23,927 research outputs found
Estimates on the first two buckling eigenvalues on spherical domains
In this paper, we study the first two eigenvalues of the buckling problem on
spherical domains. We obtain an estimate on the second eigenvalue in terms of
the first eigenvalue, which improves one recent result obtained by Wang-Xia in
[7].Comment: This article has been submitted for publication on 2009-04-2
New Congruences Modulo 2, 4, and 8 for the Number of Tagged Parts Over the Partitions with Designated Summands
Recently, Lin introduced two new partition functions PD and
PDO, which count the total number of tagged parts over all partitions of
with designated summands and the total number of tagged parts over all
partitions of with designated summands in which all parts are odd. Lin also
proved some congruences modulo 3 and 9 for PD and PDO, and
conjectured some congruences modulo 8. Very recently, Adansie, Chern, and Xia
found two new infinite families of congruences modulo 9 for PD. In this
paper, we prove the congruences modulo 8 conjectured by Lin and also find many
new congruences and infinite families of congruences modulo some small powers
of 2.Comment: 19 page
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