Let H3 be the 9-dimensional Taft Hopf algebra,let r(H3)be the corresponding Green ring of H3,and let Aut(R(H3))be the automorphism group of Green algebra R(H3)=R■Zr(H3)over the real number fieldR.We prove that the qu...Let H3 be the 9-dimensional Taft Hopf algebra,let r(H3)be the corresponding Green ring of H3,and let Aut(R(H3))be the automorphism group of Green algebra R(H3)=R■Zr(H3)over the real number fieldR.We prove that the quotient group Aut(R(H3))/T1 is isomorphic to the direct product of the dihedral group of order 12 and the cyclic group of order 2,where T1 is the isomorphism class which contains the identity map and is isomorphic to a group G={(c,d)∈R^(2)∣∣(c,d)≠(−1/3,−1/6)}with multiplication given by(c1,d1)⋅(c2,d2)=(c1+c2+2c1c2−4d1d2+2c1d2+2d1c2,d1+d2−2c1c2−2d1d2+4c1d2+4d1c2).展开更多
With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic...With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.展开更多
This paper proposes a novel cargo loading algorithm applicable to automated conveyor-type loading systems.The algorithm offers improvements in computational efficiency and robustness by utilizing the concept of discre...This paper proposes a novel cargo loading algorithm applicable to automated conveyor-type loading systems.The algorithm offers improvements in computational efficiency and robustness by utilizing the concept of discrete derivatives and introducing logistics-related constraints.Optional consideration of the rotation of the cargoes was made to further enhance the optimality of the solutions,if possible to be physically implemented.Evaluation metrics were developed for accurate evaluation and enhancement of the algorithm’s ability to efficiently utilize the loading space and provide a high level of dynamic stability.Experimental results demonstrate the extensive robustness of the proposed algorithm to the diversity of cargoes present in Business-to-Consumer environments.This study contributes practical advancements in both cargo loading optimization and automation of the logistics industry,with potential applications in last-mile delivery services,warehousing,and supply chain management.展开更多
Several challenging issues,such as the poor conductivity of sulfur,shuttle effects,large volume change of cathode,and the dendritic lithium in anode,have led to the low utilization of sulfur and hampered the commercia...Several challenging issues,such as the poor conductivity of sulfur,shuttle effects,large volume change of cathode,and the dendritic lithium in anode,have led to the low utilization of sulfur and hampered the commercialization of lithium–sulfur batteries.In this study,a novel three-dimensionally interconnected network structure comprising Co9 S8 and multiwalled carbon nanotubes(MWCNTs)was synthesized by a solvothermal route and used as the sulfur host.The assembled batteries delivered a specific capacity of1154 m Ah g-1 at 0.1 C,and the retention was 64%after 400 cycles at 0.5 C.The polar and catalytic Co9 S8 nanoparticles have a strong adsorbent effect for polysulfide,which can effectively reduce the shuttling effect.Meanwhile,the three-dimensionally interconnected CNT networks improve the overall conductivity and increase the contact with the electrolyte,thus enhancing the transport of electrons and Li ions.Polysulfide adsorption is greatly increased with the synergistic effect of polar Co9 S8 and MWCNTs in the three-dimensionally interconnected composites,which contributes to their promising performance for the lithium–sulfur batteries.展开更多
The fracture and migration patterns of direct roofs play a critical role in excavation stability and mining pressure.However,current methods fail to capture the irregular three-dimensional(3D)behavior of these roofs.I...The fracture and migration patterns of direct roofs play a critical role in excavation stability and mining pressure.However,current methods fail to capture the irregular three-dimensional(3D)behavior of these roofs.In this study,the problem was solved by introducing an innovative 2.5-dimensional(2.5D)Voronoi numerical simulation method,dividing rock layers into 2.5D Voronoi blocks and developing cohesive element-based failure models,supported by a strain-softening HoekeBrown model.The method was applied to the 8311 working face in the Taishan Mine in China,and its accuracy was confirmed through physical experiments.The following conclusions were drawn.The first roof break typically followed an"O-X"pattern.The direct roof did not break randomly over time;instead,it followed three distinct scenarios:(1)A complete break of the direct roof occurred,followed by a sequential collapse(ScenarioⅠ).