相关论文: Directional Heisenberg uncertainty product
We investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We examine the well-posedness issue and prove that the space-dependent variable order coefficient is uniquely determined among other…
As a starting point of our research, we show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to…
In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media.…
We study a class of high-frequency path functionals for diffusions with singular thresholds or boundaries, where the process exhibits either (i) skweness, oscillating coefficients, and stickiness, or (ii) sticky reflection. The functionals…
A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…
This paper is devoted to variational problems on the set of probability measures which involve optimal transport between unequal dimensional spaces. In particular, we study the minimization of a functional consisting of the sum of a term…
An optimal control problem related to the probability of transition between stable states for a thermally driven Ginzburg-Landau equation is considered. The value function for the optimal control problem with a spatial discretization is…
We obtain an optimal deviation from the mean upper bound \begin{equation} D(x)\=\sup_{f\in \F}\mu\{f-\E_{\mu} f\geq x\},\qquad\ \text{for}\ x\in\R\label{abstr} \end{equation} where $\F$ is the class of the integrable, Lipschitz functions on…
We identify shortcomings in two popular measures of localization of functions: the $L^p-L^q$ participation ratio and the mass concentration comparison. We then introduce a novel localization measure for functions on bounded subsets of…
Position uncertainty (delocalization) measures for a particle on the sphere are proposed and illustrated on several examples of states. The new measures are constructed using suitably the standard multiplication angle operator variances.…
We show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order $1$),…
Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by…
In the first part of this paper we establish, in terms of so called k-tangential sets, a kind of optimal estimate for the size and structure of the set of non-differentiability of Lipshitz functions with one-sided directional derivatives.…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
Consider a BV function on a Riemannian manifold. What is its differential? And what about the Hessian of a convex function? These questions have clear answers in terms of (co)vector/matrix valued measures if the manifold is the Euclidean…
We initiate a systematic study of intrinsic dimensional versions of classical functional inequalities which capture refined properties of the underlying objects. We focus on model spaces: Euclidean space, Hamming cube, and manifolds of…
We generalize the generalized-squeezing problem to include fractional values of the squeezing order $n$. This approach allows us to determine the locations of critical points at which qualitative changes in behaviour occur and accurately…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
This paper investigates the behavior of sets and functions at infinity by introducing new concepts, namely directional normal cones at infinity for unbounded sets, along with limiting and singular subdifferentials at infinity in the…
In this note, we study an optimal transportation problem arising in density functional theory. We derive an upper bound on the semi-classical Hohenberg-Kohn functional derived by Cotar, Friesecke and Kl\"{u}ppelberg (2012) which can be…