Results 21 to 30 of about 2,032 (227)
COMMON SOURCE OF NUMEROUS THETA FUNCTION IDENTITIES [PDF]
Glasgow Mathematical Journal, 2007 Abstract.Motivated by the recent work due to Warnaar (2005), two new and elementary proofs are presented for a very useful q-difference equation on eight shifted factorials of infinite order. As the common source of theta function identities, this q-difference equation is systematically explored to review old and establish new identities on Ramanujan's
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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 +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 ...
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Theta function identities and q series
, 2023 We establish some functional identities of theta functions, an elementary proof of classical fourth-order identities, Landen transformations, and q series from the eigenvectors of the discrete Fourier transform. Also, we derive connection between Rogers-Ramanujan type identity and theta function identity.
Masal, Hemant +2 more
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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 +3 more
wiley +1 more source
From Dedekind’s Level 12 Identities to Combinatorial Structures of Colored Partitions
AxiomsThe 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 +2 more
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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 ...
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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 +3 more
wiley +1 more source
Theta Function Identities of Level 16 and Their Applications to Colored Partitions
MathematicsTheta function identities play an important role in the theory of modular forms and partitions, with Ramanujan’s q-series providing a fundamental analytical framework.
Fatemah Mofarreh +2 more
doaj +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.
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