This is a survey of local and global classification results concerning Dupin hypersurfaces in S^(n)(or R^(n))that have been obtained in the context of Lie sphere geometry.The emphasis is on results that relate Dupin h...This is a survey of local and global classification results concerning Dupin hypersurfaces in S^(n)(or R^(n))that have been obtained in the context of Lie sphere geometry.The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres.Along with these classification results,many important concepts from Lie sphere geometry,such as curvature spheres,Lie curvatures,and Legendre lifts of submanifolds of S^(n)(or R^(n)),are described in detail.The paper also contains several important constructions of Dupin hypersurfaces with certain special properties.展开更多
Collisions between objects are a relatively common phenomenon in nature.Analyses of collision processes can greatly contribute to solving problems such as impact-rub faults and particle impacts.The coefficient of rest...Collisions between objects are a relatively common phenomenon in nature.Analyses of collision processes can greatly contribute to solving problems such as impact-rub faults and particle impacts.The coefficient of restitution is a critical parameter in the analysis of collision processes.Many experiments have shown that the coefficient of restitution is closely related to the plate thickness,and the smaller the plate thickness,the more inaccurate the coefficient of restitution predicted by the existing model,which seriously affects the process of collision analysis.To remedy this shortcoming,this paper proposes a plate thickness influence factor with the ratio of sphere diameter to plate thickness as the variable.The plate thickness influence factor can optimize the coefficient of restitution model to effectively predict the coefficient of restitution of impacting elastoplastic spheres with finite plate thickness.Finally,the validity of the new model is verified using a large amount of experimental data.展开更多
Sodium-sulfur(Na-S)and potassium-sulfur(K-S)batteries for use at room temperature have received widespread attention because of the abundance and low cost of their raw materials and their high energy density.However,t...Sodium-sulfur(Na-S)and potassium-sulfur(K-S)batteries for use at room temperature have received widespread attention because of the abundance and low cost of their raw materials and their high energy density.However,their development is restricted by the shuttling of polysulfides,large volume expansion and poor conductivity.To overcome these obstacles,an effective approach is to use carbon-based materials with abundant space for the sulfur that has sulfiphilic sites to immobilize it,and a high electrical conductivity.Hollow carbon spheres(HCSs)with a controllable structure and composition are promising for this purpose.We consider recent progress in optimizing the electrochemical performance of Na-/K-S batteries by using these materials.First,the advantages of HCSs,their synthesis methods,and strategies for preparing HCSs/sulfur composite materials are reviewed.Second,the use of HCSs in Na-/K-S batteries,along with mechanisms underlying the resulting performance improvement,are discussed.Finally,prospects for the further development of HCSs for metal−S batteries are presented.展开更多
Incorporating a selenium(Se)positive electrode into aluminum(Al)-ion batteries is an effective strategy for improving the overall battery performance.However,the cycling stability of Se positive electrodes has challen...Incorporating a selenium(Se)positive electrode into aluminum(Al)-ion batteries is an effective strategy for improving the overall battery performance.However,the cycling stability of Se positive electrodes has challenges due to the dissolution of intermediate reaction products.In this work,we aim to harness the advantages of Se while reducing its limitations by preparing a core-shell mesoporous carbon hollow sphere with a titanium nitride(C@TiN)host to load 63.9wt%Se as the positive electrode material for Al-Se batteries.Using the physical and chemical confinement offered by the hollow mesoporous carbon and TiN,the obtained core-shell mesoporous carbon hollow spheres coated with Se(Se@C@TiN)display superior utilization of the active material and remarkable cycling stability.As a result,Al-Se batteries equipped with the as-prepared Se@C@TiN composite positive electrodes show an initial discharge specific capacity of 377 mAh·g^(-1)at a current density of 1000 mA·g^(-1)while maintaining a discharge specific capacity of 86.0 mAh·g^(-1)over 200 cycles.This improved cycling performance is ascribed to the high electrical conductivity of the core-shell mesoporous carbon hollow spheres and the unique three-dimensional hierarchical architecture of Se@C@TiN.展开更多
