Related papers: A Geometrical Interpretation of Frequency
There are many striking phenomena which are attributed to ``quantum coherence''. It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical…
We present a browser application for estimating the number of frequent patterns, in particular itemsets, as well as the pattern frequency spectrum. The pattern frequency spectrum is defined as the function that shows for every value of the…
We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has mass and charge density distributing in space,…
This letter proposes an analytical approach to formulate the power system oscillation frequency under a large disturbance. A fact is revealed that the oscillation frequency is only the function of the oscillation amplitude when the system's…
The variation of the velocity of a periodic signal and its frequency along the world line of a standard emitter (at rest with an observer) are considered in a space with affine connections and metrics. It is shown that the frequency of the…
The Fourier spectrum is a family of dimensions that interpolates between the Fourier and Hausdorff dimensions and are defined in terms of certain energies which capture Fourier decay. In this paper we obtain a convenient discrete…
This letter seeks to clarify the different existing definitions of both instantaneous complex phase and frequency as well as their equivalence under standard modeling assumptions considered for transmission systems, i.e. balanced positive…
Frequency tagging is a powerful approach to investigate the neural processing of sensory features, and is recently adapted to study the neural correlates of superordinate structures, i.e., chunks, in complex sequences such as speech and…
Symmetry -- invariance to certain operators -- is a fundamental concept in many branches of physics. We propose ways to measure symmetric properties of vertices, and their surroundings, in networks. To be stable to the randomness inherent…
This paper presents methods to analyze functional brain networks and signals from graph spectral perspectives. The notion of frequency and filters traditionally defined for signals supported on regular domains such as discrete time and…
In this paper, a generalization of the concept of electrical power for periodic current and voltage waveforms based on a new generalized complex geometric algebra (GCGA) is proposed. This powerful tool permits, in n-sinusoidal/nonlinear…
The object of this contribution is twofold. On one hand, it rises some general questions concerning the definition of the electromagnetic field and its intrinsic properties, and it proposes concepts and ways to answer them. On the other…
We review the definition of geometric quantization, which begins with defining a mathematical framework for the algebra of observables that holds equally well for classical and quantum mechanics. We then discuss prequantization, and go into…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
A new approach to description of hadron spectroscopy is proposed. By assumption, the form of spectrum is dictated by the trace of energy momentum tensor in QCD. This provides the relativistic and renormalization invariance of hadron masses.…
The reflection, transmission and absorption of a symmetric electromagnetic pulse, which carrying frequency is close to the frequency of an interband transition in a QW (QW), are obtained. The energy levels of a QW are assumed discrete, one…
We consider a measurement of finite-frequency current fluctuations, using a resonance circuit as a model for the detector. We arrive at an expression for the measurable response in terms of the current-current correlators which differs from…
A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called harmonic Gaussian…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
Signals and datasets that arise in physical and engineering applications, as well as social, genetics, biomolecular, and many other domains, are becoming increasingly larger and more complex. In contrast to traditional time and image…