Results 31 to 40 of about 4,592,487 (264)

On Ramanujan's lost notebook and new tenth-order like identities for second-, sixth-, and eighth-order mock theta functions [PDF]

, 2023
Ramanujan's lost notebook contains many mock theta functions and mock theta function identities not mentioned in his last letter to Hardy. For example, we find the four tenth-order mock theta functions and their six identities.
Mortenson, Eric T.
core   +1 more source

An extension of the Andrews–Warnaar partial theta function identity [PDF]

Advances in Applied Mathematics, 2020
In this paper, by applying a range of classic summation and transformation formulas for basic hypergeometric series, we obtain a three-term identity for partial theta functions. It extends the Andrews-Warnaar partial theta function identity, and also unifies several results on partial theta functions due to Ramanujan, Lovejoy and Kim. We also establish
openaire   +4 more sources

A computational study on altered theta-gamma coupling during learning and phase coding [PDF]

, 2012
There is considerable interest in the role of coupling between theta and gamma oscillations in the brain in the context of learning and memory. Here we have used a neural network model which is capable of producing coupling of theta phase to gamma ...
Yang Zhan, Haifu Zhou (157350), Zhang Xuejuan, Kendrick Keith M., Zhan Yang, Kendrick, Keith M., Xuejuan Zhang, Zhang, Xuejuan, Zhou Haifu, Jianfeng Feng (48703), Xuejuan Zhang (157336), Zhan, Yang, Keith M. Kendrick (157342), Zhou, Haifu, Haifu Zhou, Yang Zhan (157356), Feng, Jianfeng, Jianfeng Feng, Keith M Kendrick, Feng Jianfeng   +19 more
core   +2 more sources

An isoform of 14‐3‐3 protein regulates transbilayer lipid movement at the plasma membrane

FEBS Letters, EarlyView.
Loss of 14‐3‐3ζ in CHO cells confers resistance to exogenous phosphatidylserine (PS) and impairs endocytosis‐independent inward flip‐flop of fluorescent PS at the plasma membrane. RNAi‐mediated knockdown reproduces this defect, while no additive effect is seen in ATP11C‐deficient cells.
Akiko Yamaji‐Hasegawa, Akira Hattori, Masafumi Tsujimoto, Toshihide Kobayashi   +3 more
wiley   +1 more source

Residual tail twisting in ascidian larvae is stabilized by asymmetric myofibrils that resist bilateral symmetry restoration

FEBS Letters, EarlyView.
Ascidian Ciona larvae initially show strong clockwise tail twisting, which is largely corrected during development. However, a small residual twist remains. This study shows that organized helical myofibrils in tail muscles mechanically stabilize this residual asymmetry, preventing complete restoration of bilateral symmetry and revealing how embryos ...
Yuki S. Kogure, Misaki K. Nishio, Satoru Okuda, Kohji Hotta   +3 more
wiley   +1 more source

On Parameterized Theta Function Identities

, 2023
In history, theta function identities have been studied extensively and deeply. In this paper, applying the residue theorem of an elliptic function, we obtain a parameterized theta function identity. Then, by selecting the appropriate parameter, we derive some famous Jacobi identities, as well as other relatively simple theta ...
openaire   +1 more source

A theta function identity of degree eight and Eisenstein series identities [PDF]

, 2012
In this paper we prove a theta function identity of degree eight using the theory of elliptic theta functions and the method of asymptotic analysis. This identity allows us to derive some curious Eisenstein series identities.
Liu, Zhi-Guo
core   +1 more source

From Dedekind’s Level 12 Identities to Combinatorial Structures of Colored Partitions

Axioms
The Dedekind η-function plays an important role in number theory, particularly in the study of modular forms, q-series, and partition identities. In this paper, we investigate several level-12 η-function identities and examine their combinatorial ...
Fatemah Mofarreh, Arooj Fatima, Ahmer Ali   +2 more
doaj   +1 more source

Loss of IGF‐1R impairs DNA‐PKcs recruitment to chromatin leading to defective end‐joining

Molecular Oncology, EarlyView.
IGF‐1R promotes radioresistance by facilitating DNA‐PKcs recruitment to chromatin, enabling non‐homologous end‐joining (NHEJ) repair of double‐strand breaks. Inhibition or loss of IGF‐1R disrupts this recruitment to damage sites, driving compensatory reliance on microhomology‐mediated end‐joining (MMEJ) repair.
Matthew O. Ellis, Jack V. Mills, Wojciech Niedzwiedz, Valentine M. Macaulay   +3 more
wiley   +1 more source

Theta function identities

Journal of Mathematical Analysis and Applications, 1990
All but one of the identities in the 21 chapters of Ramanujan's second Notebook had been proved by 1986. This paper proves the remaining identity, which involves a ratio of Dedekind eta functions \(\eta^ 2(z/p)/\eta^ 2(z)\) with \(p=13\). The author's method is quite general and constructs, for each odd integer \(p>1\), a class of modular functions on ...
openaire   +1 more source