In the present paper, an uncertainty principle is derived in the quantum wavelet framework. Precisely, a new uncertainty principle for the generalized q-Bessel wavelet transform, based on some q-quantum wavelet, is established. A two-parameters exten...
Quantum gravity theories rely on a minimal measurable length for their formulations, which clashes with the classical formulation of the uncertainty principle and with Lorentz invariance from general relativity. These incompatibilities led to the dev...
The free metaplectic transformation is an N-dimensional linear canonical transformation. This transformation operator is useful, especially for signal processing applications. In this paper, in order to characterize simultaneously local analysis of a...
The classical uncertainty principle inequalities are imposed over the general relativity geodesic equation as a mathematical constraint. In this way, the uncertainty principle is reformulated in terms of proper space–time length element, Planck lengt...
We develop the concept of covariance for waves and show that it plays a fundamental role in understanding the evolution of a propagating pulse. The concept clarifies several issues regarding the spread of a pulse and the motion of the mean. Exact res...
Different kinds of power quality can be sensed in a smart substation. Power quality sensing and analysis are basic functions of a smart substation for situation awareness. The uncertainty principle, which states that the time uncertainty and frequenc...
A refinement of the Heisenberg uncertainty principle has been proved by Luo using Wigner–Yanase information. Generalizations of this result have been proved by Yanagi and by other scholars for regular Quantum Fisher Information in the matrix ca...
In this work, we point out an overlooked and subtle feature of the generalized uncertainty principle (GUP) approach to quantizing gravity: namely that different pairs of modified operators with the same modified commutator,
Decision-making theory has developed over many decades at the intersection of economics, mathematics, psychology, and engineering. Its classical foundations include Bernoulli’s expected utility theory, von Neumann and Morgenstern’s ration...
We revisit the Extended Uncertainty Principle (EUP) from an operational viewpoint, replacing wavefunction-based widths with apparatus-defined position constraints such as a finite slit of width
We provide a natural derivation and interpretation for the uncertainty principle in quantum mechanics from the stochastic optimal control approach. We show that, in particular, the stochastic approach to quantum mechanics allows one to understand the...
The Heisenberg uncertainty principle is modified by the introduction of an observer-independent minimal length. In this work, we have considered the resonant gravitational wave detector in the modified uncertainty principle framework, where we have u...
In the present contribution, a preliminary analysis of the effects of the Generalized Uncertainty Principle (GUP) with a minimum length, in the context of compact stars, is performed. On basis of a deformed Poisson canonical algebra with a parametriz...
Suppose we make a series of measurements on a chosen quantum system. The outcomes of the measurements form a sequence of random events, which occur in a particular order. The system, together with a meter or meters, can be seen as following the paths...
We investigate the statistical entropy of black holes within the framework of the generalized uncertainty principle (GUP) by employing effective metrics that incorporate leading-order and all-order quantum gravitational corrections. We construct thre...
Motivated by the recent study about the extended uncertainty principle (EUP) black holes, we present in this study its extension called the generalized extended uncertainty principle (GEUP) black holes. In particular, we investigated the GEUP effects...
Recently, we published two papers in this journal. One of the papers dealt with the action of the radiation fields generated by a traveling-wave element and the other dealt with the momentum transferred by the same radiation fields and their connecti...
The linear canonical wavelet transform is a nontrivial generalization of the classical wavelet transform in the context of the linear canonical transform. In this article, we first present a direct interaction between the linear canonical transform a...
The deformed wavelet transform is a new addition to the class of wavelet transforms that heavily rely on a pair of generalized translation and dilation operators governed by the well-known Dunkl transform. In this study, we adapt the symmetrical prop...
The meaning of the quantum minimum effective length that should distinguish the quantum nature of a gravitational field is investigated in the context of manifestly covariant quantum gravity theory (CQG-theory). In such a framework, the possible occu...
The paper describes the net momentum transported by the transient electromagnetic radiation field of a long transient dipole in free space. In the dipole a current is initiated at one end and propagates towards the other end where it is absorbed. The...
The linear canonical Fourier transform is one of the most celebrated time-frequency tools for analyzing non-transient signals. In this paper, we will introduce and study the deformed Gabor transform associated with the linear canonical Dunkl transfor...
A recent addition to the class of integral transforms is the quaternion quadratic-phase Fourier transform (Q-QPFT), which generalizes various signal and image processing tools. However, this transform is insufficient for addressing the quadratic-phas...
In this paper, we obtain uncertainty principles associated with the linear canonical transform (LCT) of hypercomplex functions. First, we derive the uncertainty principle for hypercomplex functions in the time and LCT domains. Moreover, we exploit th...
In recent years, the implications of the generalized (GUP) and extended (EUP) uncertainty principles on Maxwell–Boltzmann distribution have been widely investigated. However, at high energy regimes, the validity of Maxwell–Boltzmann stati...
