The concepts and methods of topology and geometry are an indispensable part
of theoretical physics today. They have led to a deeper understanding of many
crucial aspects in condensed matter physics, cosmology, gravity, and particle
physics. Moreover, several intriguing connections between only apparently disconnected
phenomena have been revealed based on these mathematical tools.
Topological and geometrical considerations will continue to play a central role
in theoretical physics.
Let X be a projective manifold and f : X → X a rational mapping with large topological degree, dt λk−1 (f ) := the (k − 1)th dynamical degree of f . We give an elementary construction of a probability measure µf such that d−n (f n )∗ Θ → µf for every smooth probability measure Θ on X. We show t that every quasiplurisubharmonic function is µf -integrable. In particular µf does not charge either points of indeterminacy or pluripolar sets, hence µf is f -invariant with constant jacobian f ∗ µf = dt µf...
A back -propagation artificial neural net has been trained to estimate the activity values of a set of 18 N-alkyl-N-acyl- -aminoamide derivatives from the results of molecular mechanics and RHF/PM3/SCF MO semi-empirical calculations. The input descriptors include molecular properties such as the partition coefficient P, 3d structure dependent parameters, charge dependent parameters, and topological descriptors.
Subunit G of photosystem I is a nuclear-encoded protein, predicted to
form two transmembrane a-helices separated by a loop region. We use
in vitro import assays to show that the positively charged loop domain
faces the stroma, whilst the N- and C-termini most likely face the lumen.
PSI-G constructs in which a His- or Strep-tag is placed at the C-terminus
or in the loop region insert with the same topology as wild-type photosys-tem I subunit G (PSI-G).