First, we present semisimple properties of twisted products by means of constructing an algebra isomorphism between twisted products and crossed products, and point out that there exist some relations among braided bi...First, we present semisimple properties of twisted products by means of constructing an algebra isomorphism between twisted products and crossed products, and point out that there exist some relations among braided bialgebras, paired bialgebras and Yang-Baxter coalgebras. Furthermore, we give an example to illustrate these relations by using Sweedler's 4-dimensional Hopf algebra. Finally, from starting off with Yang-Baxter coalgebras, we can construct some quadratic bialgebras such that they are braided bialgebras.展开更多
Let A and B be two regular multiplier Hopf algebras.First,the notion of diagonal crossed product B#A of multiplier Hopf algebras is constructed using the bimodule algebra,which is a generalization of the diagonal cros...Let A and B be two regular multiplier Hopf algebras.First,the notion of diagonal crossed product B#A of multiplier Hopf algebras is constructed using the bimodule algebra,which is a generalization of the diagonal crossed product in the sense of Hopf algebras.The result that the product in B#A is non-degenerate is given.Next,the definition of the comultiplicationΔ#on B#A is introduced,which is composed of the multiplierΔB(b)on B⊗B and the multiplierΔA(a)on A⊗A,and the elementΔ#(b⊗a)is a two-side multiplier of B#A⊗B#A,for any b∈B and a∈A.Then,a sufficient condition for B#A to be a regular multiplier Hopf algebra is described.In particular,Delvaux's main theorem in the case of smash products is generalized.Finally,these integrals on a diagonal crossed product of multiplier Hopf algebras are considered.展开更多
M-ary spread spectrum technique has been found wide applications in wireless communications, but it needs too many orthogonal spreading codes and its despreading/demodulation is quite complex computationally, which li...M-ary spread spectrum technique has been found wide applications in wireless communications, but it needs too many orthogonal spreading codes and its despreading/demodulation is quite complex computationally, which limit its wider applications. This paper proposes a novel scheme for Code Division Multiple Access (CDMA) communication systems based on M-ary spread spectrum, where only one prototype spreading code is assigned to each user and the codes for different users are orthogonal or quasi-orthogonal with each other. The M spreading codes of each user to represent K bits data are generated by circularly shifting the assigned code and reversing its polarity. The spreading codes generated like that are called as BiOrthogonal Cyclic Codes (BOCCs). At the receiver of the system, a transform domain matched-filter implemented by means of Fast Fourier Transform (FFT) is employed to despread and demodulate the received signals, which has very low computational complexity. The results of simulation experiments and bit-error performance analysis show that the proposed scheme is practical and very useful in many cases.展开更多
In this paper, we present the general theory and universal properties of weak crossed biproducts. We prove that every weak projection of weak bialgebras induces one of these weak crossed structures. Finally, we comput...In this paper, we present the general theory and universal properties of weak crossed biproducts. We prove that every weak projection of weak bialgebras induces one of these weak crossed structures. Finally, we compute explicitly the weak crossed biproduct associated with a groupoid that admits an exact factorization.展开更多
As a critical component of alkaline fuel cells, anion exchange membranes determine the energy efficiency, output power density and the long term stability. Recently, the anion exchange membranes with gemini-cation sid...As a critical component of alkaline fuel cells, anion exchange membranes determine the energy efficiency, output power density and the long term stability. Recently, the anion exchange membranes with gemini-cation side chains exhibit superior ion conductivity due to their good nanophase separation. However, the costly and complicated synthesis limits their scaling up and commercialization. To address this problem, a convenient synthetic procedure under mild conditions is well developed. A tertiary amine precursor is introduced onto the polymer by the nucleophilic substitution reaction to avoid the conventional chloro/bromo-methylation. Followed by a simple Menshutkin reaction with 6- bromo-N,N,N-trimethylhexan-1-am inium bromide, the polym er electrolytes are obtained in a high yield. The resulting anion exchange membranes with high conductivity, good fuel cell performance and restricted swelling suggest the potential for the application in fuel cell devices.展开更多
文摘First, we present semisimple properties of twisted products by means of constructing an algebra isomorphism between twisted products and crossed products, and point out that there exist some relations among braided bialgebras, paired bialgebras and Yang-Baxter coalgebras. Furthermore, we give an example to illustrate these relations by using Sweedler's 4-dimensional Hopf algebra. Finally, from starting off with Yang-Baxter coalgebras, we can construct some quadratic bialgebras such that they are braided bialgebras.
