一些稀疏图的强边染色（英文）

图G的强边染色是指对图G进行正常边染色使得任意长度为3的路的三条边染不同的颜色.图G的强边色数,记为χ’_s(G),是使得图G是强k边着色的最小正整数kk.2015年,Zang [arXiv:1510.00785]证明了:最大度△(G)=5的图G,χ’_s(G)≤37.本文证明了:最大度△(G)=5且最大平均度小于8/3(或者14/5)的图G,χ’_s(G)≤13 (或者14).另外,本文证明了:最大度△(G)≥3的不含K_2,3-图子式的图G,χ’_s(G)≤4△(G)-6,这个界是紧的.     

Foams stabilized by mixed cationic gemini/anionic conventional surfactants

The mixed adsorption of a cationic gemini surfactant, ethanediyl-1,2-bis(dodecyldimethylammonium bromide) (abbreviated as 12-2-12), and an anionic conventional surfactant, sodium dodecyl sulfate (SDS), was examined using surface tension measurements. The viscoelastic properties of the mixed films were investigated by dilational interfacial rheology technique. The results showed that the addition of SDS promoted the close packing of adsorbed molecules at the interface, which increased the dilational elasticity of the mixed films. The stability of the foams was determined by the half-life of foam height collapse. The foams generated by 12-2-12/SDS mixtures were more stable than that formed by pure 12-2-12. In the presence of sodium bromide, the foam stability was further enhanced and the surfactant concentration required to attain the maximum effect in stabilizing foams was greatly reduced. The high foam stability could well relate to the high elasticity of the film.     

Facile preparation of hierarchically porous carbon using diatomite as both template and catalyst and methylene blue adsorption of carbon products

Hierarchically porous carbons were prepared using a facile preparation method in which diatomite was utilized as both template and catalyst. The porous structures of the carbon products and their formation mechanisms were investigated. The macroporosity and microporosity of the diatomite-templated carbons were derived from replication of diatom shell and structure-reconfiguration of the carbon film, respectively. The macroporosity of carbons was strongly dependent on the original morphology of the diatomite template. The macroporous structure composed of carbon plates connected by the pillar- and tube-like macropores resulted from the replication of the central and edge pores of the diatom shells with disk-shaped morphology, respectively. And another macroporous carbon tubes were also replicated from canoe-shaped diatom shells. The acidity of diatomite dramatically affected the porosity of the carbons, more acid sites of diatomite template resulted in higher surface area and pore volume of the carbon products. The diatomite-templated carbons exhibited higher adsorption capacity for methylene blue than the commercial activated carbon (CAC), although the specific surface area was much smaller than that of CAC, due to the hierarchical porosity of diatomite-templated carbons. And the carbons were readily reclaimed and regenerated.     

Boronic Acid functionalized core-shell polymer nanoparticles prepared by distillation precipitation polymerization for glycopeptide enrichment

The boronic acid-functionalized core-shell polymer nanoparticles, poly(N,N-methylenebisacrylamide-co-methacrylic acid)@4-vinylphenylboronic acid (poly(MBA-co-MAA)@VPBA), were successfully synthesized for enriching glycosylated peptides. Such nanoparticles were composed of a hydrophilic polymer core prepared by distillation precipitation polymerization (DPP) and a boronic acid-functionalized shell designed for capturing glycopeptides. Owing to the relatively large amount of residual vinyl groups introduced by DPP on the core surface, the VPBA monomer was coated with high efficiency, working as the shell. Moreover, the overall polymerization route, especially the use of DPP, made the synthesis of nanoparticles facile and time-saving. With the poly(MBA-co-MAA)@VPBA nanoparticles, 18?glycopeptides from horseradish peroxidase (HRP) digest were captured and identified by MALDI-TOF mass spectrometric analysis, relative to eight glycopeptides enriched by using commercially available meta-aminophenylboronic acid agarose under the same conditions. When the concentration of the HRP digest was decreased to as low as 5?nmol, glycopeptides could still be selectively isolated by the prepared nanoparticles. Our results demonstrated that the synthetic poly(MBA-co-MAA)@VPBA nanoparticles might be a promising selective enrichment material for glycoproteome analysis.     

