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
In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,t...In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.展开更多
This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ...This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.展开更多
Defect engineering by heteroatom doping gives carbon materials some new characteristics such as a different electronic structure and a high electrochemical activity,making them suitable for high-performance applicatio...Defect engineering by heteroatom doping gives carbon materials some new characteristics such as a different electronic structure and a high electrochemical activity,making them suitable for high-performance applications.N-doping has been widely investigated because of its similar atom radius to carbon,high electronegativity as well as many different configurations.We summarize the preparation methods and properties of N-doped carbon materials,and discuss their possible use in sodium ion storage.The relationships between N content/configuration and crystallinity,electronic conductivity,wettability,chemical reactivity as well as sodium ion storage performance are discussed.展开更多
Objective To investigate the effects of Qingguang'anⅡFormula(QGAⅡ)on the gut micro-biota of mice with chronic high intraocular pressure(IOP)model,and explore its key micro-biota for protecting the optic nerve.Me...Objective To investigate the effects of Qingguang'anⅡFormula(QGAⅡ)on the gut micro-biota of mice with chronic high intraocular pressure(IOP)model,and explore its key micro-biota for protecting the optic nerve.Methods A total of 10 specific pathogen free(SPF)grade female DBA/2J mice were random-ly divided into model group and QGAⅡgroup(n=5 for each group),while additional 5 SPF-grade female C57BL/6J mice were assigned to control group.Mice presented spontaneous high IOP and showed elevated approximately at the age of seven months.The high IOP was maintained until week 38,when gavage was initiated.Mice in control group underwent the same intragastric treatment,while those in QGAⅡgroup were gavaged with QGAⅡ(9.67 g/kg),once a day for four weeks.Retinal morphology was examined using hematoxylin and eosin(HE)staining,with the number of retinal ganglion cells(RGCs)counted.The expression level of Brn3a protein,a specific marker for RGCs,was detected by immunofluorescence,with the mean optical density(OD)measured for quantitative analysis.In addition,16S rDNA se-quencing was leveraged to analyze changes in the diversity of gut microbiota,including theirα-diversity(Chao1,Shannon,Pielou’s evenness,and observed species index)andβ-diversity.Venn diagrams and linear discriminant analysis effect size(LEfSe)analysis was employed to investigate the number of amplicon sequence variants(ASVs),the abundance of differential gut microbiota species,and the classification of species at both the phylum and genus levels within the three groups of mice.Results HE staining revealed that compared with control group,model group showed signif-icant reduction in the number of RGCs(P<0.01),with intracellular vacuolar degeneration and nuclear pyknosis.After QGAⅡtreatment,the number of RGCs was significantly in-creased compared with model group(P<0.01),with notable improvements in intracellular vacuolar degeneration.Immunofluorescence analysis showed that the mean OD of Brn3a protein was significantly decreased in model group compared with control group(P<0.01),while QGAⅡtreatment significantly elevated its expression level(P<0.01).Analysis ofα-diversity showed that after QGAⅡintervention,the Chao1,Shannon,and Pielou’s evenness indices were significantly increased(P<0.01),and the observed species index was elevated(P<0.05).β-Diversity analysis demonstrated distinct clustering among the three groups,indicating relatively low similarity in bacterial community structures.ASV clustering identi-fied a total of 14061 ASVs across all groups,with 9514 ASVs shared between model and QGAⅡgroups.At the phylum level,the abundance of Bacteroidetes was significantly decreased in model group compared with control group(P<0.01),while Firmicutes and the Firmicutes/Bacteroidetes(F/B)ratio were significantly increased(P<0.01).QGAⅡtreatment significantly reduced both Firmicutes abundance and the F/B ratio(P<0.01).At the genus level,Lactobacillus was dominant across all groups,with its abundance significantly in-creased in model group(P<0.01)and subsequently decreased following QGAⅡintervention(P<0.05).Conclusion QGAⅡrestructured the gut microbiota of DBA/2J mice with chronic high IOP,bringing changes in their diversity and abundance of components.Firmicutes,Bacteroidetes,Lactobacillus,along with their associated microorganisms,are likely critical components of the gut microbiota that contribute to the optic neuroprotective effects of QGAⅡon chronic high IOP mice.展开更多
In this paper,we construct a new sixth order iterative method for solving nonlinear equations.The local convergence and order of convergence of the new iterative method is demonstrated.In order to check the validity o...In this paper,we construct a new sixth order iterative method for solving nonlinear equations.The local convergence and order of convergence of the new iterative method is demonstrated.In order to check the validity of the new iterative method,we employ several chemical engineering applications and academic test problems.Numerical results show the good numerical performance of the new iterative method.Moreover,the dynamical study of the new method also supports the theoretical results.展开更多
