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 ).

     

Periodic decomposition of integer valued functions

We study those functions that can be written as a finite sum of periodic integer valued functions. On ℤ we give three different characterizations of these functions. For this we prove that the existence of a real valued periodic decomposition of a ℤ → ℤ function implies the existence of an integer valued periodic decomposition with the same periods. This result depends on the representation of the greatest common divisor of certain polynomials with integer coefficients as a linear combination of the given polynomials where the coefficients also belong to ℤ[x]. We give an example of an ℤ → {0, 1} function that has a bounded real valued periodic decomposition but does not have a bounded integer valued periodic decomposition with the same periods. It follows that the class of bounded ℤ → ℤ functions has the decomposition property as opposed to the class of bounded ℝ → ℤ functions. If the periods are pairwise commensurable or not prescribed, then we get more general results. Supported by OTKA grants T 43623 and K 61908.     

Moufang sets of mixed type F4

Moufang sets were introduced by Jacques Tits in order to understand isotropic linear algebraic groups of relative rank one, but the notion is more general. We describe a new class of Moufang sets, arising from so‐called mixed groups of type ${\mathsf{F}}_4$ in characteristic 2, obtained as the fixed point set under a suitable involution.     

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.     

末端带有溴甲基基团的柱状树枝化聚酰胺的合成与表征

采用大分子单体的方法合成了一种含大量溴甲基官能团端基,主链和侧链均为聚酰胺的功能化柱状树枝化聚酰胺.氯化亚砜的新活化工艺使整个合成过程不需要保护和去保护的步骤且减少了副反应的产生,从而使得合成和纯化更加简单.产物的结构通过红外和核磁得到了证实.由分子量测试知,聚酰胺的重均分子量(Mw)为5.01×104,分子量分布为2.74.由溶解性测试知,该聚合物能溶解于N,N′-二甲基甲酰胺、N,N′-二甲基乙酰胺、二甲亚砜、1-甲基-2-吡咯烷酮和硫酸等溶剂,溶解性能得到了大大的提高,主要是由于侧链树枝化单元和末端溴甲基存在的缘故.由粘度测试知,该聚酰胺的粘度低,主要是由于侧链树枝化单元的屏蔽效应.该聚合物的热性能也由TGA测试得到了表征,结果表明该聚酰胺具有良好的热性能.由于该聚酰胺外端具有大量的溴甲基基团,它可以作为原子转移自由基聚合反应的引发剂来合成大型的梳形聚合物,另外通过把它外围的溴甲基转化为其它的功能化基团,可以使它应用于其它更广的领域.