相关论文: Uncertainty product of the spherical Gauss-Weierst…
In the paper, asymptotic behavior of the uncertainty product for a family of zonal spherical wavelets is computed. The family contains the most popular wavelets, such as Gauss-Weierstrass, Abel-Poisson and Poisson wavelets and Mexican…
The uncertainty product of a function is a quantity that measures the trade-off between the space and the frequency localization of the function. Its boundedness from below is the content of various uncertainty principles. In the present…
In the present paper, the variances in the space and momentum domains of the spherical Abel-Poisson wavelet, as well as the limit of the uncertainty product for $\rho\to0$, where $\rho$ is the scale parameter, are computed. The values of…
Poisson wavelets are a powerful tool in analysis of spherical signals. In order to have a deeper characterization of them, we compute their uncertainty product, a quantity introduced for the first time by Narcowich and Ward in~\cite{NW96}…
The goal of this paper is to calculate exactly the average of uncertainty-product of two bounded observables and to establish its typicality over the whole set of finite dimensional quantum pure states. Here we use the uniform ensembles of…
The variance and uncertainty product of the position and momentum many-particle operators of structureless bosons interacting by a long-range inter-particle interaction and trapped in a single-well potential are investigated. In the first…
Let $X_i = {X_i(t), t \in T}$ be i.i.d. copies of a centered Gaussian process $X = {X(t), t \in T}$ with values in $\mathbb{R}^d$ defined on a separable metric space $T.$ It is supposed that $X$ is bounded. We consider the asymptotic…
In 1996 Chui and Wang proved that the uncertainty constants of scaling and wavelet functions tend to infinity as smoothness of the wavelets grows for a broad class of wavelets such as Daubechies wavelets and spline wavelets. We construct a…
We study the uncertainty relation in the product form of variances and obtain some new uncertainty relations with weight, which are shown to be tighter than those derived from the Cauchy Schwarz inequality.
In this paper, we present generalizations of some results on the asymptotic property C for wreath products. Specifically, we prove that certain wreath-like products admit asymptotic property C, thus providing some new examples for further…
Although real, normalized Gaussian wave packets minimize the product of position and momentum uncertainties, generic complex normalized Gaussian wave packets do not. We prove they minimize an alternative product of uncertainties that…
Following to the Weil method we generalize the Heisenberg-Robertson uncertainty relation for arbitrary two operators. Consideration is made in spherical coordinates, where the distant variable is restricted from one side, . By this reason…
In this paper we introduce a notion of a directional uncertainty product for multivariate periodic functions. It measures a localization of a function along a particular direction. We study properties of the uncertainty product and give an…
Unstable particles cannot be treated as asymptotic external states in $S$-matrix theory and when they occur as resonant states cannot be described by finite-order perturbation theory. The known facts concerning unstable particles are…
In this note we investigate the asymptotic behavior of plane shear thickening fluids around a bounded obstacle. Different from the Navier-Stokes case considered by Gilbarg-Weinberger in \cite{GW1978}, where the good structure of the…
In this paper we derive the tail asymptotics of the product of two dependent Weibull-type risks, which is of interest in various statistical and applied probability problems. Our results extend some recent findings of Schlueter and Fischer…
The purpose of this note is to share some observations and speculations concerning the asymptotic behavior of Gromov-Witten invariants. They may be indicative of some deep phenomena in symplectic topology that in full generality are outside…
We prove some isoperimetric type inequalities in warped product manifolds, or more generally, multiply warped product manifolds. We then relate them to inequalities involving the higher order mean-curvature integrals. We also apply our…
The uncertainty relation and the probability interpretation of quantum mechanics are intrinsically connected, as is evidenced by the evaluation of standard deviations. It is thus natural to ask if one can associate a very small uncertainty…
We consider the point indentation of a pressurized, spherical elastic shell. Previously it was shown that such shells wrinkle once the indentation reaches a threshold value. Here, we study the behaviour of this system beyond the onset of…