To achieve efficient flotation separation of brucite and calcite,flotation separation experiments were conducted on two minerals using dodecylamine(DDA)as the collector and potassium dihydrogen phosphate(PDP)as the re...To achieve efficient flotation separation of brucite and calcite,flotation separation experiments were conducted on two minerals using dodecylamine(DDA)as the collector and potassium dihydrogen phosphate(PDP)as the regulator.The action mechanism of DDA and PDP was explored through contact angle measurement,zeta potential detection,solution chemistry calculation,FTIR analysis,and XPS detection.The flotation results showed that when DDA dosage was 35 mg/L and PDP dosage was 40 mg/L,the maximum floating difference between brucite and calcite was 79.81%,and the selectivity separation index was 6.46.The detection analysis showed that the main dissolved component HPO_(4)^(2−)of PDP is selectively strongly adsorbed on the Ca site on the surface of calcite,promoting the adsorption of the main dissolved component RNH_(3)^(+)of DDA on calcite surface,while brucite is basically not affected by PDP.Therefore,PDP is an effective regulator for the reverse flotation separation of brucite and calcite in DDA system.展开更多
Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamic...Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton.展开更多
Square piles of reinforced concrete(RC)in marine environments are susceptible to chloride-inducedcorrosion.A novel reverse-seepage technique(RST)is applied to square piles to block the intrusion of chlorides.Thisresea...Square piles of reinforced concrete(RC)in marine environments are susceptible to chloride-inducedcorrosion.A novel reverse-seepage technique(RST)is applied to square piles to block the intrusion of chlorides.Thisresearch introduces a computational model designed to predict the lifespan of corrosion initiation in reinforced concretesquare piles when applied reverse-seepage pressure.The model considers the impacts of chloride binding and the tripletime-dependence property among the permeability,the corrected surface chloride concentration,and the diffusioncoefficient.The proposed numerical model is solved using the alternating direction implicit(ADI)approach,and itsaccuracy and reliability are evaluated by contrasting the computational outcomes with the analytical solution andexperimental results.Furthermore,the primary factors contributing to the corrosion of reinforced concrete square pilesare analyzed.The results indicate that applying RST can decrease the chloride penetration depth and prolong the lifespanof corrosion initiation in square piles.The water-cement ratio and reverse seepage pressure are the most influentialfactors.A water pressure of 0.4 MPa can double the life of concrete,and the durable life of concrete with a water-cementratio of 0.3 can reach 100 years.展开更多
consider a quasilinear parabolic equation in a band domain with inhomogeneous and unbounded boundary conditions.We show that,under certain conditions,the solution u of the initialboundary value problem tends to infini...consider a quasilinear parabolic equation in a band domain with inhomogeneous and unbounded boundary conditions.We show that,under certain conditions,the solution u of the initialboundary value problem tends to infinite as t→∞.Moreover,by using the zero number argument we show that for any x≠O,u_(x)(x,t)also tends as t→∞to infinity,that is,the gradient is asymptotically unbounded.展开更多
Due to rainfall infiltration,groundwater activity,geological processes,and natural erosion,soil often exhibits heterogeneity and unsaturation.Additionally,seismic events can compromise slope stability.Existing analyti...Due to rainfall infiltration,groundwater activity,geological processes,and natural erosion,soil often exhibits heterogeneity and unsaturation.Additionally,seismic events can compromise slope stability.Existing analytical solutions typically consider a single failure mode,leading to inaccurate slope stability assessments.This study analyzes the impact of matric suction through three nonlinear shear strength models and adopts a heterogeneous soil model where cohesion linearly increases with depth.An improved pseudo-dynamic method is used to account for seismic effects.Based on a three-dimensional(3D)trumpet-shaped rotational failure mechanism,a new framework is established to analyze the stability of 3D two-bench slopes in heterogeneous unsaturated soil under seismic effects.The internal energy dissipation rate and external power at failure are calculated,and the gravity increase method is introduced to derive an explicit expression for the safety factor(F_(s)).The results are compared with previously published results,demonstrating the effectiveness of the proposed method.Sensitivity analyses on different parameters are conducted,discussing the influence of various factors on F s.This study proposes a new formula for calculating the F_(s) of 3D two-bench slopes in heterogeneous unsaturated soil under seismic effects,providing a practical application for slope engineering.展开更多
基金Supported by the National Science Research Project of Anhui Educational Department(KJ2019A0487)the National Natural Science Foundation of China(11771273)。
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 Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)+2 种基金Basic Research Plan of Shanxi Province(202203021211129)Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)。
文摘In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.