(2)Regional irregular stacking in one area was followed by sequential collapse in other zones(ScenarioⅡ).(3)The staged breakdown of the direct roof led to separate and sequential collapses on the left and right flanks(ScenarioⅢ).Scenario I was quite common during the 400 m advance of the working face and occurred five times.The fracture characteristics in Scenario I led to widespread pressure on the hydraulic supports in the middle of the working face.Finally,the direct roof from the working face towards the goaf area underwent phases of overhanging,hinging,and collapsing plates.After the first and periodic breaks,the basic roof formed stable hinged plate structures reinforced by overhanging plates and irregular accumulations of the direct roof.展开更多
Lie symmetry analysis is applied to a(3+1)-dimensional combined potential Kadomtsev-Petviashvili equation with B-type Kadomtsev-Petviashvili equation(pKP-BKP equation)and the corresponding similarity reduction equatio...Lie symmetry analysis is applied to a(3+1)-dimensional combined potential Kadomtsev-Petviashvili equation with B-type Kadomtsev-Petviashvili equation(pKP-BKP equation)and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions and constants for the(3+1)-dimensional pKP-BKP equation,including the lump solution,the periodic-lump solution,the two-kink solution,the breather solution and the lump-two-kink solution,have been studied analytically and graphically.展开更多
In this paper,we investigate the(2+1)-dimensional three-component long-wave-short-wave resonance interaction system,which describes complex systems and nonlinear wave phenomena in physics.By employing the Hirota bilin...In this paper,we investigate the(2+1)-dimensional three-component long-wave-short-wave resonance interaction system,which describes complex systems and nonlinear wave phenomena in physics.By employing the Hirota bilinear method,we derive the general nondegenerate N-soliton solution of the system,where each short-wave component contains N arbitrary functions of the independent variable y.The presence of these arbitrary functions in the analytical solution enables the construction of a wide range of nondegenerate soliton types.Finally,we illustrate the structural features of several novel nondegenerate solitons,including M-shaped,multiple double-hump,and sawtooth double-striped solitons,as well as interactions between nondegenerate solitons,such as dromion-like solitons and solitoffs,with the aid of figures.展开更多
In this work,we study wave state transitions of the(2+1)-dimensional Kortewegde Vries-Sawada-Kotera-Ramani(2KdVSKR)equation by analyzing the characteristic line and phase shift.By converting the wave parameters of the...In this work,we study wave state transitions of the(2+1)-dimensional Kortewegde Vries-Sawada-Kotera-Ramani(2KdVSKR)equation by analyzing the characteristic line and phase shift.By converting the wave parameters of the N-soliton solution into complex numbers,the breath wave solution is constructed.The lump wave solution is derived through the long wave limit method.Then,by choosing appropriate parameter values,we acquire a number of transformed nonlinear waves whose gradient relation is discussed according to the ratio of the wave parameters.Furthermore,we reveal transition mechanisms of the waves by exploring the nonlinear superposition of the solitary and periodic wave components.Subsequently,locality,oscillation properties and evolutionary phenomenon of the transformed waves are presented.And we also prove the change in the geometrical properties of the characteristic lines leads to the phenomena of wave evolution.Finally,for higher-order waves,a range of interaction models are depicted along with their evolutionary phenomena.And we demonstrate that their diversity is due to the fact that the solitary and periodic wave components produce different phase shifts caused by time evolution and collisions.展开更多
Recently, during the investigations on planetary oceans, Hirota-Satsuma-Ito-type models have been developed. In this paper, for a(2+1)-dimensional generalized variable-coefficient Hirota-Satsuma-Ito system describing ...Recently, during the investigations on planetary oceans, Hirota-Satsuma-Ito-type models have been developed. In this paper, for a(2+1)-dimensional generalized variable-coefficient Hirota-Satsuma-Ito system describing the fluid dynamics of shallow-water waves in an open ocean, non-characteristic movable singular manifold and symbolic computation enable an oceanic auto-B?cklund transformation with three sets of the oceanic solitonic solutions. The results rely on the oceanic variable coefficients in that system. Future oceanic observations might detect some nonlinear features predicted in this paper, and relevant oceanographic insights might be expected.展开更多
