Related papers: Normal trace for vector fields of bounded mean osc…
Bounce-averaged theories provide a framework for simulating relatively slow processes, such as collisional transport and quasilinear diffusion, by averaging these processes over the fast periodic motions of a particle on a closed orbit.…
Given a martingale sequence of random fields that satisfies a natural assumption of boundedness, it is shown that the pointwise limit of this sequence can be modified in such a way that a certain class of moduli of continuity is preserved.…
In this note, we prove that the infimum of the mean curvature on any disconnected boundary component of an unbounded mean convex domain in $\mathbb{R}^n$ must be zero.
We study the mean field equation of motion for driven domain walls in random media. We discuss the two cases of an external constant as well as an oscillating driving force. Our main focus lies on the critical dynamics close to the…
Given the pair of vector fields $X=\partial_x+|z|^{2m}y\partial_t$ and $ Y=\partial_y-|z|^{2m}x \partial_t,$ where $(x,y,t)= (z,t)\in\mathbb{R}^3=\mathbb{C}\times\mathbb{R}$, we give a condition on a bounded domain…
Topic models are Bayesian models that are frequently used to capture the latent structure of certain corpora of documents or images. Each data element in such a corpus (for instance each item in a collection of scientific articles) is…
Gradient vector fields are fundamental objects from both theoretical and practical perspectives, since various phenomena can be modeled within this framework. The ``moduli space'' of such vector fields provides the foundation for describing…
A property of smooth convex domains $\Omega \subset \mathbb{R}^n$ is that if two points on the boundary $x, y \in \partial \Omega$ are close to each other, then their normal vectors $n(x), n(y)$ point roughly in the same direction and this…
Notions of (pointwise) tangential dimension are considered, for measures of R^n. Under regularity conditions (volume doubling), the upper resp. lower dimension at a point x of a measure can be defined as the supremum, resp. infimum, of…
The paper reports on a study of a harmonic oscillator (ho) in the twisted Moyal space, in a well defined matrix basis, generated by the vector fields…
Nontrivial twisted boundary conditions associated with extra compact dimensions produce an ambiguity in the value of the four dimensional coupling constants of the renormalizable interactions of the twisted fields' zero modes. Resolving…
In the context of boundary conformal field theory, we derive a sum rule that relates two and three point functions of the displacement operator. For four dimensional conformal field theory with a three dimensional boundary, this sum rule in…
In this note, we consider a fixed vector field $V$ on $S^2$ and study the distribution of points which lie on the nodal set (of a random spherical harmonic) where $V$ is also tangent. We show that the expected value of the corresponding…
We build up normal ordered products for fermionic open string coordinates consistent with boundary conditions. The results are obtained considering the presence of antisymmetric tensor fields. We find a discontinuity of the normal ordered…
The main goal of this article is to understand the trace properties of nonlocal minimal graphs in~$\R^3$, i.e. nonlocal minimal surfaces with a graphical structure. We establish that at any boundary points at which the trace from inside…
The trace-dev-div inequality in $H^s$ controls the trace in the norm of $H^s$ by that of the deviatoric part plus the $H^{s-1}$ norm of the divergence of a quadratic tensor field different from the constant unit matrix. This is well known…
We develop a notion of quantum observable for the general boundary formulation of quantum theory. This notion is adapted to spacetime regions rather than to hypersurfaces and naturally fits into the topological quantum field theory like…
The continuous Multiscale Entanglement Renormalization Ansatz (cMERA) [Haegeman et al., Phys. Rev. Lett. 110, 100402 (2013)] gives a variational wavefunctional for ground states of quantum field theoretic Hamiltonians. A cMERA is defined as…
In this paper we consider the normal map of a closed plane curve as a vector field on the cylinder. We interpret the critical points geometrically and study their Poincar\'{e} index, including the points at infinity. After projecting the…
I describe the recently proposed quantization of bosonic string about the mean-field ground state, paying special attention to the differences from the usual quantization about the classical vacuum which turns out to be unstable for d>2. In…