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166
Modulus and the Poincaré inequality on metric measure spaces
 Mathematische Zeitschrift
"... Abstract. We show that, in a complete metric measure space equipped with a doubling Borel regular measure, the Poincare ́ inequality with upper gradients introduced by Heinonen and Koskela [HK98] is equivalent to the Poincare ́ inequality with “approximate Lipschitz constants ” used by Semmes in [S ..."
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Cited by 39 (2 self)
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Abstract. We show that, in a complete metric measure space equipped with a doubling Borel regular measure, the Poincare ́ inequality with upper gradients introduced by Heinonen and Koskela [HK98] is equivalent to the Poincare ́ inequality with “approximate Lipschitz constants ” used by Semmes
GEOMETRY OF MODULUS SPACES
"... Abstract. Let φ be a modulus function, i.e., continuous strictly increasing function on [0, ∞), such that φ(0) = 0, φ(1) = 1, and φ(x + y) ≤ φ(x) + φ(y) for all x, y in [0, ∞). It is the object of this paper to characterize, for any Banach space X, extreme points, exposed points, and smooth point ..."
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Abstract. Let φ be a modulus function, i.e., continuous strictly increasing function on [0, ∞), such that φ(0) = 0, φ(1) = 1, and φ(x + y) ≤ φ(x) + φ(y) for all x, y in [0, ∞). It is the object of this paper to characterize, for any Banach space X, extreme points, exposed points, and smooth
BEURLING'S CRITERION AND EXTREMAL METRICS FOR FUGLEDE MODULUS
"... Abstract. For each 1 p < 1, we formulate a necessary and sufficient condition for an admissible metric to be extremal for the Fuglede pmodulus of a system of measures. When p = 2, this characterization generalizes Beurling’s criterion, a sufficient condition for an admissible metric to be extre ..."
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Cited by 2 (0 self)
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Abstract. For each 1 p < 1, we formulate a necessary and sufficient condition for an admissible metric to be extremal for the Fuglede pmodulus of a system of measures. When p = 2, this characterization generalizes Beurling’s criterion, a sufficient condition for an admissible metric
The modulus of continuity of Wegner estimates for random Schrdinger operators on metric graphs
, 2007
"... We consider an alloy type potential on an infinite metric graph. We assume a covering condition on the single site potentials. For random Schrödingers operator associated with the alloy type potential restricted to finite volume subgraphs we prove a Wegner estimate which reproduces the modulus of ..."
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Cited by 2 (1 self)
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We consider an alloy type potential on an infinite metric graph. We assume a covering condition on the single site potentials. For random Schrödingers operator associated with the alloy type potential restricted to finite volume subgraphs we prove a Wegner estimate which reproduces the modulus
Noncommutative manifolds, the instanton algebra and isospectral deformations
 Comm. Math. Phys
"... We give new examples of noncommutative manifolds that are less standard than the NCtorus or Moyal deformations of R n. They arise naturally from basic considerations of noncommutative differential topology and have nontrivial global features. The new examples include the instanton algebra and the ..."
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Cited by 167 (29 self)
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obtained from this equation as a noncommutative Grassmanian as well as the corresponding notion of admissible morphisms. This space Gr contains the suspension of a NC3sphere intimately related to quantum group deformations SUq(2) of SU(2) but for unusual values (complex values of modulus one
Introduction to pmodulus of pathfamilies and Newtonian spaces
"... Shanmugalingam Abstract. The notion of pmoduli of families of paths is a useful tool in the study of analysis in metric measure space setting. In this note we briefly ..."
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Shanmugalingam Abstract. The notion of pmoduli of families of paths is a useful tool in the study of analysis in metric measure space setting. In this note we briefly
PERTURBATIONS AND METRIC REGULARITY
, 2004
"... A point x is an approximate solution of a generalized equation b ∈ F (x) if the distance from the point b to the set F (x) is small. “Metric regularity ” of the setvalued mapping F means that, locally, a constant multiple of this distance bounds the distance from x to an exact solution. The smalles ..."
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Cited by 2 (1 self)
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A point x is an approximate solution of a generalized equation b ∈ F (x) if the distance from the point b to the set F (x) is small. “Metric regularity ” of the setvalued mapping F means that, locally, a constant multiple of this distance bounds the distance from x to an exact solution
Medical image fusion by wavelet transform modulus maxima”,
 Optics Express,
, 2001
"... Abstract Medical image fusion has been used to derive useful information from multimodality medical image data. In this research, we propose a novel method for multimodality medical image fusion. Using wavelet transform, we achieved a fusion scheme. A fusion rule is proposed and used for calculatin ..."
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Cited by 9 (0 self)
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for calculating the wavelet transformation modulus maxima of input images at different bandwidths and levels. To evaluate the fusion result, a metric based on mutual information (MI) is presented for measuring fusion effect. The performances of other two methods of image fusion based on wavelet transform
Modulusdominated SUSYbreaking soft terms in Ftheory and their test at LHC
, 2008
"... We study the general patterns of SUSYbreaking soft terms arising under the assumption of Kahler moduli dominated SUSYbreaking in string theory models. Insisting that all MSSM gauginos get masses at leading order and that the top Yukawa coupling is of order the gauge coupling constant identifies th ..."
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Cited by 27 (0 self)
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the class of viable models. These are models in which the SM fields live either in the bulk or at the intersection of local sets of Type IIB D7branes or their Ftheory relatives. General arguments allow us to compute the dependence of the Kahler metrics of MSSM fields on the local Kahler modulus
Lower Bound of the Constant Modulus Criterion for Multilevel Modulations
"... Abstract – The recently proposed lower bound of the classical blind CM criterion was shown to be able to work as an excellent blind equalizability index, which is a practical performance assessment metric in the context of inverse problems. However, there still remains the need of complementary stud ..."
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Abstract – The recently proposed lower bound of the classical blind CM criterion was shown to be able to work as an excellent blind equalizability index, which is a practical performance assessment metric in the context of inverse problems. However, there still remains the need of complementary
Results 1  10
of
166