相关论文: Improved Caffarelli-Kohn-Nirenberg Inequalities an…

Uncertainty quantification (UQ) techniques are frequently used to ascertain output variability in systems with parametric uncertainty. Traditional algorithms for UQ are either system-agnostic and slow (such as Monte Carlo) or fast with…

This paper derives a new directional uncertainty principle for quaternion valued functions subject to the quaternion Fourier transformation. This can be generalized to establish directional uncertainty principles in Clifford geometric…

We derive strong variance-based uncertainty relations for arbitrary two and more unitary operators by re-examining the mathematical foundation of the uncertainty relation. This is achieved by strengthening the celebrated Cauchy-Schwarz…

We develop a new abstract derivation of the observability inequalities at two points in time for Schr\"odinger type equations. Our approach consists of two steps. In the first step we prove a Nazarov type uncertainty principle associated…

We provide new results of first-order necessary conditions of optimality problem in the form of John's theorem and in the form of Karush-Kuhn-Tucker's theorem. We establish our result in a topological vector space for problems with…

We derive a new variational formula for the R\'enyi family of divergences, $R_\alpha(Q\|P)$, between probability measures $Q$ and $P$. Our result generalizes the classical Donsker-Varadhan variational formula for the Kullback-Leibler…

This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…

We describe modern variants of Monte Carlo methods for Uncertainty Quantification (UQ) of the Neutron Transport Equation, when it is approximated by the discrete ordinates method with diamond differencing. We focus on the mono-energetic 1D…

In this article, we establish several fundamental uncertainty principles for the Strichartz Fourier transform on the Heisenberg group, including Benedicks' theorem, the Donoho-Stark principle, the local uncertainty principle of Price, and a…

This paper presents a generalization for Differential and Integral Calculus. Just as the derivative is the instantaneous angular coefficient of the tangent line to a function, the generalized derivative is the instantaneous parameter value…

We propose a new generalised formalism for estimating the quantum phase uncertainty of pure and mixed continuous-variable quantum states and compare this with the phase uncertainty given by the quantum Fisher information. In order to…

By employing harmonic analysis techniques, we derive weak-type Caffarelli-Kohn-Nirenberg inequalities under natural parameter conditions. A key feature of these weak-type versions is that they remain valid even at critical parameter values…

In this work, we summarize the linearization method to study the Heisenberg Uncertainty Principles, and explain that the same approach can be used to handle the stability problem. As examples of application, combining with spherical…

We approach uncertainty principles of Cowling-Price-Heis-\\enberg-type as a variational principle on modulation spaces. In our discussion we are naturally led to compact localization operators with symbols in modulation spaces. The optimal…

The model of kappa-deformed space is an interesting example of a noncommutative space, since it allows a deformed symmetry. In this paper we present new results concerning different sets of derivatives on the coordinate algebra of…

We first present a generalization of the Robertson-Heisenberg uncertainty principle. This generalization applies to mixed states and contains a covariance term. For faithful states, we characterize when the uncertainty inequality is an…

We revisit the uncertainty principle from the point of view suggested by A. Wigderson and Y. Wigderson. This approach is based on a primary uncertainty principle from which one can derive several inequalities expressing the impossibility of…

Many physical and mathematical models involve random fields in their input data. Examples are ordinary differential equations, partial differential equations and integro--differential equations with uncertainties in the coefficient…

We use the Fr\"olicher-Nijenhuis formalism to reformulate the inverse problem of the calculus of variations for a system of differential equations of order 2k in terms of a semi-basic 1-form of order k. Within this general context, we use…

We investigate a phase-field version of the Faber--Krahn theorem based on a phase-field optimization problem introduced in Garcke et al. [ESAIM Control Optim. Calc. Var. 29 (2023), Paper No. 10] formulated for the principal eigenvalue of…