Results 41 to 50 of about 15,581 (265)

Some Types of Identities Involving the Legendre Polynomials

Mathematics, 2019
In this paper, a new non-linear recursive sequence is firstly introduced. Then, using this sequence, a computational problem involving the convolution of the Legendre polynomial is studied using the basic and combinatorial methods.
Shimeng Shen, Li Chen
doaj   +1 more source

Relationship Between Neurologic Symptoms and Signs and FMR1 Genotype in Premutation Carriers

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Background and Objectives Fragile X‐associated Tremor/Ataxia Syndrome (FXTAS) is the most severe late‐onset condition caused by a premutation in the FMR1 gene, characterized by expanded CGG triplet repeats of 55–200. Clinical presentations of FXTAS, including gait ataxia, kinetic tremor, cognitive decline, and rare Parkinsonism, are linked to ...
Flora Tassone, Freddy Chafota, Miguel E. Rentería, Randi J. Hagerman, Ellery Santos, Anna Atkinson, Nicholas G. Martin, Elsdon Storey, Danuta Z. Loesch   +8 more
wiley   +1 more source

Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture

Symmetry, Integrability and Geometry: Methods and Applications, 2009
We give a new theta-function identity, a special case of which is utilised to prove Kawanaka's Macdonald polynomial conjecture. The theta-function identity further yields a transformation formula for multivariable elliptic hypergeometric series which ...
Robin Langer, Michael J. Schlosser, S. Ole Warnaar   +2 more
doaj   +1 more source

On commutativity theorems for rings

International Journal of Mathematics and Mathematical Sciences, 1990
Let R be an associative ring with unity. It is proved that if R satisfies the polynomial identity [xny−ymxn,x]=0(m>1,n≥1), then R is commutative. Two or more related results are also obtained.
H. A. S. Abujabal, M. S. Khan
doaj   +1 more source

A Novel Multi-Receiver Signcryption Scheme with Complete Anonymity. [PDF]

PLoS ONE, 2016
Anonymity, which is more and more important to multi-receiver schemes, has been taken into consideration by many researchers recently. To protect the receiver anonymity, in 2010, the first multi-receiver scheme based on the Lagrange interpolating ...
Liaojun Pang, Xuxia Yan, Huiyang Zhao, Yufei Hu, Huixian Li   +4 more
doaj   +1 more source

Evaluation of Digital Technologies for Home‐Based Assessment in People With Amyotrophic Lateral Sclerosis

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Digital technologies hold promise for transforming healthcare by enhancing personalized treatments and offer valuable opportunities to improve patient care. Here, we evaluated several novel, self‐administered, home‐based, digital endpoints for their association with corresponding conventional standard clinical measures (primary) in ...
Arne Mueller, Vanessa Vallejo, Mónica Povedano Panadés, Orla Hardiman, Véronique Danel‐Brunaud, Senda Ajroud‐Driss, Philippe Couratier, Jeremy Shefner, Anna Gokey, Mike DiCesare, Erin Lennox, Jens Praestgaard, Lucie Brujin, Peggy Allred, Ram Miller   +14 more
wiley   +1 more source

A Two‐Stage Questionnaire and Actigraphy Screening for iRBD in a Multicenter Retrospective Cohort

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Isolated rapid‐eye‐movement sleep behavior disorder is a prodromal marker of synucleinopathies. However, most cases remain undiagnosed due to the insufficient predictive value of questionnaires and limited access to confirmatory video‐polysomnography. We assessed a two‐stage screening strategy combining a brief questionnaire on rapid‐
Caleb A. Massimi, Giorgio Ricciardiello Mejia, Andre Metzger, Kang Hyun Ryu, Salonee Marwaha, Eva Grzegorczyk, Li Zhou, Eliana Jacobs, Boris Gilyadov, Claudia Kunney, Liqhwa Ncube, Ankit Parekh, Emmanuel Mignot, Fanny M. Elahi, Joseph Winer, Kathleen Poston, Andreas Brink‐Kjaer, Emmanuel H. During   +17 more
wiley   +1 more source

On the Leibniz formula for divided differences

Journal of Numerical Analysis and Approximation Theory, 2006
We give an identity for the Hermite-Lagrange interpolating polynomial and a short proof of Leibniz-type formula for divided differences in case of coalescing knots.
Mircea Ivan
doaj   +2 more sources

T1 Over Squared Proton Density Ratio to Characterize Multiple Sclerosis Lesions

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Differentiating remyelinated from demyelinated lesions in MS remains challenging without histological confirmation. This study introduces the T1‐to‐PD2 ratio (TPR) imaging approach and evaluates its ability to characterize MS lesions alongside other quantitative MRI (qMRI) metrics. Methods Thirty individuals with MS (mean age: 47.5 ± 
Sarah J. Wright, Scotty G. McKay, Jean Ramos Bou, Fen Bao, Vivian B. Truong, Chenyang Li, Li Jiang, Anza B. Memon, E. Mark Haacke, Yulin Ge, Yongsheng Chen   +10 more
wiley   +1 more source

Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling Numbers

Mathematics
In this paper, we present two symbolic methods, in particular, the method starting from the source identity, umbra identity, for constructing identities of s-Appell polynomials related to Stirling numbers and binomial coefficients.
Tian-Xiao He, Emanuele Munarini
doaj   +1 more source