In our recent paper [12] we developed a new principle of “symmetrization by truncation” to obtain symmetrization inequalities of Sobolev type via truncation. In this note we consider the corresponding results for Sobolev spaces on domains, without assuming that the Sobolev functions vanish at the boundary. The explicit connection between Sobolev-Poincaré inequalities and isoperimetric inequalit...

Under high pressures the hydrogen bonds were predicted to transform from a highly asymmetric soft O-H···O to a symmetric rigid configuration in which the proton lies midway between the two oxygen atoms. Despite four decades of research on hydroxyl containing compounds, pressure induced hydrogen bond symmetrization remains elusive. Following single crystal x-ray diffraction, Mössbauer and Raman ...

We present a closed-form solution for the symmetrization problem, solving for the optimal deformation that reconciles a set of local bilateral symmetries. Given as input a set of point-pairs which should be symmetric, we first compute for each local neighborhood a transformation which would produce an approximate bilateral symmetry. We then solve for a single global symmetry which includes all ...

The study of hydrogen bonds near symmetrization limit at high pressures is of importance to understand proton dynamics in complex bio-geological processes. We report here the evidence of hydrogen bond symmetrization in the simplest amino acid-carboxylic acid complex, glycinium oxalate, at moderate pressures of 8 GPa using in-situ infrared and Raman spectroscopic investigations combined with fir...

We present two types of meta-algorithm that can greatly improve the accuracy of existing algorithms for integrating the equations of motion of dynamical systems. The first meta-algorithm takes an integrator that is time-symmetric only for constant time steps, and ensures time-symmetry even in the case of varying time steps. The second metaalgorithm can be applied to any self-starting integratio...

Let X be a random variable. We shall call an independent random variable Y to be a symmetrizer forX , ifX+Y is symmetric around zero. If Y is independent copy of −X , it is obviously a symmetrizer. A random variable is said to be symmetry resistant if the variance of any symmetrizer Y , is never smaller than the variance of X itself. For example, let X be a Bernoulli(p) random variable. If p = ...

This work interprets and generalizes consensus-type algorithms as switching dynamics leading to symmetrization of some vector variables with respect to the actions of a finite group. We show how the symmetrization framework we develop covers applications as diverse as consensus on probability distributions (either classical or quantum), uniform random state generation, and open-loop disturbance...