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This paper analyzes how the social relations of class, race, and gender present in the social formation of South Africa resulted in the constitution of a pigmentocratic system of social welfare. The study is qualitative and it's based on the theory of the consubstantiality of class, race, and gender social relations produced by South African critical sociology. For the survey of corpora, literature review and analysis of official documents were carried out. Documents from the last years of the colonial period up to the year 1996 were analyzed. The study identified that the segregation relations generated a comprehensive system of social welfare oriented towards the social empowerment and social protection of white families. Meanwhile, Blacks, Coloureds, and Asians have become increasingly deprived of rights. Even with the end of apartheid, the South African welfare system continues (re)producing pigmentocracy. It stems from the neoliberal conditions that led the transition to democracy. [ABSTRACT FROM AUTHOR]

By a φ -variety V , we mean a supervariety or a ⁎-variety generated by an associative algebra over a field F of characteristic zero. In this case, we consider its sequence of φ -codimensions c n φ (V) and say that V is minimal of polynomial growth n k if c n φ (V) grows like n k , but any proper φ -subvariety grows like n t with t < k. In this paper, we deal with minimal φ -varieties generated by unitary algebras and prove that for k ≤ 2 there is only a finite number of them. We also explicit a list of finite dimensional algebras generating such minimal φ -varieties. For k ≥ 3 , we show that the number of minimal φ -varieties can be infinity and we classify all minimal φ -varieties of polynomial growth n k by giving a recipe for the construction of their T φ -ideals. [ABSTRACT FROM AUTHOR]

Let V be a variety of associative algebras with involution ⁎ over a field F of characteristic zero. Giambruno and Mishchenko proved in [6] that the ⁎-codimension sequence of V is polynomially bounded if and only if V does not contain the commutative algebra D = F ⊕ F , endowed with the exchange involution, and M , a suitable 4-dimensional subalgebra of the algebra of 4 × 4 upper triangular matrices, endowed with the reflection involution. As a consequence the algebras D and M generate the only varieties of almost polynomial growth. In [20] the authors completely classify all subvarieties and all minimal subvarieties of the varieties var ⁎ ( D ) and var ⁎ ( M ) . In this paper we exhibit the decompositions of the ⁎-cocharacters of all minimal subvarieties of var ⁎ ( D ) and var ⁎ ( M ) and compute their ⁎-colengths. Finally we relate the polynomial growth of a variety to the ⁎-colengths and classify the varieties such that their sequence of ⁎-colengths is bounded by three. [ABSTRACT FROM AUTHOR]

In this paper, we study the growth of the codimensions of a finite dimensional-superalgebraover a field of characteristic zero. We prove thathas polynomial growth if and only if any finite dimensional-superalgebra satisfying the same-graded identities ofhas an explicit decomposition into suitable-superalgebras. We also give such a characterization by studying the decomposition of the-cocharacter of. In this case, the main tool is the representation theory of the product of symmetric groups. [ABSTRACT FROM PUBLISHER]

We study the growth of the codimensions of a *-superalgebra over a field of characteristic zero. We classify the ideals of identities of finite dimensional algebras whose corresponding codimensions are of almost polynomial growth. It turns out that these are the ideals of identities of two algebras with distinct involutions and gradings. Along the way, we also classify the finite dimensional simple *-superalgebras over an algebraically closed field of characteristic zero. [ABSTRACT FROM PUBLISHER]

Near-infraredspectroscopy (NIRS) in conjunction with multivariatecalibration have proved to be adequate techniques to predict watercontent as well as methanol concentration in a industrial multicomponentmixture. The calibration models were developed using real industrialcomplex samples of water, methanol, and several other components invariable but lower concentrations such as sulfonic acids, acetone,and methyl cyanide. These samples come from industrialdistillation of hydrated methanol. Prior to the establishment of thetwo calibration models, wavelength selection, original spectral datacompression by means of the principal components analysis technique,and preprocessing optimization were performed. Calibration was modeledaccording topartial least squares (PLS) regression which was developed using themean centering and the leave-one-out cross validation (LOOCV) methodfor the optimization of the principal components (PC) number. Bothmodels were developed in the 5369–5153 cm–1spectral region. Karl Fischer titration and gas chromatography wereused as reference methodsfor water and methanol quantification, respectively. The suitabilityof the models was evaluated through the calculation of the standarderror of calibration and standard error of prediction. For the watercontent determination the variance scaling pretreatment was appliedwith 12 PLS factors, the calibration and predictionerrors being 2.56% and 1.76% respectively. As for the methanol concentrationvariance scaling was applied in conjunction with Savitzky–Golay’ssecond order derivative with six PLS factors. In this case the calibrationand prediction errors were 0.42% and 0.90%, respectively. [ABSTRACT FROM AUTHOR]