Algorithms for finding connected separators between antipodal points

A set (or a collection of sets) contained in the Euclidean space Rm is symmetric if it is invariant under the antipodal map. Given a symmetric unicoherent polyhedron X (like an n-dimensional cube or a sphere) and an odd real function f defined on vertices of a certain symmetric triangulation of X, we algorithmically construct a connected symmetric separator of X by choosing a subcollection of the triangulation. Each element of the subcollection contains the vertices v and u such that f(v)f(u)?0.     

Backward extensions of subnormal operators

The concept of backward extension for subnormal weighted shifts is generalized to arbitrary subnormal operators. Several differences and similarities in these contexts are explored, with emphasis on the structure of the underlying measures.

     

General covariance of the non-abelian DBI-action: checks and balances

We perform three tests on our proposal to implement diffeomorphism invariance in the non-abelian D0-brane DBI action as a base-point independence constraint between matrix Riemann normal coordinate systems. First, we show that T-duality along an isometry correctly interchanges the potential and kinetic terms in the action. Second, we show that the method to impose base-point independence using an auxiliary dN²-dimensional nonlinear sigma model also works for metrics which are curved along the brane, provided a physical gauge choice is made at the end. Third, we show that without alteration this method is applicable to higher order in velocities. Testing specifically to order 4, we elucidate the range of validity of the symmetrized trace approximation to the non-abelian DBI action.     

Rank,covering number and a simple spectrum

For a dynamical system (X, B, T, μ) we investigate the connections between metric invariants, the rankr(T) and the covering numberF ^*(T) and a spectral property for having a simple spectrum. Given a positive integerr≥2, a real numberb, 0<b<1 such thatr·b≥1, we construct examples of systems withr(T)=r, F ^*(T)=b and having a simple spectrum.     

U(2, 2) Symmetry as a Common Basis for Quantum Theory and Geometrodynamics

We formulated some criticisms of the Diracequation and its Clifford-algebraic philosophy; inparticular, we show that, within a general-relativisticcontext, they seem to contain hidden action-at-distance concepts. We suggest a new model based on thefour-component Klein-Gordon equation locally invariantunder the U(2,2) gauge group. The usual Dirac equationis then obtained as a certain approximation. The geometrodynamical sector shows reasonablecorrespondence with general relativity.     

Relevance of Reflection in Static and Dynamic Light Scattering Experiments

Using a monodisperse PMMA dispersion, it was shown that light reflection at the sample cuvette walls may greatly influence the results of both static (SLS) and dynamic (DLS) light scattering experiments. Considering SLS, this reflection phenomenon mostly causes an overestimation of the scattered intensity at high scattering angles, which may give rise to the emergence of an additional, artificial peak in the lower region of the particle size distribution. On the other hand, the influcence of reflection on DLS measurements was shown to be particularly important in the upper region of the particle size distribution. The experimentally observed phenomena were explained from the basic principles of both particle sizing methods. Finally, it was shown that the disturbing effect of reflection could be avoided by modifying either the hardware or the software of the static and dynamic light scattering technique.