49,901 research outputs found
On some universal sums of generalized polygonal numbers
For those with are
called generalized -gonal numbers. Sun [13] studied for what values of
positive integers the sum is universal over (i.e., any has the form
with ). We prove that
and are universal over , as conjectured by Sun. Sun also conjectured that any can be
written as and with
; in contrast, we show that and
are universal over . Our proofs are essentially
elementary and hence suitable for general readers.Comment: Final published versio
Blow-up criteria for Boussinesq system and MHD system and Landau-Lifshitz equations in a bounded domain
In this paper, we prove some blow-up criteria for the 3D Boussinesq system
with zero heat conductivity and MHD system and Landau-Lifshitz equations in a
bounded domain.Comment: 20 page
- β¦