28 research outputs found
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.
Primitive abundant and weird numbers with many prime factors
We give an algorithm to enumerate all primitive abundant numbers (briefly,
PANs) with a fixed (the number of prime factors counted with their
multiplicity), and explicitly find all PANs up to , count all PANs
and square-free PANs up to and count all odd PANs and odd
square-free PANs up to . 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 and prove that there
are none with . Regarding PWNs with a cubic (or higher) odd prime
factor, we prove that there are none with , and we did not find
any with larger . 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
Embeddings of ultradistributions and periodic hyperfunctions in Colombeau type algebras through sequence spaces
In a recent paper, we gave a topological description of Colombeau type
algebras introducing algebras of sequences with exponential weights. Embeddings
of Schwartz' spaces into the Colombeau algebra G are well known, but for
ultradistribution and periodic hyperfunction type spaces we give new
constructions. We show that the multiplication of regular enough functions
(smooth, ultradifferentiable or quasianalytic), embedded into corresponding
algebras, is the ordinary multiplication