Electrochemical CO_(2) reduction to produce value-added chemicals and fuels is one of the research hotspots in the field of energy conversion.The development of efficient catalysts with high conductivity and readily a...Electrochemical CO_(2) reduction to produce value-added chemicals and fuels is one of the research hotspots in the field of energy conversion.The development of efficient catalysts with high conductivity and readily accessible active sites for CO_(2) electroreduction remains challenging yet indispensable.In this work,a reliable poly(ethyleneimine)(PEI)-assisted strategy is developed to prepare a hollow carbon nanocomposite comprising a single-site Ni-modified carbon shell and confined Ni nanoparticles(NPs)(denoted as Ni@NHCS),where PEI not only functions as a mediator to induce the highly dispersed growth of Ni NPs within hollow carbon spheres,but also as a nitrogen precursor to construct highly active atomically-dispersed Ni-Nx sites.Benefiting from the unique structural properties of Ni@NHCS,the aggregation and exposure of Ni NPs can be effectively prevented,while the accessibility of abundant catalytically active Ni-Nx sites can be ensured.As a result,Ni@NHCS exhibits a high CO partial current density of 26.9 mA cm^(-2) and a Faradaic efficiency of 93.0% at-1.0 V vs.RHE,outperforming those of its PEI-free analog.Apart from the excellent activity and selectivity,the shell confinement effect of the hollow carbon sphere endows this catalyst with long-term stability.The findings here are anticipated to help understand the structure-activity relationship in Ni-based carbon catalyst systems for electrocatalytic CO_(2) reduction.Furthermore,the PEI-assisted synthetic concept is potentially applicable to the preparation of high-performance metal-based nanoconfined materials tailored for diverse energy conversion applications and beyond.展开更多
Lithium-sulfur(Li-S)batteries are one of the most promising energy storage and conversion devices due to the high theoretical capacity and cost-effectiveness of sulfur.However,they still suffer from sluggish redox kin...Lithium-sulfur(Li-S)batteries are one of the most promising energy storage and conversion devices due to the high theoretical capacity and cost-effectiveness of sulfur.However,they still suffer from sluggish redox kinetics and the shuttle effect caused by complex polysulfides.In this work,graphitic carbon nitride(g-C_(3)N_(4))is utilized as a template and further hydrothermally treated with an Mn source and glucose.The pyrolysis of g-C_(3)N_(4)gives rise to N-doped carbon nanotubes,producing abundant sites for physical confinement and chemical adsorption of polysulfides,while glucose carbonization brings forth amorphous carbon and Mn source produces metal spheres.Afterward,polydopamine(PDA)induces N-doped carbon coating and promotes interface connection as well as electron immigration.This synergistic design possesses a high surface area of micropores and mesopores to aggregate sulfur and accelerate redox kinetics.As a result,the N-doped carbon nanotube with Mn spheres and PDA coating@sulfur(CN/Mn-PDA@S)exhibits a high reversible capacity of 813.5 mAh g^(-1)at 1 C with a decay rate of 0.064%per cycle and remarkable capacity retention at 2 C with rate performance up to 4 C.Therefore,the novel design of N-doped carbon nanotubes with Mn spheres and PDA coating serves as an efficient polysulfide immobilizer for Li-S batteries.展开更多
The paper is devoted to a spherically symmetric problem of General Relativity (GR) for a fluid sphere. The problem is solved within the framework of a special geometry of the Riemannian space induced by gravitation. A...The paper is devoted to a spherically symmetric problem of General Relativity (GR) for a fluid sphere. The problem is solved within the framework of a special geometry of the Riemannian space induced by gravitation. According to this geometry, the four-dimensional Riemannian space is assumed to be Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate. Such interpretation of the Riemannian space allows us to obtain complete set of GR equations for the external empty space and the internal spaces for incompressible and compressible perfect fluids. The obtained analytical solution for an incompressible fluid is compared with the Schwarzchild solution. For a sphere consisting of compressible fluid or gas, a numerical solution is presented and discussed.展开更多