Mixed micellization of binary alkanediyl-α,ω-bis(dimethyldodecylammonium bromide) homologues in aqueous solution

We report a systematic investigation on the mixed micellization of the binary homologues of Gemini surfactant 12-s-12 series that has a flexible polyethylene spacer. The results showed that the micellization behavior deviates from the ideality when the difference of the spacer lengths (Δs) of two components is larger than 6. The obvious synergism between two components occurs in the mixtures of 12-2-12/12-18-12 and 12-4-12/12-18-12. This was attributed to a relatively large difference in the molecular shape of the two components induced by the length and the configuration of the spacer chain, which yielded better steric compensation between two components within a mixed micelle than other mixed systems.     

Orientation of the Azobenzene Spacer of Carboxylic Methyl Ester Gemini Surfactants in Langmuir Monolayer

The Langmuir monolayer of carboxylic methyl ester Gemini surfactants with the azobenzene spacer, referred to as MC_m(azo)MC_m, was prepared and the π‐A isotherms were measured. The result revealed an orientational picture of the azobenzene spacer at the air/water interface. Before irradiation, the planar trans‐azobenzene group adopted an approximate configuration parallel to the interface and lay on the air/water interface. After UV‐light irradiation, the spacer became the twisted cis‐one. Because of the location of the polar headgroups at the air/water interface, the two phenyl rings were also forced to take a near‐parallel orientation with the interface to reduce the free energy. As a result, the spacer thin‐layer was "thickened", which caused an elevation in collapse pressure.     

Alkyl chain length-dependent viscoelastic properties in aqueous wormlike micellar solutions of anionic gemini surfactants with an azobenzene spacer

A homologue of carboxylate gemini surfactants with an azobenzene spacer and different lengths of the alkyl tails, referred to as C_m(azo)C_m, has been synthesized. All the surfactants formed wormlike micelles at relatively low concentrations without addition of salt. The reason was attributed to the long and rigid characteristic of the azobenzene spacer, which yielded the pseudo volume between the two tails and thus a columnar-like molecular geometry favorable for the formation of wormlike micelles. The results of rheology and FF-TEM measurements showed that the length of the alkyl tails strongly affected the viscoelastic properties of the wormlike micelle solution. With the increase of the alkyl tail length, the solutions evolved from a typically viscous fluid to a strong viscoelastic solution and then to a gel-like state. This was attributed to the different microstates as revealed by scaling law. These solutions behave as polyelectrolyte systems because of their additive-free nature.     

Evolution of cooperation among mobile agents

We study the effects of mobility on the evolution of cooperation among mobile players, which imitate collective motion of biological flocks and interact with neighbors within a prescribed radius R. Adopting the the prisoner’s dilemma game and the snowdrift game as metaphors, we find that cooperation can be maintained and even enhanced for low velocities and small payoff parameters, when compared with the case that all agents do not move. But such enhancement of cooperation is largely determined by the value of R, and for modest values of R, there is an optimal value of velocity to induce the maximum cooperation level. Besides, we find that intermediate values of R or initial population densities are most favorable for cooperation, when the velocity is fixed. Depending on the payoff parameters, the system can reach an absorbing state of cooperation when the snowdrift game is played. Our findings may help understanding the relations between individual mobility and cooperative behavior in social systems.     

符号圈拼接图的零度

令$\eta(\Gamma)$和$c(\Gamma)$是符号图$\Gamma$的零度和基本圈数. 一个符号圈拼接图是指每个块都是圈的连通符号图. 本文证明了对任意符号拼接图$\eta(\Gamma)\le c(\Gamma)+1$成立, 并且刻画了等号成立的极图, 推广了王登银等人(2022)在简单圈拼接图上的结果. 此外, 我们证明了任意的符号拼接图$\eta(\Gamma)\neq c(\Gamma)$, 给出了满足$\eta(\Gamma)=c(\Gamma)-1$的符号拼接图的一些性质并刻画处$\eta(\Gamma)=c(\Gamma)-1$的二部符号拼接图.