A scheme to a complex-valued acquisition of the Fourier transform imaging was proposed. The main idea is to project the real and the imaginary parts of a diffraction field to intensity distributions respectively. The whole procedure was algorithm i...
An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally represented as...
It is proven that, for any soft potential characterized by a finite Fourier transform $\widetildeφ(k)$, the virial and energy thermodynamic routes are equivalent for approximations such that the Fourier transform of the total correlation function...
In this work we present new methods for transforming and solving finite series by using the Laplace transform. In addition we introduce both an alternative method based on the Fourier transform and a simplified approach. The latter allows a quick sol...
Tags: python-3.x, csv, machine-learning, scikit-learn | Score: 1
Tags: python, json, python-2.7 | Score: -1
Tags: javascript, vuejs2, vuetify.js | Score: 2
We introduce the Sumudu Neural Operator (SNO), a neural operator rooted in the properties of the Sumudu Transform. We leverage the relationship between the polynomial expansions of transform pairs to decompose the input space as coefficients, which a...
The Gale transform, an involution on sets of points in projective space, appears in a multitude of guises, in subjects as diverse as optimization, coding theory, theta-functions, and recently in our proof that certain general sets of points fail to...
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using transform m...
A nonparametric method is proposed for estimating the quantile spectra and cross-spectra introduced in Li (2012; 2014) as bivariate functions of frequency and quantile level. The method is based on the quantile discrete Fourier transform (QDFT) defin...
In mathematics, the Hankel transform expresses any given function f(r) as the weighted sum of an infinite number of Bessel functions of the first kind
In this paper, we consider the following singular integral \begin{equation*} T_jf(x)=K_j*f(x), K_j(x)=\frac{x_j}{|x|^{n+1-β}}, \end{equation*} where $x\in R^n, 0\le β<n, j=1,2,\cdots, n$. When $β=0$, it corresponds to the Riesz transform. We will...
Liu, et al., 2009 developed a transformation of a class of non-Gaussian univariate distributions into Gaussian distributions. Liu and collaborators (2012) subsequently applied the transform to search for graphical causal models for a number of empiri...
Let D be a planar Lipschitz domain and consider the Beurling transform of the characteristic function of D, B(1_D). Let 1<p<\infty and 0<a<1 with ap>1. In this paper we show that if the outward unit normal N on bD, the boundary of D, belongs to the B...
Recent research has shown that dynamic zeros in shader programs of gaming applications can be effectively leveraged with a profile-guided, code-versioning transform. This transform duplicates code, specializes one path assuming certain key program op...
Human motions (especially dance motions) are very noisy, and it is hard to analyze and edit the motions. To resolve this problem, we propose a new method to decompose and modify the motions using the Hilbert-Huang transform (HHT). First, HHT decompos...
A new method for removing impulse noise from speech in the wavelet transform domain is proposed. The method utilizes the multiresolution property of the wavelet transform, which provides finer time resolution at the higher frequencies than the short-...
We derive explicit formulas for the Mellin transform and the distribution of the exponential functional for Levy processes with rational Laplace exponent. This extends recent results by Cai and Kou on the processes with hyper-exponential jumps [N. Ca...
A function $f:\mathbb{Z}_n \to \mathbb{C}$ can be represented as a linear combination $f(x)=\sum_{α\in \mathbb{Z}_n}\widehat{f}(α) χ_{α,n}(x)$ where $\widehat{f}$ is the (discrete) Fourier transform of $f$. Clearly, the basis $\{χ_{α,n}(x):=\ex...