This study focuses on a novel parameterized Wigner distribution, which is an organic integration of the free metaplectic Wigner distribution and the
A simple derivation of the bound on entropy is given and the holographic principle is discussed. We estimate the number of quantum states inside space region on the base of uncertainty relation. The result is compared with the Bekenstein formula for...
Uncertainty in biology refers to situations in which information is imperfect or unknown. Variability, on the other hand, is measured by the frequency distribution of observed data. Biological variability adds to the uncertainty. The Constrained Diso...
Quaternion Fourier transform (QFT) has gained significant attention in recent years due to its effectiveness in analyzing multi-dimensional signals and images. This article introduces two-dimensional (2D) right-sided quaternion offset linear canonica...
Although Wiener process models with the consideration of uncertainties, which are nonlinearity, random effects, and measurement errors, have been developed for lifetime prediction in the accelerated degradation test (ADT), they fail to describe the r...
Different disciplines are developing various methods for determining and dealing with uncertainties in complex systems. The constrained disorder principle (CDP) accounts for the randomness, variability, and uncertainty that characterize biological sy...
Palatini-like theories of gravity have a remarkable connection to models incorporating linear generalized uncertainty principles. Considering this, we delve into the thermodynamics of systems comprising both Bose and Fermi gases. Our analysis encompa...
Due to the limitations of traditional geometric error measurement, the measurement accuracy of long-stroke geometric errors is generally not high and the operation is complicated. In response to the above situation, in this study, a geometric error m...
The emergence of a minimal length at the Planck scale is consistent with modern developments in quantum gravity. This is taken into account by transforming the Heisenberg uncertainty principle into the generalized uncertainty principle. Here, the pos...
In this paper, we present a novel integral transform known as the one-dimensional quaternion quadratic-phase Fourier transform (1D-QQPFT). We first define the one-dimensional quaternion quadratic-phase Fourier transform (1D-QQPFT) of integrable (and...
Thermodynamic uncertainty principles make up one of the few rare anchors in the largely uncharted waters of nonequilibrium systems, the fluctuation theorems being the more familiar. In this work we aim to trace the uncertainties of thermodynamic quan...
This note is a part of my effort to rid quantum mechanics (QM) nonlocality. Quantum nonlocality is a two faced Janus: one face is a genuine quantum mechanical nonlocality (defined by the Lüders’ projection postulate). Another face is the nonlocality...
In this paper, we investigate a novel implication of the non-negligible spacetime curvature at large distances when its effects are expressed in terms of a suitably modified form of the Heisenberg uncertainty relations. Specifically, we establish a o...
In this work, we formulate a generalized uncertainty principle with both position and momentum operators modified from their canonical forms. We study whether Lorentz symmetry is violated and whether it can be saved with these modifications. The requ...
This paper presents a minimum signal model via the AC small-signal model and the uncertainty principle, which reveals the minimum AC signal that can be amplified by a bipolar transistor. The Ebers—Moll model (EM3) can describe the small signal amplif...
The special affine Fourier transform (SAFT) is an extended version of the classical Fourier transform and incorporates various signal processing tools which include the Fourier transforms, the fractional Fourier transform, the linear canonical transf...
The aim of this paper is to show some uncertainty inequalities for the linear canonical Dunkl transform (LCDT), including sharp Heisenberg-type, entropic-type, logarithmic-type, Donoho–Stark-type and local-type uncertainty principles.
In this paper, we relate Poisson’s summation formula to Heisenberg’s uncertainty principle. They both express Fourier dualities within the space of tempered distributions and these dualities are also inverse of each other. While Poisson’s summation f...
We review, as well as provide some new results regarding the study of the structure of spacetime and the singularity in the interior of the Schwarzschild black hole in both loop quantum gravity and generalized uncertainty principle approaches, using...
We study the correlation of the ground state of an N-particle Moshinsky model by computing the Shannon entropy in both position and momentum spaces. We have derived the Shannon entropy and mutual information with analytical forms of such an N-particl...
We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the Rényi and Tsallis types. Here, specific features of measurements of observa...
Several approaches to quantum gravity imply the presence of a minimal measurable length at high energies. This is in tension with the Heisenberg Uncertainty Principle. Such a contrast is then considered in phenomenological approaches to quantum gravi...
The principle of certainty of taxation is the dimension of a general requirement of certainty in the legal system. The purpose of this article is to argue the thesis that uncertainty in tax law is not always an absolute evil, sometimes it acts as a m...
By using the symmetry of the Dunkl Laplacian operator, we prove a sharp Shannon-type inequality and a logarithmic Sobolev inequality for the Dunkl transform. Combining these inequalities, we obtain a new, short proof for Heisenberg-type uncertainty p...
Thermodynamic uncertainty relations (TURs) represent one of the few broad-based and fundamental relations in our toolbox for tackling the thermodynamics of nonequilibrium systems. One form of TUR quantifies the minimal energetic cost of achieving a c...
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