Low-dimensional Bi2Fe4O9 nanosheets and microrods have been selectively prepared by a solvothermal method, from which the growth of the Bi2Fe4O9 crystals can be controlled by the variation of reaction conditions. Stru...Low-dimensional Bi2Fe4O9 nanosheets and microrods have been selectively prepared by a solvothermal method, from which the growth of the Bi2Fe4O9 crystals can be controlled by the variation of reaction conditions. Structure determination showed that the nanosheets are mainly exposed by {001} facets while the microrods are exposed by {110} facets. Ab- sorption spectra revealed that there are two bandgaps observed for both nanosheets （at 1.9 and 1.55 eV） and microrods （1.7 and 1.45 eV）, and they both would be available for the sunlight photocatalysis e ciently due to the intensive absorption ability in a wide region. Photocatalytic investigation demonstrated that the overall photocatalytic performance of the microrods is prior to that of the nanosheets due to the variation of bandgaps and exposed facets. The present report provides a useful alternative strategy for the controlling growth of nanostructures and/or microcrystals besides the present demonstration of the Bi2Fe4O9 crystals with diflerent bandgaps and facets that would be able to tune the corresponding photocatalytic ability selectively.展开更多
A two-dimensional（2D） 44 topological ZnⅡ coordination polymer {[Zn2Cl2（L）（4bpy）2]}∞（H2L = anthracene-9,10-dicarboxylic acid, 4bpy = 4,4ˊ-bipyridine） based on binuclear [Zn2Cl2] nodes has been synthesized an...A two-dimensional（2D） 44 topological ZnⅡ coordination polymer {[Zn2Cl2（L）（4bpy）2]}∞（H2L = anthracene-9,10-dicarboxylic acid, 4bpy = 4,4ˊ-bipyridine） based on binuclear [Zn2Cl2] nodes has been synthesized and characterized by IR, elemental analysis, X-ray powder diffraction and single-crystal X-ray diffraction analysis. Moreover, the luminescent properties of the correspon- ding compound have been briefly investigated.展开更多
基金Supported by the National Natural Science Foundation of China(Nos.11661014,11701499,11871063,and 11711530703)the Research Innovation Program Project of Academic Degree Graduate Students in Jiangsu(XKYCX17_029)the Excellent Doctoral Dissertation Foundation Project of Yangzhou University in 2018.
文摘Let H3 be the 9-dimensional Taft Hopf algebra,let r(H3)be the corresponding Green ring of H3,and let Aut(R(H3))be the automorphism group of Green algebra R(H3)=R■Zr(H3)over the real number fieldR.We prove that the quotient group Aut(R(H3))/T1 is isomorphic to the direct product of the dihedral group of order 12 and the cyclic group of order 2,where T1 is the isomorphism class which contains the identity map and is isomorphic to a group G={(c,d)∈R^(2)∣∣(c,d)≠(−1/3,−1/6)}with multiplication given by(c1,d1)⋅(c2,d2)=(c1+c2+2c1c2−4d1d2+2c1d2+2d1c2,d1+d2−2c1c2−2d1d2+4c1d2+4d1c2).
基金financially supported by the Scientific Research Foundation of North China University of Technology(Grant Nos.11005136024XN147-87 and 110051360024XN151-86).
文摘With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.
基金supported by the BK21 FOUR funded by the Ministry of Education of Korea and National Research Foundation of Korea,a Korea Agency for Infrastructure Technology Advancement(KAIA)grant funded by the Ministry of Land,Infrastructure,and Transport(Grant 1615013176)IITP(Institute of Information&Coummunications Technology Planning&Evaluation)-ICAN(ICT Challenge and Advanced Network of HRD)grant funded by the Korea government(Ministry of Science and ICT)(RS-2024-00438411).
文摘This paper proposes a novel cargo loading algorithm applicable to automated conveyor-type loading systems.The algorithm offers improvements in computational efficiency and robustness by utilizing the concept of discrete derivatives and introducing logistics-related constraints.Optional consideration of the rotation of the cargoes was made to further enhance the optimality of the solutions,if possible to be physically implemented.Evaluation metrics were developed for accurate evaluation and enhancement of the algorithm’s ability to efficiently utilize the loading space and provide a high level of dynamic stability.Experimental results demonstrate the extensive robustness of the proposed algorithm to the diversity of cargoes present in Business-to-Consumer environments.This study contributes practical advancements in both cargo loading optimization and automation of the logistics industry,with potential applications in last-mile delivery services,warehousing,and supply chain management.
