Este artigo utiliza ferramentas da teoria de grupos e computação simbólica para dar uma classificação das representações de grupos finitos de ordem menor ou igual a 9 que podem ser consideradas no estudo local de campos vetoriais reversíveis-equivariantes em <img border=0 width=32 height=32 src="../../../../img/revistas/aabc/v83n2/carr.jpg" align=absmiddle>4 . Os resultados são obtidos resolvendo algebricamente equações matriciais. Em particular, exibimos as involuções utilizadas no estudo local de campos vetoriais reversíveis-equivariantes. Baseado em tal abordagem, nós apresentamos, para cada elemento desta classe, uma forma normal de Belitskii simplificada.

This paper uses tools in group theory and symbolic computing to classify the representations of finite groups with order lower than, or equal to 9 that can be derived from the study of local reversible-equivariant vector fields in <img border=0 width=32 height=32 src="../../../../img/revistas/aabc/v83n2/carr.jpg" align=absmiddle>4 . The results are obtained by solving matricial equations. In particular, we exhibit the involutions used in a local study of reversible-equivariant vector fields. Based on such approach we present, for each element in this class, a simplified Belitskii normal form.

Estudou-se a agregação de surfactantes aniônicos em soluções aquosas diluídas de (hidroxipropil)celulose (HPC) sob moderada força iônica (NaCl 0,1 mol L-1). Empregaram-se os surfactantes colato de sódio (CS), deoxicolato de sódio (DC) e dodecil sulfato de sódio (SDS). Observou-se decréscimo da concentração de agregação crítica (C1) para SDS e DC em comparação à concentração micelar crítica (CMC), enquanto ocorreu aumento para CS, a 298 K. A viscosidade relativa apresentou um máximo para o sistema SDS/HPC, mas permaneceu constante para CS/HPC ou DC/HPC. Houve aumento da temperatura de turbidez para todos os sistemas. Utilizando-se espalhamento de luz dinâmico, verificou-se que, a baixas concentrações de surfactante, o modo rápido da HPC relaciona-se a agregados surfactantes/HPC e cadeias poliméricas curtas; a altas concentrações, a micelas livres. O modo lento relaciona-se a complexos surfactante/HPC ou a "clusters" de HPC. Nos sistemas sais biliares/HPC, o mecanismo de agregação pode ocorrer em duas etapas.

The aggregation of different anionic surfactants in dilute aqueous solutions of (hydroxypropyl)cellulose (HPC) under moderate ionic strength (NaCl 0.1 mol L-1) was studied. The surfactants were sodium cholate (CS), sodium deoxycholate (DC) and sodium dodecylsulphate (SDS). By fluorescence probing, the critical aggregate concentration (C1) decreased for SDS and DC in comparison to the critical micelle concentration (CMC) whereas it increased for CS at 298 K. The relative viscosity reached a maximum for SDS/HPC but remained constant for CS/HPC and DC/HPC. By light scattering, cloud points were verified to increase. By dynamic light scattering, it was concluded that, at low surfactant contents, the fast mode of HPC is related to surfactant/HPC aggregates and shorter HPC chains; at high contents, to free micelles. The slow mode is linked to interchain polymer-surfactant complexes and HPC clusters. For the bile salts/ HPC systems, the mechanism of aggregation may occur in two steps.

Fluorescence probing, viscosity and light scattering measurements have been combined to study the aggregation of different anionic surfactants mainly in dilute solutions (0.5% w/v) of (hydroxypropyl)cellulose (HPC MW 173,000), in moderate ionic strength (NaCl 0.1 mol.L-1). The set of surfactants includes natural cholesterol derivatives, sodium cholate (CS) and sodium deoxycholate (DC), and the alkylsulphate, sodium dodecylsulphate (SDS). At 298 K the critical surfactant concentration related to aggregate/HPC formation (C1) decreases for SDS and DC whereas it increases slightly for CS. At 312 K the C1 values for CS and DC are slightly shifted toward higher values whereas it is not changed for SDS. All surfactant/HPC systems increase C1 values as the HPC concentration increases to 1.2%. Above C1 the viscosity increases for all surfactant/HPC systems but it is sharper in the increasing order CS, DC and SDS. The hydrodynamic behavior indicates that CS induces higher diffusion to HPC than SDS and DC. The aggregation in the surfactant/HPC systems is analyzed through the feature of surfactant/aggregate structure (size, charge density, etc).