The BRST quantisation of the Drinfeld-Sokolov reduction applied to the case of A (1) 2 is explored to construct in an unified and systematic way the general singular vectors in W 3 and W (2) 3 Verma modules. The construction relies on the use of proper quantum analogues of the classical DS gauge fixing transformations. Furthermore the stability groups W (η) of the highest weights of the W-Verma...

This paper introduces a new algorithm to reduce the time of updating the weights of auto-association multilayer perceptrons network. The basic idea is to modify the singular value decomposition which has been used in the batch algorithm to update the weights whenever a new row is added to the input matrix. The computation analysis and the experiments show that the new algorithm speeds up the im...

In this paper we present an efficient algorithm to compute the eigen decomposition of a matrix that is a weighted sum of the self outer products of vectors such as a covariance matrix of data. A well known algorithm to compute the eigen decomposition of such matrices is though the singular value decomposition, which is available only if all the weights are nonnegative. Our proposed algorithm ac...

Sound exposure effects have been investigated by broadcasting a group of broilers with sound of Quran verses (Group B) whereas the other group is the control broilers (Group C). The growth rate comparisons in terms of weight and raw meat texture measured by shear force have been investigated. Twenty-seven broilers were randomly selected from each group on Day 24 and weight measurement was carri...

Interpolatory quadrature rules whose abscissas are zeros of a biorthogonal polynomial have proved to be useful, especially in numerical integration of singular integrands. However, the positivity of their weights has remained an open question, in some cases, since 1980. We present a general criterion for this positivity. As a consequence, we establish positivity of the weights in a quadrature r...

In the present paper, we define a Dolbeault complex with weights according to normal crossings, which is a useful tool for studying the ∂-equation on singular complex spaces by resolution of singularities (where normal crossings appear naturally). The major difficulty is to prove that this complex is locally exact. We do that by constructing a local ∂-solution operator which involves only Cauch...

In this paper we prove two extrapolation theorems for related weights. The theorems proved by C. Segovia and J.L. Torrea in [C. Segovia and J.L. Torrea, Weighted inequalities for commutators of fractional and singular integrals. Publ. Mat. 35 (1991) 209-235] are adapted for one-sided weights. We apply these extrapolation theorems to improve weighted inequalities for commutators (with symbol b d...