SL(3,3~n)和SU(3,3~n)的第一Cartan不变量

确定Cartan不变量是代数群与相关的李型有限群的模表示理论中的一个重要方面.作者利用代数群模表示理论中的一系列结果,计算了3~n个元素的有限域上特殊线性群SL(3,3~n)和特殊酉群SU(3,3~n)的第一Cartan不变量,得到如下结论:当G=SL(3,3~n)时,C_(00)~((n))=a~n+b~n+6~n-2·8~n;而当G=SU(3,3~n)时,C_(00)~((n))=a~n+b~n+6~n-2·8~n+2·(1+(-1)~n),其中a,b是多项式x~2-20x+48的两个根.另外,作者也得到了射影不可分解模U_n(0,0)的维数公式:dim U_n(0,0)=(12~n-6~n+∈)·3~(3n),其中,当G=SL(3,3~n)时,∈=1;而当G=SU(3,3~n)时,∈=-1.     

钒液流电池用隔离膜研究进展

钒液流电池是近年来发展最为迅猛的储能电池之一。隔膜作为钒电池的重要组成部分直接关系到钒电池的转化储能效率和使用寿命。本文综述了近年来钒电池用隔离膜的发展现状。全氟磺酸质子交换膜(Nafion膜)作为当前使用最为广泛的隔膜,从传导机理、交换机理和表面涂覆、交联、复合等表面改性技术方面入手做了深入的研究,并对比分析了各种改性方法的优缺点。对磺化的特种工程塑料为主的非氟耐热型质子交换膜和功能化的聚烯烃隔膜在钒电池中的当前进展做了全面总结,并对钒液流电池用电池隔膜的发展方向做了展望。     

A Theoretical Model for Release Dynamics of an Antifungal Agent Covalently Bonded to the Chitosan

The aim of the study was to create a mathematical model useful for monitoring the release of bioactive aldehydes covalently bonded to the chitosan by reversible imine linkage, considered as a polymer–drug system. For this purpose, two hydrogels were prepared by the acid condensation reaction of chitosan with the antifungal 2-formyl-phenyl-boronic acid and their particularities; influencing the release of the antifungal aldehyde by shifting the imination equilibrium to the reagents was considered, i.e., the supramolecular nature of the hydrogels was highlighted by polarized light microscopy, while scanning electron microscopy showed their microporous morphology. Furthermore, the in vitro fungicidal activity was investigated on two fungal strains and the in vitro release curves of the antifungal aldehyde triggered by the pH stimulus were drawn. The theoretical model was developed starting from the hypothesis that the imine-chitosan system, both structurally and functionally, can be assimilated, from a mathematical point of view, with a multifractal object, and its dynamics were analyzed in the framework of the Scale Relativity Theory. Thus, through Riccati-type gauges, two synchronous dynamics, one in the scale space, associated with the fungicidal activity, and the other in the usual space, associated with the antifungal aldehyde release, become operational. Their synchronicity, reducible to the isomorphism of two SL(2R)-type groups, implies, by means of its joint invariant functions, bioactive aldehyde compound release dynamics in the form of “kink–antikink pairs” dynamics of a multifractal type. Finally, the theoretical model was validated through the experimental data.     

Anti-holomorphic involutive isometry of hyper-Kähler manifolds and branes

We study complex Lagrangian submanifolds of a compact hyper-Kähler manifold and prove two results: (a) that an involution of a hyper-Kähler manifold which is antiholomorphic with respect to one complex structure and which acts non-trivially on the corresponding symplectic form always has a fixed point locus which is complex Lagrangian with respect to one of the other complex structures, and (b) there exist Lagrangian submanifolds which are complex with respect to one complex structure and are not the fixed point locus of any involution which is anti-holomorphic with respect to one of the other complex structures.     

