Related papers: Normal trace for vector fields of bounded mean osc…
This work is devoted to prove an optimum version of the trace inequality associated to the embedding $BV(\Omega)\subset L^1(\partial\Omega)$. Special emphasis is placed on the regularity that the domain $\Omega$ should exhibit for this…
We will prove that for piecewise smooth and concave domains Korn's first inequality holds for vector fields satisfying homogeneous normal or tangential boundary conditions with explicit Korn constant square root of 2.
If there is a topologically locally constant family of smooth algebraic varieties together with an admissible normal function on the total space, then the latter is constant on any fiber if this holds on some fiber. Combined with spreading…
This note presents a regularity result with proof for an initial-boundary value problem of a linear parabolic system involving curl of the unknown vector field, subjected to the boundary condition of prescribing the tangential component of…
Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a…
The standard covariant differentiation procedure for fields in vector bundles is generalised so as to be applicable to fields in general nonaffine bundles in which the fibres may have an arbitrary nonlinear structure. In addition to the…
We study the boundary behavior of the so-called ring $Q$-mappings obtained as a natural generalization of mappings with bounded distortion. We establish a series of conditions imposed on a function $Q(x)$ for the continuous extension of…
A major open question in transcendental dynamics asks if it is possible for points in a wandering domain to have bounded orbits, and more strongly, for a wandering domain to iterate only in a bounded domain. In this paper we give a partial…
Paying attention to conformal invariance as the invariance under local transformations of units of measure, we take a conformal invariant quantum field as a quantum matter theory in which one has the freedom to choose the values of units of…
We introduce a new paradigm for geometry denoising using prior knowledge about the surface normal vector. This prior knowledge comes in the form of a set of preferred normal vectors, which we refer to as label vectors. A segmentation…
We use form methods to define suitable realisations of the Laplacian on a domain $\Omega$ with Wentzell boundary conditions, i.e. such that $\partial_{\mathrm{n}}u + \beta u + \Delta u = 0$ holds in a suitable sense on the boundary of…
The direct string computation of anomalous D-brane and orientifold plane couplings is extended to include the curvature of the normal bundle. The normalization of these terms is fixed unambiguously. New, non-anomalous gravitational…
The formation of normal-state domains in type-I superconducting indium films is investigated using the high resolution magneto-optical imaging technique. The observed patterns consist of coexisting circular and lamellar normal-phase domains…
Multivariate extreme value theory assumes a multivariate domain of attraction condition for the distribution of a random vector. This necessitates that each component satisfies a marginal domain of attraction condition. An approximation of…
Variational inference approximates Bayesian posterior distributions by projecting onto a tractable family of distributions. While most theoretical analyses evaluate the quality of this approximation using global divergence measures, many…
We characterize the canonical algebras such that for all dimension vectors of homogeneous modules the corresponding module varieties are complete intersections (respectively, normal). We also investigate the sets of common zeros of…
We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…
We consider a stable but nearly unstable autoregressive process of any order. The bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with spectral radius $\rho(A_{n}) < 1$ satisfying…
In a binary classification problem the feature vector (predictor) is the input to a scoring function that produces a decision value (score), which is compared to a particular chosen threshold to provide a final class prediction (output).…
A classical statistical inequality is used to show that the distance covariance of two bounded random vectors is bounded from above by a simple function of the dimensionality and the bounds of the random vectors. Two special cases that…