.Furthermore,Zn(OTf)_(2)-based system typically exhibits poor stability at high current densities.Fortunately,the lifespan of symmetrical cells was extended by 40-fold at the high current density.When paired with an Na V_(3)O_(8)·1.5H_(2)O(NVO)cathode,the system achieves 86.5%capacity retention after 3000 cycles at a large specific current density of 10 A g^(-1).These results underscore the efficacy of the curcumin-based protective layer in enhancing the reversibility and stability of metal electrodes,specifically relieving the instability of Zn(OTf)_(2)-based systems at high current densities,advancing its commercial viability.
基金financially supported by Guangdong Major Project of Basic Research(No.2023B0303000002)Shenzhen Fundamental Research Programs(No.JCYJ20241202125404007)+1 种基金Shenzhen Key Laboratory of Advanced Energy Storage(No.ZDSYS20220401141000001)National Natural Science Foundation of China(No.52263016,22265007)。
文摘Aqueous zinc-ion batteries(AZIBs)hold great promise for next-generation energy storage but face challenges such as Zn dendrite growth,side reactions,and limited performance at low temperatures.Here,we propose an electrolyte design strategy that reconstructs the hydrogenbond network through the synergistic effect of glycerol(GL)and methylsulfonamide(MSA),enabling the formation of a(100)-oriented Zn anode.This design significantly broadens the operating current and temperature windows of AZIBs.As a result,Zn||Zn symmetric cells exhibit remarkable cycling stability,achieving 4,000 h at 1 mA cm^(-2)and 600 h at 40 mA cm^(-2)(both at 1 mAh cm^(-2)capacity);even at-20℃,Zn||Zn symmetric cells deliver ultra-stable cycling for over 5,400 h.Furthermore,Zn||VO_(2)full cells retain 77.3%of their capacity after 2,000 cycles at 30°C with a current density of 0.5 A g^(-1)and 85.4%capacity retention after 2,000 cycles at-20°C and 0.25 A g^(-1).These results demonstrate a robust pathway for enhancing the practicality and low-temperature adaptability of AZIBs.
基金supported by the National Natural Science Foundation of China(52002297)National Key R&D Program of China(2022VFB2404800)+1 种基金Wuhan Yellow Crane Talents Program,China Postdoctoral Science Foundation(No.2024M752495)the Postdoctoral Fellowship Program of CPSF(No.GZB20230552).
文摘Aqueous alkali metal-ion batteries(AAMIBs)have been recognized as emerging electrochemical energy storage technologies for grid-scale applications owning to their intrinsic safety,cost-effectiveness,and environmental sustainability.However,the practical application of AAMIBs is still severely constrained by the tendency of aqueous electrolytes to freeze at low temperatures and decompose at high temperatures,limiting their operational temperature range.Considering the urgent need for energy systems with higher adaptability and resilience at various application scenarios,designing novel electrolytes via structure modulation has increasingly emerged as a feasible and economical strategy for the performance optimization of wide-temperature AAMIBs.In this review,the latest advancement of wide-temperature electrolytes for AAMIBs is systematically and comprehensively summarized.Specifically,the key challenges,failure mechanisms,correlations between hydrogen bond behaviors and physicochemical properties,and thermodynamic and kinetic interpretations in aqueous electrolytes are discussed firstly.Additionally,we offer forward-looking insights and innovative design principles for developing aqueous electrolytes capable of operating across a broad temperature range.This review is expected to provide some guidance and reference for the rational design and regulation of widetemperature electrolytes for AAMIBs and promote their future development.
基金supported by the Anhui Provincial Science and Technology Innovation Initiative(202423i08050051)the Anhui Provincial Natural Science Foundation(2408085MB029)+1 种基金the HFIPS Director’s Fund(YZJJGGZX202201)the Natural Science Foundation of Hebei Province of China(B2024402018)。
文摘Aqueous zinc-ion batteries(AZIBs)are currently confronted with the challenge of achieving long-term cyclic stability under high current densities.This issue is primarily attributed to the excessive growth of dendrites and the occurrence of significant side reactions.Herein,sucralose(SCL),as an electrolyte additive,has been used to promote the exposure of the Zn(002)texture.The introduction of SCL can adjust the Zn~(2+)nucleation and diffusion along different crystal facets,promoting the exposure of the Zn(002)texture.By substituting water molecules in the[Zn(H_(2)O)_(6)]~(2+),SCL reconfigures the hydrogen bond network in the electrolyte,reconstructing the solvation structure and suppressing the hydrogen evolution reaction.Consequently,the Zn//Zn symmetric battery exhibits long-term cycling stability of over 4900 h at 1 mA cm^(-2)-1 mAh cm^(-2).Even at a harsh condition of 30 mA cm^(-2)-30 mAh cm^(-2)(DOD=73.3%),it can stably cycle for 171 h.The CE of the Zn//Cu half battery reaches 99.61% at 0.2 mA cm^(-2)with 0.2 mAh cm^(-2).Employing the optimized electrolyte,after 500 cycles,a high specific capacity of 420 mAh g^(-1)can be retained for the NH_4V_4O_(10)//Zn full battery at 500 mA g^(-1),corresponding to a capacity retention of 90.7%.
