scholarly journals Fourier frames for singular measures and pure type phenomena

2018 ◽  
Vol 146 (7) ◽  
pp. 2883-2896 ◽  
Author(s):  
Nir Lev
Keyword(s):  
Pure Type ◽  
Singular Measures ◽  
Fourier Frames

scholarly journals Translational absolute continuity and Fourier frames on a sum of singular measures

2018 ◽  
Vol 274 (9) ◽  
pp. 2477-2498 ◽  
Author(s):  
Xiaoye Fu ◽  
Chun-Kit Lai
Keyword(s):  
Absolute Continuity ◽  
Singular Measures ◽  
Fourier Frames

Spectral theory of substitutions

2016 ◽  
Vol 38 (4) ◽  
pp. 1289-1341 ◽  
Author(s):  
ALAN BARTLETT
Keyword(s):  
Spectral Theory ◽  
Spectral Type ◽  
Metric Space ◽  
Fourier Coefficients ◽  
Simple Algorithm ◽  
Translation Operator ◽  
Compact Metric Space ◽  
Pure Type ◽  
Singular Measures ◽  
Open Question

In this paper, we generalize and develop results of Queffélec allowing us to characterize the spectrum of an aperiodic$\mathbb{Z}^{d}$substitution. Specifically, we describe the Fourier coefficients of mutually singular measures of pure type giving rise to the maximal spectral type of the translation operator on$L^{2}$, without any assumptions on primitivity or height, and show singularity for aperiodic bijective commutative$\mathbb{Z}^{d}$substitutions. Moreover, we provide a simple algorithm to determine the spectrum of aperiodic$\mathbf{q}$-substitutions, and use this to show singularity of Queffélec’s non-commutative bijective substitution, as well as the Table tiling, answering an open question of Solomyak. Finally, we show that every ergodic matrix of measures on a compact metric space can be diagonalized, which we use in the proof of the main result.

Rurality and Party System Fragmentation in the Nigerian Presidential Elections of the Fourth Republic

2020 ◽  
Vol 11 (1) ◽  
pp. 59-85
Author(s):  
Cletus Famous Nwankwo
Keyword(s):  
Presidential Elections ◽  
Party System ◽  
Party Systems ◽  
Voting Behaviour ◽  
Composite Measure ◽  
Singular Measures ◽  
Rural And Urban ◽  
Fourth Republic ◽  
Cast Doubt ◽  
Negative Effect

AbstractThis paper examines the effect of rurality on party system fragmentation in the Nigerian presidential elections of the fourth republic. The findings show that party system fragmentation (PSF) has been characteristically low in the Nigerian presidential elections and rurality does not significantly predict party system fragmentation. Rurality has a negative effect on PSF in all the elections studied except the 2003 election but only significant in the 2011 poll. Thus, the paper cast doubt on previous studies that indicate that striking rural-urban differences manifest in party system fragmentation in African elections and attribute it to previous studies’ measure of rurality. The paper argues that the use of a composite measure of rurality instead of singular measures of rurality might provide better analysis that helps us understand the effect of rurality on party systems. Also, it argues that in the study of the rural-urban difference in voting behaviour or political behaviours more broadly, data should be aggregated based on cities and non-city areas because cities have distinctive urban characters compared with non-city places. Analyses done on states or constituencies level may not reveal the rural-urban difference because states and constituencies usually have a mix of rural and urban population and other characteristics.

A sharper stability bound of Fourier frames

1999 ◽  
Vol 5 (1) ◽  
pp. 67-71
Author(s):  
Weifeng Su ◽  
Xingwei Zhou
Keyword(s):  
Stability Bound ◽  
Fourier Frames

scholarly journals Automath and Pure Type Systems

2003 ◽  
Vol 85 (7) ◽  
pp. 30-49
Author(s):  
Fairouz Kamareddine ◽  
Twan Laan ◽  
Rob Nederpelt
Keyword(s):  
Type Systems ◽  
Pure Type ◽  
Pure Type Systems

scholarly journals Magnetic Structures in Pure Type-II Superconductors

1973 ◽  
Vol 50 (4) ◽  
pp. 1194-1215 ◽  
Author(s):  
Yasushi Wada ◽  
Yoshio Tamura
Keyword(s):  
Type Ii ◽  
Magnetic Structures ◽  
Type Ii Superconductors ◽  
Pure Type

Singular measures with absolutely continuous convolution squares

1966 ◽  
Vol 62 (3) ◽  
pp. 399-420 ◽  
Author(s):  
Edwin Hewitt ◽  
Herbert S. Zuckerman
Keyword(s):  
Abelian Groups ◽  
Natural Order ◽  
Continuous Measure ◽  
Locally Compact ◽  
Absolutely Continuous ◽  
Character Group ◽  
Locally Compact Abelian Groups ◽  
Singular Measures ◽  
Compact Abelian Groups ◽  
Nikodym Derivative

Introduction. A famous construction of Wiener and Wintner ((13)), later refined by Salem ((11)) and extended by Schaeffer ((12)) and Ivašev-Musatov ((8)), produces a non-negative, singular, continuous measure μ on [ − π,π[ such thatfor every ∈ > 0. It is plain that the convolution μ * μ is absolutely continuous and in fact has Lebesgue–Radon–Nikodým derivative f such that For general locally compact Abelian groups, no exact analogue of (1 · 1) seems possible, as the character group may admit no natural order. However, it makes good sense to ask if μ* μ is absolutely continuous and has pth power integrable derivative. We will construct continuous singular measures μ on all non-discrete locally compact Abelian groups G such that μ * μ is a absolutely continuous and for which the Lebesgue–Radon–Nikodým derivative of μ * μ is in, for all real p > 1.

The bound excitations of a single vortex in a pure type II superconductor

1968 ◽  
Vol 27 (8) ◽  
pp. 576-577 ◽  
Author(s):  
E. Brun Hansen
Keyword(s):  
Type Ii ◽  
Single Vortex ◽  
Pure Type ◽  
Type Ii Superconductor

Current distribution in a pure type II superconductor

1967 ◽  
Vol 5 (5) ◽  
pp. 375-379 ◽  
Author(s):  
R.G. Jones
Keyword(s):  
Current Distribution ◽  
Type Ii ◽  
Pure Type ◽  
Type Ii Superconductor

scholarly journals Weak normalization implies strong normalization in a class of non-dependent pure type systems

2001 ◽  
Vol 269 (1-2) ◽  
pp. 317-361 ◽  
Author(s):  
Gilles Barthe ◽  
John Hatcliff ◽  
Morten Heine Sørensen
Keyword(s):  
Type Systems ◽  
Strong Normalization ◽  
Pure Type ◽  
Pure Type Systems
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