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
In this paper,we consider a Schr¨odinger-Poisson system with sublinear nonlinearity.The growth of nonlinearity depends on potential function and a bounded function.We first obtain the existence of nontrivial solu...In this paper,we consider a Schr¨odinger-Poisson system with sublinear nonlinearity.The growth of nonlinearity depends on potential function and a bounded function.We first obtain the existence of nontrivial solution sequence with negative energy for the system via a variant Clark’s theorem.Then we get the asymptotical property of the solution sequence by L∞norm.展开更多
Simultaneously preparing sodium silicate solution with high modulus and obtaining aluminum concentrate with high Al/Si ratio from activated roasting clinker is the key to a new method for clean utilization of coal fly...Simultaneously preparing sodium silicate solution with high modulus and obtaining aluminum concentrate with high Al/Si ratio from activated roasting clinker is the key to a new method for clean utilization of coal fly ash.This study systematically investigates the leaching mechanism of SiO_(2) from activated roasting clinker in sodium silicate solution and proposes an optimized leaching process.The colloidal particles formed by the condensation of siloxane groups increase the diffusion resistance of the leaching agent in the capillary pores,and the SiO_(2) deep inside the pores is difficult to contact with the leaching agent,which is an important reason for the insufficient leaching of SiO_(2) in high modulus sodium silicate solution.A two-stage countercurrent leaching process proposed can simultaneously prepare sodium silicate solution with modulus greater than 2.5 and aluminum concentrate with high Al/Si ratio exceeding 11.This work provides a potential application solution for the development of clean and economically feasible technologies for the utilization of fly ash.展开更多
In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
Hydrogen-enriched ironmaking presents a promising approach to mitigate coke consumption and carbon emission in blast furnace(BF)operations.This work investigated the relationship between the structural features of cok...Hydrogen-enriched ironmaking presents a promising approach to mitigate coke consumption and carbon emission in blast furnace(BF)operations.This work investigated the relationship between the structural features of cokes and their reactivity towards solution loss(SL),especially under hydrogen-enriched atmospheres.Six cokes were characterized,and their SL behaviors were examined under varying atmospheres to elucidate the effects of hydrogen enrichment.The results indicate that an increase in fixed carbon content leads to a decrease in the coke reactivity index(CRI)and an increase in coke strength after reaction(CSR),in the CO_(2) atmosphere,the CSR of coke increases from 35.76%−62.83%,while in the 90CO_(2)/10H_(2) atmosphere,the CSR of coke increases from 65.67%−84.09%.There is a good linear relationship between CRI and microcrystalline structure parameters of coke.Cokes with larger crystalline size,lower amorphous content,and smaller optical texture index(OTI)values show enhanced resistance to degradation and maintain structural integrity in BF.Kinetic analysis performed with the shifted-modified-random pore model(S-MRPM)reveals that alterations in pore structure and intrinsic mineral composition significantly influence the reaction rate.The introduction of a small amount of water vapor raises SL rates,whereas a minor addition of hydrogen(<10%)decelerates SL due to its incomplete conversion to water vapor and the reduced partial pressure of the gasifying agent.Thermodynamic calculations also indicate that the introduced hydrogen does not convert into the same fraction of water vapor.The shift from chemical reaction control to gas diffusion control as the rate-determining step with rising temperatures during SL process was confirmed,and the introduction of hydrogen does not notably alter SL behavior.This result demonstrated that introducing a small amount of hydrogen(<10%)can mitigate SL rates,thereby enhancing coke strength and reducing coke consumption and carbon emissions.展开更多