We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We ...We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We provide the mathematical definitions of Hamiltonians and obtain new results for both models, in particular the resolvents equations, spectral properties and some scattering quantities.展开更多
Different-sized hollow SiO2 spheres of 249–1348 nm in diameter were successfully prepared by using Na2SiO3 as the precursor and using polystyrene and polystyrene-methyl acrylic acid latexes as the templates. The diam...Different-sized hollow SiO2 spheres of 249–1348 nm in diameter were successfully prepared by using Na2SiO3 as the precursor and using polystyrene and polystyrene-methyl acrylic acid latexes as the templates. The diameter and shell thickness of the hollow SiO2 spheres increase with increasing the latex template diameter at a given mass ratio of SiO2 to latex template. The diameter and shell thickness of the hollow SiO2 spheres also increase with increasing the mass ratios of SiO2 to latex template. The presence of carboxylic acid groups on the surfaces of polystyrene-methyl acrylic acid latex templates favors the formation of dense and uniform SiO2 shells. The hollow SiO2 sphere is constructed by mesoporous shell with large specific surface area. When glyphosate is used as a release model chemical, glyphosate release rate is tuned by varying the shell thickness.展开更多
To obtain a kind of convenient oral dosage form of protein, which can be fully absorbed and is efficient and safe, the thymosin-loaded PLA（polylactic acid） microspheres are prepared by the emulsification- solvent ev...To obtain a kind of convenient oral dosage form of protein, which can be fully absorbed and is efficient and safe, the thymosin-loaded PLA（polylactic acid） microspheres are prepared by the emulsification- solvent evaporation method and the orthogonal design is used to optimize the technology of preparation. The form of the medicament microspheres of thymosin are proved by differential thermal analysis （DTA）. The drug content is determined by the Lowry method, and the package ratio of medicament microspheres of thymosin and drug release in vitro are calculated. The results show that the average diameter and encapsulation efficiency of the product prepared according to the optimized formulation are 13. 8 μm and 80. 7%, respectively. The in vitro release behavior within 12 h can be described by the Higuchi equation with T1/2 = 295 rain. There are no significant changes in size distribution and residual drug contents after being stored at 25℃ and 40 ℃ for 90 d, respectively. Due to the fact that its thymosin content and package ratio meet the requirement, and its releasing half life is long, the thymosin-loaded PLA microsohere has a favorable application future.展开更多
Monoclinic BiVO4 hollow nanospheres were successfully prepared via template-free method using citric acid （C6H8O7） as chelating agent and characterized by X-ray diffraction patterns, transmission electron microscope...Monoclinic BiVO4 hollow nanospheres were successfully prepared via template-free method using citric acid （C6H8O7） as chelating agent and characterized by X-ray diffraction patterns, transmission electron microscope, UV-Vis DRS, and TG-DTA technique. C6H8O7 played an important role in the formation of hollow spheres. Morphology observations revealed that when appropriate amount of C6H8O7 was introduced, the cavity with the diameter of 40 nm was obtained in BiVO4 nanospheres. UV-Vis diffuse reflectance spectra indicated that the samples had absorption in both UV and visible light region. The photocatalytic activities were evaluated by the degradation of methylene blue under Xe lamp irradiation. Hollow spheres endow BiVO4 samples with greatly improved photocatalytic activity. A possible formation mechanism of hollow spheres was proposed.展开更多
Let A={A_1, A_2,…, A_(n+1)} be a simplex in E^n which its center O of circumscribed sphere is in inside of A. If R and R_i are radiuses of A_i respectively (A_i={A_1, A_2,…, A_(i-1), O, A_(i+1),…,A_(n+1)} ,i=1,2,…...Let A={A_1, A_2,…, A_(n+1)} be a simplex in E^n which its center O of circumscribed sphere is in inside of A. If R and R_i are radiuses of A_i respectively (A_i={A_1, A_2,…, A_(i-1), O, A_(i+1),…,A_(n+1)} ,i=1,2,…,n+1),then we have The equality holds if and only if A is a regular simplex.展开更多
