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Characterizing topological properties in 2D textures with magnetic structure tensors. [PDF]
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A Note On Homotopy Pushout And Homotopy Coherence
Quaestiones Mathematicae, 2003We present a self-contained argument, characterizing a homotopy pushout square by recognizing it as an initial object in a certain coherent homotopy category of spaces under a cotriad. Mathematics Subject Classification (2000): 18A30, 55P10, 55Q05.
Hardie, K.A., Kamps, K.H., Witbooi, P.J.
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Neural Computation, 1993
When training a feedforward neural network with backpropagation (Rumelhart et al. 1986), local minima are always a problem because of the nonlinearity of the system. There have been several ways to attack this problem: for example, to restart the training by selecting a new initial point, to perform the preprocessing of the input data or the neural ...
Liping Yang, Wanzhen Yu
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When training a feedforward neural network with backpropagation (Rumelhart et al. 1986), local minima are always a problem because of the nonlinearity of the system. There have been several ways to attack this problem: for example, to restart the training by selecting a new initial point, to perform the preprocessing of the input data or the neural ...
Liping Yang, Wanzhen Yu
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The homotopy limit of homotopy algebras
Russian Mathematical Surveys, 1986Translation from Usp. Mat. Nauk 41, No.3(249), 205-206 (Russian) (1986; Zbl 0605.55017).
Khinich, V. A., Shekhtman, V. V.
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Homotopy Groups and Torus Homotopy Groups
The Annals of Mathematics, 1948In recent years it has been found that the homotopy groups [9] can be made into a more powerful tool by the introduction of new operations. Two such have been defined and utilized: (i) every element of the fundamental group 7r, induces an automorphism of the n-dimensional homotopy group 7rX, so that 7rn becomes a group with operators; (ii) to every ...
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Journal of the London Mathematical Society, 1991
The object of the paper is to clarify the connections between relative homotopy and free homotopy. The main point is to indicate how relative homotopy can be calculated from free homotopy where free homotopy is allowed to include information about certain homotopy diagram-categories.
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The object of the paper is to clarify the connections between relative homotopy and free homotopy. The main point is to indicate how relative homotopy can be calculated from free homotopy where free homotopy is allowed to include information about certain homotopy diagram-categories.
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A representation of homotopy theory by homotopy spheres
1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
DRAGOTTI, SARA, MAGRO, GAETANO
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Canadian Mathematical Bulletin, 1984
AbstractA short proof of the following result of Bernstein and Ganea is given:“Let X be a topological space which is homotopy dominated by a closed connected n-dimensional manifold M. If Hn(X; Z2) ≠ 0 then X has the homotopy type of M”.It is also shown that the manifold in this theorem can be replaced by a Poincaré complex.
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AbstractA short proof of the following result of Bernstein and Ganea is given:“Let X be a topological space which is homotopy dominated by a closed connected n-dimensional manifold M. If Hn(X; Z2) ≠ 0 then X has the homotopy type of M”.It is also shown that the manifold in this theorem can be replaced by a Poincaré complex.
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The American Mathematical Monthly, 2017
As discussed in an earlier article in this MONTHLY, there is a universal construction in topology that turns any space into a Hausdorff space, which is known as the Hausdorffization, Hausdorfficati...
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As discussed in an earlier article in this MONTHLY, there is a universal construction in topology that turns any space into a Hausdorff space, which is known as the Hausdorffization, Hausdorfficati...
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