18 papers · ranked by Valyu relevance
Steven Murray, Francis Poulin
1 International Centre for Radio Astronomy Research (ICRAR), Curtin University, Bentley, WA 6102, Australia 2 ARC Centre of Excellence for All-Sky Astrophysics in 3 Dimensions (ASTRO 3D) 3 School of Earth and Space Exploration, Arizona State University, Tempe, AZ, 85281, USA 4 Department of DOI: 10.21105/joss.01397…
Cameron L. Williams
In this paper, we review the theory of the Fourier-Bessel transform. Many of the standard results for the Fourier-Bessel transform have become folklore results or predate modern functional analysis and rely on hard analysis proofs that miss the elegance of more modern machinery. This review aims to centralize some of…
A. V. Kisselev
The Hankel transform Hn[f(x)](q) = R ∞ 0 xf(x)Jn(qx)dx is studied for integer n > −1 and positive parameter q. It is proved that the Hankel transform is given by uniformly and absolutely convergent series in reciprocal powers of q, provided special conditions on the function f(x) and its derivatives are imposed. It is…
Natalie Baddour
It is well known that the Hankel transform possesses neither a shift-modulation nor a convolution-multiplication rule, both of which have found many uses when used with other integral transforms. In this paper, the generalized shift operator, as defined by Levitan, is applied to the Hankel transform. It is shown that…
Ashish Pathak, Dileep Kumar
where σ(t) = t 2ν+1 2 ν+ 1 2 Γ(ν+ 3 2 ) , j(.) = Cνx 1 2 −νJν− 1 2 , Cν = 2ν+ 1 2 Γ(ν + 1 2 ) and Jν− 1 2 denote the Bessel function of first kind of order ν − 1 2 .
Mahid M. Mangontarum, Amila P. Macodi-Ringia, Normalah S. Abdulcarim
More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such…
Nathalie Liezel R. Rojas, Eric A. Galapon
entire exponential type functions Authors: ['Nathalie Liezel R. Rojas' 'Eric A. Galapon'] We perform an asymptotic evaluation of the Hankel transform, R∞ 0 Jν(λx)f (x)dx, for arbitrarily large λ of an entire exponential type function, f (x), of type τ by shifting the contour of integration in the complex plane. Under…
Cristian Arteaga, Isabel Marrero
For μ ≥ −1/2, the authors have developed elsewhere a scheme for interpolation by Hankel translates of a basis function Φ in certain spaces of continuous functions Y*n (n ∈ ℕ) depending on a weight w. The functions Φ and w are connected through the distributional identity t4n(h**μ′Φ)(t) = 1/w(t), where h**μ′ denotes the…
Natalie Baddour
In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the ‘Fourier shell…
Paul Barry
We study Hankel transforms of sequences, where the transform elements are members of the set {−1, 0, 1}. We relate these Hankel transforms to special continued fraction expansions. In particular, we posit a conjecture relating the distribution of non-zero terms in the Hankel transform to the distribution of powers of…
Peter Frame, Aaron Towne, Mohamed Kamel Riahi
Time-delay embedding is an increasingly popular starting point for data-driven reduced-order modeling efforts. In particular, the singular value decomposition (SVD) of a block Hankel matrix formed from successive delay embeddings of the state of a dynamical system lies at the heart of several popular reduced-order…
D. R. Yafaev
We show that total multiplicities of negative and positive spectra of a self-adjoint Hankel operator H with kernel h(t) and of an operator of multiplication by some real function s(x) coincide. In particular, ±H ≥ 0 if and only if ±s(x) ≥ 0. The kernel h(t) and its "sign-function" s(x) are related by an explicit…
Xueyang Yao, Natalie Baddour, Yilun Shang
The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In the first part of this two-paper series, we proposed and evaluated the theory of the 2D Discrete Fourier Transform (DFT) in polar coordinates. The theory of…
Richard E Rosch, Brittany Scheid, Kathryn A Davis, Brian Litt + 1 more
Many biological systems display circadian and slow multi-day rhythms, such as hormonal and cardiac cycles. In patients with epilepsy, these cycles also manifest as slow cyclical fluctuations in seizure propensity. However, such fluctuations in symptoms are consequences of the complex interactions between the underlying…
Xi Chen, Wenchuan Wu, Mark Chiew
Three-dimensional (3D) encoding methods are increasingly being explored as alternatives to multi-slice two-dimensional (2D) acquisitions in fMRI, particularly in cases where high isotropic resolution is needed. 3D multi-shot EPI is the most popular 3D fMRI acquisition method, but is susceptible to physiological…
Duncan Bossion, Sutirtha Chowdhury, Pengfei Huo
We present the rigorous theoretical framework of the generalized spin mapping representation for non- adiabatic dynamics. This formalism is based on the generators of the su(N) Lie algebra to represent N discrete electronic states, thus preserving the size of the original Hilbert space in the state representation. The…
Authors not listed
This article is the second in a two-part tutorial review on electronic spin-dependent dynamics. In Part I, we presented the fundamental theory within the adiabatic Born– Huang framework that describes the interaction between nuclear motion and the elec- tronic (spin and spatial) degrees of freedom. In particular, we…
Steen Moeller, Erick O. Buko, Suhail P. Parvaze, Logan Dowdle + 3 more
To develop an extension to locally low rank (LLR) denoising techniques based on transform domain processing that reduces the number of images required in the MR image series for high-quality denoising. LLR methods with random matrix theory-based thresholds are successfully used in the denoising of MR image series in a…