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Exceptional sets for Diophantine inequalities
"... We apply Freeman’s variant of the DavenportHeilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument. Under appropriate conditions, we show that the exceptional set in the interval [−N,N] has measure O(N1−δ), ..."
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Cited by 4 (1 self)
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We apply Freeman’s variant of the DavenportHeilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument. Under appropriate conditions, we show that the exceptional set in the interval [−N,N] has measure O(N1−δ
Exceptional sets for the definition of quasiconformality
 Amer. J. Math
"... Abstract. We show that one can allow for an exceptional set in the definition of quasiconformality even when “limsup ” is replaced with “liminf.” 1. Introduction. Let X and Y be metric spaces and f: X! Y a homeomorphism. Then the distortion of f at a point x 2 X is H(x): = lim sup r!0 Hf (x, r),(1) ..."
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Cited by 8 (1 self)
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Abstract. We show that one can allow for an exceptional set in the definition of quasiconformality even when “limsup ” is replaced with “liminf.” 1. Introduction. Let X and Y be metric spaces and f: X! Y a homeomorphism. Then the distortion of f at a point x 2 X is H(x): = lim sup r!0 Hf (x, r),(1)
Exceptional sets and fiber products
, 2007
"... Exceptional sets where fibers have dimensions higher than the generic fiber dimension are of interest in mathematics and in application areas, such as the theory of overconstrained mechanisms. We show that fiber products promote such sets to become irreducible components, whereupon they can be found ..."
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Exceptional sets where fibers have dimensions higher than the generic fiber dimension are of interest in mathematics and in application areas, such as the theory of overconstrained mechanisms. We show that fiber products promote such sets to become irreducible components, whereupon they can
On the size of the exceptional set in Nevanlinna theory
 J. London Math. Soc
, 1986
"... An example of a meromorphic function F in the plane is shown, for which the exceptional set in the logarithmic derivative lemma, in fact, occurs. This example is used to show that some conditions on the size of the exceptional set are the best that we can obtain. 1. ..."
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Cited by 2 (2 self)
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An example of a meromorphic function F in the plane is shown, for which the exceptional set in the logarithmic derivative lemma, in fact, occurs. This example is used to show that some conditions on the size of the exceptional set are the best that we can obtain. 1.
EXCEPTIONAL SETS FOR THE DERIVATIVES OF BLASCHKE PRODUCTS
"... Abstract. We obtain growth estimates for the logarithmic derivative B (z)/B(z) of a Blaschke product as z → 1 and z avoids some exceptional sets. ..."
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Abstract. We obtain growth estimates for the logarithmic derivative B (z)/B(z) of a Blaschke product as z → 1 and z avoids some exceptional sets.
Exceptional sets for selfaffine fractals
, 2007
"... Under certain conditions the ‘singular value function ’ formula gives the Hausdorff dimension of selfaffine fractals for almost all parameters in a family. We show that the size of the set of exceptional parameters is small both in the sense of Hausdorff dimension and Fourier dimension. 1 ..."
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Cited by 7 (0 self)
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Under certain conditions the ‘singular value function ’ formula gives the Hausdorff dimension of selfaffine fractals for almost all parameters in a family. We show that the size of the set of exceptional parameters is small both in the sense of Hausdorff dimension and Fourier dimension. 1
On the exceptional set in the problem of Diophantus and Davenport
 In Application of Fibonacci Numbers 7
, 1998
"... this paper we consider some consequences of this hypothesis to the problem of Diophantus for linear polynomials. Definition 1 Let k 0 and l be integers. A set of linear polynomials with integral coe#cients i x+b i : i = 1, 2, . . . , m} is called a linear Diophantine mtuple with the property D ..."
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Cited by 6 (5 self)
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this paper we consider some consequences of this hypothesis to the problem of Diophantus for linear polynomials. Definition 1 Let k 0 and l be integers. A set of linear polynomials with integral coe#cients i x+b i : i = 1, 2, . . . , m} is called a linear Diophantine mtuple with the property
Exceptional Sets and Antoine’s Necklace
"... We study Cantor sets which occur as minimal sets for homeomorphisms of R n. The minimality is modelled on an infinite product of finite cyclic groups and on a generalized adding machine. An interesting example is a homeomorphisms on R 3 which has Antoine’s Necklace as a minimal set. We also discuss ..."
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We study Cantor sets which occur as minimal sets for homeomorphisms of R n. The minimality is modelled on an infinite product of finite cyclic groups and on a generalized adding machine. An interesting example is a homeomorphisms on R 3 which has Antoine’s Necklace as a minimal set. We also discuss
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