Developing reliable and efficient anode materials is essential for the successfully practical application of sodium-ion batteries.Herein,employing a straightforward and rapid chemical vapor deposition technique,two-di...Developing reliable and efficient anode materials is essential for the successfully practical application of sodium-ion batteries.Herein,employing a straightforward and rapid chemical vapor deposition technique,two-dimensional layered ternary indium phosphorus sulfide(In_(2)P_(3)S_(9)) nanosheets are prepared.The layered structure and ternary composition of the In_(2)P_(3)S_(9) electrode result in impressive electrochemical performance,including a high reversible capacity of 704 mA h g^(-1) at 0.1 A g^(-1),an outstanding rate capability with 425 mA h g^(-1) at 5 A g^(-1),and an exceptional cycling stability with a capacity retention of88% after 350 cycles at 1 A g^(-1).Furthermore,sodium-ion full cell also affords a high capacity of 308 and114 mA h g^(-1) at 0.1 and 5 A g^(-1).Ex-situ X-ray diffraction and ex-situ high-resolution transmission electron microscopy tests are conducted to investigate the underlying Na-storage mechanism of In_(2)P_(3)S_(9).The results reveal that during the first cycle,the P-S bond is broken to form the elemental P and In_(2)S_(3),collectively contributing to a remarkably high reversible specific capacity.The excellent electrochemical energy storage results corroborate the practical application potential of In_(2)P_(3)S_(9) for sodium-ion batteries.展开更多
This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional ...This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.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
When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, ...When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.展开更多
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ...For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.展开更多
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
支持等式测试的标识加密(identity-based encryption with equality test, IBEET)体制解决了传统等式测试方案中证书管理的问题,得到了广泛的关注.但现有的IBEET体制难以抵抗渗透攻击,且都是基于国外密码算法设计,不具有自主知识产权....支持等式测试的标识加密(identity-based encryption with equality test, IBEET)体制解决了传统等式测试方案中证书管理的问题,得到了广泛的关注.但现有的IBEET体制难以抵抗渗透攻击,且都是基于国外密码算法设计,不具有自主知识产权.基于此,提出一种支持等式测试并具有密码逆向防火墙的SM9标识加密方案(SM9 identity-based encryption scheme with equality test and cryptographic reverse firewalls, SM9-IBEET-CRF).该方案在用户与云服务器的上行信道间部署密码逆向防火墙(cryptographic reverse firewalls,CRF),对用户发出的信息执行重随机化以达到抵抗渗透攻击的作用.该方案拓展国密算法SM9至IBEET领域中,提升其运行效率并丰富国密算法在云计算领域的研究.给出了SM9-IBEET-CRF的形式化定义和安全模型,并在随机预言机模型中考虑2种不同的敌手将此方案在选择密文攻击下的不可区分性与单向性分别形式化地规约到BDH困难假设上.同时,该方案通过考虑第3种敌手证明CRF的部署为其带来维持功能性、保留安全性以及抵抗渗透性.实验仿真和分析结果展示了该方案的有效性.展开更多
基金Financial supports from the National Natural Science Foundation of China(22265018 and 21961019)the Key Project of Natural Science Foundation of Jiangxi Province(20232ACB204010)。
文摘Developing reliable and efficient anode materials is essential for the successfully practical application of sodium-ion batteries.Herein,employing a straightforward and rapid chemical vapor deposition technique,two-dimensional layered ternary indium phosphorus sulfide(In_(2)P_(3)S_(9)) nanosheets are prepared.The layered structure and ternary composition of the In_(2)P_(3)S_(9) electrode result in impressive electrochemical performance,including a high reversible capacity of 704 mA h g^(-1) at 0.1 A g^(-1),an outstanding rate capability with 425 mA h g^(-1) at 5 A g^(-1),and an exceptional cycling stability with a capacity retention of88% after 350 cycles at 1 A g^(-1).Furthermore,sodium-ion full cell also affords a high capacity of 308 and114 mA h g^(-1) at 0.1 and 5 A g^(-1).Ex-situ X-ray diffraction and ex-situ high-resolution transmission electron microscopy tests are conducted to investigate the underlying Na-storage mechanism of In_(2)P_(3)S_(9).The results reveal that during the first cycle,the P-S bond is broken to form the elemental P and In_(2)S_(3),collectively contributing to a remarkably high reversible specific capacity.The excellent electrochemical energy storage results corroborate the practical application potential of In_(2)P_(3)S_(9) for sodium-ion batteries.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12275172 and 11905124)。
文摘This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.
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.
文摘When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.
文摘For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.
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).
文摘支持等式测试的标识加密(identity-based encryption with equality test, IBEET)体制解决了传统等式测试方案中证书管理的问题,得到了广泛的关注.但现有的IBEET体制难以抵抗渗透攻击,且都是基于国外密码算法设计,不具有自主知识产权.基于此,提出一种支持等式测试并具有密码逆向防火墙的SM9标识加密方案(SM9 identity-based encryption scheme with equality test and cryptographic reverse firewalls, SM9-IBEET-CRF).该方案在用户与云服务器的上行信道间部署密码逆向防火墙(cryptographic reverse firewalls,CRF),对用户发出的信息执行重随机化以达到抵抗渗透攻击的作用.该方案拓展国密算法SM9至IBEET领域中,提升其运行效率并丰富国密算法在云计算领域的研究.给出了SM9-IBEET-CRF的形式化定义和安全模型,并在随机预言机模型中考虑2种不同的敌手将此方案在选择密文攻击下的不可区分性与单向性分别形式化地规约到BDH困难假设上.同时,该方案通过考虑第3种敌手证明CRF的部署为其带来维持功能性、保留安全性以及抵抗渗透性.实验仿真和分析结果展示了该方案的有效性.
