A lot of combinatorial objects have a natural bialgebra structure. In this paper, we prove that the vector space spanned by labeled simple graphs is a bialgebra with the conjunction product and the unshuffle coproduct...A lot of combinatorial objects have a natural bialgebra structure. In this paper, we prove that the vector space spanned by labeled simple graphs is a bialgebra with the conjunction product and the unshuffle coproduct. In fact, it is a Hopf algebra since it is graded connected. The main conclusions are that the vector space spanned by labeled simple graphs arising from the unshuffle coproduct is a Hopf algebra and that there is a Hopf homomorphism from permutations to label simple graphs.展开更多
A 3D nanostructured scaffold as the host for zinc enables effective inhibition of anodic dendrite growth.However,the increased electrode/electrolyte interface area provided by using 3D matrices exacerbates the passiva...A 3D nanostructured scaffold as the host for zinc enables effective inhibition of anodic dendrite growth.However,the increased electrode/electrolyte interface area provided by using 3D matrices exacerbates the passivation and localized corrosion of the Zn anode,ultimately bringing about the degradation of the electrochemical performance.Herein,a nanoscale coating of inorganic-organic hybrid(α-In_(2)Se_(3)-Nafion)onto a flexible carbon nanotubes(CNTs)framework(ISNF@CNTs)is designed as a Zn plating/stripping scaffold to ensure uniform Zn nucleation,thus achieving a dendrite-free and durable Zn anode.The intro-duced inorganic-organic interfacial layer is dense and sturdy,which hinders the direct exposure of deposited Zn to electrolytes and mitigates the side reactions.Meanwhile,the zincophilic nature of ISNF can largely reduce the nucleation energy barrier and promote the ion-diffusion transportation.Consequently,the ISNF@CNTs@Zn electrode exhibits a low-voltage hysteresis and a superior cycling life(over 1500 h),with dendrite-free Zn-plating behaviors in a typical symmetrical cell test.Additionally,the superior feature of ISNF@CNTs@Zn anode is further demonstrated by Zn-MnO_(2)cells in both coin and flexible quasi-solid-state configurations.This work puts forward an inspired remedy for advanced Zn-ion batteries.展开更多
Low methanol permeability of proton exchange membranes (PEMs) is greatly important for direct methanol fuel cells (DMFCs). Here, sulfonated poly (ether ether ketone) (SPEEK) based semiinterpenetrating polymer networks...Low methanol permeability of proton exchange membranes (PEMs) is greatly important for direct methanol fuel cells (DMFCs). Here, sulfonated poly (ether ether ketone) (SPEEK) based semiinterpenetrating polymer networks (semi-IPNs) are successfully prepared by interpenetrating SPEEK into the in-situ synthesized crosslinking networks. The polymeric networks are formed by the covalent bonds between bromobenzyl groups of bro mo methylated poly (phenylene oxide) and amine groups of diamine linkers as well as the ionic bonds between amine species and sulfonated groups. Two linkers without and with sulfonated groups are applied to fabricate the semi-IPNs. The core properties of the membranes, like phase separation, water uptake, proton conductivity and methanol permeability, are systematically studied and compared. The DMFCs assembled by using the semi-IPN membranes display better performance than Nafion 117 in high concentration methanol solutions. The present work provides a facile way to prepare PEMs with enhanced DMFC performance.展开更多
文摘A lot of combinatorial objects have a natural bialgebra structure. In this paper, we prove that the vector space spanned by labeled simple graphs is a bialgebra with the conjunction product and the unshuffle coproduct. In fact, it is a Hopf algebra since it is graded connected. The main conclusions are that the vector space spanned by labeled simple graphs arising from the unshuffle coproduct is a Hopf algebra and that there is a Hopf homomorphism from permutations to label simple graphs.
基金Natural Science Foundation for Young Scientists of Henan Province,Grant/Award Number:202300410071Key Research Project of Henan Provincial Higher Education,Grant/Award Number:21A140007National Natural Science Foundation of China,Grant/Award Numbers:62174049,52003073,52102285。
文摘A 3D nanostructured scaffold as the host for zinc enables effective inhibition of anodic dendrite growth.However,the increased electrode/electrolyte interface area provided by using 3D matrices exacerbates the passivation and localized corrosion of the Zn anode,ultimately bringing about the degradation of the electrochemical performance.Herein,a nanoscale coating of inorganic-organic hybrid(α-In_(2)Se_(3)-Nafion)onto a flexible carbon nanotubes(CNTs)framework(ISNF@CNTs)is designed as a Zn plating/stripping scaffold to ensure uniform Zn nucleation,thus achieving a dendrite-free and durable Zn anode.The intro-duced inorganic-organic interfacial layer is dense and sturdy,which hinders the direct exposure of deposited Zn to electrolytes and mitigates the side reactions.Meanwhile,the zincophilic nature of ISNF can largely reduce the nucleation energy barrier and promote the ion-diffusion transportation.Consequently,the ISNF@CNTs@Zn electrode exhibits a low-voltage hysteresis and a superior cycling life(over 1500 h),with dendrite-free Zn-plating behaviors in a typical symmetrical cell test.Additionally,the superior feature of ISNF@CNTs@Zn anode is further demonstrated by Zn-MnO_(2)cells in both coin and flexible quasi-solid-state configurations.This work puts forward an inspired remedy for advanced Zn-ion batteries.
基金support of the National Natural Science Foundation of China(Nos. 21603197, 21703212,21233006 and 21473164)Natural Science Foundation of Hubei Province of China(No.2016CFB181)+1 种基金Fundamental Research Funds for the Central University, China University of Geosciences (Wuhan)(No. CUGL180403)China University of Geosciences (Wuhan) for the program of Center for Advanced Energy Research and Technologies
文摘Low methanol permeability of proton exchange membranes (PEMs) is greatly important for direct methanol fuel cells (DMFCs). Here, sulfonated poly (ether ether ketone) (SPEEK) based semiinterpenetrating polymer networks (semi-IPNs) are successfully prepared by interpenetrating SPEEK into the in-situ synthesized crosslinking networks. The polymeric networks are formed by the covalent bonds between bromobenzyl groups of bro mo methylated poly (phenylene oxide) and amine groups of diamine linkers as well as the ionic bonds between amine species and sulfonated groups. Two linkers without and with sulfonated groups are applied to fabricate the semi-IPNs. The core properties of the membranes, like phase separation, water uptake, proton conductivity and methanol permeability, are systematically studied and compared. The DMFCs assembled by using the semi-IPN membranes display better performance than Nafion 117 in high concentration methanol solutions. The present work provides a facile way to prepare PEMs with enhanced DMFC performance.
