source stringclasses 1
value | date int32 1.99k 2k | text stringlengths 200 988k | token_count int32 37 403k | category stringclasses 1
value |
|---|---|---|---|---|
redpajama_arxiv | 1,998 | Introduction
A knot is an embedding of a circle S^1 in a 3-manifold M , usually taken to be
R^3 or S^3 .
In the 1920's Alexander and Briggs and Reidemeister
observed that questions about ambient isotopy of polygonal knots in
R^3 can be reduced to combinatorial
questions about knot diagrams. These are labeled planar... | 18,765 | academic |
redpajama_arxiv | 1,998 | Introduction
Cluster cooling flows present a most intriguing conspiracy. X-ray
observations have revealed large quantities of hot, diffuse gas in
most if not all clusters (e.g. Fabian 1994). In many clusters
(70--90\%) the central gas densities are high enough that the radiative
cooling
time becomes shorter than the H... | 11,415 | academic |
redpajama_arxiv | 1,998 | "INTRODUCTION\n\n Conclusions and Acknowledgements\n\nI hope that these lectures succeed in providin(...TRUNCATED) | 61,651 | academic |
redpajama_arxiv | 1,998 | "Introduction\n\nString junctions play an important \nrole in understanding non-perturbative aspects(...TRUNCATED) | 3,867 | academic |
redpajama_arxiv | 1,998 | "Introduction\n\nSmoothed particle hydrodynamics (SPH) is a Lagrangian method introduced\nspecifical(...TRUNCATED) | 19,576 | academic |
redpajama_arxiv | 1,998 | "Introduction\n\nIn standard hierarchical scenarios for galaxy formation, mergers of\ngalaxies are c(...TRUNCATED) | 11,217 | academic |
redpajama_arxiv | 1,998 | "Guidelines\n\nThe thermodynamics of inflationary expansion can be either isentropic\n or\nnon-isent(...TRUNCATED) | 1,956 | academic |
redpajama_arxiv | 1,998 | "Introduction\n\n \nAll pion-nucleon ( N ) measurements (differential cross sections, partial-total (...TRUNCATED) | 5,235 | academic |
redpajama_arxiv | 1,998 | "INTRODUCTION\n\nA protoneutron (PNS) star forms in the aftermath of a successful\nsupernova explosi(...TRUNCATED) | 24,534 | academic |
redpajama_arxiv | 1,998 | "Introduction\n\nInspired by the discovery of a sharp antiferromagnetic resonance,\nlater denoted th(...TRUNCATED) | 8,288 | academic |
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