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Control of integral manifolds loosing their attractivity in time
Journal of Mathematical Analysis and Applications, 2006 The work is devoted to the investigation of the integral manifolds of the nonautonomous slow–fast systems, which change their attractivity in time. The method used here is based on gluing attracting and repelling integral manifolds by using an additional
K R Schneider, Vladimir Sobolev
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A Symplectic Integrator for Riemannian Manifolds
Journal of Nonlinear Science, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Leimkuhler, B., Patrick, G. W.
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2010
Manifold learning has been successfully used for finding dominant factors (low-dimensional manifold) in a high-dimensional data set. However, most existing manifold learning algorithms only consider one manifold based on one dissimilarity matrix. For utilizing multiple manifolds, a key question is how different pieces of information can be integrated ...
Heeyoul Choi +4 more
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Manifold learning has been successfully used for finding dominant factors (low-dimensional manifold) in a high-dimensional data set. However, most existing manifold learning algorithms only consider one manifold based on one dissimilarity matrix. For utilizing multiple manifolds, a key question is how different pieces of information can be integrated ...
Heeyoul Choi +4 more
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2013
After giving some definitions and results on orientability of smooth manifolds, the problems treated in the present chapter are concerned with orientation of smooth manifolds; especially the orientation of several manifolds introduced in the previous chapter, such as the cylindrical surface, the Mobius strip, and the real projective space ℝP2.
Pedro M. Gadea +2 more
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After giving some definitions and results on orientability of smooth manifolds, the problems treated in the present chapter are concerned with orientation of smooth manifolds; especially the orientation of several manifolds introduced in the previous chapter, such as the cylindrical surface, the Mobius strip, and the real projective space ℝP2.
Pedro M. Gadea +2 more
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1988
The integral of an n-form on an n-manifold is defined by piecing together integrals over sets in ℝn using a partition of unity subordinate to an atlas. The change-of-variables theorem guarantees that the integral is well defined, independent of the choice of atlas and partition of unity.
Ralph Abraham +2 more
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The integral of an n-form on an n-manifold is defined by piecing together integrals over sets in ℝn using a partition of unity subordinate to an atlas. The change-of-variables theorem guarantees that the integral is well defined, independent of the choice of atlas and partition of unity.
Ralph Abraham +2 more
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2020
The purpose of this chapter is to generalize the theory of integration known for functions defined on open subsets of \(\mathbb {R}^n\) to manifolds. As a first step, we explain how differential forms defined on an open subset of \(\mathbb {R}^n\) are integrated.
Jean Gallier, Jocelyn Quaintance
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The purpose of this chapter is to generalize the theory of integration known for functions defined on open subsets of \(\mathbb {R}^n\) to manifolds. As a first step, we explain how differential forms defined on an open subset of \(\mathbb {R}^n\) are integrated.
Jean Gallier, Jocelyn Quaintance
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2001
Integration over n-dimensional manifolds reduces through charts to integration in ℝ n . The objects integrated on oriented manifolds are n-forms, for the following reason. For an ordinary function f : M → ℝ, the contribution of a chart domain U to the integral would clearly depend on the choice of chart h But for an n-form, the integral of its ...
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Integration over n-dimensional manifolds reduces through charts to integration in ℝ n . The objects integrated on oriented manifolds are n-forms, for the following reason. For an ordinary function f : M → ℝ, the contribution of a chart domain U to the integral would clearly depend on the choice of chart h But for an n-form, the integral of its ...
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1996
In this chapter, we define the integral of a k-form over a compact oriented k-manifold, and prove the important generalized Stokes’ theorem, which can be regarded as a far-reaching generalization of the fundamental theorem of calculus. We also define the integral of a function over a (not necessarily oriented) manifold, and describe the integral of a ...
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In this chapter, we define the integral of a k-form over a compact oriented k-manifold, and prove the important generalized Stokes’ theorem, which can be regarded as a far-reaching generalization of the fundamental theorem of calculus. We also define the integral of a function over a (not necessarily oriented) manifold, and describe the integral of a ...
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2003
In Chapter 11, we introduced line integrals of covector fields, which generalize ordinary integrals to the setting of curves in manifolds. It is also useful to generalize multiple integrals to manifolds. In this chapter, we carry out that generalization.
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In Chapter 11, we introduced line integrals of covector fields, which generalize ordinary integrals to the setting of curves in manifolds. It is also useful to generalize multiple integrals to manifolds. In this chapter, we carry out that generalization.
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On the Optimal Stabilization of an Integral Manifold
Journal of Mathematical Sciences, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vasilina, G. K., Tleubergenov, M. I.
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