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On Density and Sigma-Porosity in Some Families of Darboux Functions 一些达布函数族的密度和sigma -孔隙度
IF 0.2
Real Analysis Exchange Pub Date : 2022-06-01 DOI: 10.14321/realanalexch.47.1.1590599512
G. Ivanova, Irena Domnik
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引用次数: 0
A Brief Exposition of the Space of Relatively Bounded Nonlinear Operators 相对有界非线性算子空间的简要说明
IF 0.2
Real Analysis Exchange Pub Date : 2022-06-01 DOI: 10.14321/realanalexch.47.1.1610537860
P. Viswanathan
{"title":"A Brief Exposition of the Space of Relatively Bounded Nonlinear Operators","authors":"P. Viswanathan","doi":"10.14321/realanalexch.47.1.1610537860","DOIUrl":"https://doi.org/10.14321/realanalexch.47.1.1610537860","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43317551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximating the Decreasing Rearrangement 近似递减重排
IF 0.2
Real Analysis Exchange Pub Date : 2022-06-01 DOI: 10.14321/realanalexch.47.1.1596546460
Martin E. Price
{"title":"Approximating the Decreasing Rearrangement","authors":"Martin E. Price","doi":"10.14321/realanalexch.47.1.1596546460","DOIUrl":"https://doi.org/10.14321/realanalexch.47.1.1596546460","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47233762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Comments on Charges on the Boolean Algebra of Regular Open Sets 正则开集布尔代数上电荷的注释
IF 0.2
Real Analysis Exchange Pub Date : 2022-06-01 DOI: 10.14321/realanalexch.47.1.1600145293
K. B. Bhaskara Rao
{"title":"Comments on Charges on the Boolean Algebra of Regular Open Sets","authors":"K. B. Bhaskara Rao","doi":"10.14321/realanalexch.47.1.1600145293","DOIUrl":"https://doi.org/10.14321/realanalexch.47.1.1600145293","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49062513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Set of Points at which an Increasing Continuous Singular Function has a Nonzero Finite Derivative 关于递增连续奇异函数具有非零有限导数的点集
IF 0.2
Real Analysis Exchange Pub Date : 2021-11-29 DOI: 10.14321/realanalexch.47.2.1638769133
Marta Kossaczká, L. Zajícek
{"title":"On the Set of Points at which an Increasing Continuous Singular Function has a Nonzero Finite Derivative","authors":"Marta Kossaczká, L. Zajícek","doi":"10.14321/realanalexch.47.2.1638769133","DOIUrl":"https://doi.org/10.14321/realanalexch.47.2.1638769133","url":null,"abstract":"Sanchez, Viader, Paradis and Carrillo (2016) proved that there exists an increasing continuous singular function $f$ on $[0,1]$ such that the set $A_f$ of points where $f$ has a nonzero finite derivative has Hausdorff dimension 1 in each subinterval of $[0,1]$. We prove a stronger (and optimal) result showing that a set $A_f$ as above can contain any prescribed $F_{sigma}$ null subset of $[0,1]$.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45668327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ON FUNCTIONS DETERMINED BY DENSE SETS 关于稠密集确定的函数
IF 0.2
Real Analysis Exchange Pub Date : 2021-11-01 DOI: 10.14321/REALANALEXCH.46.2.0423
Nicholas P. M. Kayban, Xianfu Wang
{"title":"ON FUNCTIONS DETERMINED BY DENSE SETS","authors":"Nicholas P. M. Kayban, Xianfu Wang","doi":"10.14321/REALANALEXCH.46.2.0423","DOIUrl":"https://doi.org/10.14321/REALANALEXCH.46.2.0423","url":null,"abstract":"We show that a few basic classes of lower semicontinuous functions on ℝn are densely recoverable. Specifically, we show that the sum of a convex and a continuous function, the difference of two convex and lower semicontinuous functions, a K-increasing function (where K is a cone of nonempty interior), and differences of K-increasing functions are all functions uniquely determined by their values on a dense set in ℝn. Thus, sets of such functions of each type are densely recoverable sets. In general, the sum and difference of two densely recoverable sets of functions is shown to not be densely recoverable.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48717237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
SOME REMARKS ON WASHEK PFEFFER'S CONTRIBUTIONS IN GENERAL TOPOLOGY 浅谈washek pfeffer在一般拓扑中的贡献
IF 0.2
Real Analysis Exchange Pub Date : 2021-11-01 DOI: 10.14321/REALANALEXCH.46.2.0297
G. Gruenhage
{"title":"SOME REMARKS ON WASHEK PFEFFER'S CONTRIBUTIONS IN GENERAL TOPOLOGY","authors":"G. Gruenhage","doi":"10.14321/REALANALEXCH.46.2.0297","DOIUrl":"https://doi.org/10.14321/REALANALEXCH.46.2.0297","url":null,"abstract":"Washek Pfeffer's contributions in general topology are discussed, especially his paper with van Douwen on $D$-spaces and his work with Prikry on small spaces.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46769933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
TOGO NISHIURA November 10, 1931 — February 12, 2021 TOGO NISHIURA November 10, 1931 — February 12, 2021
IF 0.2
Real Analysis Exchange Pub Date : 2021-11-01 DOI: 10.14321/realanalexch.46.2.0301
P. Humke
{"title":"TOGO NISHIURA November 10, 1931 — February 12, 2021","authors":"P. Humke","doi":"10.14321/realanalexch.46.2.0301","DOIUrl":"https://doi.org/10.14321/realanalexch.46.2.0301","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45990637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
INEQUALITIES FOR WEIGHTED ARITHMETIC AND GEOMETRIC MEANS 加权算术不等式与几何平均
IF 0.2
Real Analysis Exchange Pub Date : 2021-11-01 DOI: 10.14321/realanalexch.46.2.0359
H. Alzer
{"title":"INEQUALITIES FOR WEIGHTED ARITHMETIC AND GEOMETRIC MEANS","authors":"H. Alzer","doi":"10.14321/realanalexch.46.2.0359","DOIUrl":"https://doi.org/10.14321/realanalexch.46.2.0359","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49490082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
OPTIMAL QUANTIZATION FOR MIXED DISTRIBUTIONS 混合分布的最优量化
IF 0.2
Real Analysis Exchange Pub Date : 2021-11-01 DOI: 10.14321/REALANALEXCH.46.2.0451
M. Roychowdhury
{"title":"OPTIMAL QUANTIZATION FOR MIXED DISTRIBUTIONS","authors":"M. Roychowdhury","doi":"10.14321/REALANALEXCH.46.2.0451","DOIUrl":"https://doi.org/10.14321/REALANALEXCH.46.2.0451","url":null,"abstract":"The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability distribution by a discrete distribution. Mixed distributions are an exciting new area for optimal quantization. In this paper, we have determined the optimal sets of n-means, the nth quantization errors, and the quantization dimensions of different mixed distributions. Besides, we have discussed whether the quantization coefficients for the mixed distributions exist. The results in this paper will give a motivation and insight into more general problems in quantization for mixed distributions.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45607039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
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