On the peirce decompositions for freudenthal—kantor triple systems

It is the object of this paper to investigate the Peirce decomposition for Freudenthal-Kantor triple systems, by making use of the concept of anti-derivation of the triple systems.     

马来松香酸和纳米氧化铝颗粒协同稳定具有pH响应性的Pickering乳液

使用有机颗粒稳定Pickering乳液受到越来越多的关注, 润湿性可调的有机颗粒且结合纳米无机颗粒协同稳定不同类型的Pickering乳液却鲜有报道. 系统研究了基于具有多羧酸基团的松香基衍生物马来松香(MPA)与纳米Al₂O₃颗粒在不同pH条件下形成的乳液类型及相关机理. 研究发现, 在单一MPA颗粒体系条件下, pH可以诱导乳液的类型由W/O Pickering乳液到O/W Pickering乳液, 到最后O/W乳液的转变, MPA的亲水性随着pH升高而增强是该乳液转变的原因. 当纳米Al₂O₃颗粒加入到MPA中后, 吸附在MPA颗粒上的亲水性Al₂O₃导致MPA颗粒亲水性增加, 从而可以使W/O Pickering乳液转变为O/W Pickering乳液(pH=1). 当pH=6时, MPA分子与纳米Al₂O₃颗粒同时具有较强的亲水性且分别无法形成稳定的乳液, 但两者的混合体系可以形成稳定的W/O Pickering乳液, 这是因为MPA分子与纳米Al₂O₃颗粒可以在水溶液中形成疏水性较强的络合物. 另外, 研究了MPA浓度及油相体积分数对乳液外观及粒径的影响, 发现随着MPA浓度增加Pickering乳液的粒径逐渐减小, 增加油相的体积分数会引起粒径的增大. 最后, 利用Zeta电势、颗粒在油水界面吸附率、接触角及表/界面张力研究了稳定Pickering乳液的稳定机理, 在油水界面上吸附的类似盔甲状颗粒层及颗粒层之间形成的网状结构是乳液液滴保持稳定的原因. 为Pickering乳液的绿色化制备提供了一种新的途径, 将在化妆品、医药及新材料等领域得到重要应用.     

Prediction of breakthrough curves for multicomponent adsorption in a fixed-bed column using logistic and Gompertz functions

In order to facilely predict the multicomponent breakthrough curves and avoid the complicated numerical solution, this work proposes two empirical models based on the logistic and Gompertz functions. The S-shaped and bell-like curves correspond to the adsorption and displacement processes respectively. The equilibrium loading of each component can be calculated by integration of the measured breakthrough curves. The effects of the model parameters on the breakthrough curves are investigated. The applicability of the two empirical models is validated by three binary and four ternary adsorption systems, including the gas–solid and liquid–solid adsorption. The residual plot and coefficient of determination (R²) are used to evaluate their fitting quality. The results indicate that the fitting curves agree well with the experimental data and all of the residuals are distributed randomly. The five model parameters (k, τ, k*, τ* and c) are easily obtained by the nonlinear regression. For example, the fitting results are k = 1.37 × 10^?2 min^?1, τ = 292 min, k* = 1.25 × 10^?2 min^?1, τ* = 453 min and c = 85.3 for adsorption of n-butyl acetate and p-xylene on granular activated carbon. On the whole, the Gompertz model is superior to the logistic model in terms of the fitting accuracy. The significance of this work is to provide a simple and practical method for prediction of the multicomponent breakthrough curves.     

Normal polytopes: Between discrete,continuous, and random

The first three sections of this survey represent an updated and much expanded version of the abstract of my talk at FPSAC'2010: new results are incorporated and several concrete conjectures on the interactions between the three perspectives on normal polytopes in the title are proposed. The last section outlines new challenges in general convex polytopes, motivated by the study of normal polytopes.     