The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding sto...The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding stochastic and impulse. For the stochastic model without impulses, the existence and uniqueness of solution, and the existence of positive periodic solutions are proved, and a sufficient condition for strategy extinction is given. For the stochastic model with impulses, the existence of positive periodic solutions is proved. Numerical results show that noise and impulses directly affect the model, but the periodicity of the model does not change.展开更多
An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solutio...An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solution is proved.展开更多
In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave so...In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave solutions for this model under the influence of advection term and distributed delay.The obtained results indicate that weak kernel and strong kernel can both deduce the existence of periodic traveling wave solutions.Finally,we apply the main results in this paper to Logistic model and Nicholson’s blowflies model.展开更多
This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of norm...This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.展开更多
On a compact Riemann surface with finite punctures P_(1),…P_(k),we define toric curves as multivalued,totallyunramified holomorphic maps to P^(n)with monodromy in a maximal torus of PSU(n+1).Toric solutions to SU(n+1...On a compact Riemann surface with finite punctures P_(1),…P_(k),we define toric curves as multivalued,totallyunramified holomorphic maps to P^(n)with monodromy in a maximal torus of PSU(n+1).Toric solutions to SU(n+1)Todasystems on X\{P_(1);…;P_(k)}are recognized by the associated toric curves in.We introduce character n-ensembles as-tuples of meromorphic one-forms with simple poles and purely imaginary periods,generating toric curves on minus finitelymany points.On X,we establish a correspondence between character-ensembles and toric solutions to the SU(n+1)system with finitely many cone singularities.Our approach not only broadens seminal solutions with two conesingularities on the Riemann sphere,as classified by Jost-Wang(Int.Math.Res.Not.,2002,(6):277-290)andLin-Wei-Ye(Invent.Math.,2012,190(1):169-207),but also advances beyond the limits of Lin-Yang-Zhong’s existencetheorems(J.Differential Geom.,2020,114(2):337-391)by introducing a new solution class.展开更多
Arsenic-contained acid polymetallic solutions(AAPS)are produced from the H2SO4 leaching of dust generated during nonferrous metals pyrometallurgy such as copper,lead,and zinc.It is difficult to selectively remove As a...Arsenic-contained acid polymetallic solutions(AAPS)are produced from the H2SO4 leaching of dust generated during nonferrous metals pyrometallurgy such as copper,lead,and zinc.It is difficult to selectively remove As and efficiently recover valuable metals simultaneously.In this study,arsenic was removed from an acid polymetallic solution containing As,Cd,and Zn via scorodite formation using a hydrothermal method.First,a thermodynamic analysis of the Cd^(2+)-Zn^(2+)-Fe^(3+)-AsO_(4)^(3−)-SO_(4)^(2−)-H_(2)O system showed that the pH range for selective As removal as FeAsO4 was 1.8−3.9,and a higher pH will result in the precipitation of Cd in the form of Cd_(5)H_(2)(AsO_(4))_(4).Second,the experimental investigations,including neutralization and hydrothermal processes,showed that 88.96%As was selectively removed as scorodite with a flower cluster morphology in a hydrothermal process after adjusting the pH of AAPS to 1.0 via a neutralization process,while the total loss ratios of Cd and Zn were 2.44%and 1.13%,respectively.This study realized selective separation of Zn and Cd from AAPS by controlling the pH to avoid their loss into scorodite.展开更多