Guizhou Province is part of the glutinous rice cultivation sphere in our country.Its rice production and germplasm resources play an important role.The southeast region is the centre of the Guizhou glutinous rice cult...Guizhou Province is part of the glutinous rice cultivation sphere in our country.Its rice production and germplasm resources play an important role.The southeast region is the centre of the Guizhou glutinous rice cultivation and characterized by waxy wo,which is treasure of the original farming culture of southeast Guizhou region and an important symbol for ethnic cultural identity of the region.展开更多
文摘This is a survey of local and global classification results concerning Dupin hypersurfaces in S^(n)(or R^(n))that have been obtained in the context of Lie sphere geometry.The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres.Along with these classification results,many important concepts from Lie sphere geometry,such as curvature spheres,Lie curvatures,and Legendre lifts of submanifolds of S^(n)(or R^(n)),are described in detail.The paper also contains several important constructions of Dupin hypersurfaces with certain special properties.
基金Supported by Joint Fund of the Ministry of Education of China (Grant No.8091B022203)Youth Talent Support Project (Grant No.2022-JCJQ-QT-059)。
文摘Collisions between objects are a relatively common phenomenon in nature.Analyses of collision processes can greatly contribute to solving problems such as impact-rub faults and particle impacts.The coefficient of restitution is a critical parameter in the analysis of collision processes.Many experiments have shown that the coefficient of restitution is closely related to the plate thickness,and the smaller the plate thickness,the more inaccurate the coefficient of restitution predicted by the existing model,which seriously affects the process of collision analysis.To remedy this shortcoming,this paper proposes a plate thickness influence factor with the ratio of sphere diameter to plate thickness as the variable.The plate thickness influence factor can optimize the coefficient of restitution model to effectively predict the coefficient of restitution of impacting elastoplastic spheres with finite plate thickness.Finally,the validity of the new model is verified using a large amount of experimental data.
文摘Sodium-sulfur(Na-S)and potassium-sulfur(K-S)batteries for use at room temperature have received widespread attention because of the abundance and low cost of their raw materials and their high energy density.However,their development is restricted by the shuttling of polysulfides,large volume expansion and poor conductivity.To overcome these obstacles,an effective approach is to use carbon-based materials with abundant space for the sulfur that has sulfiphilic sites to immobilize it,and a high electrical conductivity.Hollow carbon spheres(HCSs)with a controllable structure and composition are promising for this purpose.We consider recent progress in optimizing the electrochemical performance of Na-/K-S batteries by using these materials.First,the advantages of HCSs,their synthesis methods,and strategies for preparing HCSs/sulfur composite materials are reviewed.Second,the use of HCSs in Na-/K-S batteries,along with mechanisms underlying the resulting performance improvement,are discussed.Finally,prospects for the further development of HCSs for metal−S batteries are presented.
基金supported by the National Natural Science Foundation of China(No.52374350)China Postdoctoral Science Foundation(Nos.2020M680347 and 2021T140051)the Fundamental Research Funds for the Central Universities(No.FRF-TP-20-045A1)。
文摘Incorporating a selenium(Se)positive electrode into aluminum(Al)-ion batteries is an effective strategy for improving the overall battery performance.However,the cycling stability of Se positive electrodes has challenges due to the dissolution of intermediate reaction products.In this work,we aim to harness the advantages of Se while reducing its limitations by preparing a core-shell mesoporous carbon hollow sphere with a titanium nitride(C@TiN)host to load 63.9wt%Se as the positive electrode material for Al-Se batteries.Using the physical and chemical confinement offered by the hollow mesoporous carbon and TiN,the obtained core-shell mesoporous carbon hollow spheres coated with Se(Se@C@TiN)display superior utilization of the active material and remarkable cycling stability.As a result,Al-Se batteries equipped with the as-prepared Se@C@TiN composite positive electrodes show an initial discharge specific capacity of 377 mAh·g^(-1)at a current density of 1000 mA·g^(-1)while maintaining a discharge specific capacity of 86.0 mAh·g^(-1)over 200 cycles.This improved cycling performance is ascribed to the high electrical conductivity of the core-shell mesoporous carbon hollow spheres and the unique three-dimensional hierarchical architecture of Se@C@TiN.
