Results 281 to 290 of about 527,719 (327)
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Ab Initio Machine Learning in Chemical Compound Space
Chemical Reviews, 2021Bing Huang, O Anatole Von Lilienfeld
exaly
2017
The main objectives in this chapter are to generalize the basic geometric ideas in \(\mathbb{R}^{2}\) or \(\mathbb{R}^{3}\) to nontrivial higher-dimensional spaces \(\mathbb{R}^{n}\). Our approach is to start from geometric concepts in \(\mathbb{R}^{2}\) or \(\mathbb{R}^{3}\) and then extend them to \(\mathbb{R}^{n}\) in a purely algebraic manner.
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The main objectives in this chapter are to generalize the basic geometric ideas in \(\mathbb{R}^{2}\) or \(\mathbb{R}^{3}\) to nontrivial higher-dimensional spaces \(\mathbb{R}^{n}\). Our approach is to start from geometric concepts in \(\mathbb{R}^{2}\) or \(\mathbb{R}^{3}\) and then extend them to \(\mathbb{R}^{n}\) in a purely algebraic manner.
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2011
In this chapter we consider affine spaces on which a distance has been defined. Thus we have a model of classical Euclidean Geometry, where, for instance, Pythagoras’ Theorem works well. We give a short method to compute the distance between two varieties of arbitrary dimension.
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In this chapter we consider affine spaces on which a distance has been defined. Thus we have a model of classical Euclidean Geometry, where, for instance, Pythagoras’ Theorem works well. We give a short method to compute the distance between two varieties of arbitrary dimension.
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Blockchain-Empowered Space-Air-Ground Integrated Networks: Opportunities, Challenges, and Solutions
IEEE Communications Surveys and Tutorials, 2022Yuntao Wang, Zhou, Jianbing Ni
exaly
1980
We shall consider a classical Euclidean space in which the points M are marked by a system of general coordinates y1 where i = 1,2,...n, n being the number of dimensions. This can be any number, but for definiteness we may think of it as equal to 3. In this space a point M’, infinitesimally close to M, has coordinates differing from those of M by dyi ...
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We shall consider a classical Euclidean space in which the points M are marked by a system of general coordinates y1 where i = 1,2,...n, n being the number of dimensions. This can be any number, but for definiteness we may think of it as equal to 3. In this space a point M’, infinitesimally close to M, has coordinates differing from those of M by dyi ...
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An integrated space-to-ground quantum communication network over 4,600 kilometres
Nature, 2021Yu-Ao Chen, Qiang Zhang, Teng-Yun Chen
exaly