Related papers: Asymmetry measures for convex distance functions
The axial gauge is applied to the analysis of Euclidean quantum gravity on manifolds with boundary. A set of boundary conditions which are completely invariant under infinitesimal diffeomorphisms require that spatial components of metric…
A variety of gauges are used in cosmological perturbation theory. These are often chosen in order to attribute physical properties to a particular choice of coordinates, or otherwise to simplify the form of the resultant equations.…
A new similarity measure for two sets of S-parameters is proposed. It is constructed with the modified Hausdorff distance applied to S-parameter points in 3D space with real, imaginary and normalized frequency axes. New S-parameters…
This paper contains a new concept to measure the width and thickness of a convex body in the hyperbolic plane. We compare the known concepts with the new one and prove some results on bodies of constant width, constant diameter and given…
Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite dimensional. We consider nonconvex optimization and generalized equations…
The solution to fine tuning is one of the principal motivations for supersymmetry. However constraints on the parameter space of the Minimal Supersymmetric Standard Model (MSSM) suggest it may also require fine tuning (although to a much…
We study the isoperimetric problem for the radially symmetric measures. Applying the spherical symmetrization procedure and variational arguments we reduce this problem to a one-dimensional ODE of the second order. Solving numerically this…
We present a formalism for analysis of linear Cauchy data on a Kottler metric. Our method removes redundancy due to gauge transformations and constraints. A set of four gauge-invariant, scalar functions on the Cauchy surface is produced and…
We consider models with a noncompact symmetry in the framework of $\mathcal{N}=1$ supersymmetry. Contrary to the conventional approach, the noncompact symmetry is realized linearly on all fields without constraints. The models are…
We employ methods of geometry and generalized convergence to construct a geometric measure that serves as an alternative to the integer-dimension Hausdorff measure. This construction prioritizes integration, yields the Area Formula as a…
Let $\mu$ be a probability measure on a separable Banach space $X$. A subset $U\subset X$ is $\mu$-continuous if $\mu(\partial U)=0$. In the paper the $\mu$-continuity and uniform $\mu$-continuity of convex bodies in $X$, especially of…
The purpose of this paper is to investigate the gauge symmetry of classical field theories in integral formalism. A gauge invariant theory is defined in terms of the invariance of the physical observables under the coordinate…
We study the effect of a hidden gauge symmetry on complex holomorphic systems. For this purpose, we show that intrinsically any holomorphic system has this gauge symmetry. We establish that this symmetry is related to the Cauchy-Riemann…
We study in general spacetime dimension the symmetry of the theory obtained by gauging a non-anomalous finite normal Abelian subgroup $A$ of a $\Gamma$-symmetric theory. Depending on how anomalous $\Gamma$ is, we find that the symmetry of…
We prove an isoperimetric inequality for probability measures $\mu$ on $\mathbb{R}^n$ with density proportional to $\exp(-\phi(\lambda | x|))$, where $|x|$ is the euclidean norm on $\mathbb{R}^n$ and $\phi$ is a non-decreasing convex…
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…
A planar point set is in convex position precisely when it has a convex polygonization, that is, a polygonization with maximum interior angle measure at most \pi. We can thus talk about the convexity of a set of points in terms of the…
Symmetry is ubiquitous throughout nature and can often give great insights into the formation, structure and stability of objects studied by mathematicians, physicists, chemists and biologists. However, perfect symmetry occurs rarely so…
The problem of measuring an unbounded system attribute near a singularity has been discussed. Lenses have been introduced as formal objects to study increasingly precise measurements around the singularity and a specific family of lenses…
Counting integer points in large convex bodies with smooth boundaries containing isolated flat points is oftentimes an intermediate case between balls (or convex bodies with smooth boundaries having everywhere positive curvature) and cubes…