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LATERAL COMPLETION FOR ARBITRARY LATTICE GROUPS
"... to construct, for a given lattice group G, a canonical extension, G, with the property that if M is a subset of ô such that xAy=0 if x, y e M and Xyéy, then M has a supremum in G. The problem was first solved, for conditionally complete vector lattices, by Nakano [7] and was also treated ..."
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to construct, for a given lattice group G, a canonical extension, G, with the property that if M is a subset of ô such that xAy=0 if x, y e M and Xyéy, then M has a supremum in G. The problem was first solved, for conditionally complete vector lattices, by Nakano [7] and was also treated
A Note on the SetTheoretic Representation of Arbitrary Lattices
, 2003
"... Every lattice is isomorphic to a lattice whose elements are sets of sets and whose operations are intersection and the operation ∨ ∗ defined by A ∨ ∗ B = A ∪ B ∪ {Z: (∃X ∈ A)(∃Y ∈ B)X ∩ Y ⊆ Z}. This representation spells out precisely Birkhoff’s and Frink’s representation of arbitrary lattices, wh ..."
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Every lattice is isomorphic to a lattice whose elements are sets of sets and whose operations are intersection and the operation ∨ ∗ defined by A ∨ ∗ B = A ∪ B ∪ {Z: (∃X ∈ A)(∃Y ∈ B)X ∩ Y ⊆ Z}. This representation spells out precisely Birkhoff’s and Frink’s representation of arbitrary lattices
Fully homomorphic encryption using ideal lattices
 In Proc. STOC
, 2009
"... We propose a fully homomorphic encryption scheme – i.e., a scheme that allows one to evaluate circuits over encrypted data without being able to decrypt. Our solution comes in three steps. First, we provide a general result – that, to construct an encryption scheme that permits evaluation of arbitra ..."
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Cited by 663 (17 self)
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of arbitrary circuits, it suffices to construct an encryption scheme that can evaluate (slightly augmented versions of) its own decryption circuit; we call a scheme that can evaluate its (augmented) decryption circuit bootstrappable. Next, we describe a public key encryption scheme using ideal lattices
Multidimensional Windows Over Arbitrary Lattices And Their Application To FIR Filter Design
"... This paper presents some applications to FIR filter design of multiD windows over arbitrary lattices and with arbitrary center of spatial symmetry. First, classic windows (such as Hamming, Blackman, etc.) are extended to windows over 1D and multiD lattices with arbitrary spatial symmetry centers ( ..."
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Cited by 1 (0 self)
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This paper presents some applications to FIR filter design of multiD windows over arbitrary lattices and with arbitrary center of spatial symmetry. First, classic windows (such as Hamming, Blackman, etc.) are extended to windows over 1D and multiD lattices with arbitrary spatial symmetry centers
THE STRONG INDEPENDENCE THEOREM FOR AUTOMORPHISM GROUPS AND CONGRUENCE LATTICES OF ARBITRARY LATTICES
, 1999
"... In the book, General Lattice Theory, the first author raised the following problem (Problem II.18): Let L be a nontrivial lattice and let G be a group. Does there exist a lattice K such that K and L have isomorphic congruence lattices and the automorphism group of K is isomorphic to G? The finite ..."
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Cited by 2 (1 self)
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In the book, General Lattice Theory, the first author raised the following problem (Problem II.18): Let L be a nontrivial lattice and let G be a group. Does there exist a lattice K such that K and L have isomorphic congruence lattices and the automorphism group of K is isomorphic to G? The finite
Transmultiplexing Of Multidimensional Signals Over Arbitrary Lattices With Perfect Reconstruction
 in Proc. IEEE Int. Conf. on Acoust., Speech, and Signal Process
, 1995
"... This research addresses the frequency multiplexing of multidimensional signals, having different bandwidths or defined on different lattices, with perfect or near perfect reconstruction i.e. zero or low crosstalk between signals and zero or low distortion of individual signals. The paper discusses i ..."
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Cited by 2 (2 self)
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This research addresses the frequency multiplexing of multidimensional signals, having different bandwidths or defined on different lattices, with perfect or near perfect reconstruction i.e. zero or low crosstalk between signals and zero or low distortion of individual signals. The paper discusses
Neutral stability in Josephson junction arrays with arbitrary lattice geometry
"... Abstract We consider DCbiased arrays of overdamped Josephson junctions with different lattice geometries, and demonstrate that, with suitable choice of bias currents, it is possible for the inphase state of the array to exhibit socalled "neutral stability". This ..."
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Abstract We consider DCbiased arrays of overdamped Josephson junctions with different lattice geometries, and demonstrate that, with suitable choice of bias currents, it is possible for the inphase state of the array to exhibit socalled "neutral stability". This
Results 1  10
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