We consider the following simplified model for the Belousov-Zhabotinskii(B-Z) reaction:?u/?t=u(1-u-rv)+d?~2u/?x^2,?v/?t=-suv+?~2v/?x^2,where r and s are positive parameters, and d is the diffusing constant for the con...We consider the following simplified model for the Belousov-Zhabotinskii(B-Z) reaction:?u/?t=u(1-u-rv)+d?~2u/?x^2,?v/?t=-suv+?~2v/?x^2,where r and s are positive parameters, and d is the diffusing constant for the concen-tration u. Seeking travelling wave front solution and making an ansatz for the solution,we obtain a nonlinear system of algebraic equations. The system is solved using WuElimination and then we are able to find several exact solutions which are of interest.展开更多
In this paper, the magneto hydrodynamic (MHD) flow of viscous fluid in a channel with non-parallel plates is studied. The governing partial differential equation was transformed into a system of dimensionless non-simi...In this paper, the magneto hydrodynamic (MHD) flow of viscous fluid in a channel with non-parallel plates is studied. The governing partial differential equation was transformed into a system of dimensionless non-similar coupled ordinary differential equation. The transformed conservations equations were solved by using new algorithm. Basically, this new algorithm depends mainly on the Taylor expansion application with the coefficients of power series resulting from integrating the order differential equation. Results obtained from new algorithm are compared with the results of numerical Range-Kutta fourth-order algorithm with help of the shooting algorithm. The comparison revealed that the resulting solutions were excellent agreement. Thermo-diffusion and diffusion-thermo effects were investigated to analyze the behavior of temperature and concentration profile. Also the influences of the first order chemical reaction and the rate of mass and heat transfer were studied. The computed analytical solution result for the velocity, temperature and concentration distribution with the effect of various important dimensionless parameters was analyzed and discussed graphically.展开更多
A reaction-diffusion model for a single species with age structure and nonlocal reaction for periodic time t is derived. Some results about the model with monotone birth function are firstly introduced, and then by co...A reaction-diffusion model for a single species with age structure and nonlocal reaction for periodic time t is derived. Some results about the model with monotone birth function are firstly introduced, and then by constructing two auxiliary equations and squeezing method, the spreading speed for the system with nonmonotone birth function is obtained.展开更多
Two types of carbides M23C6 and M7C3 precipitate orderly as carbon concentration in a high Cr-Ni austenitic steel increases during carburization process. The mathematical model that describes diffusion of carbon and t...Two types of carbides M23C6 and M7C3 precipitate orderly as carbon concentration in a high Cr-Ni austenitic steel increases during carburization process. The mathematical model that describes diffusion of carbon and the precipitation of M23C6 and M7C3 has been studied. A criterion to judge when the transformation of M23C6 to M7C3 is over and M7C3 precipitates directly has been given in simulated calculation. By applying the model, the carburization of HK40 steel has been calculated by means of finite difference computation techniques. The pack carburization tests for the HK40 steel have been carried out at 1273 K. The comparison between the experimental and the calculated results show acceptable agreement.展开更多
A class of nonlinear two-species competitive singularly perturbed initial-boundary-value problems for reaction-diffusion systems are studied. Under suitable assumptions, by using the stretched variable, the formal asy...A class of nonlinear two-species competitive singularly perturbed initial-boundary-value problems for reaction-diffusion systems are studied. Under suitable assumptions, by using the stretched variable, the formal asymptotic expansion for the problems is constructed. The uniform validity of the solution for initial-boundary-value problems is obtained by using the theory of differential inequalities.展开更多
The stochastic cracking and healing behaviors of reaction-diffusion growth of thin filmswere studied by means of Markov processes analysis. We chose the thermal growth ofoxide scales on metals as an example of reactio...The stochastic cracking and healing behaviors of reaction-diffusion growth of thin filmswere studied by means of Markov processes analysis. We chose the thermal growth ofoxide scales on metals as an example of reaction-diffusion growth. The thermal growthof oxide films follows power law when no cracking occurs. Our results showed that thegrowth kinetics under stochastic cracking and healing conditions was different fromthat without cracking. It might be altered to either pseudo-linear or pseudo-power lawsdependent upon the intensity and frequency of the cracking of the films. When thehoping items dominated, the growth followed pseudo-linear law; when the diffusionalitems dominated, it followed pseudo-power law with the exponentials lower than theintrinsical values. The numerical results were in good agreement with the meassuredkinetics of isothermal and cyclic oxidation of NiAl-0.1 Y (at. %) alloys in air at 1273K.展开更多