基金National Natural Science Foundation of China(No.51974209)the Natural Science Foundation of Hubei Province of China(Nos.2013CFA021,2017CFB401,2018CFA022)。
文摘Several challenging issues,such as the poor conductivity of sulfur,shuttle effects,large volume change of cathode,and the dendritic lithium in anode,have led to the low utilization of sulfur and hampered the commercialization of lithium–sulfur batteries.In this study,a novel three-dimensionally interconnected network structure comprising Co9 S8 and multiwalled carbon nanotubes(MWCNTs)was synthesized by a solvothermal route and used as the sulfur host.The assembled batteries delivered a specific capacity of1154 m Ah g-1 at 0.1 C,and the retention was 64%after 400 cycles at 0.5 C.The polar and catalytic Co9 S8 nanoparticles have a strong adsorbent effect for polysulfide,which can effectively reduce the shuttling effect.Meanwhile,the three-dimensionally interconnected CNT networks improve the overall conductivity and increase the contact with the electrolyte,thus enhancing the transport of electrons and Li ions.Polysulfide adsorption is greatly increased with the synergistic effect of polar Co9 S8 and MWCNTs in the three-dimensionally interconnected composites,which contributes to their promising performance for the lithium–sulfur batteries.
基金supported by the Autonomous General Projects of the State Key Laboratory of Coal Mine Disaster Dynamics and Control,Chongqing University,China(Grant No.2011DA105287-MS202209)the National Natural Science Foundation of China,China(Grant Nos.52304149 and 52204127).
文摘The fracture and migration patterns of direct roofs play a critical role in excavation stability and mining pressure.However,current methods fail to capture the irregular three-dimensional(3D)behavior of these roofs.In this study,the problem was solved by introducing an innovative 2.5-dimensional(2.5D)Voronoi numerical simulation method,dividing rock layers into 2.5D Voronoi blocks and developing cohesive element-based failure models,supported by a strain-softening HoekeBrown model.The method was applied to the 8311 working face in the Taishan Mine in China,and its accuracy was confirmed through physical experiments.The following conclusions were drawn.The first roof break typically followed an"O-X"pattern.The direct roof did not break randomly over time;instead,it followed three distinct scenarios:(1)A complete break of the direct roof occurred,followed by a sequential collapse(ScenarioⅠ).(2)Regional irregular stacking in one area was followed by sequential collapse in other zones(ScenarioⅡ).(3)The staged breakdown of the direct roof led to separate and sequential collapses on the left and right flanks(ScenarioⅢ).Scenario I was quite common during the 400 m advance of the working face and occurred five times.The fracture characteristics in Scenario I led to widespread pressure on the hydraulic supports in the middle of the working face.Finally,the direct roof from the working face towards the goaf area underwent phases of overhanging,hinging,and collapsing plates.After the first and periodic breaks,the basic roof formed stable hinged plate structures reinforced by overhanging plates and irregular accumulations of the direct roof.
文摘Lie symmetry analysis is applied to a(3+1)-dimensional combined potential Kadomtsev-Petviashvili equation with B-type Kadomtsev-Petviashvili equation(pKP-BKP equation)and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions and constants for the(3+1)-dimensional pKP-BKP equation,including the lump solution,the periodic-lump solution,the two-kink solution,the breather solution and the lump-two-kink solution,have been studied analytically and graphically.
基金supported by the National Natural Science Foundation of China,Grant No.12375006。
文摘In this paper,we investigate the(2+1)-dimensional three-component long-wave-short-wave resonance interaction system,which describes complex systems and nonlinear wave phenomena in physics.By employing the Hirota bilinear method,we derive the general nondegenerate N-soliton solution of the system,where each short-wave component contains N arbitrary functions of the independent variable y.The presence of these arbitrary functions in the analytical solution enables the construction of a wide range of nondegenerate soliton types.Finally,we illustrate the structural features of several novel nondegenerate solitons,including M-shaped,multiple double-hump,and sawtooth double-striped solitons,as well as interactions between nondegenerate solitons,such as dromion-like solitons and solitoffs,with the aid of figures.
