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Let be a locally compact Hausdorff space. We show that any local -linear map (where" local" is a weaker notion than -linearity) between Banach -modules are" nearly -linear" and" nearly bounded". As an application, a local -linear map between Hilbert -modules is automatically -linear. If, in addition, contains no isolated point, then any -linear map between Hilbert -modules is automatically bounded. Another application is that if a sequence of maps between two Banach spaces" preserve -sequences"(or" preserve ultra- -sequences"), then is bounded for large enough and they have a common bound. Moreover, we will show that if is a bijective" biseparating" linear map from a" full" essential Banach -module into a" full" Hilbert -module (where is another locally compact Hausdorff space), then is" nearly bounded"(in fact, it is automatically bounded if or contains no isolated point) and there exists a homeomorphism such that ( ).

We study deformations of maximally supersymmetric gauge theories by higher dimensional operators in various spacetime dimensions. We classify infinitesimal deformations that preserve all 16 supersymmetries, while allowing the possibility of breaking either Lorentz or R-symmetry, using an on-shell algebraic method developed by Movshev and Schwarz. We also consider the problem of extending the deformation beyond the first order.

We explore ideas for speeding up HFE-based signature schemes. In particular, we propose an HFEv^− system with odd characteristic and a secret map of degree 2. Changing the characteristic of the system has a profound effect, which we attempt to explain and also demonstrate through experiment. We discuss known attacks which could possibly topple such systems, especially algebraic attacks. After testing the resilience of these schemes against F4, we suggest parameters that yield acceptable security levels.

No abstract uploaded!