We introduce a suitable adapted ordering for the twisted N = 2 superconformal algebra (i.e. with mixed boundary conditions for the fermionic fields). We show that the ordering kernels for complete Verma modules have two elements and the ordering kernels for G-closed Verma modules just one. Therefore, spaces of singular vectors may be two-dimensional for complete Verma modules whilst for G-close...

Abstract The principal component analysis (PCA) method and the singular value decomposition (SVD) are widely used for foreground subtraction in 21 cm intensity mapping experiments. We show their equivalence, point out that condition completely clean separation of foregrounds cosmic signal using PCA/SVD is unrealistic. propose a PCA-based method, dubbed “singular vector projection (SVP)” which e...

Given an m×n matrix A and an integer k less than the rank of A, the “best” rank k approximation to A that minimizes the error with respect to the Frobenius norm is Ak, which is obtained by projecting A on the top k left singular vectors of A. While Ak is routinely used in data analysis, it is difficult to interpret and understand it in terms of the original data, namely the columns and rows of ...

The problem of describing the singular vectors of W 3 and W (2) 3 Verma modules is addressed, viewing these algebras as BRST quantized Drinfeld-Sokolov (DS) reductions of A (1) 2. Singular vectors of an A (1) 2 Verma module are mapped into W algebra singular vectors and are shown to differ from the latter by terms trivial in the BRST cohomology. These maps are realized by quantum versions of th...

We generalize Khintchine’s method of constructing totally irrational singular vectors and linear forms. The main result the paper shows existence forms with large uniform Diophantine exponents on certain subsets ℝn, in particular any analytic submanifold ℝn dimension ≥2 which is not contained a proper rational affine subspace.