Results 141 to 150 of about 1,750 (289)

Finite Biorthogonal Polynomials Suggested by the Finite Orthogonal Polynomials Mnp,qx$$ {M}_n^{\left(p,q\right)}(x) $$

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Constructing a biorthogonal structure from scratch, that is, defining a biorthogonal pair is quite tough. Because here the orthogonality must be established between two different sets. There are four known univariate biorthogonal polynomial sets, suggested by Laguerre, Jacobi, Hermite and Szegő‐Hermite polynomials, in the literature.
Esra Güldoğan Lekesiz
wiley   +1 more source

A quick proof of reciprocity for Hecke Gauss sums

, 2013
In this note we present a short and elementary proof of Heckeʼs reciprocity law for Hecke–Gauss sums of number ...
Boylan, Hatice, Skoruppa, Nils-Peter
core   +1 more source

A Novel Optimized Local Linearization Hybrid Block Method for Chaotic Systems: Applications to Stretch‐Twist‐Fold Flow and Bond Orbital Chaotic Attractors

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT The numerical approximation of nonlinear chaotic differential systems, such as the modified stretch‐twist‐fold (STF) flow and multi‐bond chaotic attractors, presents a significant challenge due to their sensitive dependence on initial conditions and complex dynamics where analytical solutions are unattainable.
Shina Daniel Oloniiju, Anastacia Dlamini
wiley   +1 more source

Practical Guide and Best Practices for Diffusion NMR Processing With GNAT

Magnetic Resonance in Chemistry, EarlyView.
A practical and reproducible workflow for diffusion‐NMR (DOSY) data analysis is introduced through a step‐by‐step GNAT tutorial. By establishing clear processing guidelines, validation strategies, and reporting standards, this work aims to reduce variability in diffusion measurements and promote more transparent, comparable, and reliable DOSY studies ...
Tadeu Luiz Gomes Cabral, Guilherme Dal Poggetto, Claudio F. Tormena, Mathias Nilsson   +3 more
wiley   +1 more source

Pure Gaussian Apodisation Reduces Integral Crosstalk Sensitivity in Quantitative NMR

Magnetic Resonance in Chemistry, EarlyView.
Exponential apodisation redistributes peak area away from its centre, which increases crosstalk with neighbouring peaks and reduces integral trueness when integrating between defined regions. A pure Gaussian apodisation limits wing growth: Crosstalk between peaks is not worsened, and trueness is conserved during integration.
A. Flook, C. S. Raman, G. C. Lloyd‐Jones   +2 more
wiley   +1 more source

On the Location of Gauss Sums [PDF]

Mathematical Tables and Other Aids to Computation, 1956
openaire   +1 more source

Simultaneous T2, T2*, and R2′ Mapping for Multiple Sclerosis Using Nonlinear Model‐Based Reconstruction of Undersampled Radial RARE‐EPI MRI

Magnetic Resonance in Medicine, EarlyView.
ABSTRACT Purpose To demonstrate the synergy of undersampled radial 2in1‐RARE‐EPI acquisition and nonlinear model‐based reconstruction for accelerated and simultaneous T2, T2*, and R2′ mapping in brains of patients with multiple sclerosis (MS). Methods 2in1‐RARE‐EPI combines a RARE module with an EPI module to capture T2 and T2* information.
Jose Raul Velasquez Vides, Carl J. J. Herrmann, Thomas Gladytz, Hoby P. Hetherington, Hendrik Mattern, Xiaoqing Wang, Jason M. Millward, Shahriar Shalikar, Igor Fabian Tellez Ceja, Beate Endemann, Sonia Waiczies, Joseph Kuchling, Friedemann Paul, Georg Rose, Min‐Chi Ku, Franz Schmitt, Thoralf Niendorf   +16 more
wiley   +1 more source

Denoising of ASL Data Using Deep Learning Priors Generated From Distribution Remapping

Magnetic Resonance in Medicine, EarlyView.
ABSTRACT Purpose To develop an effective deep learning (DL)–based method to denoise arterial spin labeling (ASL) data. Methods Conventional DL–based ASL denoising methods often suffer from overfitting and poor generalization when training data are limited.
Ziyang Xu, Rong Guo, Ziwen Ke, Yudu Li, Yibo Zhao, Wen Jin, Ruihao Liu, Ziyu Meng, Yao Li, Zhi‐Pei Liang   +9 more
wiley   +1 more source

Gauss Sums forO(2n+1,q)

, 1998
For a nontrivial additive characterλand a multiplicative characterχof the finite field withqelements (qis a power of an odd prime), the “Gauss” sum ∑λ(trw) overw∈SO(2n+1,q) and ∑χ(detw)λ(trw) overw∈O(2n+1,q) are considered.
Kim, Dae San
core   +1 more source

An Improved Air Film Model for Studying the Tilt Characteristics of Aerostatic Thrust Bearings

International Journal of Mechanical System Dynamics, EarlyView.
ABSTRACT In this study, an improved mass‐spring model that treats the lubricating air film as distributed springs is proposed to calculate the static and dynamic angular stiffness of aerostatic thrust bearings. The proposed model refines the traditional mass‐spring model by introducing the spatially varying mechanical properties of the air film and the
Hui Zhuang, Jianguo Ding, Yu Chang
wiley   +1 more source