The generialized Kuramoto Sivashinski equation and Fisher equation in chemical reaction diffusion was studied in this paper. By introducing a new method, the anthors obtained the exact traveling wave solution for th...The generialized Kuramoto Sivashinski equation and Fisher equation in chemical reaction diffusion was studied in this paper. By introducing a new method, the anthors obtained the exact traveling wave solution for the two types of reaction diffusion equations.展开更多
Microstructures in the liver are primarily composed of hepatocytes, hepatic blood, and biliary vessels. Because each hepatocyte comes in contact with both vessels, these vessels form three-dimensional (3D) periodic ne...Microstructures in the liver are primarily composed of hepatocytes, hepatic blood, and biliary vessels. Because each hepatocyte comes in contact with both vessels, these vessels form three-dimensional (3D) periodic network patterns. Confocal microscope images are useful for observing 3D structures;however, it is necessary to explicitly describe the vessel structures using 3D images of sinusoidal endothelial cells. For this purpose, we propose a new approach for image segmentation based on the Turing reaction-diffusion model, in which temporal and spatial patterns are self-organized. Turing conditions provided reliable tools for describing the 3D structures. Moreover, using the proposed method, the sinusoidal patterns of rats fed a high-fat/high-cholesterol diet were examined;these rats exhibited pathological features similar to those of human patients with nonalcoholic steatohepatitis related to metabolic syndrome. The findings showed that the parameter in diffusion terms differed significantly among the experimental groups. This observation provided a heuristic argument for parameter selection leading to pattern recognition problems in diseased rats.展开更多
A PPh_(3)-catalyzed ring-opening addition reaction of cyclopropenones with alkyl bromides has been successfully established.This reaction offers a concise and practical approach for the assembly ofα,β-disubstituted ...A PPh_(3)-catalyzed ring-opening addition reaction of cyclopropenones with alkyl bromides has been successfully established.This reaction offers a concise and practical approach for the assembly ofα,β-disubstituted acrylates with exclusive E-stereoselectivity at room temperature.Mechanistic investigations indicated that both the hydrogen atom on vinyl group and one oxygen atom on ester group ofα,β-disubstituted acrylates derive from H2O in dimethyl sulfoxide(DMSO).Furthermore,a gram-scale experiment and late-stage modification of the products were accomplished,thereby expanding the application potential of this methodology in organic synthesis.展开更多
The poor electrical conductivity of metal-organic frameworks(MOFs)limits their electrocatalytic performance in the oxygen evolution reaction(OER).In this study,a Py@Co-MOF composite material based on pyrene(Py)molecul...The poor electrical conductivity of metal-organic frameworks(MOFs)limits their electrocatalytic performance in the oxygen evolution reaction(OER).In this study,a Py@Co-MOF composite material based on pyrene(Py)molecules and{[Co2(BINDI)(DMA)_(2)]·DMA}_(n)(Co-MOF,H4BINDI=N,N'-bis(5-isophthalic acid)naphthalenediimide,DMA=N,N-dimethylacetamide)was synthesized via a one-pot method,leveragingπ-πinteractions between pyrene and Co-MOF to modulate electrical conductivity.Results demonstrate that the Py@Co-MOF catalyst exhibited significantly enhanced OER performance compared to pure Co-MOF or pyrene-based electrodes,achieving an overpotential of 246 mV at a current density of 10 mA·cm^(-2) along with excellent stability.Density functional theory(DFT)calculations reveal that the formation of O*in the second step is the rate-determining step(RDS)during the OER process on Co-MOF,with an energy barrier of 0.85 eV due to the weak adsorption affinity of the OH*intermediate for Co sites.CCDC:2419276.展开更多
The coupling of the sun's gravitational field with processes of diffusion and convection exerts a significant influence on the dynamical behavior of the core 3He nuclear reaction-diffusion system. Stability analys...The coupling of the sun's gravitational field with processes of diffusion and convection exerts a significant influence on the dynamical behavior of the core 3He nuclear reaction-diffusion system. Stability analyses of the system are made in this paper by using the theory of nonequilibrium dynamics. It is showed that, in the nuclear reaction regions extending from the center to about 0.38 times of the radius of the sun, the gravitational field enables the core 3He nuclear reaction-diffusion system to become unstable and, after the instability, new states to appear in the system have characteristic of time oscillation. This may change the production rates of both 7Be and 8B neutrinos.展开更多
