text stringlengths 1 1.3M | id stringlengths 2 2.39k | metadata dict |
|---|---|---|
\section{Introduction}
Evolution algebras were introduced by Tian in his book \cite{T1} (see also \cite{TV}) to model the self reproduction process in non-Mendelian genetics. As shown in \cite{T1}, the theory of evolution algebras is connected to many areas of Mathematics, like, for example, graph theory, group theory... | proofpile-arXiv_065-3842 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
The most studied example of quantum field theory in curved spacetime is probably the theory of a scalar field in de Sitter space. Indeed the model is simple enough to be solved analytically and therefore the properties of the field can be studied in detail. In particular the thermal properties of... | proofpile-arXiv_065-6373 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
Fifth generation (5G) communication networks will likely adopt \ac{mm-wave} and massive \ac{MIMO} technologies, thanks to a number of favorable properties. In particular, operating at carrier frequencies beyond 30 GHz, with large available bandwidths, \ac{mm-wave} can provide extremely high data... | proofpile-arXiv_065-7442 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
"\\section{Introduction} \nOne of the most intriguing and mysterious objects in the Universe is the(...TRUNCATED) | proofpile-arXiv_065-9775 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
"\\section*{Abstract}\n{\\bf\nThe abstract is in boldface, and should fit in 8 lines.\nIt should be (...TRUNCATED) | proofpile-arXiv_065-10081 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
"\\section{\\label{sec:introduction}Introduction}\nImagining oneself attempting to swim in a pool of(...TRUNCATED) | proofpile-arXiv_065-10753 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
"\\section{Introduction}\r\nThere is extensive experimental evidence, eg.\\ in Refs.~\\cite{Adams:20(...TRUNCATED) | proofpile-arXiv_065-11401 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
"\\section{\\label{sec:Introduction} Introduction}\n{\nAs the temperature is increased, strongly int(...TRUNCATED) | proofpile-arXiv_065-14643 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
"\\section{Introduction}\n\n\\setcounter{equation}{0}\n\n\\renewcommand{\\mathcal X}{{X}}\n\\newcomm(...TRUNCATED) | proofpile-arXiv_066-681 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
"\\section{Introduction}\n\nFor a metric space $(X,d)$ with a notion of volume and boundary, an isop(...TRUNCATED) | proofpile-arXiv_066-1310 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
End of preview. Expand in Data Studio
This dataset is a 0.1% sample of Dolma v1.7, equating to around ~3B tokens and uploaded directly as a Hugging Face dataset.
As a pure sample, it maintains the ODC-BY license.
- Downloads last month
- 208