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In this article we outline the historical development and key results obtained to date for free parafermionic spin chains. The concept of free parafermions provides a natural N-state generalization of free fermions, which have long underpinned the ex
Externí odkaz:
http://arxiv.org/abs/2311.04582
Autor:
Thackeray, Henry Robert
For each positive integer n, if the sum of the factors of n is divided by n, then the result is called the abundancy index of n. If the abundancy index of some positive integer m equals the abundancy index of n but m is not equal to n, then m and n a
Externí odkaz:
http://arxiv.org/abs/2310.15900
Autor:
Henry, Robert A., Batchelor, Murray T.
Publikováno v:
SciPost Phys. 15, 016 (2023)
Certain spin chains, such as the quantum Ising chain, have free fermion spectra which can be expressed as the sum of decoupled two-level fermionic systems. Free parafermions are a simple generalisation of this idea to $Z(N)$-symmetric clock models. I
Externí odkaz:
http://arxiv.org/abs/2301.11031
Autor:
Henry, Robert D.1 (AUTHOR) henryr@hope.edu
Publikováno v:
BMC Pregnancy & Childbirth. 9/17/2024, Vol. 24 Issue 1, p1-13. 13p.
Autor:
Thackeray, Henry Robert
For positive integers $n$ and $k$ such that $k$ is at most $n$, we find an explicit one-to-one correspondence between the following two sets: the set of words consisting of $k$ $R$s, $k$ $U$s, and $n - k$ $D$s, where the first letter of the word is n
Externí odkaz:
http://arxiv.org/abs/2208.04395
Autor:
Thackeray, Henry Robert
An s-cap n-flat is given by a set of s points, no three of which are on a common line, in an n-dimensional affine space over the field of three elements. The cap set problem in dimension n is: what is the maximum s such that there is an s-cap n-flat?
Externí odkaz:
http://arxiv.org/abs/2206.09804
Autor:
Thackeray, Henry Robert
An s-cap n-flat, or an n-dimensional cap of size s, is a pair (S,F) where F is an n-dimensional affine space over Z/3Z and the size-s subset S of F contains no triple of collinear points. The cap set problem in dimension n asks for the largest s for
Externí odkaz:
http://arxiv.org/abs/2206.09719
Autor:
Cheng, Bing, Ran, Rui, Qu, Yanyan, Verkerk, Ruud, Henry, Robert, Dekker, Matthijs, He, Hongju
Publikováno v:
In Agriculture Communications June 2024 2(2)
Autor:
Nicole Deflaux, Margaret Sunitha Selvaraj, Henry Robert Condon, Kelsey Mayo, Sara Haidermota, Melissa A. Basford, Chris Lunt, Anthony A. Philippakis, Dan M. Roden, Joshua C. Denny, Anjene Musick, Rory Collins, Naomi Allen, Mark Effingham, David Glazer, Pradeep Natarajan, Alexander G. Bick
Publikováno v:
Nature Communications, Vol 14, Iss 1, Pp 1-10 (2023)
Abstract Recently, large scale genomic projects such as All of Us and the UK Biobank have introduced a new research paradigm where data are stored centrally in cloud-based Trusted Research Environments (TREs). To characterize the advantages and drawb
Externí odkaz:
https://doaj.org/article/5b19d5111ef64f9c86ba31efe3a52fc4
Autor:
Dhondge, Harshal V., Barvkar, Vitthal T., Dastager, Syed G., Dharne, Mahesh S., Rajput, Vinay, Pable, Anupama A., Henry, Robert J., Nadaf, Altafhusain B.
Publikováno v:
In International Journal of Food Microbiology 2 March 2024 413