منابع مشابه
Uniqueness theorems for polyhedra.
In 1813, Cauchy2 gave the first proof of the theorem that two closed convex polyhedra in three-dimensional space are congruent if their faces are congruent in pairs and are joined to each other in the same order: in effect, the a priori possibility of rotations of the faces about the edges-which are obviously seen to be possible for some easily constructed open polyhedra-cannot occur for closed...
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A toric polyhedron is a reduced closed subscheme of a toric variety that are partial unions of the orbits of the torus action. We prove vanishing theorems for toric polyhedra. We also give a proof of the E1-degeneration of Hodge to de Rham type spectral sequence for toric polyhedra in any characteristic. Finally, we give a very powerful extension theorem for ample line bundles.
متن کاملUniqueness Theorems for Cauchy Integrals
If μ is a finite complex measure in the complex plane C we denote by C 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 = 0 at μ-almost every point. We show that if μ is reflectionless and its Cauchy maximal function Cμ ∗ is summable with respect to |μ| then μ is trivial. An example of a reflectionless m...
متن کاملUniqueness Theorems for Rational Functions
In his book on the theory of meromorphic functions, R. Nevanlinna proved a number of "uniqueness theorems." The most important of them states that if two functions w=f(x) and w = g(x), meromorphic in the whole x-plane, assume five values of w (finite or infinite) at the same points x they must be identical. If we understand by the distribution of a function w = (x) with respect to a given va...
متن کاملUniqueness theorems for kernel methods
This paper has three goals: to find uniqueness theorems for some well-known kernel methods, and thereby to better understand their behavior; to derive theorems which apply to more general families of kernel methods; and to collect results which are hoped to be useful to workers who would like to prove uniqueness theorems for their own algorithms. Knowing when a solution is unique has the obviou...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1966
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.55.6.1398