Mach's principle. Part 1. Initial state of the universe the universe

The integral formulation of equations of general relativity proposed earlier as a mathematical tool for Mach's principle forbids the conventional singular cosmologies but is compatible with the de Sitter initial space.     

Complementary control by additives of the kinetics of amorphous CaCO3 mineralization at an organic interface: in-situ synchrotron x-ray observations

The kinetics of biomimetic mineralization at a fatty acid monolayer interface have been measured in situ by synchrotron x-ray reflectivity. The formation of biologically relevant amorphous calcium carbonate films is affected by soluble macromolecules, supersaturation rate of change, and Mg cations. We find that these solution conditions influence mineral film formation in a complementary fashion. Poly(sodium acrylate) extends the lifetime of metastable amorphous calcium carbonate, solution saturation controls the mineral film growth rate, and Mg cations create a longer induction time. This is the first quantification of potentially competitive biomineralization mechanisms that addresses nucleation and growth of the amorphous mineral phases, which are important in biomineralization.     

The weakly neighborly polyhedral maps on the 2-manifold with euler characteristic −1

A weakly neighborly polyhedral map (w.n.p. map) is a two-dimensional cell-complex which decomposes a closed 2-manifold without boundary, such that for every two vertices there is a 2-cell containing them. We prove that there are just four w.n.p. maps with Euler characteristic –1 and we describe them.