Carbenes as one of the most important class of intermediates have been widely utilized in various organic synthetic transformations.Carbene insertion-initiated ring-opening reactions of cyclic ethers offer a valuable ...Carbenes as one of the most important class of intermediates have been widely utilized in various organic synthetic transformations.Carbene insertion-initiated ring-opening reactions of cyclic ethers offer a valuable strategy for constructing new carbon-oxygen bonds.In comparison with traditional thermal or metal-mediated carbene transfer reactions,visible-light-promoted multi-component reaction strategy provides a mild and eco-friendly approach to access densely functionalized molecules.Recently,visible-light-induced multi-component carbene transfer reactions of diazo compounds have been rapidly developed and attracted a great deal of research interest of chemists owing to their advantages of simple operation,mild condition,high atom economy and rich structural diversity.This paper summarizes the recent research progress on the visible-light-promoted multi-component carbene transfer reactions of diazo compounds via ring-opening of cyclic ethers with various nucleophiles.The reaction patterns of different nucleophiles and their corresponding mechanism are described in this review.The future research direction and challenges in this area are also discussed.展开更多
Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region....Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region. A non-equidistant finite difference method is presented according to the property of boundary layer. The region is divided into an inner boundary layer region and an outer boundary layer region according to transition point of Shishkin. The steps sizes are equidistant in the outer boundary layer region. The step sizes are gradually increased in the inner boundary layer region such that half of the step sizes are different from each other. Truncation error is estimated. The proposed method is stable and uniformly convergent with the order higher than 2. Numerical results are given, which are in agreement with the theoretical result.展开更多
Transition metal-catalyzed C—C coupling reactions are a core strategy for the construction of carbon-carbon bonds in organic synthesis.Their development has not only promoted the synthesis of drugs,materials,and natu...Transition metal-catalyzed C—C coupling reactions are a core strategy for the construction of carbon-carbon bonds in organic synthesis.Their development has not only promoted the synthesis of drugs,materials,and natural products,but also promoted the development of new synthetic methods,and has also made breakthroughs in mechanism innovation and catalyst design.On this basis,a copper-catalyzed radical reaction between ketones is reported,enabling the synthesis of 2-carbonyl-1,4-diones.The method exhibits excellent applicability to multiple structural types of ketones,including aliphatic ketones with diverse substituents,aromatic ketones,and various simple ketones not limited to acetone,with wide applications,easy implementation,low catalyst toxicity,and low cost,cost-effective,and the product is easy to separate and purify.展开更多
Against the backdrop of escalating global climate change and energy crises,the resource utilization of carbon dioxide(CO_(2)),a major greenhouse gas,has become a crucial pathway for achieving carbon peaking and carbon...Against the backdrop of escalating global climate change and energy crises,the resource utilization of carbon dioxide(CO_(2)),a major greenhouse gas,has become a crucial pathway for achieving carbon peaking and carbon neutrality goals.The hydrogenation of CO_(2)to methanol not only enables carbon sequestration and recycling,but also provides a route to produce high value-added fuels and basic chemical feedstocks,holding significant environmental and economic potential.However,this conversion process is thermodynamically and kinetically limited,and traditional catalyst systems(e.g.,Cu/ZnO/Al_(2)O_(3))exhibit inadequate activity,selectivity,and stability under mild conditions.Therefore,the development of novel high-performance catalysts with precisely tunable structures and functionalities is imperative.Metal-organic frameworks(MOFs),as crystalline porous materials with high surface area,tunable pore structures,and diverse metal-ligand compositions,have the great potential in CO_(2)hydrogenation catalysis.Their structural design flexibility allows for the construction of well-dispersed active sites,tailored electronic environments,and enhanced metal-support interactions.This review systematically summarizes the recent advances in MOF-based and MOF-derived catalysts for CO_(2)hydrogenation to methanol,focusing on four design strategies:(1)spatial confinement and in situ construction,(2)defect engineering and ion-exchange,(3)bimetallic synergy and hybrid structure design,and(4)MOF-derived nanomaterial synthesis.These approaches significantly improve CO_(2)conversion and methanol selectivity by optimizing metal dispersion,interfacial structures,and reaction pathways.The reaction mechanism is further explored by focusing on the three main reaction pathways:the formate pathway(HCOO*),the RWGS(Reverse Water Gas Shift reaction)+CO*hydrogenation pathway,and the trans-COOH pathway.In situ spectroscopic studies and