基金The National Natural Science Foundation of China(No.11371088,11571173,11871144)the Natural Science Foundation of Jiangsu Province(No.BK20171348)。
文摘Let A and B be two regular multiplier Hopf algebras.First,the notion of diagonal crossed product B#A of multiplier Hopf algebras is constructed using the bimodule algebra,which is a generalization of the diagonal crossed product in the sense of Hopf algebras.The result that the product in B#A is non-degenerate is given.Next,the definition of the comultiplicationΔ#on B#A is introduced,which is composed of the multiplierΔB(b)on B⊗B and the multiplierΔA(a)on A⊗A,and the elementΔ#(b⊗a)is a two-side multiplier of B#A⊗B#A,for any b∈B and a∈A.Then,a sufficient condition for B#A to be a regular multiplier Hopf algebra is described.In particular,Delvaux's main theorem in the case of smash products is generalized.Finally,these integrals on a diagonal crossed product of multiplier Hopf algebras are considered.
基金Supported by the National Natural Science Foundation of China (No.60172029).
文摘M-ary spread spectrum technique has been found wide applications in wireless communications, but it needs too many orthogonal spreading codes and its despreading/demodulation is quite complex computationally, which limit its wider applications. This paper proposes a novel scheme for Code Division Multiple Access (CDMA) communication systems based on M-ary spread spectrum, where only one prototype spreading code is assigned to each user and the codes for different users are orthogonal or quasi-orthogonal with each other. The M spreading codes of each user to represent K bits data are generated by circularly shifting the assigned code and reversing its polarity. The spreading codes generated like that are called as BiOrthogonal Cyclic Codes (BOCCs). At the receiver of the system, a transform domain matched-filter implemented by means of Fast Fourier Transform (FFT) is employed to despread and demodulate the received signals, which has very low computational complexity. The results of simulation experiments and bit-error performance analysis show that the proposed scheme is practical and very useful in many cases.
基金supported by Xunta de Galicia (Grant No. PGIDT07PXB322079PR)Ministerio de Educación (Grant Nos. MTM2007-62427, MTM2006-14908-CO2-01)FEDER
文摘In this paper, we present the general theory and universal properties of weak crossed biproducts. We prove that every weak projection of weak bialgebras induces one of these weak crossed structures. Finally, we compute explicitly the weak crossed biproduct associated with a groupoid that admits an exact factorization.
基金supported by the National Natural Science Foundation of China (21720102003, 91534203 and 21522607)the Fundamental Research Funds for the Central Universities (WK2060190072 and WK2340000066)
文摘As a critical component of alkaline fuel cells, anion exchange membranes determine the energy efficiency, output power density and the long term stability. Recently, the anion exchange membranes with gemini-cation side chains exhibit superior ion conductivity due to their good nanophase separation. However, the costly and complicated synthesis limits their scaling up and commercialization. To address this problem, a convenient synthetic procedure under mild conditions is well developed. A tertiary amine precursor is introduced onto the polymer by the nucleophilic substitution reaction to avoid the conventional chloro/bromo-methylation. Followed by a simple Menshutkin reaction with 6- bromo-N,N,N-trimethylhexan-1-am inium bromide, the polym er electrolytes are obtained in a high yield. The resulting anion exchange membranes with high conductivity, good fuel cell performance and restricted swelling suggest the potential for the application in fuel cell devices.