Results 11  20
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1,142
New Data Structures for Orthogonal Range Searching
, 2001
"... We present new general techniques for static orthogonal range searching problems intwo and higher dimensions. For the general range reporting problem in R 3, we achieve query time O(log n + k) using space O(n log1+ " n), where n denotes the number of storedpoints and k the number of point ..."
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Cited by 80 (2 self)
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We present new general techniques for static orthogonal range searching problems intwo and higher dimensions. For the general range reporting problem in R 3, we achieve query time O(log n + k) using space O(n log1+ " n), where n denotes the number of storedpoints and k the number
On asymptotic stability of solitary waves in a nonlinear Schrödinger equation
, 2007
"... The longtime asymptotics is analyzed for finite energy solutions of the 1D Schrödinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U(1). For initial states close to a solitary wave, the solution converges to a sum of another s ..."
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Cited by 142 (6 self)
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The longtime asymptotics is analyzed for finite energy solutions of the 1D Schrödinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U(1). For initial states close to a solitary wave, the solution converges to a sum of another
Sum rules and the Szegő condition for orthogonal polynomials on the real line
, 2002
"... We study the Case sum rules, especially C 0, for general Jacobi matrices. We establish situations where the sum rule is valid. Applications include an extension of Shohat's theorem to cases with an infinite point spectrum and a proof that if lim n(an 1) = and lim nbn = exist and 2 jj, th ..."
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Cited by 34 (17 self)
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We study the Case sum rules, especially C 0, for general Jacobi matrices. We establish situations where the sum rule is valid. Applications include an extension of Shohat's theorem to cases with an infinite point spectrum and a proof that if lim n(an 1) = and lim nbn = exist and 2 jj
Limiting spectral distribution of sums of unitary and orthogonal matrices
, 2013
"... We show that the empirical eigenvalue measure for sum of d independent Haar distributed ndimensional unitary matrices, converge for n → ∞ to the Brown measure of the free sum of d Haar unitary operators. The same applies for independent Haar distributed ndimensional orthogonal matrices. As a bypr ..."
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Cited by 5 (0 self)
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We show that the empirical eigenvalue measure for sum of d independent Haar distributed ndimensional unitary matrices, converge for n → ∞ to the Brown measure of the free sum of d Haar unitary operators. The same applies for independent Haar distributed ndimensional orthogonal matrices. As a
Eigenvalues of a real supersymmetric tensor
 J. Symbolic Comput
"... In this paper, we define the symmetric hyperdeterminant, eigenvalues and Eeigenvalues of a real supersymmetric tensor. We show that eigenvalues are roots of a onedimensional polynomial, and when the order of the tensor is even, Eeigenvalues are roots of another onedimensional polynomial. These t ..."
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Cited by 145 (62 self)
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eigenvalues, and the number of its Eeigenvalues is strictly less than n(m − 1) n−1 when m ≥ 4. We show that the product of all the eigenvalues is equal to the value of the symmetric hyperdeterminant, while the sum of all the eigenvalues is equal to the sum of the diagonal elements of that supersymmetric
Sums of random symmetric matrices and quadratic optimization under orthogonality constraints
 MATHEMATICAL PROGRAMMING (2006), ONLINE FIRST ISSUE, DOI
"... Let Bi be deterministic real symmetric m × m matrices, and ξi be independent random scalars with zero mean and “of order of one” (e.g., ξi ∼ N (0, 1)). We are interested to know under what conditions “typical norm ” of the random matrix SN = N� ξiBi is of order of 1. An evident necessary condition ..."
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Cited by 30 (3 self)
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{�SN �> Ωm 1/6} ≤ O(1) exp{−O(1)Ω 2} for all Ω> 0 We outline some applications of this result, primarily in investigating the quality of semidefinite relaxations of a general quadratic optimization problem with orthogonality constraints Opt = max Xj∈Rm×m � F (X1,..., Xk) : XjX T j = I, j = 1,..., k
Weakly Distributive Categories
 Journal of Pure and Applied Algebra
, 1991
"... There are many situations in logic, theoretical computer science, and category theory where two binary operationsone thought of as a (tensor) "product", the other a "sum"play a key role. In distributive and autonomous categories these operations can be regarded as, respect ..."
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Cited by 137 (20 self)
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There are many situations in logic, theoretical computer science, and category theory where two binary operationsone thought of as a (tensor) "product", the other a "sum"play a key role. In distributive and autonomous categories these operations can be regarded as
Adaptive resource allocation in multiuser OFDM systems with proportional rate constraints
 IEEE Trans. Wireless Commun
, 2005
"... Abstract—Multiuser orthogonal frequency division multiplexing (MUOFDM) is a promising technique for achieving high downlink capacities in future cellular and wireless local area network (LAN) systems. The sum capacity of MUOFDM is maximized when each subchannel is assigned to the user with the b ..."
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Cited by 127 (9 self)
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Abstract—Multiuser orthogonal frequency division multiplexing (MUOFDM) is a promising technique for achieving high downlink capacities in future cellular and wireless local area network (LAN) systems. The sum capacity of MUOFDM is maximized when each subchannel is assigned to the user
M2branes, 3Lie Algebras and Plücker relations
, 2008
"... We solve the Jacobi identity of metric 3Lie algebras for which an associated Lie algebra either does not admit biinvariant 4forms or it is the sum of up to three abelian directions and a semisimple Lie algebra. In all cases, we find that the structure constants of the metric 3Lie algebras are s ..."
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Cited by 119 (2 self)
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are sums of orthogonal simple 4forms verifying a conjecture in math/0211170. In particular, there is no metric 3Lie algebra associated to a u(N) Lie alebra for N> 2. We examine the implication of this result on the existence of a multiple M2brane theory based on metric 3Lie algebras.
Results 11  20
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