[PDF] Top 20 Badly approximable points on manifolds
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Badly approximable points on manifolds
... of them. Khintchine [28] proved that Bad(n) ∩ V n had zero 1-dimensional Lebesgue measure. Baker [4] generalised this to arbitrary C 1 submanifold of R n . Apparently, Bad(n) can be relatively easily replaced with Bad(r) ... See full document
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A note on badly approximable linear forms on manifolds
... regarding badly approximable points in sub- manifolds of a Euclidian ...weighted badly ap- proximable points on any non-degenerate C 1 submanifold of R n ... See full document
17
A note on badly approximable linear forms on manifolds
... regarding badly approximable points in sub- manifolds of a Euclidian ...weighted badly ap- proximable points on any non-degenerate C 1 submanifold of R n ... See full document
16
A note on badly approximable linear forms on manifolds
... regarding badly approximable points in sub- manifolds of a Euclidian ...weighted badly ap- proximable points on any non-degenerate C 1 submanifold of R n ... See full document
17
A note on badly approximable linear forms on manifolds
... regarding badly approximable points in sub- manifolds of a Euclidian ...weighted badly ap- proximable points on any non-degenerate C 1 submanifold of R n ... See full document
17
Badly approximable points in twisted Diophantine approximation and Hausdorff dimension
... Best approximations vectors have often been used in proofs, but not al- ways explicitly. In particular, Voronoi [24] selected some points in a lattice that correspond exactly to the best approximation vectors (see ... See full document
17
Decaying and non-decaying badly approximable numbers
... of badly approximable points which are not only non-decaying, but non-decaying when multiplied by any chosen sequence of rational numbers, with as little decay in the Lagrange values as ... See full document
7
Uniformly de Bruijn sequences and symbolic Diophantine approximation on fractals
... rational points of the Cantor set (see Section 6), and a Dirichlet-type theorem was proven [12, Corollary ...“badly approximable” ...of badly approximable points, the set of ... See full document
18
Decaying and non-decaying badly approximable numbers
... of badly approximable points which are not only non-decaying, but non-decaying when multiplied by any chosen sequence of rational numbers, with as little decay in the Lagrange values as ... See full document
8
Decaying and non-decaying badly approximable numbers
... of badly approximable points which are not only non-decaying, but non-decaying when multiplied by any chosen sequence of rational numbers, with as little decay in the Lagrange values as ... See full document
8
Badly approximable points in twisted Diophantine approximation and Hausdorff dimension
... In the 1-dimensional case, it is well known that the set of badly ap- proximable numbers has Lebesgue measure zero but maximal Hausdorff dimension. In the n-dimensional case, it is also a classical result that ... See full document
18
Non-planarity and metric Diophantine approximation for systems of linear forms
... We remark that the equivalence given by Lemma 6.3 is specific to the notion of ex- tremality and cannot be obtained in relation to the more ‘fine tuned’ forms of Diophantine approximation appearing in Khintchine type ... See full document
30
Uniformly de Bruijn sequences and symbolic Diophantine approximation on fractals
... are) badly symbolically approximable numbers whose base b expan- sions are not uniformly de ...of badly symbolically approximable numbers was given in [11, Lemma ...of badly ... See full document
24
Badly approximable points on planar curves and winning
... Denote by Bad (i, j) the set of (i, j)-badly approximable points in R 2 . In the case i = j = 1/2, the set under consideration is the standard set of simultaneously badly approximable ... See full document
56
Diophantine Approximation on Manifolds and the Distribution of Rational Points: Contributions to the Convergence Theory
... be replaced by the condition that (1.18) is satisfied for at least one point α ∈ [0, 1]. In other words, all that is required is that there exists at least one point on the curve that is non-degenerate. Using fibering ... See full document
25
Semi parabolic bifurcations in complex dimension two
... the right hand of Figure 1 because the set T \ K + is small. But we note that G + is harmonic where it is nonzero, so points of T \ K + must be present in the apparent boundaries between regions of di↵erent color. ... See full document
26
Medical DR image alignment based improved tangent space
... Learning with the label value can be regarded[8] as the problem of approximating a multivariate function from labeled data points. The function can be real valued as in regression or binary valued as in ... See full document
7
Horosphere slab separation theorems in manifolds without conjugate points
... B ( p, r ) is either convex or empty. The result follows easily if p ∈ A. So, assume that p ∈ / A. Let q be in A and r = d ( p, q ) . It is clear that G = A ∩ ¯ B ( p, r ) is a closed no-empty convex subset of B ¯ ( p, r ... See full document
6
Stirring and transport enhancement in a continuously modulated free-surface flow
... In each case presented in figure 13 the rate of tracer loss decreases over time, such that the curves level off. This indicates that an unmixed core remains in the eddy region. In fact there are two cores, which – as is ... See full document
34
The strengths and weaknesses of L2 approximable regressors
... If the normalized regressors are L2-approximable, then, using Properties 2 and 3 and stochastic limit results from Davidson 1994, it is possible to replace independent errors by martinga[r] ... See full document
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