density functional theory(DFT)calculations elucidate the formation and transformation of key intermediates,as well as the roles of active sites,metal-support interfaces,oxygen vacancies,and promoters.Additionally,representative catalytic performance data for MOFbased systems are compiled and compared,demonstrating their advantages over traditional catalysts in terms of CO_(2)conversion,methanol selectivity,and space-time yield.Future perspectives for MOF-based CO_(2)hydrogenation catalysts will prioritize two main directions:structural design and mechanistic understanding.The precise construction of active sites through multi-metallic synergy,defect engineering,and interfacial electronic modulation should be made to enhance catalyst selectivity and stability.In addition,advanced in situ characterization techniques combined with theoretical modeling are essential to unravel the detailed reaction mechanisms and intermediate behaviors,thereby guiding rational catalyst design.Moreover,to enable industrial application,challenges related to thermal/hydrothermal stability,catalyst recyclability,and cost-effective large-scale synthesis must be addressed.The development of green,scalable preparation methods and the integration of MOF catalysts into practical reaction systems(e.g.,flow reactors)will be crucial for bridging the gap between laboratory research and commercial deployment.Ultimately,multi-scale structure-performance optimization and catalytic system integration will be vital for accelerating the industrialization of MOF-based CO_(2)-to-methanol technologies.展开更多
This paper deals with an initial boundary value problem for the strongly coupledreaction-diffusion systems with a full matrix of diffusion coefficients. The global existence ofsolutions is proved by using the techniqu...This paper deals with an initial boundary value problem for the strongly coupledreaction-diffusion systems with a full matrix of diffusion coefficients. The global existence ofsolutions is proved by using the techniques based on invariant regions, Lyapunov functionalmethods, and local Lp prior estimates independent of time.展开更多
The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved i...The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved in L2(Rn )× L2(Rn ) .展开更多
Silica nanoparticles-stabilized cobalt and nitrogen-doped carbon materials were synthesized through pyrolysis of metal-organic-framework of ZIF-67 supported by silica nanoparticles.The experimental results reveal that...Silica nanoparticles-stabilized cobalt and nitrogen-doped carbon materials were synthesized through pyrolysis of metal-organic-framework of ZIF-67 supported by silica nanoparticles.The experimental results reveal that the introduction of the silica nanoparticles can stabilize the microstructure of the derived CoN-C materials,which in turn exhibits the promising electrocatalytic activity towards both oxygen reduction and oxygen evolution reactions.The optimized sample exhibits a better oxygen reduction activity than commercial Pt/C catalyst as confirmed by the positive shift of half-wave potential by 20 mV while it has a low overpotential of 273 mV for oxygen evolution reactions with the retained performance over 80%after 25,000 s of continuous operation.It is demonstrated that the introduction of support frame might be an effective way to improve the activity and stability of metal-organic-framework derived electrocatalyst with stabilized microstructure.展开更多
基金This work is supporred the National Natural Science Foundation of China.
文摘We consider the following simplified model for the Belousov-Zhabotinskii(B-Z) reaction:?u/?t=u(1-u-rv)+d?~2u/?x^2,?v/?t=-suv+?~2v/?x^2,where r and s are positive parameters, and d is the diffusing constant for the concen-tration u. Seeking travelling wave front solution and making an ansatz for the solution,we obtain a nonlinear system of algebraic equations. The system is solved using WuElimination and then we are able to find several exact solutions which are of interest.
文摘In this paper, the magneto hydrodynamic (MHD) flow of viscous fluid in a channel with non-parallel plates is studied. The governing partial differential equation was transformed into a system of dimensionless non-similar coupled ordinary differential equation. The transformed conservations equations were solved by using new algorithm. Basically, this new algorithm depends mainly on the Taylor expansion application with the coefficients of power series resulting from integrating the order differential equation. Results obtained from new algorithm are compared with the results of numerical Range-Kutta fourth-order algorithm with help of the shooting algorithm. The comparison revealed that the resulting solutions were excellent agreement. Thermo-diffusion and diffusion-thermo effects were investigated to analyze the behavior of temperature and concentration profile. Also the influences of the first order chemical reaction and the rate of mass and heat transfer were studied. The computed analytical solution result for the velocity, temperature and concentration distribution with the effect of various important dimensionless parameters was analyzed and discussed graphically.
