In this study, we developed a general method to analytically tackle a kind of movable boundary problem from the viewpoint of energy variation. Having grouped the adhesion of a micro-beam, droplet and carbon nanotube ...In this study, we developed a general method to analytically tackle a kind of movable boundary problem from the viewpoint of energy variation. Having grouped the adhesion of a micro-beam, droplet and carbon nanotube （CNT） ring on a substrate into one framework, we used the developed line of reasoning to investigate the adhesion behaviors of these systems. Based upon the derived governing equations and transversality conditions, explicit solutions involving the critical parameters and morphologies for the three systems are successfully obtained, and then the parameter analogies and common characteristics of them are thor- oughly investigated. The presented method has been verified via the concept of energy release rate in fracture mechanics. Our analyses provide a new approach for exploring the mechanism of different systems with similarities as well as for understanding the unity of nature. The analysis results may be beneficial for the design of nano-structured materi- als, and hold potential for enhancing their mechanical, chemical, optical and electronic properties.展开更多
The well-known tower theorem of groups （resp. Lie algebras） shows that the tower of automorphism groups （resp. derivation algebras） of a finite group （resp. a finite dimensional Lie algebra） with trivial center ...The well-known tower theorem of groups （resp. Lie algebras） shows that the tower of automorphism groups （resp. derivation algebras） of a finite group （resp. a finite dimensional Lie algebra） with trivial center terminates after finitely many steps. We generalize these results for Lie rings, and present some necessary and sufficient conditions for Lie rings to be complete.展开更多
Reaction products of 2,4,6-tris(4-phenyl-phenoxy)-1,3,5-triazine derived from 4-phenylphenol cyanate ester and phenyl glycidyl ether were analyzed. In addition to an isocyanurate compound and an oxazolidone compound w...Reaction products of 2,4,6-tris(4-phenyl-phenoxy)-1,3,5-triazine derived from 4-phenylphenol cyanate ester and phenyl glycidyl ether were analyzed. In addition to an isocyanurate compound and an oxazolidone compound which were well known as reaction products of cyanate esters and epoxy resins, compounds with hybrid ring structure of cyanurate/isocyanurate were determined. Gibbs free energies of the compound having hybrid ring structure of cyanurate/isocyanurate with two isocyanurate moiety were found to be lower than that of the compound with cyanurate ring structure through calculations. Calculation data supported the existence of hybrid ring structure of cy-anurate/isocyanurate. It was revealed that isomerization from cyanurate to isocyanurate occurs via hybrid ring structure of cyanurate/isocyanurate in the reaction of aryl cyanurate and epoxy.展开更多
Let R be a finite chain ring with maximal ideal （7） and residue field F,and letγ be of nilpotency index t. To every code C of length n over R, a tower of codes C = （C ： γ0） C_ （C： 7） C ... C_ （C： γ2） C_ ...Let R be a finite chain ring with maximal ideal （7） and residue field F,and letγ be of nilpotency index t. To every code C of length n over R, a tower of codes C = （C ： γ0） C_ （C： 7） C ... C_ （C： γ2） C_ .-. C_ （C：γ^t-1） can be associated with C, where for any r C R, （C ： r） = {e C Rn I re E C}. Using generator elements of the projection of such a tower of codes to the residue field F, we characterize cyclic codes over R. This characterization turns the condition for codes over R to be cyclic into one for codes over the residue field F. Furthermore, we obtain a characterization of cyclic codes over the formal power series ring of a finite chain ring.展开更多
