ABSTRACT Future large-scale structure surveys will measure the locations and shapes of billions galaxies. The precision such catalogues require meticulous treatment systematic contamination observed fields. We compare several existing methods for removing systematics from galaxy clustering measurements. show how all methods, including popular pseudo-C? Mode Projection Template Subtraction can b...

In this paper, properties of ideal I semiprime ring R with multiplicative generalized (α,β)- reverse derivation determined not necessarily additive map d is studied. We previous studies for different derivations to F. show that [β(p),d(p)]I=0 all p∈I or [d(p)],α(p)]I=0 under the given conditions. Also, we give relationship between and anti-automorphism α automorphism β R. Under conditions, exam...

We show that P (n)∗(P (n)) for p = 2 with its geometrically induced structure maps is not an Hopf algebroid because neither the augmentation nor the coproduct ∆ are multiplicative. As a consequence the algebra structure of P (n)∗(P (n)) is slightly different from what was supposed to be the case. We give formulas for (xy) and ∆(xy) and show that the inversion of the formal group of P (n) is ind...

Let Mn be the semigroup of n× n complex matrices under the usual multiplication, and let S be different subgroups or semigroups in Mn including the (special) unitary group, (special) general linear group, the semigroups of matrices with bounded ranks. Suppose Λk(A) is the rank-k numerical range and rk(A) is the rank-k numerical radius of A ∈ Mn. Multiplicative maps φ : S → Mn satisfying rk(φ(A)...