منابع مشابه
Balancing Unit Vectors
Theorem A. Let x1, . . . , x2k+1 be unit vectors in a normed plane. Then there exist signs ε1, . . . , ε2k+1 ∈ {±1} such that ‖ P 2k+1 i=1 εixi‖ ≤ 1. We use the method of proof of the above theorem to show the following point facility location result, generalizing Proposition 6.4 of Y. S. Kupitz and H. Martini (1997). Theorem B. Let p0, p1, . . . , pn be distinct points in a normed plane such t...
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When dealing with privatized data, it is important to be able to protect against malformed user inputs. This becomes difficult in MPC systems as each server should not contain enough information to know what values any user has submitted. In this paper, we implement an MPC technique to verify blinded user inputs are unit vectors. In addition, we introduce a BGW circuit which can securely aggreg...
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متن کاملPolynomial interpolation on the unit sphere II
The problem of interpolation at (n+1) points on the unit sphere S by spherical polynomials of degree at most n is proved to have a unique solution for several sets of points. The points are located on a number of circles on the sphere with even number of points on each circle. The proof is based on a method of factorization of polynomials.
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The problem of interpolation at (n + 1) 2 points on the unit sphere S 2 by spherical polynomials of degree at most n is proved to have a unique solution for several sets of points. The points are located on a number of circles on the sphere with even number of points on each circle. The proof is based on a method of factorization of polynomials.
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ژورنال
عنوان ژورنال: Geophysical Journal International
سال: 1979
ISSN: 0956-540X,1365-246X
DOI: 10.1111/j.1365-246x.1979.tb04802.x