A mixed-valent hexanuclear complex [Cu^ⅡCu^Ⅰ2（pbi）2Br2]2 （pbi = （2-（2-pyridyl）-benzimidazole） exhibiting a dimeric unit bridged by two Br atoms was synthesized by hydrothermal reaction Interestingly, there ex...A mixed-valent hexanuclear complex [Cu^ⅡCu^Ⅰ2（pbi）2Br2]2 （pbi = （2-（2-pyridyl）-benzimidazole） exhibiting a dimeric unit bridged by two Br atoms was synthesized by hydrothermal reaction Interestingly, there exist intramolecular and intermolecular n^zstacking interactions as well as metalaromatic ring interactions in the title complex. The crystal belongs to the monoclinic system, space group P1, with a = 7.1061（9）, b = 12.1008（13）, c = 14.0711（17） A, α=91.742（8）,β=100.155（9）, γ=90.486（7）°, V = 1190.3（2） A^3, Z = 2, C48H32Br4CucoNt2, Mr = 1477.74, Dc= 2.061 g/cm^3, F（000） = 718, μ（MoKα） = 6.039 mm^-1, the final R = 0.0481 and wR = 0.0974 for 3426 observed reflections （I 〉 2σ（I））.展开更多
Making full use of coordination-driven self-assembly strategy,we herein described the selective synthesis of a molecular Borromean rings and two cases of “U”-shaped tweezer-like molecular assemblies in high yield by...Making full use of coordination-driven self-assembly strategy,we herein described the selective synthesis of a molecular Borromean rings and two cases of “U”-shaped tweezer-like molecular assemblies in high yield by using bipyridyl ligands based on biphenyl unit and half-sandwich binuclear rhodium(III)/iridium(III) building blocks.The selective synthesis was realized by adjusting the length of dipyridyl arms.The utilization of curved U-shaped bipyridyl ligand L1 led to tweezer-like molecular assemblies.Subsequently,olefinic bonds were introduced to elongate dipyridyl arms obtaining ligand L2.The ligand L2 has two stable conformations,U-shape and Z-shape,which facilitated the formation of different topologies including the tetranuclear macrocycle and Borromean rings with different building blocks in this work.These structures in solid and solution all have been further confirmed by single-crystal X-ray diffraction,NMR analysis,and mass spectrometry.In addition,as an important driving force,π-π stacking interactions not only played a significant role in the stability of structures but also further triggered photothermal conversion in solution.The experimental results demonstrated that compounds 1a and 2 had good NIR photothermal conversion efficiency (11.83% and 17.76%),and further analysis found the photothermal conversion efficiency had a gradual increase in the trend with the π-π stacking interactions increasing.This research expands the application of topological structures in materials science and provides a new idea for the synthesis of novel photothermal conversion materials.展开更多
基金supported by the National Natural Science Foundation of China (11272357 and 11102140)Doctoral Fund of Ministry of Education of China (200804251520 and 20110141120024)Natural Science Foundation of Shandong Province (ZR2009AQ006)
文摘In this study, we developed a general method to analytically tackle a kind of movable boundary problem from the viewpoint of energy variation. Having grouped the adhesion of a micro-beam, droplet and carbon nanotube （CNT） ring on a substrate into one framework, we used the developed line of reasoning to investigate the adhesion behaviors of these systems. Based upon the derived governing equations and transversality conditions, explicit solutions involving the critical parameters and morphologies for the three systems are successfully obtained, and then the parameter analogies and common characteristics of them are thor- oughly investigated. The presented method has been verified via the concept of energy release rate in fracture mechanics. Our analyses provide a new approach for exploring the mechanism of different systems with similarities as well as for understanding the unity of nature. The analysis results may be beneficial for the design of nano-structured materi- als, and hold potential for enhancing their mechanical, chemical, optical and electronic properties.
基金supported in part by NSFC (10371032)Doctoral Foundation of Ministry of Education(20050512002)+1 种基金Youth Foundation of Tianyuan(10726020)Youth Foundation of Hubei Provincial Department of Education(Q20081008)
文摘The well-known tower theorem of groups （resp. Lie algebras） shows that the tower of automorphism groups （resp. derivation algebras） of a finite group （resp. a finite dimensional Lie algebra） with trivial center terminates after finitely many steps. We generalize these results for Lie rings, and present some necessary and sufficient conditions for Lie rings to be complete.