基金Supported by National Science Foundation of China(11971027,12171497)。
文摘This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.
文摘Defect engineering by heteroatom doping gives carbon materials some new characteristics such as a different electronic structure and a high electrochemical activity,making them suitable for high-performance applications.N-doping has been widely investigated because of its similar atom radius to carbon,high electronegativity as well as many different configurations.We summarize the preparation methods and properties of N-doped carbon materials,and discuss their possible use in sodium ion storage.The relationships between N content/configuration and crystallinity,electronic conductivity,wettability,chemical reactivity as well as sodium ion storage performance are discussed.
基金National Natural Science Foundation of China(81904260)Scientific Research Project of Hunan Province Department of Education(22B0398)Scientific Research Project of Traditional Chinese Medicine of Hunan Province(D2022045).
文摘Objective To investigate the effects of Qingguang'anⅡFormula(QGAⅡ)on the gut micro-biota of mice with chronic high intraocular pressure(IOP)model,and explore its key micro-biota for protecting the optic nerve.Methods A total of 10 specific pathogen free(SPF)grade female DBA/2J mice were random-ly divided into model group and QGAⅡgroup(n=5 for each group),while additional 5 SPF-grade female C57BL/6J mice were assigned to control group.Mice presented spontaneous high IOP and showed elevated approximately at the age of seven months.The high IOP was maintained until week 38,when gavage was initiated.Mice in control group underwent the same intragastric treatment,while those in QGAⅡgroup were gavaged with QGAⅡ(9.67 g/kg),once a day for four weeks.Retinal morphology was examined using hematoxylin and eosin(HE)staining,with the number of retinal ganglion cells(RGCs)counted.The expression level of Brn3a protein,a specific marker for RGCs,was detected by immunofluorescence,with the mean optical density(OD)measured for quantitative analysis.In addition,16S rDNA se-quencing was leveraged to analyze changes in the diversity of gut microbiota,including theirα-diversity(Chao1,Shannon,Pielou’s evenness,and observed species index)andβ-diversity.Venn diagrams and linear discriminant analysis effect size(LEfSe)analysis was employed to investigate the number of amplicon sequence variants(ASVs),the abundance of differential gut microbiota species,and the classification of species at both the phylum and genus levels within the three groups of mice.Results HE staining revealed that compared with control group,model group showed signif-icant reduction in the number of RGCs(P<0.01),with intracellular vacuolar degeneration and nuclear pyknosis.After QGAⅡtreatment,the number of RGCs was significantly in-creased compared with model group(P<0.01),with notable improvements in intracellular vacuolar degeneration.Immunofluorescence analysis showed that the mean OD of Brn3a protein was significantly decreased in model group compared with control group(P<0.01),while QGAⅡtreatment significantly elevated its expression level(P<0.01).Analysis ofα-diversity showed that after QGAⅡintervention,the Chao1,Shannon,and Pielou’s evenness indices were significantly increased(P<0.01),and the observed species index was elevated(P<0.05).β-Diversity analysis demonstrated distinct clustering among the three groups,indicating relatively low similarity in bacterial community structures.ASV clustering identi-fied a total of 14061 ASVs across all groups,with 9514 ASVs shared between model and QGAⅡgroups.At the phylum level,the abundance of Bacteroidetes was significantly decreased in model group compared with control group(P<0.01),while Firmicutes and the Firmicutes/Bacteroidetes(F/B)ratio were significantly increased(P<0.01).QGAⅡtreatment significantly reduced both Firmicutes abundance and the F/B ratio(P<0.01).At the genus level,Lactobacillus was dominant across all groups,with its abundance significantly in-creased in model group(P<0.01)and subsequently decreased following QGAⅡintervention(P<0.05).Conclusion QGAⅡrestructured the gut microbiota of DBA/2J mice with chronic high IOP,bringing changes in their diversity and abundance of components.Firmicutes,Bacteroidetes,Lactobacillus,along with their associated microorganisms,are likely critical components of the gut microbiota that contribute to the optic neuroprotective effects of QGAⅡon chronic high IOP mice.
