The standard topological approach to indistinguishable particles formulates exchange statistics by using the fundamental group analyze connectedness of configuration space. Although successful in two and more dimensions, this gives only trivial or near one dimension because two-body coincidences are excluded from Instead, we include these path-ambiguous singular points consider space as an orbi...

Using nuclear magnetic resonance and quasi-elastic neutron scattering spectroscopic techniques, we obtain experimental evidence of a well-defined dynamic crossover temperature T(L) in supercooled water. We consider three different geometrical environments: (i) water confined in a nanotube (quasi-one-dimensional water), (ii) water in the first hydration layer of the lysozyme protein (quasi-two-d...

This paper introduces the dimension distribution for a square integrable function f on [0, 1]. The dimension distribution is used to relate several definitions of the effective dimension of a function. Functions of low effective dimension can be easy to integrate numerically. Many commonly considered quadrature test functions are sums or products of univariate functions, and as a result have pa...

We prove that every commutative differential graded algebra whose cohomology is a simply-connected Poincaré duality algebra is quasi-isomorphic to one whose underlying algebra is simply-connected and satisfies Poincaré du-ality in the same dimension. This has application in particular to the study of CDGA models of configuration spaces on a closed manifold.

We prove the existence of quasi-stationary symmetric solutions with exactly n ≥ 0 zeros and uniqueness for n = 0 for the Schrödinger-Newton model in one dimension and in two dimensions along with an angular momentum m ≥ 0. Our result is based on an analysis of the corresponding system of second-order differential equations.