文摘Electrochemical CO_(2) reduction to produce value-added chemicals and fuels is one of the research hotspots in the field of energy conversion.The development of efficient catalysts with high conductivity and readily accessible active sites for CO_(2) electroreduction remains challenging yet indispensable.In this work,a reliable poly(ethyleneimine)(PEI)-assisted strategy is developed to prepare a hollow carbon nanocomposite comprising a single-site Ni-modified carbon shell and confined Ni nanoparticles(NPs)(denoted as Ni@NHCS),where PEI not only functions as a mediator to induce the highly dispersed growth of Ni NPs within hollow carbon spheres,but also as a nitrogen precursor to construct highly active atomically-dispersed Ni-Nx sites.Benefiting from the unique structural properties of Ni@NHCS,the aggregation and exposure of Ni NPs can be effectively prevented,while the accessibility of abundant catalytically active Ni-Nx sites can be ensured.As a result,Ni@NHCS exhibits a high CO partial current density of 26.9 mA cm^(-2) and a Faradaic efficiency of 93.0% at-1.0 V vs.RHE,outperforming those of its PEI-free analog.Apart from the excellent activity and selectivity,the shell confinement effect of the hollow carbon sphere endows this catalyst with long-term stability.The findings here are anticipated to help understand the structure-activity relationship in Ni-based carbon catalyst systems for electrocatalytic CO_(2) reduction.Furthermore,the PEI-assisted synthetic concept is potentially applicable to the preparation of high-performance metal-based nanoconfined materials tailored for diverse energy conversion applications and beyond.
基金support from the National Natural Science Foundation of China(No.22179109).
文摘Lithium-sulfur(Li-S)batteries are one of the most promising energy storage and conversion devices due to the high theoretical capacity and cost-effectiveness of sulfur.However,they still suffer from sluggish redox kinetics and the shuttle effect caused by complex polysulfides.In this work,graphitic carbon nitride(g-C_(3)N_(4))is utilized as a template and further hydrothermally treated with an Mn source and glucose.The pyrolysis of g-C_(3)N_(4)gives rise to N-doped carbon nanotubes,producing abundant sites for physical confinement and chemical adsorption of polysulfides,while glucose carbonization brings forth amorphous carbon and Mn source produces metal spheres.Afterward,polydopamine(PDA)induces N-doped carbon coating and promotes interface connection as well as electron immigration.This synergistic design possesses a high surface area of micropores and mesopores to aggregate sulfur and accelerate redox kinetics.As a result,the N-doped carbon nanotube with Mn spheres and PDA coating@sulfur(CN/Mn-PDA@S)exhibits a high reversible capacity of 813.5 mAh g^(-1)at 1 C with a decay rate of 0.064%per cycle and remarkable capacity retention at 2 C with rate performance up to 4 C.Therefore,the novel design of N-doped carbon nanotubes with Mn spheres and PDA coating serves as an efficient polysulfide immobilizer for Li-S batteries.
文摘The paper is devoted to a spherically symmetric problem of General Relativity (GR) for a fluid sphere. The problem is solved within the framework of a special geometry of the Riemannian space induced by gravitation. According to this geometry, the four-dimensional Riemannian space is assumed to be Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate. Such interpretation of the Riemannian space allows us to obtain complete set of GR equations for the external empty space and the internal spaces for incompressible and compressible perfect fluids. The obtained analytical solution for an incompressible fluid is compared with the Schwarzchild solution. For a sphere consisting of compressible fluid or gas, a numerical solution is presented and discussed.
