Results 51 to 60 of about 4,592,487 (264)
On Somos's theta-function identities of level 14
, 2017 M. Somos discovered around 6200 theta-function identities of different levels using the computer and offered no proof for them.
Vasuki, K. R., Veeresha, R. G.
core +1 more source
On zeta function identities involving sums of squares and the zeta–theta correspondence [PDF]
, 2011 We prove two identities involving Dirichlet series, in the denominators of whose terms sums of two, three and four squares appear. These follow from two classical identities of Jacobi involving the four Jacobian Theta Functions θ1(z;q), θ2(z;q), θ3(z;q ...
Dutt, Somjit, Somjit Dutt
core +1 more source
Some Remarks on Very-Well-Poised 8ϕ7 Series
Symmetry, Integrability and Geometry: Methods and Applications, 2012 Nonpolynomial basic hypergeometric eigenfunctions of the Askey-Wilson second order difference operator are known to be expressible as very-well-poised 8ϕ7 series.
Jasper V. Stokman
doaj +1 more source
Elevated Connectivity During Language Processing Is Associated With Cognitive Performance in SeLECTS
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Self‐Limited Epilepsy with Centrotemporal Spikes (SeLECTS) is associated with language impairments despite seizures originating in the motor cortex, suggesting aberrant cross‐network interactions. Here we tested whether functional connectivity in SeLECTS during language tasks predicts language performance.
Wendy Qi +8 more
wiley +1 more source
New proofs of Ramanujan’s identities on false theta functions [PDF]
The Ramanujan Journal, 2018 We provide new proofs to five of Ramanujan's intriguing identities on false theta functions without using the Rogers-Fine identity and Bailey transforms.
openaire +3 more sources
A Combinatorial Proof of the Farkas-Kra Theta Function Identities and Their Generalizations
, 1995 Recently, Farkas acid Kra found some cubic theta function identities from their work on automorphic forms. Shortly thereafter, Farkas and Ropeliovich were able to generalize these to pth order theta function identities using the theory of elliptic ...
Garvan, F.G.
core +1 more source
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Variants in SLC6A1, encoding the GABA transporter 1 (GAT‐1), cause epilepsy, autism spectrum disorder, and developmental delay via loss of GABA uptake, impaired trafficking, and ER retention. We previously found that 4‐Phenylbutyrate (PBA), an FDA‐approved drug, restores GABA uptake and reduces seizures in SLC6A1‐related disorders ...
Melissa B. DeLeeuw +5 more
wiley +1 more source
Automatic Proof of Theta-Function Identities [PDF]
, 2019 This is a tutorial for using two new MAPLE packages, thetaids and ramarobinsids. The thetaids package is designed for proving generalized eta-product identities using the valence formula for modular functions. We show how this package can be used to find theta-function identities as well as prove them.
Frye, Jie, Garvan, Frank
openaire +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 +10 more
wiley +1 more source
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Treatment of disorders of consciousness (DoC) remains a major clinical challenge, and noninvasive, targeted modulation of deep brain structures has emerged as a promising therapeutic strategy. We aimed to evaluate the feasibility/safety and preliminary effects of thalamic temporal interference stimulation (TIS) targeting centromedian‐
Gengyao Hu +7 more
wiley +1 more source