The stress gradient of surrounding rock and reasonable prestress of support are the keys to ensuring the stability of roadways.The elastic-plastic analytical solution for surrounding rock was derived based on unified ...The stress gradient of surrounding rock and reasonable prestress of support are the keys to ensuring the stability of roadways.The elastic-plastic analytical solution for surrounding rock was derived based on unified strength theory.A model for solving the stress gradient of the surrounding rock with the intermediate principal stress parameter b was established.The correctness and applicability of the solution for the stress gradient in the roadway surrounding rock was verified via multiple methods.Furthermore,the laws of stress,displacement,and the plastic zone of the surrounding rock with different b values and prestresses were revealed.As b increases,the stress gradient in the plastic zone increases,and the displacement and plastic zone radius decrease.As the prestress increases,the peak stress shifts toward the sidewalls,and the stress and stress gradient increments decrease.In addition,the displacement increment and plastic zone increment were proposed to characterize the support effect.The balance point of the plastic zone area appears before that of the displacement zone.The relationship between the stress gradient compensation coefficient and the prestress is obtained.This study provides a research method and idea for determining the reasonable prestress of support in roadways.展开更多
This study investigates the effects of varying Sc content on phase composition,corrosion resistance and passive film characteristic of Al_(1.2)CoCrFeNiSc_(x)(x=0,0.1,0.2,0.3)high-entropy alloys in 0.5 mol/L H_(2)SO_(4...This study investigates the effects of varying Sc content on phase composition,corrosion resistance and passive film characteristic of Al_(1.2)CoCrFeNiSc_(x)(x=0,0.1,0.2,0.3)high-entropy alloys in 0.5 mol/L H_(2)SO_(4) solution.The addition of Sc causes the alloys to form a Laves phase which is a(Ni,Co)_(2)Sc intermetallic compound with face centred cubic(FCC)structure and lattice parameter of 0.695 nm.During the potentiodynamic polarization process,Laves phase is severely corroded due to its large grain orientation spread value and high electrochemical activity.Sc deteriorates the corrosion resistance of the alloy primarily by significantly accelerating the corrosion rate rather than altering the corrosion tendency.Al_(1.2)CoCrFeNiSc_(x) alloys exhibit poorer corrosion resistance in 0.5 mol/L H_(2)SO_(4) than in 3.5 wt.%NaCl solution,with severe intergranular corrosion observed on the alloy surface.The passive films on Sc-free alloys primarily composed of Al_(2)O_(3) and Cr_(2)O_(3),while for Sc-containing alloys,the film mainly contains Al_(2)O_(3),Cr_(2)O_(3) and Sc_(2)O_(3).In addition,the passive films on Sc-free alloys behave as an n-type semiconductor,while the passive films on Sc-containing alloys surface exhibit the electronic characteristics of p-n junctions.As the Sc content rises,the defect density in passive film increases from 10^(21) cm^(-3) to 10^(23) cm^(-3),which leads to a less compact and less protective passive film,ultimately decreasing the alloy’s corrosion resistance.This work holds significant guiding significance for the engineering application of high-entropy alloys in acidic environments and is conducive to the development of high-performance corrosion-resistant alloys.展开更多
In practical engineering construction,multi-layered barriers containing geomembranes are extensively applied to retard the migration of pollutants.However,the associated analytical theory on pollutants diffusion still...In practical engineering construction,multi-layered barriers containing geomembranes are extensively applied to retard the migration of pollutants.However,the associated analytical theory on pollutants diffusion still needs to be further improved.In this work,general analytical solutions are derived for one-dimensional diffusion of degradable organic contaminant(DOC)in the multi-layered media containing geomembranes under a time-varying concentration boundary condition,where the variable substitution and separated variable approaches are employed.These analytical solutions with clear expressions can be used not only to study the diffusion behaviors of DOC in bottom and vertical composite barrier systems,but also to verify other complex numerical models.The proposed general analytical solutions are then fully validated via three comparative analyses,including comparisons with the experimental measurements,an existing analytical solution,and a finite-difference solution.Ultimately,the influences of different factors on the composite cutoff wall’s(CCW,which consists of two soil-bentonite layers and a geomembrane)service performance are investigated through a composite vertical barrier system as the application example.The findings obtained from this investigation can provide scientific guidance for the barrier performance evaluation and the engineering design of CCWs.This application example also exhibits the necessity and effectiveness of the developed analytical solutions.展开更多
