These lectures will address two questions. Is there a simple variational principle underlying the existence of secondary motifs in the native state of proteins? Is there a general approach which can qualitatively capture the salient features of the folding process and which may be useful for interpreting and guiding experiments? Here, we present three different approaches to the first question,...

A twistor Cech cohomological characterization of mixed frequency zero rest-mass elds is developed. Using a Cech form of the cup product we derive an expression for the symplectic product of two real mixed frequency scalar elds in terms of a single vertex diagram. An expression for the frequency splitting complex structure of quantum eld theory is derived, and presented by its action on a mixed ...

The geometrical (superembedding) approach is used as a tool for deriving from the worldvolume dynamics of superbranes field theoretical models exhibiting partial supersymmetry breaking. In this way we obtain nonlinear actions for Goldstone superfields associated with physical degrees of freedom of the superbranes.

Using the tools of category theory and diierential geometry, we extend the geometric notions consequent of Gaussian detection problems to non-Gaussian ones. The nominal probability measures associated with the hypotheses in a binary detection problem form points on an innnite dimensional manifold. These measures may correspond to non-additive as well as additive noise situations and can express...

1. Geometry of primitive ideals. 1.1. Let G be a complex algebraic group with Lie algebra g. I would like to have a geometric picture for the structure of primitive ideals of the enveloping algebra U(g). The only universal answer known so far is the "orbit method," saying that primitive ideals should correspond to coadjoint orbits in the dual g* of g. Sometimes this principle doesn't work, howe...

Failures in composite materials occur mainly due to interlaminar fracture, also called delamination, between laminates. This indicates that characterizing interlaminar fracture toughness is the most effective factor in the fracture of composite materials. This study reports investigation on mixed-mode interlaminar fracture behaviour in woven carbon fibre/polyetherimide (CF/PEI) thermoplastic co...

We study the propagation of brittle fractures coupled to large out-of-plane bending, as when a brittle elastic thin sheet is cut by a moving object. Taking into account the separation of the film's bending and stretching energies and using fracture theory we show that such cracks propagate according to a simple set of geometrical rules in the limit of small thickness. In particular, this provid...