New representation and factorizations of the higher-order ultraspherical-type differential equations

The paper deals with the class of linear differential equations of any even order 2α+4$2\alpha +4$, α∈_N0$\alpha \in {\mathbb{N}}_0$, which are associated with the so-called ultraspherical-type polynomials. These polynomials form an orthogonal system on the interval [−1,1]$[-1,1]$ with respect to the ultraspherical weight function (1−x²)^α${(1-x^2)}^{\alpha }$ and additional point masses of equal size at the two endpoints. The differential equations of “ultraspherical-type” were developed by R. Koekoek in 1994 by utilizing special function methods. In the present paper, a new and completely elementary representation of these higher-order differential equations is presented. This result is used to deduce the orthogonality relation of the ultraspherical-type polynomials directly from the differential equation property. Moreover, we introduce two types of factorizations of the corresponding differential operators of order 2α+4$2\alpha +4$ into a product of α+2$\alpha +2$ linear second-order operators.     

Site- and event-specific wastewater-based epidemiology: Current status and future perspectives

Wastewater-based epidemiology (WBE) can provide objective and reliable data to monitor spatio‐temporal patterns of licit and illicit drug use. Numerous studies have been published relating to sampling, sample stability, validation of analytical protocols and the back-calculation of drug consumption. The majority of these studies focus on sampling from municipal sewage treatment plants, but an increasing number of studies have used WBE to monitor community-specific substance use and use during special events. This paper presents a systematic review of published WBE studies of drug use trends in educational institutions and prisons, as well as during music festivals, sporting events, and holidays. A discussion on the application and benefits of using wastewater-based epidemiology in these specific cases is presented together with an examination of current challenges and future perspectives.     

宽带隙Cu(In,Al)Se2薄膜的制备及表征

以特殊脉冲电沉积方法制备CuInSe2(CIS)前驱体薄膜, 通过真空蒸镀法在CIS薄膜上沉积Al膜, 经硒化退火后在氧化铟锡(ITO)基底上制备了Cu(InAl)Se2(CIAS)薄膜. 采用扫描电子显微镜(SEM)、X射线能谱(EDS)、X射线衍射(XRD)、X射线光电子能谱(XPS)、紫外-可见吸收光谱(UV-Vis)对其形貌、结构、成分及光学吸收性质进行了表征. 结果表明, 制备的CIAS薄膜颗粒均匀, 表面平整致密, 呈黄铜矿结构. 薄膜在可见光区具有良好的吸收, 带隙约为1.65 eV.     

可逆加成-断裂链转移自由基聚合与点击化学相结合在制备特殊结构聚合物中的应用

可逆加成一断裂链转移(RAFT)聚合作为一种新型活性自由基聚合方法,由于其具有单体适用面广、聚合条件温和、不受聚合方法的限制等优点,已经成为聚合物分子设计的有效手段之一.点击化学(Click chaemistry)是近几年发展起来的一种快速合成的新方法,是指选用易得原料,通过可靠、高效而又具有选择性的化学反应来实现碳杂...     

应用特征波段和反射变形差的方法进行土壤属性估算

传统的土壤分析是昂贵的、费时的并且可能带来环境污染问题。应用近红外光谱分析技术测定土壤参数具有快速、花费少和非破坏性的特点。利用GPS野外定位,在江西省的红壤站、鄱阳湖站和千烟州站周边共取得41个耕层(0～20 cm)土壤样品。通过对土壤样品高光谱反射率的室内分析测定,研究了土壤在紫外/可见光/近红外波段光谱的反射特性。研究的目的是应用波谱反射建立一个新的研究方法来估算土壤属性含量值。随后应用多元线性逐步回归方法对反射光谱数据进行分析,“B22+H13”光谱数据作为自变量,土壤属性含量作为因变量,建立了土壤属性含量的高光谱预测模型, 并对模型的稳定性和预测能力进行了检验。结果是土壤的pH、有机碳、全氮、全磷、阳离子代换量和碱解氮的相关系数都达到了0.80,而TK、速效磷、速效钾的相关系数在0.68左右。结果表明,应用此方法估算一些土壤属性含量是可行的。     

Necessity of acceleration‐induced nonlocality

The purpose of this paper is to explain clearly why nonlocality must be an essential part of the theory of relativity. In the standard local version of this theory, Lorentz invariance is extended to accelerated observers by assuming that they are pointwise inertial. This locality postulate is exact when dealing with phenomena involving classical point particles and rays of radiation, but breaks down for electromagnetic fields, as field properties in general cannot be measured instantaneously. The problem is corrected in nonlocal relativity by supplementing the locality postulate with a certain average over the past world line of the observer.