基金supported by the National Natural Science Foundation of China(12371255,11975306)the Xuzhou Basic Research Program Project(KC23048)+1 种基金the Six Talent Peaks Project in Jiangsu Province(JY-059)the 333 Project in Jiangsu Province and the Fundamental Research Funds for the Central Universities of CUMT(2024ZDPYJQ1003).
文摘In this work,we study wave state transitions of the(2+1)-dimensional Kortewegde Vries-Sawada-Kotera-Ramani(2KdVSKR)equation by analyzing the characteristic line and phase shift.By converting the wave parameters of the N-soliton solution into complex numbers,the breath wave solution is constructed.The lump wave solution is derived through the long wave limit method.Then,by choosing appropriate parameter values,we acquire a number of transformed nonlinear waves whose gradient relation is discussed according to the ratio of the wave parameters.Furthermore,we reveal transition mechanisms of the waves by exploring the nonlinear superposition of the solitary and periodic wave components.Subsequently,locality,oscillation properties and evolutionary phenomenon of the transformed waves are presented.And we also prove the change in the geometrical properties of the characteristic lines leads to the phenomena of wave evolution.Finally,for higher-order waves,a range of interaction models are depicted along with their evolutionary phenomena.And we demonstrate that their diversity is due to the fact that the solitary and periodic wave components produce different phase shifts caused by time evolution and collisions.
基金financially supported by the Scientific Research Foundation of North China University of Technology (Grant Nos.11005136024XN147-87 and 110051360024XN151-86)。
文摘Recently, during the investigations on planetary oceans, Hirota-Satsuma-Ito-type models have been developed. In this paper, for a(2+1)-dimensional generalized variable-coefficient Hirota-Satsuma-Ito system describing the fluid dynamics of shallow-water waves in an open ocean, non-characteristic movable singular manifold and symbolic computation enable an oceanic auto-B?cklund transformation with three sets of the oceanic solitonic solutions. The results rely on the oceanic variable coefficients in that system. Future oceanic observations might detect some nonlinear features predicted in this paper, and relevant oceanographic insights might be expected.
基金This work was supported by the National Natu-ral Science Foundation of China （No.21571166 and No.51271173） and the National Basic Research Pro- gram of China （No.2012CB922001）.
文摘Low-dimensional Bi2Fe4O9 nanosheets and microrods have been selectively prepared by a solvothermal method, from which the growth of the Bi2Fe4O9 crystals can be controlled by the variation of reaction conditions. Structure determination showed that the nanosheets are mainly exposed by {001} facets while the microrods are exposed by {110} facets. Ab- sorption spectra revealed that there are two bandgaps observed for both nanosheets （at 1.9 and 1.55 eV） and microrods （1.7 and 1.45 eV）, and they both would be available for the sunlight photocatalysis e ciently due to the intensive absorption ability in a wide region. Photocatalytic investigation demonstrated that the overall photocatalytic performance of the microrods is prior to that of the nanosheets due to the variation of bandgaps and exposed facets. The present report provides a useful alternative strategy for the controlling growth of nanostructures and/or microcrystals besides the present demonstration of the Bi2Fe4O9 crystals with diflerent bandgaps and facets that would be able to tune the corresponding photocatalytic ability selectively.
基金Supported by the key project of Science,the Technology Department of Henan province(No.112102210371)the science and technology research projects of Education Department of Henan province(No.12B150003)
文摘A two-dimensional（2D） 44 topological ZnⅡ coordination polymer {[Zn2Cl2（L）（4bpy）2]}∞（H2L = anthracene-9,10-dicarboxylic acid, 4bpy = 4,4ˊ-bipyridine） based on binuclear [Zn2Cl2] nodes has been synthesized and characterized by IR, elemental analysis, X-ray powder diffraction and single-crystal X-ray diffraction analysis. Moreover, the luminescent properties of the correspon- ding compound have been briefly investigated.
