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Computable error bounds for asymptotic approximations of the quadratic discriminant function 二次判别函数渐近逼近的可计算误差界
IF 0.2 4区 数学
Hiroshima Mathematical Journal Pub Date : 2020-11-01 DOI: 10.32917/hmj/1607396491
Y. Fujikoshi
{"title":"Computable error bounds for asymptotic approximations of the quadratic discriminant function","authors":"Y. Fujikoshi","doi":"10.32917/hmj/1607396491","DOIUrl":"https://doi.org/10.32917/hmj/1607396491","url":null,"abstract":"A bstract . This paper is concerned with computable error bounds for asymptotic approximations of the expected probabilities of misclassification (EPMC) of the quadratic discriminant function Q . A location and scale mixture expression for Q is given as a special case of a general discriminant function including the linear and quadratic discriminant functions. Using the result, we provide computable error bounds for asymptotic approximations of the EPMC of Q when both the sample size and the dimensionality are large. The bounds are numerically explored. Similar results are given for a quadratic discriminant function Q 0 when the covariance matrix is known.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49585899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Table of Contents, Hiroshima Math. J., Volume 50, (2020) 目录，广岛数学。J.，第50卷，（2020）
IF 0.2 4区 数学
Hiroshima Mathematical Journal Pub Date : 2020-11-01 DOI: 10.32917/hmj/1607396495
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引用次数: 0
Notes on constructions of knots with the same trace 同迹结的构造注释
IF 0.2 4区 数学
Hiroshima Mathematical Journal Pub Date : 2020-10-26 DOI: 10.32917/h2021005
Keiji Tagami
{"title":"Notes on constructions of knots with the same trace","authors":"Keiji Tagami","doi":"10.32917/h2021005","DOIUrl":"https://doi.org/10.32917/h2021005","url":null,"abstract":"The $m$-trace of a knot is the $4$-manifold obtained from $mathbf{B}^4$ by attaching a $2$-handle along the knot with $m$-framing. In 2015, Abe, Jong, Luecke and Osoinach introduced a technique to construct infinitely many knots with the same $m$-trace, which is called the operation $(ast m)$. In this paper, we prove that their technique can be explained in terms of Gompf and Miyazaki's dualizable pattern. In addition, we show that the family of knots admitting the same $4$-surgery given by Teragaito can be explained by the operation $(ast m)$.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44538739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Dwork hypersurfaces of degree six and Greene’s hypergeometric function 六次Dwork超曲面与Greene超几何函数
IF 0.2 4区 数学
Hiroshima Mathematical Journal Pub Date : 2020-10-25 DOI: 10.32917/h2020097
Satoshi Kumabe
{"title":"Dwork hypersurfaces of degree six and Greene’s hypergeometric function","authors":"Satoshi Kumabe","doi":"10.32917/h2020097","DOIUrl":"https://doi.org/10.32917/h2020097","url":null,"abstract":"In this paper, we give a formula for the number of rational points on the Dwork hypersurfaces of degree six over finite fields by using Greene's finite-field hypergeometric function, which is a generalization of Goodson's formula for the Dwork hypersurfaces of degree four [1, Theorem 1.1]. Our formula is also a higher-dimensional and a finite field analogue of MatsumotoTerasoma-Yamazaki's formula. Furthermore, we also explain the relation between our formula and Miyatani's formula.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":"47 18","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41248741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A criterion for the existence of a plane model with two inner Galois points for algebraic curves 代数曲线上具有两个内Galois点的平面模型存在性的一个判据
IF 0.2 4区 数学
Hiroshima Mathematical Journal Pub Date : 2020-10-02 DOI: 10.32917/H2020094
Kazuki Higashine
{"title":"A criterion for the existence of a plane model with two inner Galois points for algebraic curves","authors":"Kazuki Higashine","doi":"10.32917/H2020094","DOIUrl":"https://doi.org/10.32917/H2020094","url":null,"abstract":"A criterion for the existence of a plane model with two non-smooth Galois points for algebraic curves is presented, which is a generalization of Fukasawa's criterion for two smooth Galois points. Owing to this generalized criterion, multiplicities and order sequences at Galois points can be described in detail.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41809900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Consistent variable selection criteria in multivariate linear regression even when dimension exceeds sample size 在多元线性回归中，即使维度超过样本量，变量选择标准也保持一致
IF 0.2 4区 数学
Hiroshima Mathematical Journal Pub Date : 2020-07-31 DOI: 10.32917/hmj/1607396493
