scholarly journals On a class of singular measures satisfying a strong annular decay condition

2019 ◽  
Vol 147 (10) ◽  
pp. 4409-4423
Author(s):  
Ángel Arroyo ◽  
José G. Llorente
Keyword(s):  
Singular Measures ◽  
Decay Condition

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.

scholarly journals Large solutions of semilinear elliptic equations with nonlinear gradient terms

1999 ◽  
Vol 22 (4) ◽  
pp. 869-883 ◽  
Author(s):  
Alan V. Lair ◽  
Aihua W. Wood
Keyword(s):  
Positive Solutions ◽  
Compact Support ◽  
Elliptic Equations ◽  
Nonnegative Function ◽  
Semilinear Elliptic Equations ◽  
Decay Condition ◽  
Large Solutions ◽  
Semilinear Elliptic ◽  
The Given

We show that large positive solutions exist for the equation(P±):Δu±|∇u|q=p(x)uγinΩ⫅RN(N≥3)for appropriate choices ofγ>1,q>0in which the domainΩis either bounded or equal toRN. The nonnegative functionpis continuous and may vanish on large parts ofΩ. IfΩ=RN, thenpmust satisfy a decay condition as|x|→∞. For(P+), the decay condition is simply∫0∞tϕ(t)dt<∞, whereϕ(t)=max|x|=tp(x). For(P−), we require thatt2+βϕ(t)be bounded above for some positiveβ. Furthermore, we show that the given conditions onγandpare nearly optimal for equation(P+)in that no large solutions exist if eitherγ≤1or the functionphas compact support inΩ.

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.

scholarly journals Generalized powers and measures

2021 ◽  
Vol 41 (6) ◽  
pp. 747-754
Author(s):  
Zbigniew Burdak ◽  
Marek Kosiek ◽  
Patryk Pagacz ◽  
Krzysztof Rudol ◽  
Marek Słociński
Keyword(s):  
Invariant Subspaces ◽  
Unitary Operators ◽  
Singular Measures ◽  
Special Classes

Using the winding of measures on torus in "rational directions" special classes of unitary operators and pairs of isometries are defined. This provides nontrivial examples of generalized powers. Operators related to winding Szegö-singular measures are shown to have specific properties of their invariant subspaces.

Asymptotically compatible discretization of multidimensional nonlocal diffusion models and approximation of nonlocal Green’s functions

2018 ◽  
Vol 39 (2) ◽  
pp. 607-625 ◽  
Author(s):  
Qiang Du ◽  
Yunzhe Tao ◽  
Xiaochuan Tian ◽  
Jiang Yang
Keyword(s):  
Green's Functions ◽  
Numerical Solutions ◽  
Green’S Functions ◽  
Diffusion Equations ◽  
Nonlocal Diffusion ◽  
Optimal Order ◽  
Numerical Approximations ◽  
Splitting Technique ◽  
Singular Measures ◽  
Nonlocal Models

AbstractNonlocal diffusion equations and their numerical approximations have attracted much attention in the literature as nonlocal modeling becomes popular in various applications. This paper continues the study of robust discretization schemes for the numerical solution of nonlocal models. In particular, we present quadrature-based finite difference approximations of some linear nonlocal diffusion equations in multidimensions. These approximations are able to preserve various nice properties of the nonlocal continuum models such as the maximum principle and they are shown to be asymptotically compatible in the sense that as the nonlocality vanishes, the numerical solutions can give consistent local limits. The approximation errors are proved to be of optimal order in both nonlocal and asymptotically local settings. The numerical schemes involve a unique design of quadrature weights that reflect the multidimensional nature and require technical estimates on nonconventional divided differences for their numerical analysis. We also study numerical approximations of nonlocal Green’s functions associated with nonlocal models. Unlike their local counterparts, nonlocal Green’s functions might become singular measures that are not well defined pointwise. We demonstrate how to combine a splitting technique with the asymptotically compatible schemes to provide effective numerical approximations of these singular measures.

scholarly journals Generalized cluster trees and singular measures

2019 ◽  
Vol 47 (4) ◽  
pp. 2174-2203 ◽  
Author(s):  
Yen-Chi Chen
Keyword(s):  
Singular Measures

scholarly journals A non-existence result for nonlinear parabolic equations with singular measures as data

2009 ◽  
Vol 139 (2) ◽  
pp. 381-392 ◽  
Author(s):  
Francesco Petitta
Keyword(s):  
Laplace Operator ◽  
Lower Order ◽  
Parabolic Equations ◽  
Existence Result ◽  
Nonlinear Parabolic Equations ◽  
Parabolic Problems ◽  
Singular Measures ◽  
Nonlinear Parabolic ◽  
Image Position ◽  
Lower Order Terms

In this paper we prove a non-existence result for nonlinear parabolic problems with zero lower-order terms whose model iswhere Δp=div(|∇u|p−2∇u) is the usual p-laplace operator, λ is measure concentrated on a set of zero parabolic r-capacity (1<p<r) and q is large enough.

SINGULARITY FEATURES OF PORE-SIZE SOIL DISTRIBUTION: SINGULARITY STRENGTH ANALYSIS AND ENTROPY SPECTRUM

Fractals ◽  
2001 ◽  
Vol 09 (03) ◽  
pp. 305-316 ◽  
Author(s):  
F. J. CANIEGO ◽  
M. A. MARTÍN ◽  
F. SAN JOSÉ
Keyword(s):  
Image Analysis ◽  
Pore Size ◽  
Soil Samples ◽  
Second Step ◽  
Strength Analysis ◽  
Entropy Spectrum ◽  
Singular Measures ◽  
Experimental Measure ◽  
Soil Distribution ◽  
Smooth Density

In this paper, several features of pore-size soil distribution are first analyzed, suggesting that they are closer to those of singular measures than to those of distributions with smooth density. In a second step, the weighted singularity strength of an experimental measure obtained by image analysis of soil samples is evaluated. The results of this analysis show the singular nature of pore-size distribution. Finally, the distribution is characterized by means of a spectrum of entropies computed on distorted measures associated with the original experimental measure.

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