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A Simple Proof of the Restricted Isometry Property for Random Matrices
 CONSTR APPROX
, 2008
"... We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candès and Tao) for random matrices that underlies Compressed Sensing. Our approach has two main ingredients: (i) concentration inequalities for random inner products that have recently provided algorithmical ..."
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Cited by 631 (64 self)
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algorithmically simple proofs of the Johnson–Lindenstrauss lemma; and (ii) covering numbers for finitedimensional balls in Euclidean space. This leads to an elementary proof of the Restricted Isometry Property and brings out connections between Compressed Sensing and the Johnson–Lindenstrauss lemma. As a result
PVS: A Prototype Verification System
 CADE
, 1992
"... PVS is a prototype system for writing specifications and constructing proofs. Its development has been shaped by our experiences studying or using several other systems and performing a number of rather substantial formal verifications (e.g., [5,6,8]). PVS is fully implemented and freely available. ..."
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Cited by 655 (16 self)
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PVS is a prototype system for writing specifications and constructing proofs. Its development has been shaped by our experiences studying or using several other systems and performing a number of rather substantial formal verifications (e.g., [5,6,8]). PVS is fully implemented and freely available
The elementary proof of the prime number theorem
 Math Intelligencer
, 2009
"... rime numbers are the atoms of our mathematical universe. Euclid showed that there are infinitely many primes, but the subtleties of their distribution continue to fascinate mathematicians. Letting p(n) denote the number of primes p B n, Gauss conjectured in the early nineteenth century that pðnÞ n=l ..."
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Cited by 1 (0 self)
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rime numbers are the atoms of our mathematical universe. Euclid showed that there are infinitely many primes, but the subtleties of their distribution continue to fascinate mathematicians. Letting p(n) denote the number of primes p B n, Gauss conjectured in the early nineteenth century that pðnÞ
The PCP theorem by gap amplification
 In Proceedings of the ThirtyEighth Annual ACM Symposium on Theory of Computing
, 2006
"... The PCP theorem [3, 2] says that every language in NP has a witness format that can be checked probabilistically by reading only a constant number of bits from the proof. The celebrated equivalence of this theorem and inapproximability of certain optimization problems, due to [12], has placed the PC ..."
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Cited by 166 (8 self)
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The PCP theorem [3, 2] says that every language in NP has a witness format that can be checked probabilistically by reading only a constant number of bits from the proof. The celebrated equivalence of this theorem and inapproximability of certain optimization problems, due to [12], has placed
The Prime Number Theorem . . .
"... In this article, we survey and announce a recent unconditional proof of the prime number theorem for RankinSelberg Lfunctions attached to automorphic cuspidal representations of GLn over Q. Applications of this prime number theorem to Selberg’s orthogonality conjecture and factorization of automor ..."
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Cited by 7 (0 self)
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In this article, we survey and announce a recent unconditional proof of the prime number theorem for RankinSelberg Lfunctions attached to automorphic cuspidal representations of GLn over Q. Applications of this prime number theorem to Selberg’s orthogonality conjecture and factorization
(Almost) Real Proof of the Prime Number Theorem
, 2017
"... We explain a fairly simple proof of the Prime Number Theorem that uses only basic real analysis and the elementary arithmetic of complex numbers. This includes the ζfunction (as realdifferentiable function) and the Fourier transform on R, but neither Fourier inversion nor anything from complex an ..."
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We explain a fairly simple proof of the Prime Number Theorem that uses only basic real analysis and the elementary arithmetic of complex numbers. This includes the ζfunction (as realdifferentiable function) and the Fourier transform on R, but neither Fourier inversion nor anything from complex
DIMENSIONS OF FORMAL FIBERS OF HEIGHT ONE PRIME IDEALS
, 2010
"... This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sublicensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express o ..."
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or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs
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