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Real Hypersurfaces in Complex Two-Plane Grassmannians
Berndt, Ju¨rgen,Suh, Young Jin 경북대학교 위상수학 기하학연구센터 1999 硏究論文集 Vol.8 No.-
The complex two-plane Grassmannian G_2(C^m+2) is equipped with both a Ka¨hler and a quaternionic Ka¨hler structure. By applying these two structures to the normal bundle of a real hypersurface M in G_2(C^(m+2)) one gets a one- and a three-dimensional distribution on M. We classify all real hypersurfaces M in G_2(C^(m+2)), m≥3, for which these two distributions are invariant under the shape operator of M.
Finite and infinite Rogers–Ramanujan continued fractions in Ramanujan's lost notebook
Berndt, Bruce C.,Kang, Soon-Yi,Sohn, Jaebum Elsevier 2015 Journal of number theory Vol.148 No.-
<P><B>Abstract</B></P> <P>Some entries on both finite and infinite Rogers–Ramanujan continued fractions in Ramanujan's lost notebook are examined.</P>
Character analogues of theorems of Ramanujan, Koshliakov and Guinand
Berndt, B.C.,Dixit, A.,Sohn, J. Academic Press 2011 Advances in applied mathematics Vol.46 No.1
We derive analogues of theorems of Ramanujan, Koshliakov, and Guinand involving primitive characters and modified Bessel functions. As particular examples, transformation formulas involving the Legendre symbol and sums-of-divisors functions are established.
PROOFS OF CONJECTURES OF SANDON AND ZANELLO ON COLORED PARTITION IDENTITIES
Berndt, Bruce C.,Zhou, Roberta R. Korean Mathematical Society 2014 대한수학회지 Vol.51 No.5
In a recent systematic study, C. Sandon and F. Zanello offered 30 conjectured identities for partitions. As a consequence of their study of partition identities arising from Ramanujan's formulas for multipliers in the theory of modular equations, the present authors in an earlier paper proved three of these conjectures. In this paper, we provide proofs for the remaining 27 conjectures of Sandon and Zanello. Most of our proofs depend upon known modular equations and formulas of Ramanujan for theta functions, while for the remainder of our proofs it was necessary to derive new modular equations and to employ the process of duplication to extend Ramanujan's catalogue of theta function formulas.
Reflections of the Mongolian Great Election Year 2004-2005
Berndt H. Brikell 서울행정학회 2008 서울행정학회 학술대회 발표논문집 Vol.- No.-
During the Great Election year there were held election for Parliament, locally and regionally, as well as for President. There are mainly two topics of special interest for me in these elections; First the contents of the politics an second the procedure by which the elections were managed. As I was a single observer this cannot be presented as some kind of overall picture of the elections but just snapshots of the facilities, and how they were managed, that I visited or where people I interviewed had been. Of the contents of the politics involved varies according to the level of the election. In the parliamentary election the big issue was if the MPRP had done a good job the last four years if office or not. The opposition did not entirely buy this discourse but made certain offers to the voters. In the end it showed that the confidence of the MPRP was a bit overrated. As for the way the elections were executed there was a lot of accusations of cheating and buying votes and similar charges. This gave some consequences concerning changes I procedure on the local and regional election later that year and the Presidential election the following year. Concluding remarks on the elections and their content states first that after the Parliamentary election and its result, the steam sort of went out of the Motherland Coalition, and the results of the local, regional and Presidential elections were rather clear victories for the MPRP. The reasons behind this have at least partly to do with how Mongolians view politics and its difference to administration and bureaucracy. In other words, who is a politician and who is a bureaucrat?