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Random Systematic Exact Value
"... We consider a technique to determine the initial beam conditions of the DARHT II accelerator by measuring the beam size under three different magnetic transport settings. This may be time gated to resolve the parameters as a function of time within the 2000 nsec pulse. This technique leads to three ..."
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We consider a technique to determine the initial beam conditions of the DARHT II accelerator by measuring the beam size under three different magnetic transport settings. This may be time gated to resolve the parameters as a function of time within the 2000 nsec pulse. This technique leads to three equations in three unknowns with solution giving the accelerator exit beam radius, tilt, and emittance. We find that systematic errors cancel and so are not a problem in unfolding the initial beam conditions. Random uncorrelated shot to shot errors can be managed by one of three strategies: 1) make the transport system optically demagnifying; 2) average over many individual shots; or 3) make the random uncorrelated shot to shot errors sufficiently small.
Some Exact Values of Sr
"... In Problem 07003, Hongwei Chen requests a general formula in terms of the digamma function for the sum of the series n=1 ..."
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In Problem 07003, Hongwei Chen requests a general formula in terms of the digamma function for the sum of the series n=1
Exact Matrix Completion via Convex Optimization
, 2008
"... We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfe ..."
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Cited by 860 (27 self)
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by solving a simple convex optimization program. This program finds the matrix with minimum nuclear norm that fits the data. The condition above assumes that the rank is not too large. However, if one replaces the 1.2 exponent with 1.25, then the result holds for all values of the rank. Similar results hold
On some exact values of threecolor . . .
, 2012
"... For graphs G1, G2, G3, the threecolor Ramsey number R(G1, G2, G3) is the smallest integer n such that if we arbitrarily color the edges of the complete graph of order n with 3 colors, then it contains a monochromatic copy of Gi in color i, for some 1 ≤ i ≤ 3. First, we prove that the conjectured eq ..."
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equality R3(C2n, C2n, C2n) = 4n, if true, implies that R3(P2n+1, P2n+1, P2n+1) = 4n + 1 for all n ≥ 3. We also obtain two new exact values R(P8, P8, P8) = 14 and R(P9, P9, P9) = 17, furthermore we do so without help of computer algorithms. Our results agree with a formula R(Pn, Pn, Pn) = 2n−2+(n mod 2
1 MORE EXACT VALUES OF THE HYPERBOLIC FUNCTIONS
"... In a previous paper [3] many exact values of the hyperbolic functions were found. It was shown that if n is any integer, 2 ..."
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In a previous paper [3] many exact values of the hyperbolic functions were found. It was shown that if n is any integer, 2
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
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Cited by 548 (13 self)
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, and that outputs samples in exact accordance with the desired distribution. The method uses couplings, which have also played a role in other sampling schemes; however, rather than running the coupled chains from the present into the future, one runs from a distant point in the past up until the present, where
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of the N = 2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira– Spencer theory, which may be viewed as the closed string analog of the Chern–Simon theory. Using the mirror map this leads to computation of the ‘number ’ of holomorphic curves of higher genus curves in Calabi–Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N = 2 theory. Relations with c = 1 strings are also pointed out.
Finding exact values for infinite sums
 this MAGAZINE
, 1999
"... [1]: From the wellknown results, ..."
An Exact Value for Avogadro’s Number
"... Avogadro’s number, NA, is the fundamental physical constant that links the macroscopic physical world of objects that we can see and feel with the submicroscopic, invisible world of atoms. In theory, NA specifies the exact number of atoms in a palmsized specimen of a physical element such as carbon ..."
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Avogadro’s number, NA, is the fundamental physical constant that links the macroscopic physical world of objects that we can see and feel with the submicroscopic, invisible world of atoms. In theory, NA specifies the exact number of atoms in a palmsized specimen of a physical element
Results 1  10
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2,269,557