Covering the alternating groups by products of cycle classes

Given integers k,l?2, where either l is odd or k is even, we denote by n=n(k,l) the largest integer such that each element of An is a product of k cycles of length l. For an odd l, k is the diameter of the undirected Cayley graph Cay(An,Cl), where Cl is the set of all l-cycles in An. We prove that if k?2 and l?9 is odd and divisible by 3, then . This extends earlier results by Bertram [E. Bertram, Even permutations as a product of two conjugate cycles, J. Combin. Theory 12 (1972) 368-380] and Bertram and Herzog [E. Bertram, M. Herzog, Powers of cycle-classes in symmetric groups, J. Combin. Theory Ser. A 94 (2001) 87-99].     

A result on the Gelfand-Kirillov dimension of representations of classical groups

Let be the reductive dual pair . We show that if is a representation of (respectively ) obtained from duality correspondence with some representation of (respectively ), then its Gelfand-Kirillov dimension is less than or equal to
(respectively ).

     

Automorphism Groups of Restricted Cartan-Type Lie Superalgebras

Let X denote the restricted Lie superalgebras of Cartan type W, S, H, or K over a field of characteristic p > 3, and 𝔄 the corresponding underlying superalgebra of X. Employing the invariance of the filtration of X we construct an isomorphism of Aut X to Aut(𝔄:X), the admissible automorphism group of the associative super-commutative superalgebra 𝔄. Moreover, it is proved that the group isomorphism above maps the standard normal series of Aut X to the one of Aut(𝔄:X), and also maps the homogeneous automorphism group of X to the admissible homogeneous automorphism group of 𝔄.     

Influence of the nature of membrane ionogenic groups on water dissociation and electrolyte ion transport: A rotating membrane disk study

Polarization properties of electromembrane systems (EMS) consisting of a heterogeneous membrane, either the MK-41 phosphonic acid membrane or the MK-40 sulfonic acid membrane, and dilute sodium chloride solutions are investigated with the rotating membrane disk method. For the MK-41/0.01 M NaCl and MK-41/0.001 M NaCl EMS, effective ion transport numbers and partial current-voltage curves (CVC) are measured for sodium and hydrogen ions, and limiting-current densities and the diffusion-layer thickness are calculated as functions of the rotation rate of the membrane disk. With the theory of the overlimiting state of EMS, internal parameters of the systems under investigation—the diffusion-layer thickness, the space-charge distribution, and electric-field strengths in the diffusion layer and in the membrane—are calculated from experimentally obtained CVC and the dependence of effective transport numbers on current density. The catalytic influence of ionogenic groups on the dissociation rate of water is analyzed quantitatively. Partial CVC for H⁺ ions are calculated for the space-charge region in MK-40 and MK-41 membranes. Analogous CVC for bipolar membranes containing sulfonic acid and phosphonic acid groups are compared. The dissociation mechanism of water is the same in all EMS and is independent of the membrane type and the nature of the functional groups.     

Carboxyl groups in pre-treated regenerated cellulose fibres

The influence of peroxide bleaching and slack-mercerization on the amount of acidic groups in regenerated fibres (viscose, modal and lyocell) were studied. Conductometric titration was used to determine the total content of acidic carboxylic groups. Polyelectrolyte titration was used for surface and total charge determination, and to obtain information about the charge distribution and accessibilities of charged groups. Changes in fibre crystallinity to pre-treatment processes were characterized using iodine sorption (Schwertassek method) and correlated to treatments and the amount of carboxylic groups. For all three types of fibres the amount of accessible carboxyl groups was lowered by an increase in the degree of crystallinity. Bleaching with hydrogen peroxide causes some oxidative cellulose damage and, therefore, a larger amount of carboxyl groups (presumably formed at the end of cellulose chains). Slack-mercerization did not significantly change the total amount of acidic groups in the fibres, but their accessibility to cationic polyelectrolytes, in particular to polymers with high molecular weight was substantially lowered. Lidija Fras Zemljič, Zdenka Peršin, and Karin Stana Kleinschek are the members of the European Polysaccharide Network of Excellence (EPNOE).     

Effective strategy for the systematic synthesis of hydrazine derivatives

A new and efficient strategy for the systematic synthesis of hydrazine derivatives is reported. It allows the synthesis of up to tetrasubstituted hydrazine derivatives with minimal number of steps using only one protecting group or without any of them at all. Simple and readily available starting materials such as hydrazine hydrate or phenylhydrazine can be used. A variety of substrates were used to investigate scope and limitations of this strategy, additionally one full synthetic sequence was performed.     

类固醇类环境内分泌干扰物羟基衍生化研究

采用气相色谱-质谱联用技术(GC-MS),以N,O-双三甲基硅基三氟乙酰胺为衍生化试剂,系统研究了4种类固醇类环境内分泌干扰物雌酮(E1)、17β-雌二醇(E2)、雌三醇(E3)、17α-乙炔基雌二醇(EE2)的羟基衍生化行为,考察了BSTFA用量、衍生化温度和时间对类固醇类环境内分泌干扰物衍生化效果的影响以及衍生化产物的稳定性、标准曲线、仪器检出限等,并对衍生化产物特征碎片离子的裂解机理进行了解释.结果表明:对于100 μL 0.01 g/L标准混合溶液,BSTFA的最佳用量为25 μL;衍生化过程不需要加热,常温下(20 ℃)下反应10 min就可取得最佳的衍生化效果;衍生化产物的稳定性较好,在-20 ℃下放置48 h,相对响应因子RRF基本没有降低.在优化的实验条件下,各待测物具有良好的线性相关性,E1和E2的检出限为0.3 μg/L,EE2和E3的检出限为5 μg/L.     

Poly(diphenylacetylene)s with Electron‐Donating Alkoxy and Electron‐Withdrawing Fluoroalkyl Groups: Effect of the Substituent on Fluorescence

New poly(diphenylacetylene)s with alkoxy and fluoroalkyl groups as electron‐donating and electron‐withdrawing groups, respectively, were synthesized by using a WCl₆‐n‐Ph₄Sn catalyst. The polymer solutions emitted strong, bluish‐green lights when photo‐excited. The polymers that contained the electron‐donating alkoxy groups showed longer fluorescence‐maximum peaks when compared to the polymers that contained the electron‐withdrawing fluoroalkyl groups. However, such an effect of the substituent on the absorption property was not clearly seen. The emission bands of the solid films did not show any significant red shift, relative to that of the dilute solution.