基金Supported by the NSF of China(11171120)Supported by the Doctoral Program of Higher Education of China(20094407110001)Supported by the NSF of Guangdong Province(10151063101000003)
文摘A reaction-diffusion model for a single species with age structure and nonlocal reaction for periodic time t is derived. Some results about the model with monotone birth function are firstly introduced, and then by constructing two auxiliary equations and squeezing method, the spreading speed for the system with nonmonotone birth function is obtained.
基金This work was supported by the National Natural Science Foundation of China under grant No.50071016.
文摘Two types of carbides M23C6 and M7C3 precipitate orderly as carbon concentration in a high Cr-Ni austenitic steel increases during carburization process. The mathematical model that describes diffusion of carbon and the precipitation of M23C6 and M7C3 has been studied. A criterion to judge when the transformation of M23C6 to M7C3 is over and M7C3 precipitates directly has been given in simulated calculation. By applying the model, the carburization of HK40 steel has been calculated by means of finite difference computation techniques. The pack carburization tests for the HK40 steel have been carried out at 1273 K. The comparison between the experimental and the calculated results show acceptable agreement.
文摘A class of nonlinear two-species competitive singularly perturbed initial-boundary-value problems for reaction-diffusion systems are studied. Under suitable assumptions, by using the stretched variable, the formal asymptotic expansion for the problems is constructed. The uniform validity of the solution for initial-boundary-value problems is obtained by using the theory of differential inequalities.
基金supported by Hundred-Talent Project of Chinese Academy of Sciencesby the National Natural Science Foundation of China for Young Scientist
文摘The stochastic cracking and healing behaviors of reaction-diffusion growth of thin filmswere studied by means of Markov processes analysis. We chose the thermal growth ofoxide scales on metals as an example of reaction-diffusion growth. The thermal growthof oxide films follows power law when no cracking occurs. Our results showed that thegrowth kinetics under stochastic cracking and healing conditions was different fromthat without cracking. It might be altered to either pseudo-linear or pseudo-power lawsdependent upon the intensity and frequency of the cracking of the films. When thehoping items dominated, the growth followed pseudo-linear law; when the diffusionalitems dominated, it followed pseudo-power law with the exponentials lower than theintrinsical values. The numerical results were in good agreement with the meassuredkinetics of isothermal and cyclic oxidation of NiAl-0.1 Y (at. %) alloys in air at 1273K.
文摘The generialized Kuramoto Sivashinski equation and Fisher equation in chemical reaction diffusion was studied in this paper. By introducing a new method, the anthors obtained the exact traveling wave solution for the two types of reaction diffusion equations.
文摘Microstructures in the liver are primarily composed of hepatocytes, hepatic blood, and biliary vessels. Because each hepatocyte comes in contact with both vessels, these vessels form three-dimensional (3D) periodic network patterns. Confocal microscope images are useful for observing 3D structures;however, it is necessary to explicitly describe the vessel structures using 3D images of sinusoidal endothelial cells. For this purpose, we propose a new approach for image segmentation based on the Turing reaction-diffusion model, in which temporal and spatial patterns are self-organized. Turing conditions provided reliable tools for describing the 3D structures. Moreover, using the proposed method, the sinusoidal patterns of rats fed a high-fat/high-cholesterol diet were examined;these rats exhibited pathological features similar to those of human patients with nonalcoholic steatohepatitis related to metabolic syndrome. The findings showed that the parameter in diffusion terms differed significantly among the experimental groups. This observation provided a heuristic argument for parameter selection leading to pattern recognition problems in diseased rats.
文摘A PPh_(3)-catalyzed ring-opening addition reaction of cyclopropenones with alkyl bromides has been successfully established.This reaction offers a concise and practical approach for the assembly ofα,β-disubstituted acrylates with exclusive E-stereoselectivity at room temperature.Mechanistic investigations indicated that both the hydrogen atom on vinyl group and one oxygen atom on ester group ofα,β-disubstituted acrylates derive from H2O in dimethyl sulfoxide(DMSO).Furthermore,a gram-scale experiment and late-stage modification of the products were accomplished,thereby expanding the application potential of this methodology in organic synthesis.
