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Pure Point Dynamical and Diffraction Spectra
"... Abstract. We show that for multicolored Delone point sets with finite local complexity and uniform cluster frequencies the notions of pure point diffraction and pure point dynamical spectrum are equivalent. 1 ..."
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Abstract. We show that for multicolored Delone point sets with finite local complexity and uniform cluster frequencies the notions of pure point diffraction and pure point dynamical spectrum are equivalent. 1
Which distributions of matter diffract? Some answers
, 2002
"... This review revolves around the question which general distribution of scatterers (in a Euclidean space) results in a pure point diffraction spectrum. Firstly, we treat mathematical diffration theory and state conditions under which such a distribution has pure point diffraction. We explain how a cu ..."
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Cited by 8 (3 self)
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This review revolves around the question which general distribution of scatterers (in a Euclidean space) results in a pure point diffraction spectrum. Firstly, we treat mathematical diffration theory and state conditions under which such a distribution has pure point diffraction. We explain how a
Weighted Dirac combs with pure point diffraction
, 2004
"... A class of translation bounded complex measures, which have the form of weighted Dirac combs, on locally compact Abelian groups is investigated. Given such a Dirac comb, we are interested in its diffraction spectrum which emerges as the Fourier transform of the autocorrelation measure. We present a ..."
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Cited by 71 (36 self)
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sufficient set of conditions to ensure that the diffraction measure is a pure point measure. Simultaneously, we establish a natural link to the cut and project formalism and to the theory of almost periodic measures. Our conditions are general enough to cover the known theory of model sets, but also
Dynamical Systems on Translation Bounded Measures: PURE POINT DYNAMICAL AND DIFFRACTION SPECTRA
, 2003
"... Certain topological dynamical systems are considered that arise from actions of σcompact locally compact Abelian groups on compact spaces of translation bounded measures. Such a measure dynamical system is shown to have pure point dynamical spectrum if and only if its diffraction spectrum is pure ..."
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Cited by 58 (30 self)
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Certain topological dynamical systems are considered that arise from actions of σcompact locally compact Abelian groups on compact spaces of translation bounded measures. Such a measure dynamical system is shown to have pure point dynamical spectrum if and only if its diffraction spectrum
Kolakoski(3,1) is a (deformed) model set
, 2004
"... Abstract. Unlike the (classical) Kolakoski sequence on the alphabet {1, 2}, its analogue on {1, 3} can be related to a primitive substitution rule. Using this connection, we prove that the corresponding biinfinite fixed point is a regular generic model set and thus has a pure point diffraction spec ..."
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Cited by 5 (1 self)
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spectrum. The Kolakoski(3, 1) sequence is then obtained as a deformation, without losing the pure point diffraction property. 1.
Kolakoski(2m,2n) are limitperiodic model sets
 J. Math. Phys
"... Abstract. We consider (generalized) Kolakoski sequences on an alphabet with two even numbers. They can be related to a primitive substitution rule of constant length ℓ. Using this connection, we prove that they have pure point dynamical and pure point diffractive spectrum, where we make use of the s ..."
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Cited by 9 (4 self)
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Abstract. We consider (generalized) Kolakoski sequences on an alphabet with two even numbers. They can be related to a primitive substitution rule of constant length ℓ. Using this connection, we prove that they have pure point dynamical and pure point diffractive spectrum, where we make use
Network Centric Warfare: Developing and Leveraging Information Superiority
 Command and Control Research Program (CCRP), US DoD
, 2000
"... the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technolo ..."
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Cited by 308 (5 self)
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the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technologies. The CCRP pursues a broad program of research and analysis in information superiority, information operations, command and control theory, and associated operational concepts that enable us to leverage shared awareness to improve the effectiveness and efficiency of assigned missions. An important aspect of the CCRP program is its ability to serve as a bridge between the operational, technical, analytical, and educational communities. The CCRP provides leadership for the command and control research community by: n n
Deformation of Delone dynamical systems and pure point spectrum
 J. Fourier Anal. Appl
, 2005
"... Abstract. This paper deals with certain dynamical systems built from point sets and, more generally, measures on locally compact Abelian groups. These systems arise in the study of quasicrystals and aperiodic order, and important subclasses of them exhibit pure point diffraction spectra. We discuss ..."
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Cited by 18 (11 self)
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Abstract. This paper deals with certain dynamical systems built from point sets and, more generally, measures on locally compact Abelian groups. These systems arise in the study of quasicrystals and aperiodic order, and important subclasses of them exhibit pure point diffraction spectra. We discuss
DIFFRACTION
, 1972
"... This is not a complete review of the diffraction dissociation phenomena, but only a summary, albeit incomplete, of the papers presented to the Conference. A more leisurely and complete discussion of the subject can be found in recent reviews by Kane ’ and Lubatti. 2 I have tried to summarize the da ..."
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This is not a complete review of the diffraction dissociation phenomena, but only a summary, albeit incomplete, of the papers presented to the Conference. A more leisurely and complete discussion of the subject can be found in recent reviews by Kane ’ and Lubatti. 2 I have tried to summarize
Results 1  10
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