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The Partial Derivative of Okamoto's Functions with Respect to the Parameter 冈本函数对参数的偏导数
IF 0.2
Real Analysis Exchange Pub Date : 2021-10-22 DOI: 10.14321/realanalexch.48.1.1638769133
Nathan Dalaklis, K. Kawamura, Tobey Mathis, Michalis Paizanis
{"title":"The Partial Derivative of Okamoto's Functions with Respect to the Parameter","authors":"Nathan Dalaklis, K. Kawamura, Tobey Mathis, Michalis Paizanis","doi":"10.14321/realanalexch.48.1.1638769133","DOIUrl":"https://doi.org/10.14321/realanalexch.48.1.1638769133","url":null,"abstract":"The differentiability of the one parameter family of Okomoto's functions as functions of $x$ has been analyzed extensively since their introduction in 2005. As an analogue to a similar investigation, in this paper, we consider the partial derivative of Okomoto's functions with respect to the parameter $a$. We place a significant focus on $a = 1/3$ to describe the properties of a nowhere differentiable function $K(x)$ for which the set of points of infinite derivative produces an example of a measure zero set with Hausdorff dimension $1$.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44296262","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: 2
The exponential matrix: an explicit formula by an elementary method 指数矩阵:用初等方法得到的显式公式
IF 0.2
Real Analysis Exchange Pub Date : 2021-10-14 DOI: 10.14321/realanalexch.46.1.0099
O. D. de Oliveira
{"title":"The exponential matrix: an explicit formula by an elementary method","authors":"O. D. de Oliveira","doi":"10.14321/realanalexch.46.1.0099","DOIUrl":"https://doi.org/10.14321/realanalexch.46.1.0099","url":null,"abstract":"We show an explicit formula, with a quite easy deduction, for the exponential matrix $e^{tA}$ of a real square matrix $A$ of order $ntimes n$. The elementary method developed requires neither Jordan canonical form, nor eigenvectors, nor resolution of linear systems of differential equations, nor resolution of linear systems with constant coefficients, nor matrix inversion, nor complex integration, nor functional analysis. The basic tools are power series and the method of partial fraction decomposition. Two examples are given. A proof of one well-known stability result is given.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"31 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84848513","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
Ideal extensions of Olivier's theorem 奥利维尔定理的理想扩展
IF 0.2
Real Analysis Exchange Pub Date : 2021-10-14 DOI: 10.14321/realanalexch.46.1.0261
Ladislav Misík, J. Tóth
{"title":"Ideal extensions of Olivier's theorem","authors":"Ladislav Misík, J. Tóth","doi":"10.14321/realanalexch.46.1.0261","DOIUrl":"https://doi.org/10.14321/realanalexch.46.1.0261","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41529170","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: 2
Strong derivative and the essentially Riemann integral 强导数和本质上的黎曼积分
IF 0.2
Real Analysis Exchange Pub Date : 2021-10-14 DOI: 10.14321/realanalexch.46.1.0233
Immanuel D. Calunod, I. Garces
{"title":"Strong derivative and the essentially Riemann integral","authors":"Immanuel D. Calunod, I. Garces","doi":"10.14321/realanalexch.46.1.0233","DOIUrl":"https://doi.org/10.14321/realanalexch.46.1.0233","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47690486","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
Variational measure with respect to measurable gauges 相对于可测量量规的变分测量
IF 0.2
Real Analysis Exchange Pub Date : 2021-10-14 DOI: 10.14321/realanalexch.46.1.0247
N. Singh, S. P. S. Kainth
{"title":"Variational measure with respect to measurable gauges","authors":"N. Singh, S. P. S. Kainth","doi":"10.14321/realanalexch.46.1.0247","DOIUrl":"https://doi.org/10.14321/realanalexch.46.1.0247","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46592971","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
Non-isolated, non-strictly monotone points of iterates of continuous functions 连续函数迭代的非孤立非严格单调点
IF 0.2
Real Analysis Exchange Pub Date : 2021-10-14 DOI: 10.14321/realanalexch.46.1.0051
V. Murugan, Rajendran Palanivel
{"title":"Non-isolated, non-strictly monotone points of iterates of continuous functions","authors":"V. Murugan, Rajendran Palanivel","doi":"10.14321/realanalexch.46.1.0051","DOIUrl":"https://doi.org/10.14321/realanalexch.46.1.0051","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44900237","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: 2
Open and surjective mapping theorems for differentiable maps with critical points 具有临界点的可微映射的开映射和满射映射定理
IF 0.2
Real Analysis Exchange Pub Date : 2021-10-14 DOI: 10.14321/realanalexch.46.1.0107
Liangpan Li
{"title":"Open and surjective mapping theorems for differentiable maps with critical points","authors":"Liangpan Li","doi":"10.14321/realanalexch.46.1.0107","DOIUrl":"https://doi.org/10.14321/realanalexch.46.1.0107","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43768341","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: 2
Sufficient conditions for convergence of riemann sums for function space defined by the $k$-modulus of continuity 用连续的k模定义函数空间的黎曼和收敛的充分条件
IF 0.2
Real Analysis Exchange Pub Date : 2021-10-14 DOI: 10.14321/realanalexch.46.1.0037
Igor E. Preobrazhenskii, P. Demidov
{"title":"Sufficient conditions for convergence of riemann sums for function space defined by the $k$-modulus of continuity","authors":"Igor E. Preobrazhenskii, P. Demidov","doi":"10.14321/realanalexch.46.1.0037","DOIUrl":"https://doi.org/10.14321/realanalexch.46.1.0037","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46000745","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
Continuous functions in rings generated by a single Darboux function 由单个达布函数生成的环中的连续函数
IF 0.2
Real Analysis Exchange Pub Date : 2021-10-14 DOI: 10.14321/realanalexch.46.1.0083
Paweł Barbarski
{"title":"Continuous functions in rings generated by a single Darboux function","authors":"Paweł Barbarski","doi":"10.14321/realanalexch.46.1.0083","DOIUrl":"https://doi.org/10.14321/realanalexch.46.1.0083","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43796622","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
Quantitative Straightening of Distance Spheres 距离球的定量矫直
IF 0.2
Real Analysis Exchange Pub Date : 2021-07-20 DOI: 10.14321/realanalexch.48.1.1626760923
G. David, McKenna Kaczanowski, D. Pinkerton
{"title":"Quantitative Straightening of Distance Spheres","authors":"G. David, McKenna Kaczanowski, D. Pinkerton","doi":"10.14321/realanalexch.48.1.1626760923","DOIUrl":"https://doi.org/10.14321/realanalexch.48.1.1626760923","url":null,"abstract":"We study\"distance spheres\": the set of points lying at constant distance from a fixed arbitrary subset $K$ of $[0,1]^d$. We show that, away from the regions where $K$ is\"too dense\"and a set of small volume, we can decompose $[0,1]^d$ into a finite number of sets on which the distance spheres can be\"straightened\"into subsets of parallel $(d-1)$-dimensional planes by a bi-Lipschitz map. Importantly, the number of sets and the bi-Lipschitz constants are independent of the set $K$.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43262151","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
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