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value | date int32 2.02k 2.02k | text stringlengths 200 1.26M | token_count int32 33 389k | category stringclasses 1
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redpajama_arxiv | 2,017 | Introduction
As it is well-known (see ), a Hamiltonian system is called completely integrable if and only if it possesses the maximal number of independent Poisson-commuting first integrals of motion. In the present article we shall work in the holomorphic category and associate to a complex surface endowed with a hol... | 8,401 | academic |
redpajama_arxiv | 2,017 | Preliminaries
A net (x_)_ A in a vector lattice X is order convergent to x X if there exists a net (y_)_ B , possibly over a different index set, such that y_ 0 and for each B there exists _0 A satisfying x_-x y_ for all _0 . We will write x_ ox to denote this convergence. Recall that a net (x_) in a vector lattice X ... | 14,569 | academic |
redpajama_arxiv | 2,017 | Introduction
All graphs considered in this paper are finite, undirected and contain no loops nor multiple edges.
For every k 1 , the set 1,,k is denoted k .
The size of a graph G , denoted G , is the number of vertices in G .
For a vertex v of G , the set of vertices adjacent to v in G is denoted N(v) .
For a set X of... | 11,659 | academic |
redpajama_arxiv | 2,017 | Introduction
Impressive achievements in investigations and applications of optical vortex beams and optical angular momentum (AM) motivated the prediction and generation of free-electron vortex states carrying orbital angular momentum .
These electron vortices are currently attracting considerable attention in severa... | 7,123 | academic |
redpajama_arxiv | 2,017 | Introduction
Magnetic skyrmions are nanoscale whirling spin configurations . Their small size, topological protection and the fact that they can be manipulated by small in-plane current densities have opened a new paradigm to manipulate the magnetization at the nanoscale. This has led to proposals for novel memory and... | 4,156 | academic |
redpajama_arxiv | 2,017 | "Introduction\n\nRandom fields governed by systems of stochastic partial differential\nequations (SP(...TRUNCATED) | 9,065 | academic |
redpajama_arxiv | 2,017 | "Introduction\n\nThe apparent rise in political incivility has attracted substantial attention\nfrom(...TRUNCATED) | 4,475 | academic |
redpajama_arxiv | 2,017 | "Introduction\n\nAstrophysical and cosmological evidences suggest that non-baryonic cold dark matter(...TRUNCATED) | 8,535 | academic |
redpajama_arxiv | 2,017 | "Motivation and outlook\n\nThe study and characterisation of supersymmetric and asymptotically AdS _(...TRUNCATED) | 8,867 | academic |
redpajama_arxiv | 2,017 | "Introduction\n\n \n According to the World Health Organization, breast cancer is one of the most fr(...TRUNCATED) | 4,336 | academic |
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