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GBsplines of arbitrary order’
, 1998
"... Explicit formulae and recurrence relations for the calculation of generalized Bsplines (GBsplines) of arbitrary order are given. We derive main properties of GBsplines and their series, i.e. partition of unity, shapepreserving properties, invariance with respect to affine transformations, etc. I ..."
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Explicit formulae and recurrence relations for the calculation of generalized Bsplines (GBsplines) of arbitrary order are given. We derive main properties of GBsplines and their series, i.e. partition of unity, shapepreserving properties, invariance with respect to affine transformations, etc
Perturbative gadgets at arbitrary orders
, 2008
"... Adiabatic quantum algorithms are often most easily formulated using manybody interactions. However, experimentally available interactions are generally twobody. In 2004, Kempe, Kitaev, and Regev introduced perturbative gadgets, by which arbitrary threebody effective interactions can be obtained u ..."
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Cited by 10 (0 self)
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so that one can directly obtain arbitrary kbody effective interactions from twobody Hamiltonians. These effective interactions arise from the k th order in perturbation theory. 1 Perturbative Gadgets Perturbative gadgets were introduced to construct a twolocal Hamiltonian whose low energy
Arbitrary–order trigonometric Fourier
"... collocation methods for multifrequency oscillatory systems ..."
On weak Brownian motions of arbitrary order
"... We show the existence, for any k 2 N, of processes which have the same kmarginals as Brownian motion, although they are not Brownian motions. For k = 4, this proves a conjecture of Stoyanov. The law ~ P of such a "weak Brownian motion of order k" can be constructed to be equivalent to Wi ..."
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Cited by 19 (3 self)
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to Wiener measure P on C[0; 1]. On the other hand, there are weak Brownian motions of arbitrary order whose law is singular to Wiener measure. We also show that, for any " ? 0, there are weak Brownian motions whose law coincides with Wiener measure outside of any interval of length ".
THETA FUNCTIONS OF ARBITRARY ORDER AND THEIR DERIVATIVES
, 2004
"... In this paper we establish the relationships between theta functions of arbitrary order and their derivatives. We generalize our previous work [4] and prove that for any n> 1 the map sending an abelian variety to the set of Gauss images of its points of order 2n is an embedding into an appropria ..."
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Cited by 1 (1 self)
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In this paper we establish the relationships between theta functions of arbitrary order and their derivatives. We generalize our previous work [4] and prove that for any n> 1 the map sending an abelian variety to the set of Gauss images of its points of order 2n is an embedding
Arbitraryorder Hermite generating functions for obtaining arbitraryorder coherent and squeezed
 A
, 1995
"... For use in calculating higherorder coherent and squeezed state quantities, we derive generalized generating functions for the Hermite polynomials. They are given by ∑ ∞ n=0 z jn+k Hjn+k(x)/(jn + k)!, for arbitrary integers j ≥ 1 and k ≥ 0. Along the way, the sums with the Hermite polynomials repl ..."
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Cited by 5 (1 self)
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For use in calculating higherorder coherent and squeezed state quantities, we derive generalized generating functions for the Hermite polynomials. They are given by ∑ ∞ n=0 z jn+k Hjn+k(x)/(jn + k)!, for arbitrary integers j ≥ 1 and k ≥ 0. Along the way, the sums with the Hermite polynomials
Muffintin orbitals of arbitrary order
 Phys. Rev. B
, 2000
"... We have derived orbital basis sets from scattering theory. They are expressed as polynomial approximations to the energy dependence of a set of partial waves, in quantized form. The corresponding matrices, as well as the Hamiltonian and overlap matrices, are specified by the values on the energy mes ..."
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Cited by 6 (0 self)
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We have derived orbital basis sets from scattering theory. They are expressed as polynomial approximations to the energy dependence of a set of partial waves, in quantized form. The corresponding matrices, as well as the Hamiltonian and overlap matrices, are specified by the values on the energy mesh of the screened resolvent and its first energy derivative. These orbitals are a generalization of the 3rdgeneration linear MTOs and should be useful for electronicstructure calculations in general. Typeset using REVTEX 1 For electrons in condensed matter, it is often desirable to express the oneelectron wave functions, Ψi (r), with energies, εi, in a certain range in terms of a minimal set of energyindependent orbitals, χRL (r). Here, R labels sites and L the local symmetry (e.g. L≡lm). The simplest example of such an orbital is the Wannier function, χ (r − R), for an isolated band. A more realistic example is illustrated in Fig.1, the conductionband orbital of a cuprate hightemperature superconductor. This orbital is centered on Cu, has antibonding
Bootstrapping data arrays of arbitrary order
, 2011
"... In this paper we study a bootstrap strategy for estimating the variance of a mean taken over large multifactor crossed random effects data sets. We apply bootstrap reweighting independently to the levels of each factor, giving each observation the product of its factor weights. No exact bootstrap ex ..."
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Cited by 4 (1 self)
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In this paper we study a bootstrap strategy for estimating the variance of a mean taken over large multifactor crossed random effects data sets. We apply bootstrap reweighting independently to the levels of each factor, giving each observation the product of its factor weights. No exact bootstrap exists for this problem (McCullagh, 2000). We show that the proposed bootstrap is mildly conservative, under sufficient conditions that allow very unbalanced and heteroscedastic inputs. Earlier results for a resampling bootstrap only apply to two factors and are not suitable to online computation. The proposed reweighting approach can be implemented in parallel and online settings. The results for this method apply to any number of factors. The method is illustrated using a 3 factor data set of comment lengths from Facebook.
Results 1  10
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