20 papers · ranked by Valyu relevance
Peter D. Miller, David A. Smith
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial interval. We provide conditions on the regularity of both the data and weight for…
Sultan Aitzhan, Sambhav Bhandari, David A. Smith
We describe a new form of diagonalization for linear two point constant coefficient differential operators with arbitrary linear boundary conditions. Although the diagonalization is in a weaker sense than that usually employed to solve initial boundary value problems (IBVP), we show that it is sufficient to solve IBVP…
D. A. Smith
A method for solving linear initial boundary value problems was recently reimplemented as a true spectral transform method. As part of this reformulation, the precise sense in which the spectral transforms diagonalize the underlying spatial differential operator was elucidated. That work concentrated on two point…
P. Hashemzadeh, A. S. Fokas, S. A. Smitheman
Integral representations for the solution of linear elliptic partial differential equations (PDEs) can be obtained using Green's theorem. However, these representations involve both the Dirichlet and the Neumann values on the boundary, and for a well-posed boundary-value problem (BVPs) one of these functions is…
Kehe Zhu
There is a canonical unitary transformation from L 2 (R) onto the Fock space F 2 , called the Bargmann transform. The purpose of this article is to translate some important results and operators from the context of L 2 (R) to that of F 2 . Examples include the Fourier transform, the Hilbert transform, Gabor frames…
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…
Maurice Pierre
We provide an introduction to the Fractional Fourier Transform Fθ and draw a connection between it and the unit complex number e iθ. Motivated by this, we define an entirely new object associated with any unit quaternion e iξ1 cos η + e iξ2 j sin η, which we call the Versor Transform V(ξ1,η,ξ2) . This transform, which…
Nabil Mlaiki, Noor Jamal, Muhammad Sarwar, Manel Hleili + 2 more
'Khursheed J. Ansari' 'Naeem Saleem'] Integral transforms are used in many research articles in the literature, due to their interesting applications in the solutions of problems of applied science and engineering. In many situations, researchers feel difficulties in applying a given transform to solve differential or…
Authors not listed
This report compares various simulation and data analysis methods for free induction decay (FID) signals in Nuclear Magnetic Resonance (NMR) Spectroscopy. The methods discussed include discrete fast Fourier transformation (FFT), least squares fitting (LSF), short-time Fourier transformation (STFT), and wavelet…
Yuzhou Chang, Jixin Liu, Anjun Ma, Sizun Jiang + 11 more
Tissue module (TM) is a spatially organized tissue region and executes specialized biological functions, recurring and varying at different tissue sites. However, the computational identification of TMs poses challenges due to their convoluted biological functions, poorly-defined molecular features, and varying…
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…
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…
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…
A.C. Geiger, C.J. Smith, N. Takanti, D.M. Harmon + 2 more
Fourier transform fluorescence recovery after photobleaching (FT-FRAP) with patterned illumination is theorized and demonstrated for quantitatively evaluating normal and anomalous diffusion. Diffusion characterization is routinely performed to assess mobility in cell biology, pharmacology, and food science.…
Hari M. Srivastava, Waseem Z. Lone, Firdous A. Shah, Ahmed I. Zayed + 1 more
'Jean-Pierre Gazeau'] The discrete Fourier transform is considered as one of the most powerful tools in digital signal processing, which enable us to find the spectrum of finite-duration signals. In this article, we introduce the notion of discrete quadratic-phase Fourier transform, which encompasses a wider class of…
Justin D Silverman, Alex Washburne, Sayan Mukherjee, Lawrence A David
High-throughput DNA sequencing technologies have revolutionized the study of microbial communities (microbiota) and have revealed their importance in both human health and disease. However, due to technical limitations, data from microbiota surveys reflect the relative abundance of bacterial taxa and not their absolute…
Ricardo M. Campello de Souza, H. M. de Oliveira, A. N. Kauffman
– In this paper, the k-trigonometric functions over the Galois Field GF(q) are introduced and their main properties derived. This leads to the definition of the cask(.) function over GF(q), which in turn leads to a finite field Hartley Transform . The main properties of this new discrete transform are presented and…
Authors not listed
Considering transformation products (TPs) in environmental studies remains a huge challenge for scientists, from identification in samples via mass spectrometry through to inclusion in chemical regulation. This article introduces FAIR-TPs, a website to browse openly-available TP data collated from literature sources.…
Jean Gaudart, Stanislas Rebaudet, Gaetan Texier, Robert Barrais + 2 more
The aim of the present study was to develop a method for multiscale analysis of non-stationary and non-periodic epidemic time series. Indeed, the epidemiologists may need to know the features, at different resolutions, of short duration outbreaks that did not exhibit periodic cycles. Among of the large number of…
Yichen Ding, Varun Gudapati, Ruiyuan Lin, Yanan Fei + 8 more
Recent advances in light-sheet fluorescence microscopy (LSFM) enable 3-dimensional (3-D) imaging of cardiac architecture and mechanics in toto. However, segmentation of the cardiac trabecular network to quantify cardiac injury remains a challenge. We hereby employed “subspace approximation with augmented kernels (Saak)…