文摘The poor electrical conductivity of metal-organic frameworks(MOFs)limits their electrocatalytic performance in the oxygen evolution reaction(OER).In this study,a Py@Co-MOF composite material based on pyrene(Py)molecules and{[Co2(BINDI)(DMA)_(2)]·DMA}_(n)(Co-MOF,H4BINDI=N,N'-bis(5-isophthalic acid)naphthalenediimide,DMA=N,N-dimethylacetamide)was synthesized via a one-pot method,leveragingπ-πinteractions between pyrene and Co-MOF to modulate electrical conductivity.Results demonstrate that the Py@Co-MOF catalyst exhibited significantly enhanced OER performance compared to pure Co-MOF or pyrene-based electrodes,achieving an overpotential of 246 mV at a current density of 10 mA·cm^(-2) along with excellent stability.Density functional theory(DFT)calculations reveal that the formation of O*in the second step is the rate-determining step(RDS)during the OER process on Co-MOF,with an energy barrier of 0.85 eV due to the weak adsorption affinity of the OH*intermediate for Co sites.CCDC:2419276.
文摘The coupling of the sun's gravitational field with processes of diffusion and convection exerts a significant influence on the dynamical behavior of the core 3He nuclear reaction-diffusion system. Stability analyses of the system are made in this paper by using the theory of nonequilibrium dynamics. It is showed that, in the nuclear reaction regions extending from the center to about 0.38 times of the radius of the sun, the gravitational field enables the core 3He nuclear reaction-diffusion system to become unstable and, after the instability, new states to appear in the system have characteristic of time oscillation. This may change the production rates of both 7Be and 8B neutrinos.
基金Science and Technology Foundation of Guizhou Province(No.QKHJC-ZK[2024]654)Guizhou Provincial University Key Laboratory of Advanced Functional Electronic Materials(No.QJJ[2023]021).
文摘Carbenes as one of the most important class of intermediates have been widely utilized in various organic synthetic transformations.Carbene insertion-initiated ring-opening reactions of cyclic ethers offer a valuable strategy for constructing new carbon-oxygen bonds.In comparison with traditional thermal or metal-mediated carbene transfer reactions,visible-light-promoted multi-component reaction strategy provides a mild and eco-friendly approach to access densely functionalized molecules.Recently,visible-light-induced multi-component carbene transfer reactions of diazo compounds have been rapidly developed and attracted a great deal of research interest of chemists owing to their advantages of simple operation,mild condition,high atom economy and rich structural diversity.This paper summarizes the recent research progress on the visible-light-promoted multi-component carbene transfer reactions of diazo compounds via ring-opening of cyclic ethers with various nucleophiles.The reaction patterns of different nucleophiles and their corresponding mechanism are described in this review.The future research direction and challenges in this area are also discussed.
基金supported by the Educational Department Foundation of Fujian Province of China(Nos. JA08140 and A0610025)the Scientific Research Foundation of Zhejiang University of Scienceand Technology (No. 2008050)the National Natural Science Foundation of China (No. 50679074)
文摘Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region. A non-equidistant finite difference method is presented according to the property of boundary layer. The region is divided into an inner boundary layer region and an outer boundary layer region according to transition point of Shishkin. The steps sizes are equidistant in the outer boundary layer region. The step sizes are gradually increased in the inner boundary layer region such that half of the step sizes are different from each other. Truncation error is estimated. The proposed method is stable and uniformly convergent with the order higher than 2. Numerical results are given, which are in agreement with the theoretical result.
基金Project supported by the Basic Research Support Program for Outstanding Young Teachers in Provincial Undergraduate Colleges and Universities in Heilongjiang Province(No.YQJH2024096)the Heilongjiang Province Natural Joint Guidance Cultivation Project(No.PL2024H198)。
文摘Transition metal-catalyzed C—C coupling reactions are a core strategy for the construction of carbon-carbon bonds in organic synthesis.Their development has not only promoted the synthesis of drugs,materials,and natural products,but also promoted the development of new synthetic methods,and has also made breakthroughs in mechanism innovation and catalyst design.On this basis,a copper-catalyzed radical reaction between ketones is reported,enabling the synthesis of 2-carbonyl-1,4-diones.The method exhibits excellent applicability to multiple structural types of ketones,including aliphatic ketones with diverse substituents,aromatic ketones,and various simple ketones not limited to acetone,with wide applications,easy implementation,low catalyst toxicity,and low cost,cost-effective,and the product is easy to separate and purify.
基金Supported by the National Key Research and Development Program of China(2023YFB4104500,2023YFB4104502)the National Natural Science Foundation of China(22138013)the Taishan Scholar Project(ts201712020).