基金supported by the Natural Science Foundation of China(Nos.52125202,52202100,and U24A2065)the Natural Science Foundation of Jiangsu Province(BK20243016)Fundamental Research Funds for the Central Universities,China Postdoctoral Science Foundation(No.2024T171166).
文摘Aqueous zinc-ion batteries(AZIBs)have garnered considerable attention as promising post-lithium energy storage technologies owing to their intrinsic safety,cost-effectiveness,and competitive gravimetric energy density.However,their practical commercialization is hindered by critical challenges on the anode side,including dendrite growth and parasitic reactions at the anode/electrolyte interface.Recent studies highlight that rational electrolyte structure engineering offers an effective route to mitigate these issues and strengthen the electrochemical performance of the zinc metal anode.In this review,we systematically summarize state-of-the-art strategies for electrolyte optimization,with a particular focus on the zinc salts regulation,electrolyte additives,and the construction of novel electrolytes,while elucidating the underlying design principles.We further discuss the key structure–property relationships governing electrolyte behavior to provide guidance for the development of next-generation electrolytes.Finally,future perspectives on advanced electrolyte design are proposed.This review aims to serve as a comprehensive reference for researchers exploring high-performance electrolyte engineering in AZIBs.
基金the fundamental Research Funds for the central Universities(x2wjD2240360)for the funding supportMeanwhile,Engineering and Physical Sciences Research Council(EPSRC,EP/V027433/3)+2 种基金UK Research and Innovation(UKRI)under the UK government’s Horizon Europe funding(101077226,EP/Y008707/1)Faraday Institution(EP/S003053/1)Degradation project(FIRG001),Royal Society(IEC\NSFC\233361),QUB Agility Fund and Wright Technology and Research Centre(W-Tech,R5240MEE)Funding from UK aid from the UK Government through the Faraday Institution and the Transforming Energy Access Programme(Grant number FIRG050-Device engineering of Zn-based hybrid micro-flow batteries and by-product H2 collection for Emerging Economies)。
文摘Aqueous zinc metal batteries(AZMBs)face significant challenges in achieving reversibility and cycling stability,primarily due to hydrogen evolution reactions(HER)and zinc dendrite growth.In this study,by employing carefully designed cells that approximate the structural characteristics of practical batteries,we revisit this widely held view through in-operando X-ray radiography to examine zinc dendrite formation and HER under nearpractical operating conditions.While conventional understanding emphasizes the severity of these processes,our findings suggest that zinc dendrites and HER are noticeably less pronounced in dense,real-operation configurations compared to modified cells,possibly due to a more uniform electric field and the suppression of triple-phase boundaries.This study indicates that other components,such as degradation at the cathode current collector interface and configuration mismatches within the full cell,may also represent important barriers to the practical application of AZMBs,particularly during the early stages of electrodeposition.
基金support from the Key projects of scientific research projects of universities in Anhui Province(2024AH050360).
文摘MnO_(2) stands out among cathode materials for aqueous zinc-ion batteries(AZIBs)high capacity and voltage,it has poor stability and slow Zn^(2+) kinetics.Herein,we propose a dual-regulation strategy integrating copper doping and carbon-based confinement.Residual carbon(RC),derived from acid-washed coal gasification fine slag(CGFS),serves as a conductive and porous framework for the directional growth of Cu-doped MnO_(2) nanowires(CMO@RC).The synergistic modulation of Cu-induced electronic structure tuning and carbon confinement induced mechanical/electrical stabilization significantly enhances Zn^(2+) transport and electrochemical performance.CMO@RC achieves a high capacity of 563 mA·h·g^(−1) at 0.1 A·g^(−1) and maintains 106%after 1000 cycles at 1 A·g^(−1).Kinetic analyses confirm the dual-path Zn^(2+) diffusion and accelerated reaction kinetics,while DFT calculations reveal that Cu doping enhances Mn 3d orbital hybridization and electron interaction with carbon,elevating the density of states near the Fermi level and reducing charge transfer barriers.Furthermore,pouch cell testing demonstrates outstanding flexibility and mechanical resilience.This study provides a cost-effective and scalable strategy for high-performance AZIBs,leveraging both experimental and theoretical validations.
基金Supported by National Natural Science Foundation of China(Grant No.62173161).
文摘Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challenging.By utilizing classification techniques,we establish all solutions of the Yang-Baxter-like matrix equation in this paper when the coefficient matrix A is similar to non-diagonalizable matrix diag(λ,J_(2)(λ))withλ̸=0.More specifically,we divide the non-diagonal elements of the solution into 10 different cases.By discussing each situation,we establish all solutions of the Yang-Baxter-like matrix equation.The results of this work enrich the existing ones.
基金supported by the National Natural Science Foundation of China(12401279,12371219)the Academic and Technical Leaders Training Plan of Jiangxi Province(20212BCJ23027).
文摘This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic field is assumed to satisfy the Neumann boundary condition,which was first investigated by Kazhikhov in 1987.We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data.More precisely,our result can be regarded as a natural generalization of Kazhikov’s result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12361040,12061064)the National Science Foundation of Gansu Province(Grant No.22JR5RA264)State Scholarship Fund(Grant No.20230862021).
文摘In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.
