source stringclasses 1
value | date int32 2.02k 2.02k | text stringlengths 200 1.22M | token_count int32 36 314k | category stringclasses 1
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redpajama_arxiv | 2,016 | Introduction
Let G be a simple undirected graph with the vertex set V(G) and the edge set E(G) . A vertex with degree one is called a pendant vertex. The distance between the vertices u and v in graph G is denoted by d_G(u,v) . A cycle C is called chordless if C has no cycle chord (that is an edge not in the edge set ... | 3,607 | academic |
redpajama_arxiv | 2,016 | Principle of nano strain-amplifier
Figure (a) and 1(b) show the concept of the conventional structures of piezoresistive sensors. The piezoresistive elements are either released from, or kept on, the substrate. The sensitivity ( S ) of the sensors is defined based on the ratio of the relative resistance change ... | 2,529 | academic |
redpajama_arxiv | 2,016 | Introduction
Gas has a fundamental role in shaping the evolution of galaxies,
through its accretion on to massive haloes, cooling and subsequent
fuelling of star formation, to the triggering of extreme luminous
activity around super massive black holes. Determining how the
physical state of gas in galaxies changes as ... | 9,308 | academic |
redpajama_arxiv | 2,016 | Introduction
Given >0 , we consider the problem
where ^N is a Lipschitz, bounded domain, 1<p<2^*-1 , >0 is a fixed
parameter, and both U H^1_0() and are unknown. More precisely,
we investigate conditions on p and (and also ) for the solvability of
the problem.
The main interest in relies on the investigation of stan... | 13,999 | academic |
redpajama_arxiv | 2,016 | Introduction
Despite the immense popularity and availability of online video content via outlets such as Youtube and Facebook,
most work on object detection
focuses on static images.
Given the breakthroughs of deep convolutional neural networks
for detecting objects in static images,
the application of these method... | 4,367 | academic |
redpajama_arxiv | 2,016 | Introduction
The wave-particle duality is an alternative statement of the complementarity principle, and it establishes the relation between corpuscular and undulatorythe corpuscular and the ondulatory nature of quantum entities . It can be illustrated in a two-way interferometer, where the apparatus can be set to obs... | 8,025 | academic |
redpajama_arxiv | 2,016 | "#1\n\nequation0\n[1]\n\n#1\n\nsection.equation\n=msbm10 scaled 1\n=msbm7 scaled 1\n=msbm5 scaled 1\(...TRUNCATED) | 16,978 | academic |
redpajama_arxiv | 2,016 | "Introduction\n\n \nIn recent years there has been a resurgence of interest in the\nproperties of me(...TRUNCATED) | 10,037 | academic |
redpajama_arxiv | 2,016 | "Introduction\n\n \n\nThe production of hadrons and jets at a future Electron Ion Collider (EIC) wil(...TRUNCATED) | 8,039 | academic |
redpajama_arxiv | 2,016 | "Introduction\n\nCompact stars have a large number of pulsation modes that have been extensively stu(...TRUNCATED) | 5,210 | academic |
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