文摘Against the backdrop of escalating global climate change and energy crises,the resource utilization of carbon dioxide(CO_(2)),a major greenhouse gas,has become a crucial pathway for achieving carbon peaking and carbon neutrality goals.The hydrogenation of CO_(2)to methanol not only enables carbon sequestration and recycling,but also provides a route to produce high value-added fuels and basic chemical feedstocks,holding significant environmental and economic potential.However,this conversion process is thermodynamically and kinetically limited,and traditional catalyst systems(e.g.,Cu/ZnO/Al_(2)O_(3))exhibit inadequate activity,selectivity,and stability under mild conditions.Therefore,the development of novel high-performance catalysts with precisely tunable structures and functionalities is imperative.Metal-organic frameworks(MOFs),as crystalline porous materials with high surface area,tunable pore structures,and diverse metal-ligand compositions,have the great potential in CO_(2)hydrogenation catalysis.Their structural design flexibility allows for the construction of well-dispersed active sites,tailored electronic environments,and enhanced metal-support interactions.This review systematically summarizes the recent advances in MOF-based and MOF-derived catalysts for CO_(2)hydrogenation to methanol,focusing on four design strategies:(1)spatial confinement and in situ construction,(2)defect engineering and ion-exchange,(3)bimetallic synergy and hybrid structure design,and(4)MOF-derived nanomaterial synthesis.These approaches significantly improve CO_(2)conversion and methanol selectivity by optimizing metal dispersion,interfacial structures,and reaction pathways.The reaction mechanism is further explored by focusing on the three main reaction pathways:the formate pathway(HCOO*),the RWGS(Reverse Water Gas Shift reaction)+CO*hydrogenation pathway,and the trans-COOH pathway.In situ spectroscopic studies and density functional theory(DFT)calculations elucidate the formation and transformation of key intermediates,as well as the roles of active sites,metal-support interfaces,oxygen vacancies,and promoters.Additionally,representative catalytic performance data for MOFbased systems are compiled and compared,demonstrating their advantages over traditional catalysts in terms of CO_(2)conversion,methanol selectivity,and space-time yield.Future perspectives for MOF-based CO_(2)hydrogenation catalysts will prioritize two main directions:structural design and mechanistic understanding.The precise construction of active sites through multi-metallic synergy,defect engineering,and interfacial electronic modulation should be made to enhance catalyst selectivity and stability.In addition,advanced in situ characterization techniques combined with theoretical modeling are essential to unravel the detailed reaction mechanisms and intermediate behaviors,thereby guiding rational catalyst design.Moreover,to enable industrial application,challenges related to thermal/hydrothermal stability,catalyst recyclability,and cost-effective large-scale synthesis must be addressed.The development of green,scalable preparation methods and the integration of MOF catalysts into practical reaction systems(e.g.,flow reactors)will be crucial for bridging the gap between laboratory research and commercial deployment.Ultimately,multi-scale structure-performance optimization and catalytic system integration will be vital for accelerating the industrialization of MOF-based CO_(2)-to-methanol technologies.
基金Supported by the Henan Innovation Project for University Prominent Research Talents (2003KJCX008)
文摘This paper deals with an initial boundary value problem for the strongly coupledreaction-diffusion systems with a full matrix of diffusion coefficients. The global existence ofsolutions is proved by using the techniques based on invariant regions, Lyapunov functionalmethods, and local Lp prior estimates independent of time.
文摘The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved in L2(Rn )× L2(Rn ) .
基金Funded by the National Natural Science Foundation of China Guangdong(No.22279096)。
文摘Silica nanoparticles-stabilized cobalt and nitrogen-doped carbon materials were synthesized through pyrolysis of metal-organic-framework of ZIF-67 supported by silica nanoparticles.The experimental results reveal that the introduction of the silica nanoparticles can stabilize the microstructure of the derived CoN-C materials,which in turn exhibits the promising electrocatalytic activity towards both oxygen reduction and oxygen evolution reactions.The optimized sample exhibits a better oxygen reduction activity than commercial Pt/C catalyst as confirmed by the positive shift of half-wave potential by 20 mV while it has a low overpotential of 273 mV for oxygen evolution reactions with the retained performance over 80%after 25,000 s of continuous operation.It is demonstrated that the introduction of support frame might be an effective way to improve the activity and stability of metal-organic-framework derived electrocatalyst with stabilized microstructure.