基金supported by the National Natural Science Foundation of China (No.12271518)the Key Program of the National Natural Science Foundation of China (No.62333016)。
文摘In this paper,we construct a new sixth order iterative method for solving nonlinear equations.The local convergence and order of convergence of the new iterative method is demonstrated.In order to check the validity of the new iterative method,we employ several chemical engineering applications and academic test problems.Numerical results show the good numerical performance of the new iterative method.Moreover,the dynamical study of the new method also supports the theoretical results.
基金the General Program of the National Natural Science Foundation of China(Nos.51974064,52174239)the National Key R&D Program of China(No.2021YFC2902400)the Outstanding Postdoctoral Program of Jiangsu Province,China(No.2022ZB521).
文摘To achieve efficient flotation separation of brucite and calcite,flotation separation experiments were conducted on two minerals using dodecylamine(DDA)as the collector and potassium dihydrogen phosphate(PDP)as the regulator.The action mechanism of DDA and PDP was explored through contact angle measurement,zeta potential detection,solution chemistry calculation,FTIR analysis,and XPS detection.The flotation results showed that when DDA dosage was 35 mg/L and PDP dosage was 40 mg/L,the maximum floating difference between brucite and calcite was 79.81%,and the selectivity separation index was 6.46.The detection analysis showed that the main dissolved component HPO_(4)^(2−)of PDP is selectively strongly adsorbed on the Ca site on the surface of calcite,promoting the adsorption of the main dissolved component RNH_(3)^(+)of DDA on calcite surface,while brucite is basically not affected by PDP.Therefore,PDP is an effective regulator for the reverse flotation separation of brucite and calcite in DDA system.
基金Supported by the National Natural Science Foundation of China(12275172)。
文摘Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton.
基金Projects(52178371,52108355,52178321)supported by the National Natural Science Foundation of ChinaProject(202305)supported by the Research Project of Engineering Research Centre of Rock-Soil Drilling&Excavation and Protection,Ministry of Education,China。
文摘Square piles of reinforced concrete(RC)in marine environments are susceptible to chloride-inducedcorrosion.A novel reverse-seepage technique(RST)is applied to square piles to block the intrusion of chlorides.Thisresearch introduces a computational model designed to predict the lifespan of corrosion initiation in reinforced concretesquare piles when applied reverse-seepage pressure.The model considers the impacts of chloride binding and the tripletime-dependence property among the permeability,the corrected surface chloride concentration,and the diffusioncoefficient.The proposed numerical model is solved using the alternating direction implicit(ADI)approach,and itsaccuracy and reliability are evaluated by contrasting the computational outcomes with the analytical solution andexperimental results.Furthermore,the primary factors contributing to the corrosion of reinforced concrete square pilesare analyzed.The results indicate that applying RST can decrease the chloride penetration depth and prolong the lifespanof corrosion initiation in square piles.The water-cement ratio and reverse seepage pressure are the most influentialfactors.A water pressure of 0.4 MPa can double the life of concrete,and the durable life of concrete with a water-cementratio of 0.3 can reach 100 years.
基金The National Natural Science Foundation of China(12001375)。
文摘consider a quasilinear parabolic equation in a band domain with inhomogeneous and unbounded boundary conditions.We show that,under certain conditions,the solution u of the initialboundary value problem tends to infinite as t→∞.Moreover,by using the zero number argument we show that for any x≠O,u_(x)(x,t)also tends as t→∞to infinity,that is,the gradient is asymptotically unbounded.
基金Project(51378510)supported by the National Natural Science Foundation of China。
文摘Due to rainfall infiltration,groundwater activity,geological processes,and natural erosion,soil often exhibits heterogeneity and unsaturation.Additionally,seismic events can compromise slope stability.Existing analytical solutions typically consider a single failure mode,leading to inaccurate slope stability assessments.This study analyzes the impact of matric suction through three nonlinear shear strength models and adopts a heterogeneous soil model where cohesion linearly increases with depth.An improved pseudo-dynamic method is used to account for seismic effects.Based on a three-dimensional(3D)trumpet-shaped rotational failure mechanism,a new framework is established to analyze the stability of 3D two-bench slopes in heterogeneous unsaturated soil under seismic effects.The internal energy dissipation rate and external power at failure are calculated,and the gravity increase method is introduced to derive an explicit expression for the safety factor(F_(s)).The results are compared with previously published results,demonstrating the effectiveness of the proposed method.Sensitivity analyses on different parameters are conducted,discussing the influence of various factors on F s.This study proposes a new formula for calculating the F_(s) of 3D two-bench slopes in heterogeneous unsaturated soil under seismic effects,providing a practical application for slope engineering.
