Let M be a(2 k + 2 l + 2)-dimensional smooth manifold. For such M, Bande and Hadjar introduce a new geometric structure called contact pair which roughly is a couple of 1-forms of constant classes with complementary k...Let M be a(2 k + 2 l + 2)-dimensional smooth manifold. For such M, Bande and Hadjar introduce a new geometric structure called contact pair which roughly is a couple of 1-forms of constant classes with complementary kernels and foliations. We show the relationship between a pair of vector fields for a contact pair and a quadruple of functions on M. This is a generalization of the classical result for contact manifolds.展开更多
In this paper, the extremal problem, min, of two convex bodies K and L in ?n is considered. For K to be in extremal position in terms of a decomposition of the identity, give necessary conditions together with the opt...In this paper, the extremal problem, min, of two convex bodies K and L in ?n is considered. For K to be in extremal position in terms of a decomposition of the identity, give necessary conditions together with the optimization theorem of John. Besides, we also consider the weaker optimization problem: min. As an application, we give the geometric distance between the unit ball B2n and a centrally symmetric convex body K.展开更多
In this paper, we consider the extremal problem of the ;p-norm： min{;p（TK）, o E TK C L, T E GL（n）}, where K, L are two convex bodies in Rn. Using the optimization theorem of John, we give necessary conditions for...In this paper, we consider the extremal problem of the ;p-norm： min{;p（TK）, o E TK C L, T E GL（n）}, where K, L are two convex bodies in Rn. Using the optimization theorem of John, we give necessary conditions for K to be in extremal position in terms of a decomposition of the identity. Fhrthermore, the weaker optimization problem, min{（lp（TK））p ： TK C B2n,TK Sn-1 ≠ O,T E GL（n）}, is also considered. As an application, the geometric distance between the unit ball B2n and a centrally symmetric convex body K is obtained.展开更多
Aprotic Li-CO_(2)batteries have attracted growing interest due to their high theoretical energy density and its ability to use green house gas CO_(2)for energy storage.However,the poor ability of activating CO_(2)in o...Aprotic Li-CO_(2)batteries have attracted growing interest due to their high theoretical energy density and its ability to use green house gas CO_(2)for energy storage.However,the poor ability of activating CO_(2)in organic electrolyte often leads to the premature termination of CO_(2)reduction reaction(CO_(2)RR)directly.Here in this work,cetyl trimethyl ammonium bromide(CTAB)was introduced into a dimethyl sulfoxide(DMSO)based Li-CO_(2)battery for the first time to enhance the CO_(2)RR.Significantly improved electrochemical performances,including reduced discharge over-potential and increased discharge capacity,can be achieved with the addition of CTAB.Ab initio molecular dynamics(AIMD)simulations show that quaternary ammonium group CTA^(+) can accelerate CO_(2)reduction process by forming more stable contact ion pair(CIP)with CO_(2)^(–),reducing the energy barrier for CO_(2)RR,thus improving the CO_(2)reduction process.In addition,adding CTA^(+) is also favorable for the solution-phase growth of discharge products because of the improved migration ability of stable CTA^(+)-CO_(2)^(–) CIP in the electrolyte,which is beneficial for improving the utilization ratio of cathode.This work could facilitate the development of CO_(2)RR by providing a novel understanding of CO_(2)RR mechanism in organic system.展开更多
Let M be a 2n-dimensional smooth manifold associated with the structure of symplectic pair which is a pair of closed 2-forms of constant ranks with complementary kernel foliations. Let Q ■M be a codimension 2 compact...Let M be a 2n-dimensional smooth manifold associated with the structure of symplectic pair which is a pair of closed 2-forms of constant ranks with complementary kernel foliations. Let Q ■M be a codimension 2 compact submanifold. We show some sufficient and necessary conditions on the existence of the structure of contact pair (α,β) on Q, which is a pair of 1-forms of constant classes whose characteristic foliations are transverse and complementary such that α and β restrict to contact forms on the leaves of the characteristic foliations of β and α, respectively. This is a generalization of the neighborhood theorem for contact-type hypersurfaces in symplectic topology.展开更多
基金supported by the National Natural Science Foundation of China(11671209,11871278)by the Starting Foundation for Research of Jinan University
文摘Let M be a(2 k + 2 l + 2)-dimensional smooth manifold. For such M, Bande and Hadjar introduce a new geometric structure called contact pair which roughly is a couple of 1-forms of constant classes with complementary kernels and foliations. We show the relationship between a pair of vector fields for a contact pair and a quadruple of functions on M. This is a generalization of the classical result for contact manifolds.
