Results 351 to 360 of about 5,495,109 (374)
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1999
A useful characterization of closed sets, and a definition of the closure of a set. Definition of a neighborhood. Convergence of a sequence in ℝ n . If the sequence does not converge, it diverges. Definition of a Cauchy sequence. Cauchy’s convergence criterion.
Knut Sydsæter, Arne Strøm, Peter Berck
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A useful characterization of closed sets, and a definition of the closure of a set. Definition of a neighborhood. Convergence of a sequence in ℝ n . If the sequence does not converge, it diverges. Definition of a Cauchy sequence. Cauchy’s convergence criterion.
Knut Sydsæter, Arne Strøm, Peter Berck
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2016
The central projection of circles with different radii may result in conics of any type. Depending on whether the projection cone C, i.e., the connection of the circles and the center C of the projection, avoids, touches, or intersects the vanishing plane, the image of the circle is an ellipse, a parabola, or a hyperbola.
Hellmuth Stachel +2 more
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The central projection of circles with different radii may result in conics of any type. Depending on whether the projection cone C, i.e., the connection of the circles and the center C of the projection, avoids, touches, or intersects the vanishing plane, the image of the circle is an ellipse, a parabola, or a hyperbola.
Hellmuth Stachel +2 more
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Hypersurfaces of Euclidean Space as Gradient Ricci Solitons
, 2014In this paper we obtain some necessary and sufficient conditions for a hypersurface of a Euclidean space to be a gradient Ricci soliton. We also study the geo- metry of a special type of compact Ricci solitons isometrically immersed into a Euclidean ...
Hana Al-Sodais +2 more
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Polyharmonic maps into the Euclidean space
, 2013We study polyharmonic (k-harmonic) maps between Riemannian manifolds with finite j-energies (j=1, cdots, 2k-2). We show if the domain is complete and the target is the Euclidean space, then such a map is harmonic.
Nobumitsu Nakauchi, H. Urakawa
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Applications to Euclidean Space
1972We recall the definition of the $$ standard\,n - sphere\quad {{\mathbb{S}}^n} = \{ x \in {{\mathbb{R}}^{{n + 1}}}|\left\| x \right\| = 1\} $$ and $$ standard\,n - ball\quad {{\mathbb{B}}^n} = \{ y \in {{\mathbb{R}}^n}|\left\| y \right\| \leqslant 1\}, $$ where \( ||x|| = \sqrt {\sum\nolimits_{i = 0}^n {x_i^2} } . \).
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Spherical Submanifolds of a Euclidean Space
The Quarterly Journal of Mathematics, 2002In this paper, we are interested in extending the study of spherical curves in R 3 to the submanifolds in the Euclidean space R n+p. More precisely, we are interested in obtaining conditions under which an n-dimensional compact submanifold M of a Euclidean space R n+p lies on the ...
Haila Alodan, Sharief Deshmukh
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L2-Net: Deep Learning of Discriminative Patch Descriptor in Euclidean Space
Computer Vision and Pattern Recognition, 2017Yurun Tian, Bin Fan, Fuchao Wu
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Introductory Mathematical Analysis for Quantitative Finance, 2020
D. Ritelli, G. Spaletta
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D. Ritelli, G. Spaletta
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Euclidean Space and Continuous Space
2014This chapter introduces Euclidean spaces, topological spaces, and their relationships to discrete spaces. We first introduce the concept of metrics, the distance measure of Euclidean spaces. Then, we introduce general continuous spaces—topological space. At the end, we discuss the relationship between continuous spaces and discrete spaces.
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