Related papers: On Singular Points and Oscillatory Integrals
The oscillator, inherently, turns the phase noise of its internal components into frequency noise, which results into a multiplication by 1/f^2 in the phase-noise power spectral density. This phenomenon is known as the Leeson effect. This…
We review the method of the differential equations for the evaluation of multi-loop Feynman integrals. In particular, we focus on the series expansion approach for solving the system of differential equation and we discuss how to perform…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
We obtain rigorous results concerning the evaluation of integrals on the two sphere using complex methods. It is shown that for regular as well as singular functions which admit poles, the integral can be reduced to the calculation of…
We introduce the novel concept of a non-stationary iterated function system by considering a countable sequence of distinct set-valued maps $\{\mathcal{F}_k\}_{k\in \mathbb{N}}$ where each $\mathcal{F}_k$ maps $\mathcal{H}(X)\to…
This article introduces an effective generalization of the polar flavor of the Fourier Theorem based on a new method of analysis. Under the premises of the new theory an ample class of functions become viable as bases, with the further…
We generalize the position- and momentum-space entanglement cuts to a family of cuts corresponding to regions in the classical phase space. We explicitly compute the entanglement spectra of free fermionic many-body wavefunctions for a…
In this paper we revisit some quadrature methods for highly oscillatory integrals of the form $\int_{-1}^1f(x)e^{{\rm i}\omega x}dx, \omega>0$. Exponentially Fitted (EF) rules depend on frequency dependent nodes which start off at the…
The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From…
An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicate the intrinsic limitations of spectral methods when it comes…
In this paper, using generalized k-fractional integral operator (in terms of the Gauss hypergeometric function), we establish new results on generalized k-fractional integral inequalities by considering the extended Chebyshev functional in…
We discuss the notion of resonance, as well as the existence and uniqueness of periodic solutions for a forced simple harmonic oscillator. While this topic is elementary, and well-studied for sinusoidal forcing, this does not seem to be the…
The evolution of any factorized time-reversible symplectic integrators, when applied to the harmonic oscillator, can be exactly solved in a closed form. The resulting modified Hamiltonians demonstrate the convergence of the Lie series…
We develop a new and further generalized form of the fractional kinetic equation involving generalized k-Bessel function. The manifold generality of the generalized k-Bessel function is discussed in terms of the solution of the fractional…
Phase response curves are important for analysis and modeling of oscillatory dynamics in various applications, particularly in neuroscience. Standard experimental technique for determining them requires isolation of the system and…
There are three main types of numerical computations for the Bessel function of the second kind: series expansion, continued fraction, and asymptotic expansion. In addition, they are combined in the appropriate domain for each. However,…
We study some conformally invariant integral equations using the method of moving spheres.
Fresnel's equations describe reflection and transmission of electromagnetic waves at an interface between two media. It turns out that these equations can be used in quasistatics and even statics, for example to straightforwardly calculate…
An oscillator algebra and the associated Fock space with reflecting boundary and generalized statistics are constructed and is generalized to the multicomponent case. The oscillator algebra depends manifestly on the reflection factor and…
In this paper we consider a nonlinear generalization of the isotonic oscillator in the same spirit as one considers the generalization of the harmonic oscillator with a truly nonlinear restoring force. The corresponding potential being…