文摘In this paper, the extremal problem, min, of two convex bodies K and L in ?n is considered. For K to be in extremal position in terms of a decomposition of the identity, give necessary conditions together with the optimization theorem of John. Besides, we also consider the weaker optimization problem: min. As an application, we give the geometric distance between the unit ball B2n and a centrally symmetric convex body K.
基金Supported by National Natural Science Foundation of China (Grant No. 10971128)Shanghai Leading Academic Discipline Project (Grant No. S30104)Doctoral Fund of Henan Polytechnic University (Grant No. B2011-024)
文摘In this paper, we consider the extremal problem of the ;p-norm： min{;p（TK）, o E TK C L, T E GL（n）}, where K, L are two convex bodies in Rn. Using the optimization theorem of John, we give necessary conditions for K to be in extremal position in terms of a decomposition of the identity. Fhrthermore, the weaker optimization problem, min{（lp（TK））p ： TK C B2n,TK Sn-1 ≠ O,T E GL（n）}, is also considered. As an application, the geometric distance between the unit ball B2n and a centrally symmetric convex body K is obtained.
基金National Science Foundation of China(Nos.21701145 and 21701146)China Postdoctoral Science Foundation(Nos.2017M610459 and 2018T110739)。
文摘Aprotic Li-CO_(2)batteries have attracted growing interest due to their high theoretical energy density and its ability to use green house gas CO_(2)for energy storage.However,the poor ability of activating CO_(2)in organic electrolyte often leads to the premature termination of CO_(2)reduction reaction(CO_(2)RR)directly.Here in this work,cetyl trimethyl ammonium bromide(CTAB)was introduced into a dimethyl sulfoxide(DMSO)based Li-CO_(2)battery for the first time to enhance the CO_(2)RR.Significantly improved electrochemical performances,including reduced discharge over-potential and increased discharge capacity,can be achieved with the addition of CTAB.Ab initio molecular dynamics(AIMD)simulations show that quaternary ammonium group CTA^(+) can accelerate CO_(2)reduction process by forming more stable contact ion pair(CIP)with CO_(2)^(–),reducing the energy barrier for CO_(2)RR,thus improving the CO_(2)reduction process.In addition,adding CTA^(+) is also favorable for the solution-phase growth of discharge products because of the improved migration ability of stable CTA^(+)-CO_(2)^(–) CIP in the electrolyte,which is beneficial for improving the utilization ratio of cathode.This work could facilitate the development of CO_(2)RR by providing a novel understanding of CO_(2)RR mechanism in organic system.
基金This work was supported in part by the National Natural Science Foundation of China (Grant No. 11671209).
文摘Let M be a 2n-dimensional smooth manifold associated with the structure of symplectic pair which is a pair of closed 2-forms of constant ranks with complementary kernel foliations. Let Q ■M be a codimension 2 compact submanifold. We show some sufficient and necessary conditions on the existence of the structure of contact pair (α,β) on Q, which is a pair of 1-forms of constant classes whose characteristic foliations are transverse and complementary such that α and β restrict to contact forms on the leaves of the characteristic foliations of β and α, respectively. This is a generalization of the neighborhood theorem for contact-type hypersurfaces in symplectic topology.