Integrability and solvability of polynomial Liénard differential systems

We provide the necessary and sufficient conditions of Liouvillian integrability for Liénard differential systems describing nonlinear oscillators with a polynomial damping and a polynomial restoring force. We prove that Liénard differential systems are not Darboux integrable excluding subfamilies with certain restrictions on the degrees of the polynomials arising in the systems. We demonstrate that if the degree of a polynomial responsible for the restoring force is greater than the degree of a polynomial producing the damping, then a generic Liénard differential system is not Liouvillian integrable with the exception of linear Liénard systems. However, for any fixed degrees of the polynomials describing the damping and the restoring force we present subfamilies possessing Liouvillian first integrals. As a by-product of our results, we find a number of novel Liouvillian integrable subfamilies. In addition, we study the existence of nonautonomous Darboux first integrals and nonautonomous Jacobi last multipliers with a time-dependent exponential factor.     

The spectral curve theory for (k,l)-symmetric CMC surfaces

Constant mean curvature surfaces in $S^3$ can be studied via their associated family of flat connections. In the case of tori this approach has led to a deep understanding of the moduli space of all CMC tori. For compact CMC surfaces of higher genus the theory is far more involved due to the non abelian nature of their fundamental group. In this paper we extend the spectral curve theory for tori developed in Hitchin (1990), Pinkall and Sterling (1989) and for genus 2 surfaces (Heller, 2014) to CMC surfaces in $S^3$ of genus $g=k\cdot l$ with commuting ${\mathbb{Z}}_{k+1}$ and ${\mathbb{Z}}_{l+1}$ symmetries. We determine their associated family of flat connections via certain flat line bundle connections parametrized by the spectral curve. We generalize the flow on spectral data introduced in Heller (2015) and prove the short time existence of this flow for certain families of initial surfaces. In this way we obtain countably many $1-$parameter families of new CMC surfaces of higher genus with prescribed branch points and prescribed umbilics.     

Rational functions with identical measure of maximal entropy

We discuss when two rational functions f and g   can have the same measure of maximal entropy. The polynomial case was completed by Beardon, Levin, Baker–Eremenko, Schmidt–Steinmetz, etc., 1980s–1990s, and we address the rational case following Levin and Przytycki (1997). We show: _μf=_μg${\mu }_f={\mu }_g$ implies that f and g   share an iterate (fⁿ=g^m$f^n=g^m$ for some n and m) for general f   with degree d≥3$d\ge 3$. And for generic f∈_Ratd≥3$f\in {\mathrm{Rat}}_{d\ge 3}$, _μf=_μg${\mu }_f={\mu }_g$ implies g=fⁿ$g=f^n$ for some n≥1$n\ge 1$. For generic f∈_Rat2$f\in {\mathrm{Rat}}_2$, _μf=_μg${\mu }_f={\mu }_g$ implies that g=fⁿ$g=f^n$ or _σf°fⁿ${\sigma }_f°f^n$ for some n≥1$n\ge 1$, where _σf∈_PSL2(C)${\sigma }_f\in {\mathit{PSL}}_2(\mathbb{C})$ permutes two points in each fiber of f. Finally, we construct examples of f and g   with _μf=_μg${\mu }_f={\mu }_g$ such that fⁿ≠σ°g^m$f^n\ne \sigma °g^m$ for any σ∈_PSL2(C)$\sigma \in {\mathit{PSL}}_2(\mathbb{C})$ and m,n≥1$m,n\ge 1$.     

自主协同系统的宏观稳定机理研究

为保证自主协同机群的内聚性, 实现多机的有效沟通和协作, 借鉴蜂王信息素机理, 抽象出跟踪型多无人机自主协同系统的宏观运动特征. 通过构造Lyapunov函数, 分析该系统的稳定性, 进而得到系统的稳定性判据. 仿真结果表明: 本文所提的稳定控制机理不仅能够保证自主协同系统的稳定性, 还能够通过调整相关控制参数有效地控制系统规模.