为筛选出适于新疆阿拉尔垦区种植的棉花品种(系)及优质的亲本材料,同时明确棉花选育中与高产优质有关的关键指标,选取12个不同株型的棉花品种(系)为研究对象,采用逼近理想解排序法(dynamic technique for order preference by similarit...为筛选出适于新疆阿拉尔垦区种植的棉花品种(系)及优质的亲本材料,同时明确棉花选育中与高产优质有关的关键指标,选取12个不同株型的棉花品种(系)为研究对象,采用逼近理想解排序法(dynamic technique for order preference by similarity to an ideal solution,DTOPSIS)对参试品种(系)进行综合评价并筛选出综合表现较优的品种(系),同时结合株型性状与产量及其构成因素、纤维品质指标进行相关分析,探究影响阿拉尔垦区棉花产量和品质的关键农艺性状。结果表明,塔河2号主要性状适应当地栽培种植,17-1612和AW04可作为提高产量或品质的优良亲本材料;在当地棉花育种实践中,宜选择株型较紧凑的品种;单株果枝数可作为选育高产优质棉花品种(系)的侧重性正向性状指标,株高、内围铃数和茎粗可作为关键性状指标。研究结果可为当地高产优质棉花新品种选育提供理论依据。展开更多
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
In this article,by employing the Hirota bilinear approach and the long wave limit method,we not only derive soliton solutions,lump solutions,and hybrid solutions for the(2+1)-dimensional Yu-Toda-Sasa-Fukuyama(YTSF)equ...In this article,by employing the Hirota bilinear approach and the long wave limit method,we not only derive soliton solutions,lump solutions,and hybrid solutions for the(2+1)-dimensional Yu-Toda-Sasa-Fukuyama(YTSF)equation,but also analyze the dynamical behaviors of nonlinear local wave propagation in shallow water.Firstly,based on the Hirota bilinear approach,one to four-order soliton solutions of the YTSF equation are obtained,and the effects of different parameters on the amplitude,propagation trajectory,and displacement of solitons are investigated.Secondly,using the long wave limit approach,one to three-order lump solutions and various physical quantities of the YTSF equation are derived.It is found that the real and imaginary parts of the parameter pi dominate the propagation trajectory and the shape of lump waves,respectively.Furthermore,we construct the hybrid solution for the YTSF equation,leading to the conclusion that the interaction between lumps and solitons constitutes an elastic collision.To intuitively understand the dynamic behaviors of these solutions,we conduct numerical simulations to present vivid three-dimensional visualizations.展开更多
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 National Natural Science Foundation of China(12226412)Natural Science Foundation of Jiangsu Province(BK20221339)。
文摘In this paper,we consider a Schr¨odinger-Poisson system with sublinear nonlinearity.The growth of nonlinearity depends on potential function and a bounded function.We first obtain the existence of nontrivial solution sequence with negative energy for the system via a variant Clark’s theorem.Then we get the asymptotical property of the solution sequence by L∞norm.
基金Project(52374362)supported by the National Natural Science Foundation of ChinaProject(2022YFC3900901)supported by the National Key Research and Development Program of China。
文摘Simultaneously preparing sodium silicate solution with high modulus and obtaining aluminum concentrate with high Al/Si ratio from activated roasting clinker is the key to a new method for clean utilization of coal fly ash.This study systematically investigates the leaching mechanism of SiO_(2) from activated roasting clinker in sodium silicate solution and proposes an optimized leaching process.The colloidal particles formed by the condensation of siloxane groups increase the diffusion resistance of the leaching agent in the capillary pores,and the SiO_(2) deep inside the pores is difficult to contact with the leaching agent,which is an important reason for the insufficient leaching of SiO_(2) in high modulus sodium silicate solution.A two-stage countercurrent leaching process proposed can simultaneously prepare sodium silicate solution with modulus greater than 2.5 and aluminum concentrate with high Al/Si ratio exceeding 11.This work provides a potential application solution for the development of clean and economically feasible technologies for the utilization of fly ash.
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
基金supported by National Natural Science Foundation of China(22178002,22178001)Natural Science Foundation of Anhui Province(2308085Y19)Excellent Youth Research Project of Anhui Provincial Department of Education(2022AH030045).
