Related papers: On uncertainty principles in the finite dimensiona…
Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…
The purpose of this article is to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform (QFT). We study some fundamental properties of this extension such as scaling, translation,…
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…
We present a new strategic voting model where we use uncertainty representation to model preferences. Specifically, we use probability sets as uncertainty representations, together with lower and upper expected utility gains to take…
We give a general method of deriving statistical limit theorems, such as the central limit theorem and its functional version, in the setting of ergodic measure preserving transformations. This method is applicable in situations where the…
In the present paper, in terms of the measurability concept introduced in the previous works of the author, a quantum theory is studied. Within the framework of this concept, several examples are considered using the Schrodinger picture;…
In the present work the role that a generalized uncertainty principle could play in the quantization of the electromagnetic field is analyzed. It will be shown that we may speak of a Fock space, a result that implies that the concept of…
I will attempt to represent a symbol to a ps.d.o., using two bases and a lifting functional. The representation is based upon an invariance principle and conditions on the boundary, defined by first surfaces to the symbol.
The aim of this note is twofold. Firstly, we prove an abstract version of the Calder\'on transference principle for inequalities of admissible type in the general commutative multilinear and multiparameter setting. Such an operation does…
We analyse a second-order SPDE model in multiple space dimensions and develop estimators for the parameters of this model based on discrete observations of a solution in time and space on a bounded domain. While parameter estimation for one…
The present work aims to search for an implementation of a new symmetry in the space-time by introducing the idea of an invariant minimum speed scale ($V$). Such a lowest limit $V$, being unattainable by the particles, represents a…
The goal of this paper is to prove a uniqueness result for a stochastic heat equation with a randomly perturbed potential, which can be considered as a variant of Hardy's uncertainty principle for stochastic heat evolutions.
We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. R\'enyi entropy is used as uncertainty measure associated with the distribution…
We present details of our effective computational methods based on the real-space finite-difference formalism to elucidate electronic and magnetic properties of the two-dimensional (2D) materials within the framework of the density…
Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator $[\hat{x}, \hat{p}] = i f(\hat{p})$. We apply this deformed quantization to free scalar field theory for $f_\pm =1\pm \beta p^2$.…
In this note we provide a negative answer to a question raised by M. Kreisel concerning a condition on the short-time Fourier transform that would imply the HRT conjecture. In particular we provide a new type of uncertainty principle for…
Uncertainty estimation has been widely studied in medical image segmentation as a tool to provide reliability, particularly in deep learning approaches. However, previous methods generally lack effective supervision in uncertainty…
The uncertainty relation is a fundamental concept in quantum theory, plays a pivotal role in various quantum information processing tasks. In this study, we explore the additive uncertainty relation pertaining to two or more observables, in…
In this paper, we have given a new definition of continuous fractional wavelet transform in $\mathbb{R}^N$, namely the multidimensional fractional wavelet transform (MFrWT) and studied some of the basic properties along with the inner…