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Factoring wavelet transforms into lifting steps
 J. Fourier Anal. Appl
, 1998
"... ABSTRACT. This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This dec ..."
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Cited by 573 (8 self)
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in the biorthogonal, i.e, nonunitary case. Like the lattice factorization, the decomposition presented here asymptotically reduces the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining a waveletlike transform that maps integers to integers. 1.
NONUNITARY VALUATION SUBALGEBRAS
, 1973
"... Let U be a commutative ring with identity. The approach of this paper is to consider U as an algebra over another commutative ring R with identity and then to study the structure of U in terms of its multiplicatively closed J?submodules which we call subalgebras. We introduce the notion ..."
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Let U be a commutative ring with identity. The approach of this paper is to consider U as an algebra over another commutative ring R with identity and then to study the structure of U in terms of its multiplicatively closed J?submodules which we call subalgebras. We introduce the notion
A nonunitary quantum circuit
, 2004
"... The quantum circuit is generalized to include nonunitary gates operated by quantum measurement, in order to reduce the number of the overhead of qubits required to ensure fault tolerance. A specific type of onequbit nonunitary gates, together with the controllednot gate and all onequbit unitary ..."
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Cited by 4 (0 self)
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The quantum circuit is generalized to include nonunitary gates operated by quantum measurement, in order to reduce the number of the overhead of qubits required to ensure fault tolerance. A specific type of onequbit nonunitary gates, together with the controllednot gate and all one
On Nonunitary Representations of the Heisenberg Group
"... Let $G $ be a connected, simply connected nilpotent Lie group and $\mathfrak{g} $ be it $s $ Lie algebra. Irreducible unitary representations can be described by the orbit method due to A.Kirillov$([K]) $. Let $f $ be an element of the dual space $\mathfrak{g}’ $ of $\mathfrak{g} $. Let $G_{f} $ be ..."
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Let $G $ be a connected, simply connected nilpotent Lie group and $\mathfrak{g} $ be it $s $ Lie algebra. Irreducible unitary representations can be described by the orbit method due to A.Kirillov$([K]) $. Let $f $ be an element of the dual space $\mathfrak{g}’ $ of $\mathfrak{g} $. Let $G
Quantum mechanics with nonunitary symmetries
, 2000
"... This article shows that one can consistently incorporate nonunitary representations of at least one group into the “ordinary ” nonrelativistic quantum mechanics. This group turns out to be Lorentz group thus giving us an alternative approach to QFT for combining the quantum mechanics and special the ..."
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This article shows that one can consistently incorporate nonunitary representations of at least one group into the “ordinary ” nonrelativistic quantum mechanics. This group turns out to be Lorentz group thus giving us an alternative approach to QFT for combining the quantum mechanics and special
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
Results 1  10
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151,302