文摘Hydrogen-enriched ironmaking presents a promising approach to mitigate coke consumption and carbon emission in blast furnace(BF)operations.This work investigated the relationship between the structural features of cokes and their reactivity towards solution loss(SL),especially under hydrogen-enriched atmospheres.Six cokes were characterized,and their SL behaviors were examined under varying atmospheres to elucidate the effects of hydrogen enrichment.The results indicate that an increase in fixed carbon content leads to a decrease in the coke reactivity index(CRI)and an increase in coke strength after reaction(CSR),in the CO_(2) atmosphere,the CSR of coke increases from 35.76%−62.83%,while in the 90CO_(2)/10H_(2) atmosphere,the CSR of coke increases from 65.67%−84.09%.There is a good linear relationship between CRI and microcrystalline structure parameters of coke.Cokes with larger crystalline size,lower amorphous content,and smaller optical texture index(OTI)values show enhanced resistance to degradation and maintain structural integrity in BF.Kinetic analysis performed with the shifted-modified-random pore model(S-MRPM)reveals that alterations in pore structure and intrinsic mineral composition significantly influence the reaction rate.The introduction of a small amount of water vapor raises SL rates,whereas a minor addition of hydrogen(<10%)decelerates SL due to its incomplete conversion to water vapor and the reduced partial pressure of the gasifying agent.Thermodynamic calculations also indicate that the introduced hydrogen does not convert into the same fraction of water vapor.The shift from chemical reaction control to gas diffusion control as the rate-determining step with rising temperatures during SL process was confirmed,and the introduction of hydrogen does not notably alter SL behavior.This result demonstrated that introducing a small amount of hydrogen(<10%)can mitigate SL rates,thereby enhancing coke strength and reducing coke consumption and carbon emissions.
基金Supported by the National Natural Science Foundation of China(10671182)。
文摘The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding stochastic and impulse. For the stochastic model without impulses, the existence and uniqueness of solution, and the existence of positive periodic solutions are proved, and a sufficient condition for strategy extinction is given. For the stochastic model with impulses, the existence of positive periodic solutions is proved. Numerical results show that noise and impulses directly affect the model, but the periodicity of the model does not change.
基金Supported by Scientific Research Fund of Hunan Provincial Education Departmen(t23A0361)。
文摘An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solution is proved.
基金Supported by the National Natural Science Foundation of China(12261050)Science and Technology Project of Department of Education of Jiangxi Province(GJJ2201612 and GJJ211027)Natural Science Foundation of Jiangxi Province of China(20212BAB202021)。
文摘In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave solutions for this model under the influence of advection term and distributed delay.The obtained results indicate that weak kernel and strong kernel can both deduce the existence of periodic traveling wave solutions.Finally,we apply the main results in this paper to Logistic model and Nicholson’s blowflies model.
基金Supported by National Natural Science Foundation of China(11671403,11671236)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.
基金supported by the National Natural Science Foundation of China(11931009,12271495,11971450,and 12071449)Anhui Initiative in Quantum Information Technologies(AHY150200)the Project of Stable Support for Youth Team in Basic Research Field,Chinese Academy of Sciences(YSBR-001).
文摘On a compact Riemann surface with finite punctures P_(1),…P_(k),we define toric curves as multivalued,totallyunramified holomorphic maps to P^(n)with monodromy in a maximal torus of PSU(n+1).Toric solutions to SU(n+1)Todasystems on X\{P_(1);…;P_(k)}are recognized by the associated toric curves in.We introduce character n-ensembles as-tuples of meromorphic one-forms with simple poles and purely imaginary periods,generating toric curves on minus finitelymany points.On X,we establish a correspondence between character-ensembles and toric solutions to the SU(n+1)system with finitely many cone singularities.Our approach not only broadens seminal solutions with two conesingularities on the Riemann sphere,as classified by Jost-Wang(Int.Math.Res.Not.,2002,(6):277-290)andLin-Wei-Ye(Invent.Math.,2012,190(1):169-207),but also advances beyond the limits of Lin-Yang-Zhong’s existencetheorems(J.Differential Geom.,2020,114(2):337-391)by introducing a new solution class.
文摘In this paper,by using the method of Lyapunov-Schmidt reduction,we obtain the existence of multi-bump solutions for planar Schrödinger-Poisson system.