R. Oda
{"title":"Consistent variable selection criteria in multivariate linear regression even when dimension exceeds sample size","authors":"R. Oda","doi":"10.32917/hmj/1607396493","DOIUrl":"https://doi.org/10.32917/hmj/1607396493","url":null,"abstract":"","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":"50 1","pages":"339-374"},"PeriodicalIF":0.2,"publicationDate":"2020-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44008384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Bifurcation diagram of a Robin boundary value problem arising in MEMS MEMS中Robin边值问题的分岔图
IF 0.2 4区 数学
Hiroshima Mathematical Journal Pub Date : 2020-07-08 DOI: 10.32917/h2021029
Jong-Shenq Guo, N. Kavallaris, Chi-Jen Wang, C. Yu
{"title":"Bifurcation diagram of a Robin boundary value problem arising in MEMS","authors":"Jong-Shenq Guo, N. Kavallaris, Chi-Jen Wang, C. Yu","doi":"10.32917/h2021029","DOIUrl":"https://doi.org/10.32917/h2021029","url":null,"abstract":"We consider a parabolic problem with Robin boundary condition which arises when the edge of a micro-electro-mechanical-system (MEMS) device is connected with a flexible nonideal support. Then via a rigorous analysis we investigate the structure of the solution set of the corresponding steady-state problem. We show that a critical value (the pull-in voltage) exists so that the system has exactly two stationary solutions when the applied voltage is lower than this critical value, one stationary solution for applying this critical voltage, and no stationary solution above the critical voltage.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41760528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A time-periodic oscillatory hexagonal solution in a 2-dimensional integro-differential reaction-diffusion system 二维积分-微分反应-扩散系统的时间周期振荡六方解
IF 0.2 4区 数学
Hiroshima Mathematical Journal Pub Date : 2020-07-01 DOI: 10.32917/hmj/1595901630
Shunsuke Kobayashi, T. Sakamoto, Yasuhide Uegata, S. Yazaki
{"title":"A time-periodic oscillatory hexagonal solution in a 2-dimensional integro-differential reaction-diffusion system","authors":"Shunsuke Kobayashi, T. Sakamoto, Yasuhide Uegata, S. Yazaki","doi":"10.32917/hmj/1595901630","DOIUrl":"https://doi.org/10.32917/hmj/1595901630","url":null,"abstract":"An oscillatory hexagonal solution in a two component reaction-di¤usion system with a non-local term is studied. By applying the center manifold theory, we obtain a four-dimensional dynamical system that informs us about the bifurcation structure around the trivial solution. Our results suggest that the oscillatory hexagonal solution can bifurcate from a stationary hexagonal solution via the Hopf bifurcation. This provides a reasonable explanation for the existence of the oscillatory hexagon.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46173597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Calderón-Zygmund operators with variable kernels acting on weak Musielak-Orlicz Hardy spaces 弱Musielak-Orlicz-Hardy空间上的变核Calderón-Zygmund算子
IF 0.2 4区 数学
Hiroshima Mathematical Journal Pub Date : 2020-07-01 DOI: 10.32917/hmj/1595901624
Bo Li
{"title":"Calderón-Zygmund operators with variable kernels acting on weak Musielak-Orlicz Hardy spaces","authors":"Bo Li","doi":"10.32917/hmj/1595901624","DOIUrl":"https://doi.org/10.32917/hmj/1595901624","url":null,"abstract":"","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":"50 1","pages":"151-168"},"PeriodicalIF":0.2,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45765451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic bias of $C_p$ type criterion for model selection in the GEE when the sample size and the cluster sizes are large 当样本容量和聚类容量较大时，$C_p$类型准则在GEE模型选择中的渐近偏差
IF 0.2 4区 数学
Hiroshima Mathematical Journal Pub Date : 2020-07-01 DOI: 10.32917/hmj/1595901629
Tomoharu Sato
{"title":"Asymptotic bias of $C_p$ type criterion for model selection in the GEE when the sample size and the cluster sizes are large","authors":"Tomoharu Sato","doi":"10.32917/hmj/1595901629","DOIUrl":"https://doi.org/10.32917/hmj/1595901629","url":null,"abstract":"A bstract . In this paper, we evaluate the asymptotic bias of C p type criterion for model selection in the GEE (generalized estimating equation) method when the sample and cluster sizes are large. We present the asymptotic properties of GEE estimator and the model selection criterion. Then, we present the order of the asymptotic bias of PMSEG (the prediction mean squared error in the GEE).","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46432242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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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