文摘We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We provide the mathematical definitions of Hamiltonians and obtain new results for both models, in particular the resolvents equations, spectral properties and some scattering quantities.
基金Projects (11KJB530002, CX10B-259Z) supported by Research Funds from Jiangsu Provincial Department of Education, ChinaProject (10zxfk35) supported by Sichuan Province Nonmetallic Composites and Functional Materials Key Laboratory Project, China
文摘Different-sized hollow SiO2 spheres of 249–1348 nm in diameter were successfully prepared by using Na2SiO3 as the precursor and using polystyrene and polystyrene-methyl acrylic acid latexes as the templates. The diameter and shell thickness of the hollow SiO2 spheres increase with increasing the latex template diameter at a given mass ratio of SiO2 to latex template. The diameter and shell thickness of the hollow SiO2 spheres also increase with increasing the mass ratios of SiO2 to latex template. The presence of carboxylic acid groups on the surfaces of polystyrene-methyl acrylic acid latex templates favors the formation of dense and uniform SiO2 shells. The hollow SiO2 sphere is constructed by mesoporous shell with large specific surface area. When glyphosate is used as a release model chemical, glyphosate release rate is tuned by varying the shell thickness.
文摘To obtain a kind of convenient oral dosage form of protein, which can be fully absorbed and is efficient and safe, the thymosin-loaded PLA（polylactic acid） microspheres are prepared by the emulsification- solvent evaporation method and the orthogonal design is used to optimize the technology of preparation. The form of the medicament microspheres of thymosin are proved by differential thermal analysis （DTA）. The drug content is determined by the Lowry method, and the package ratio of medicament microspheres of thymosin and drug release in vitro are calculated. The results show that the average diameter and encapsulation efficiency of the product prepared according to the optimized formulation are 13. 8 μm and 80. 7%, respectively. The in vitro release behavior within 12 h can be described by the Higuchi equation with T1/2 = 295 rain. There are no significant changes in size distribution and residual drug contents after being stored at 25℃ and 40 ℃ for 90 d, respectively. Due to the fact that its thymosin content and package ratio meet the requirement, and its releasing half life is long, the thymosin-loaded PLA microsohere has a favorable application future.
文摘Monoclinic BiVO4 hollow nanospheres were successfully prepared via template-free method using citric acid （C6H8O7） as chelating agent and characterized by X-ray diffraction patterns, transmission electron microscope, UV-Vis DRS, and TG-DTA technique. C6H8O7 played an important role in the formation of hollow spheres. Morphology observations revealed that when appropriate amount of C6H8O7 was introduced, the cavity with the diameter of 40 nm was obtained in BiVO4 nanospheres. UV-Vis diffuse reflectance spectra indicated that the samples had absorption in both UV and visible light region. The photocatalytic activities were evaluated by the degradation of methylene blue under Xe lamp irradiation. Hollow spheres endow BiVO4 samples with greatly improved photocatalytic activity. A possible formation mechanism of hollow spheres was proposed.
文摘Let A={A_1, A_2,…, A_(n+1)} be a simplex in E^n which its center O of circumscribed sphere is in inside of A. If R and R_i are radiuses of A_i respectively (A_i={A_1, A_2,…, A_(i-1), O, A_(i+1),…,A_(n+1)} ,i=1,2,…,n+1),then we have The equality holds if and only if A is a regular simplex.
基金Supported by General Humanity and Social Science Research Fundfrom Ministry of Education in 2009(09XJC770001)~~
文摘Guizhou Province is part of the glutinous rice cultivation sphere in our country.Its rice production and germplasm resources play an important role.The southeast region is the centre of the Guizhou glutinous rice cultivation and characterized by waxy wo,which is treasure of the original farming culture of southeast Guizhou region and an important symbol for ethnic cultural identity of the region.
