On the functional equation $f^n=e^{P_1}+\cdots+e^{P_m}$ and rigidity theorems for holomorphic curves

the effect of functional/notional approach on the proficiency level of efl learners and its evaluation through functional test

in fact, this study focused on the following questions: 1. is there any difference between the effect of functional/notional approach and the structural approaches to language teaching on the proficiency test of efl learners? 2. can a rather innovative language test referred to as "functional test" ge devised so so to measure the proficiency test of efl learners, and thus be as much reliable an...

On Family Rigidity Theorems

Rigidity and Holomorphic Segre Transversality for Holomorphic Segre Maps

Let Hn and HN denote the complexifications of Heisenberg hypersurfaces in Cn and CN , respectively. We show that non-degenerate holomorphic Segre mappings from Hn into HN with N ≤ 2n− 2 possess a partial rigidity property. As an application, we prove that the holomorphic Segre non-transversality for a holomorphic Segre map from Hn into HN with N ≤ 2n− 2 propagates along Segre varieties. We also...

On Family Rigidity Theorems II

In [LM], we proved a family version of the famous Witten rigidity theorems and several family vanishing theorems for elliptic genera. In this paper, we gerenalize our theorems [LM] in two directions. First we establish a family rigidity theorem for the Dirac operator on loop space twisted by general positive energy loop group representations. Second we prove a family rigidity theorem for spin-m...

Membranes Wrapped on Holomorphic Curves

We construct supergravity solutions dual to the twisted field theories arising when M-theory membranes wrap holomorphic curves in Calabi–Yau n-folds. The solutions are constructed in an Abelian truncation of maximal D = 4 gauged supergravity and then uplifted to D = 11. For four-folds and five-folds we find new smooth AdS/CFT examples and for all cases we analyse the nature of the singularities...