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Uniqueness theorem for unbounded domain
, 1995
"... We prove in this paper the uniqueness theorem for a certain class of harmonic functions defined in unbounded domain lying in a band. 1 ..."
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We prove in this paper the uniqueness theorem for a certain class of harmonic functions defined in unbounded domain lying in a band. 1
Black hole uniqueness theorems
 In: Proceedings of the 11th International Conference on General Relativity and Gravitation
, 1987
"... I review the black hole uniqueness theorem and the no hair theorems established for physical black hole stationary states by the early 80’. This review presents the original and decisive work of Carter, Robinson, Mazur and Bunting on the problem of no bifurcation and uniqueness of physical black hol ..."
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Cited by 4 (0 self)
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I review the black hole uniqueness theorem and the no hair theorems established for physical black hole stationary states by the early 80’. This review presents the original and decisive work of Carter, Robinson, Mazur and Bunting on the problem of no bifurcation and uniqueness of physical black
The uniqueness theorem for entanglement measures
 quantph/0105017. 7 A. Khinchin, Mathematical Foundations of Information Theory (New
, 1957
"... Abstract We review the mathematics of the theory of entanglement measures. As well as giving proofs from first principles for some wellknown and important results, we provide a sharpened version of a uniqueness theorem which gives necessary and sufficient conditions for an entanglement measure to c ..."
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Cited by 23 (3 self)
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Abstract We review the mathematics of the theory of entanglement measures. As well as giving proofs from first principles for some wellknown and important results, we provide a sharpened version of a uniqueness theorem which gives necessary and sufficient conditions for an entanglement measure
A Uniqueness Theorem for Clustering
"... Despite the widespread use of Clustering, there is distressingly little general theory of clustering available. Questions like “What distinguishes a clustering of data from other data partitioning?”, “Are there any principles governing all clustering paradigms?”, “How should a user choose an appropr ..."
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Cited by 24 (7 self)
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Despite the widespread use of Clustering, there is distressingly little general theory of clustering available. Questions like “What distinguishes a clustering of data from other data partitioning?”, “Are there any principles governing all clustering paradigms?”, “How should a user choose an appropriate clustering algorithm for a particular task?”, etc. are almost completely unanswered by the existing body of clustering literature. We consider an axiomatic approach to the theory of Clustering. We adopt the framework of Kleinberg, [Kle03]. By relaxing one of Kleinberg’s clustering axioms, we sidestep his impossibility result and arrive at a consistent set of axioms. We suggest to extend these axioms, aiming to provide an axiomatic taxonomy of clustering paradigms. Such a taxonomy should provide users some guidance concerning the choice of the appropriate clustering paradigm for a given task. The main result of this paper is a set of abstract properties that characterize the SingleLinkage clustering function. This characterization result provides new insight into the properties of desired data groupings that make SingleLinkage the appropriate choice. We conclude by considering a taxonomy of clustering functions based on abstract properties that each satisfies. 1
Uniqueness theorems for Cauchy integrals
"... Abstract. If µ is a finite complex measure in the complex plane C we denote by C µ its Cauchy integral defined in the sense of principal value. The measure µ is called reflectionless if it is continuous (has no atoms) and C µ = 0 at µalmost every point. We show that if µ is reflectionless and its C ..."
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Cited by 6 (1 self)
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Abstract. If µ is a finite complex measure in the complex plane C we denote by C µ its Cauchy integral defined in the sense of principal value. The measure µ is called reflectionless if it is continuous (has no atoms) and C µ = 0 at µalmost every point. We show that if µ is reflectionless and its Cauchy maximal function C µ ∗ is summable with respect to µ then µ is trivial. An example of a reflectionless measure whose maximal function belongs to the ”weak ” L 1 is also constructed, proving that the above result is sharp in its scale. We also give a partial geometric description of the set of reflectionless measures on the line and discuss connections of our results with the notion of sets of finite perimeter in the sense of De Giorgi. 1.
Uniqueness theorem for entire functions
"... Let G(k) = ∫ 1 0 g(x)ekx dx, g ∈ L 1 (0, 1). The main result of this paper is the following theorem. Theorem. If lim sup k→+ ∞ G(k)  < ∞, then g = 0. There exists g ̸ ≡ 0, g ∈ C ∞ 0 (0, 1), such that G(kj) = 0, kj < kj+1, limj→ ∞ kj = ∞, limk→ ∞ G(k)  does not exist, lim sup k→+ ∞ G(k) ..."
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Let G(k) = ∫ 1 0 g(x)ekx dx, g ∈ L 1 (0, 1). The main result of this paper is the following theorem. Theorem. If lim sup k→+ ∞ G(k)  < ∞, then g = 0. There exists g ̸ ≡ 0, g ∈ C ∞ 0 (0, 1), such that G(kj) = 0, kj < kj+1, limj→ ∞ kj = ∞, limk→ ∞ G(k)  does not exist, lim sup k→+ ∞ G
An Existence and Uniqueness Theorem for
"... Abstract: For a pair of plane curves β and γ, we give a sufficient and necessary condition for the existence of a unique plane curve α that rolls on β, while a reference point P traces γ. This study was motivated by rolling curve solutions to a few classical problems of the calculus of variations. 1 ..."
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Abstract: For a pair of plane curves β and γ, we give a sufficient and necessary condition for the existence of a unique plane curve α that rolls on β, while a reference point P traces γ. This study was motivated by rolling curve solutions to a few classical problems of the calculus of variations
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