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Controlling DNA Three‐Way Junction Conformations via Base Pairing
Small Structures, Volume 7, Issue 4, April 2026.Atomistic molecular dynamics simulations reveal how base pairing determines the Ys‐, T‐, and newly identified Ya‐shaped forms of DNA three‐way junctions, uncovering the dynamic interplay between base‐pairing and junction conformation. DNA three‐way junctions, the simplest form of branched DNA, are widely used scaffolds in nanotechnology and ...
Richard Jacobi, Leticia González
wiley +1 more source
A combinatorial proof for the positivity of the normalized Jacobi triple product tails
For \(k\geq 1\), we prove that \[ [q^n z^s]J_k(z,q)\geq 0, \qquad (n\geq 0,\ s\in\mathbb Z) \] for the normalized Jacobi triple product tails \[ J_k(z,q)= \frac{ \sum_{j=k}^{\infty}(-1)^{j-k} q^{\binom{j+1}{2}}(z^{-j}+\cdots+z^j)} {(zq,q/z;q)_\infty}. \]
Xiangyu Ding, Lisa Hui Sun
core +1 more source
Gaussian sums, Dedekind sums and the Jacobi triple product identity
Kyushu Journal of Mathematics, 1995 Let \(e(x)=\exp (2\pi ix)\). The Gaussian sum identity \[ \sum^q_{r=1} e (r^2/q) = \prod^{q-2}_{\substack{ r=1\\ (r\text{ odd})}} \bigl\{e(r/q) - e(-r/ q)\bigr\} \] is deduced from the Jacobi triple product identity for the theta function \[ \vartheta (\tau,z) = \sum^\infty_{n=- \infty} e(n^2 \tau/2+nz). \]
openaire +3 more sources
The Triple Helix of University-Industry-Government Relations [PDF]
, 2012 Etzkowitz & Leydesdorff (2000) further elaborated the Triple Helix of University-Industry-Government Relations (cf. Etzkowitz & Leydesdorff, 1995; Lowe, 1982) into a model for studying knowledge-based economies.
Leydesdorff, Loet +2 more
core +1 more source
Tiling proofs of Jacobi triple product and Rogers-Ramanujan identities
, 2020 We use the method of tiling to give elementary combinatorial proofs of some celebrated $q$-series identities, such as Jacobi triple product identity, Rogers-Ramanujan identities, and some identities of Rogers. We give a tiling proof of the q-binomial theorem and a tiling interpretation of the q-binomial coefficients. A new generalized $ k $-product $q$-
openaire +3 more sources
Publications de l'Institut Mathematique, 2020 We establish a set of two new relationships involving R?,R? and Rm-functions, which are based on Jacobi?s famous triple-product identity. We, also provide answer for an open problem of Srivastava, Srivastava, Chaudhary and Uddin, which suggest to find an inter-relationships between R?,R? and Rm(m ?
openaire +3 more sources
A simple proof of Jacobi’s triple product identity [PDF]
Proceedings of the American Mathematical Society, 1965 openaire +2 more sources
p-adic vertex operator algebras. [PDF]
Res Number Theory, 2023 Franc C, Mason G.
europepmc +1 more source
On general series-product identities [PDF]
, 2013 [[abstract]]We derive the general series-product identities from which we deduce several applications, including an identity of Gauss, the generalization of Winquist's identity by Carlitz and Subbarao, an identity for , the quintuple product identity ...
Chen, Sin-Da; Huang, Sen-Shan
core
On the infinite Borwein product raised to a positive real power. [PDF]
Ramanujan J, 2023 Schlosser MJ, Zhou NH.
europepmc +1 more source