基金Project(23B05465) supported by the Scientific Research Fund of Hunan Provincial Education Department,China。
文摘Arsenic-contained acid polymetallic solutions(AAPS)are produced from the H2SO4 leaching of dust generated during nonferrous metals pyrometallurgy such as copper,lead,and zinc.It is difficult to selectively remove As and efficiently recover valuable metals simultaneously.In this study,arsenic was removed from an acid polymetallic solution containing As,Cd,and Zn via scorodite formation using a hydrothermal method.First,a thermodynamic analysis of the Cd^(2+)-Zn^(2+)-Fe^(3+)-AsO_(4)^(3−)-SO_(4)^(2−)-H_(2)O system showed that the pH range for selective As removal as FeAsO4 was 1.8−3.9,and a higher pH will result in the precipitation of Cd in the form of Cd_(5)H_(2)(AsO_(4))_(4).Second,the experimental investigations,including neutralization and hydrothermal processes,showed that 88.96%As was selectively removed as scorodite with a flower cluster morphology in a hydrothermal process after adjusting the pH of AAPS to 1.0 via a neutralization process,while the total loss ratios of Cd and Zn were 2.44%and 1.13%,respectively.This study realized selective separation of Zn and Cd from AAPS by controlling the pH to avoid their loss into scorodite.
基金Project(52274130)supported by the National Natural Science Foundation of ChinaProject(ZR2024ZD22)supported by the Major Basic Research Project of the Shandong Provincial Natural Science Foundation,China+2 种基金Project(2023375)supported by the Guizhou University Research and Innovation Team,ChinaProject(Leading Fund(2023)09)supported by the Natural Science Research Fund of Guizhou University,ChinaProject(JYBSYS2021101)supported by the Open Fund of Key Laboratory of Safe and Effective Coal Mining,Ministry of Education,China。
文摘The stress gradient of surrounding rock and reasonable prestress of support are the keys to ensuring the stability of roadways.The elastic-plastic analytical solution for surrounding rock was derived based on unified strength theory.A model for solving the stress gradient of the surrounding rock with the intermediate principal stress parameter b was established.The correctness and applicability of the solution for the stress gradient in the roadway surrounding rock was verified via multiple methods.Furthermore,the laws of stress,displacement,and the plastic zone of the surrounding rock with different b values and prestresses were revealed.As b increases,the stress gradient in the plastic zone increases,and the displacement and plastic zone radius decrease.As the prestress increases,the peak stress shifts toward the sidewalls,and the stress and stress gradient increments decrease.In addition,the displacement increment and plastic zone increment were proposed to characterize the support effect.The balance point of the plastic zone area appears before that of the displacement zone.The relationship between the stress gradient compensation coefficient and the prestress is obtained.This study provides a research method and idea for determining the reasonable prestress of support in roadways.
基金Project(ZR2021QE136)supported by the Natural Science Foundation of Shandong Province,ChinaProject(52301106)supported by the National Natural Science Foundation of China+1 种基金Project(2022KJ273)supported by the Development Plan of Shandong Province Young Innovation Team of Higher Education Institutions,ChinaProject(2024HWYQ-074)supported by the Shandong Provincial Natural Science Fund for Excellent Young Scientists Fund Program(Overseas),China。
文摘This study investigates the effects of varying Sc content on phase composition,corrosion resistance and passive film characteristic of Al_(1.2)CoCrFeNiSc_(x)(x=0,0.1,0.2,0.3)high-entropy alloys in 0.5 mol/L H_(2)SO_(4) solution.The addition of Sc causes the alloys to form a Laves phase which is a(Ni,Co)_(2)Sc intermetallic compound with face centred cubic(FCC)structure and lattice parameter of 0.695 nm.During the potentiodynamic polarization process,Laves phase is severely corroded due to its large grain orientation spread value and high electrochemical activity.Sc deteriorates the corrosion resistance of the alloy primarily by significantly accelerating the corrosion rate rather than altering the corrosion tendency.Al_(1.2)CoCrFeNiSc_(x) alloys exhibit poorer corrosion resistance in 0.5 mol/L H_(2)SO_(4) than in 3.5 wt.%NaCl solution,with severe intergranular corrosion observed on the alloy surface.The passive films on Sc-free alloys primarily composed of Al_(2)O_(3) and Cr_(2)O_(3),while for Sc-containing alloys,the film mainly contains Al_(2)O_(3),Cr_(2)O_(3) and Sc_(2)O_(3).In addition,the passive films on Sc-free alloys behave as an n-type semiconductor,while the passive films on Sc-containing alloys surface exhibit the electronic characteristics of p-n junctions.As the Sc content rises,the defect density in passive film increases from 10^(21) cm^(-3) to 10^(23) cm^(-3),which leads to a less compact and less protective passive film,ultimately decreasing the alloy’s corrosion resistance.This work holds significant guiding significance for the engineering application of high-entropy alloys in acidic environments and is conducive to the development of high-performance corrosion-resistant alloys.