文摘Reaction products of 2,4,6-tris(4-phenyl-phenoxy)-1,3,5-triazine derived from 4-phenylphenol cyanate ester and phenyl glycidyl ether were analyzed. In addition to an isocyanurate compound and an oxazolidone compound which were well known as reaction products of cyanate esters and epoxy resins, compounds with hybrid ring structure of cyanurate/isocyanurate were determined. Gibbs free energies of the compound having hybrid ring structure of cyanurate/isocyanurate with two isocyanurate moiety were found to be lower than that of the compound with cyanurate ring structure through calculations. Calculation data supported the existence of hybrid ring structure of cy-anurate/isocyanurate. It was revealed that isomerization from cyanurate to isocyanurate occurs via hybrid ring structure of cyanurate/isocyanurate in the reaction of aryl cyanurate and epoxy.
基金supported by the Natural Science Foundation of Hubei Province (B20114410)the Natural Science Foundation of Hubei Polytechnic University (12xjz14A)
文摘Let R be a finite chain ring with maximal ideal （7） and residue field F,and letγ be of nilpotency index t. To every code C of length n over R, a tower of codes C = （C ： γ0） C_ （C： 7） C ... C_ （C： γ2） C_ .-. C_ （C：γ^t-1） can be associated with C, where for any r C R, （C ： r） = {e C Rn I re E C}. Using generator elements of the projection of such a tower of codes to the residue field F, we characterize cyclic codes over R. This characterization turns the condition for codes over R to be cyclic into one for codes over the residue field F. Furthermore, we obtain a characterization of cyclic codes over the formal power series ring of a finite chain ring.
基金This work was supported by the 973 Program of the MOST (001CB108906), the NNSFC (90206040, 20425313, 20521101, 20333070, and 20303021), the NSF of Fujian Province (2005HZ01-1) and the Chinese Academy of Sciences
文摘A mixed-valent hexanuclear complex [Cu^ⅡCu^Ⅰ2（pbi）2Br2]2 （pbi = （2-（2-pyridyl）-benzimidazole） exhibiting a dimeric unit bridged by two Br atoms was synthesized by hydrothermal reaction Interestingly, there exist intramolecular and intermolecular n^zstacking interactions as well as metalaromatic ring interactions in the title complex. The crystal belongs to the monoclinic system, space group P1, with a = 7.1061（9）, b = 12.1008（13）, c = 14.0711（17） A, α=91.742（8）,β=100.155（9）, γ=90.486（7）°, V = 1190.3（2） A^3, Z = 2, C48H32Br4CucoNt2, Mr = 1477.74, Dc= 2.061 g/cm^3, F（000） = 718, μ（MoKα） = 6.039 mm^-1, the final R = 0.0481 and wR = 0.0974 for 3426 observed reflections （I 〉 2σ（I））.
基金supported by the National Natural Science Foundation of China(Nos.22031003,21720102004)the Shanghai Science Technology Committee(No.19DZ2270100)G.-X.J.thanks the Alexander von Humboldt Foundation for a Humboldt Research Award.
文摘Making full use of coordination-driven self-assembly strategy,we herein described the selective synthesis of a molecular Borromean rings and two cases of “U”-shaped tweezer-like molecular assemblies in high yield by using bipyridyl ligands based on biphenyl unit and half-sandwich binuclear rhodium(III)/iridium(III) building blocks.The selective synthesis was realized by adjusting the length of dipyridyl arms.The utilization of curved U-shaped bipyridyl ligand L1 led to tweezer-like molecular assemblies.Subsequently,olefinic bonds were introduced to elongate dipyridyl arms obtaining ligand L2.The ligand L2 has two stable conformations,U-shape and Z-shape,which facilitated the formation of different topologies including the tetranuclear macrocycle and Borromean rings with different building blocks in this work.These structures in solid and solution all have been further confirmed by single-crystal X-ray diffraction,NMR analysis,and mass spectrometry.In addition,as an important driving force,π-π stacking interactions not only played a significant role in the stability of structures but also further triggered photothermal conversion in solution.The experimental results demonstrated that compounds 1a and 2 had good NIR photothermal conversion efficiency (11.83% and 17.76%),and further analysis found the photothermal conversion efficiency had a gradual increase in the trend with the π-π stacking interactions increasing.This research expands the application of topological structures in materials science and provides a new idea for the synthesis of novel photothermal conversion materials.
