The three-form multiplet in N=2 superspace

We present an N=2 multiplet including a three-index antisymmetric tensor gauge potential, and describe it as a solution to the Bianchi identities for the associated fieldstrength superform, subject to some covariant constraints, in extended central charge superspace. We find that this solution is given in terms of an 8+8 tensor multiplet subject to an additional constraint. We give the transformation laws for the multiplet as well as invariant superfield and component field lagrangians, and mention possible couplings to other multiplets. We also allude to the relevance of the 3--form geometry for generic invariant supergravity actions.Comment: 12 pages, LaTeX (2.09). (Final version to appear in Z.Phys.C

On the relation between (C,E,P)–algebras and asymptotic algebras

On several occasions, the question has been asked whether (C,E,P)–algebras as introduced by Marti (1999), go beyond the framework of asymptotic algebras as deï¬ned by Delcroix and Scarpalezos (1998). This note summarizes the constructions and clariï¬es the relation between the corresponding algebras.

The N=2 vector-tensor multiplet, central charge superspace, and Chern-Simons couplings

We present a new, alternative interpretation of the vector-tensor multiplet as a 2-form in central charge superspace. This approach provides a geometric description of the (non-trivial) central charge transformations ab initio and is naturally generalized to include couplings of Chern-Simons forms to the antisymmetric tensor gauge field, giving rise to a N=2 supersymmetric version of the Green-Schwarz anomaly cancellation mechanism.Comment: 11 pages, LaTe

Pointvalue characterizations in multi-parameter algebras

We extend classical results from the Colombeau algebra, concerning point-value characterizations of generalized functions, to the more general case of multi-parameter (C,E,P)–algebras. Our investigations include considerations about different definitions of subspaces related to tempered generalized functions.Algebra of generalized functions, pointvalue characterization, tempered generalized functions

Primitive abundant and weird numbers with many prime factors

We give an algorithm to enumerate all primitive abundant numbers (briefly, PANs) with a fixed $\Omega$ (the number of prime factors counted with their multiplicity), and explicitly find all PANs up to $\Omega=6$, count all PANs and square-free PANs up to $\Omega=7$ and count all odd PANs and odd square-free PANs up to $\Omega=8$. We find primitive weird numbers (briefly, PWNs) with up to 16 prime factors, improving the previous results of [Amato-Hasler-Melfi-Parton] where PWNs with up to 6 prime factors have been given. The largest PWN we find has 14712 digits: as far as we know, this is the largest example existing, the previous one being 5328 digits long [Melfi]. We find hundreds of PWNs with exactly one square odd prime factor: as far as we know, only five were known before. We find all PWNs with at least one odd prime factor with multiplicity greater than one and $\Omega = 7$ and prove that there are none with $\Omega < 7$. Regarding PWNs with a cubic (or higher) odd prime factor, we prove that there are none with $\Omega\le 7$, and we did not find any with larger $\Omega$. Finally, we find several PWNs with 2 square odd prime factors, and one with 3 square odd prime factors. These are the first such examples.Comment: New section on open problems. A mistake in table 2 corrected (# odd PAN with Omega=8). New PWN in table 5, last line, 2 squared prime factors, Omega=15. Updated bibliograph