基金Project(2023YFC3707800)supported by the National Key Research and Development Program of China。
文摘In practical engineering construction,multi-layered barriers containing geomembranes are extensively applied to retard the migration of pollutants.However,the associated analytical theory on pollutants diffusion still needs to be further improved.In this work,general analytical solutions are derived for one-dimensional diffusion of degradable organic contaminant(DOC)in the multi-layered media containing geomembranes under a time-varying concentration boundary condition,where the variable substitution and separated variable approaches are employed.These analytical solutions with clear expressions can be used not only to study the diffusion behaviors of DOC in bottom and vertical composite barrier systems,but also to verify other complex numerical models.The proposed general analytical solutions are then fully validated via three comparative analyses,including comparisons with the experimental measurements,an existing analytical solution,and a finite-difference solution.Ultimately,the influences of different factors on the composite cutoff wall’s(CCW,which consists of two soil-bentonite layers and a geomembrane)service performance are investigated through a composite vertical barrier system as the application example.The findings obtained from this investigation can provide scientific guidance for the barrier performance evaluation and the engineering design of CCWs.This application example also exhibits the necessity and effectiveness of the developed analytical solutions.
文摘为筛选出适于新疆阿拉尔垦区种植的棉花品种(系)及优质的亲本材料,同时明确棉花选育中与高产优质有关的关键指标,选取12个不同株型的棉花品种(系)为研究对象,采用逼近理想解排序法(dynamic technique for order preference by similarity to an ideal solution,DTOPSIS)对参试品种(系)进行综合评价并筛选出综合表现较优的品种(系),同时结合株型性状与产量及其构成因素、纤维品质指标进行相关分析,探究影响阿拉尔垦区棉花产量和品质的关键农艺性状。结果表明,塔河2号主要性状适应当地栽培种植,17-1612和AW04可作为提高产量或品质的优良亲本材料;在当地棉花育种实践中,宜选择株型较紧凑的品种;单株果枝数可作为选育高产优质棉花品种(系)的侧重性正向性状指标,株高、内围铃数和茎粗可作为关键性状指标。研究结果可为当地高产优质棉花新品种选育提供理论依据。
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金Supported by the National Natural Science Foundation of China(12001424,12271324)the Natural Science Basic research program of Shaanxi Province(2021JZ-21)+1 种基金the China Postdoctoral Science Foundation(2020M673332)Xi’an University,Xi’an Science and Technology Plan Wutongshu Technology Transfer Action Innovation Team(25WTZD07)。
文摘In this article,by employing the Hirota bilinear approach and the long wave limit method,we not only derive soliton solutions,lump solutions,and hybrid solutions for the(2+1)-dimensional Yu-Toda-Sasa-Fukuyama(YTSF)equation,but also analyze the dynamical behaviors of nonlinear local wave propagation in shallow water.Firstly,based on the Hirota bilinear approach,one to four-order soliton solutions of the YTSF equation are obtained,and the effects of different parameters on the amplitude,propagation trajectory,and displacement of solitons are investigated.Secondly,using the long wave limit approach,one to three-order lump solutions and various physical quantities of the YTSF equation are derived.It is found that the real and imaginary parts of the parameter pi dominate the propagation trajectory and the shape of lump waves,respectively.Furthermore,we construct the hybrid solution for the YTSF equation,leading to the conclusion that the interaction between lumps and solitons constitutes an elastic collision.To intuitively understand the dynamic behaviors of these solutions,we conduct numerical simulations to present vivid three-dimensional visualizations.
