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Extremal Area of Polygons, sliding along a circle 多边形的极值区域，沿圆滑动
IF 0.5 4区 数学
Hokkaido Mathematical Journal Pub Date : 2020-01-29 DOI: 10.14492/hokmj/2020-312
D. Siersma
{"title":"Extremal Area of Polygons, sliding along a circle","authors":"D. Siersma","doi":"10.14492/hokmj/2020-312","DOIUrl":"https://doi.org/10.14492/hokmj/2020-312","url":null,"abstract":"We determine all critical configurations for the Area function on polygons with vertices on a circle or an ellipse. For isolated critical points we compute their Morse index, resp index of the gradient vector field. We relate the computation at an isolated degenerate point to an eigenvalue question about combinations. In the even dimensional case non-isolated singularities occur as `zigzag trains'.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46857910","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
Singular limit problem of abstract second order evolution equations 抽象二阶演化方程的奇异极限问题
IF 0.5 4区 数学
Hokkaido Mathematical Journal Pub Date : 2019-12-21 DOI: 10.14492/hokmj/2021-504
R. Ikehata, M. Sobajima
{"title":"Singular limit problem of abstract second order evolution equations","authors":"R. Ikehata, M. Sobajima","doi":"10.14492/hokmj/2021-504","DOIUrl":"https://doi.org/10.14492/hokmj/2021-504","url":null,"abstract":"We consider the singular limit problem in a real Hilbert space for abstract second order evolution equations with a parameter $varepsilon in (0,1]$. We first give an alternative proof of the celebrated results due to Kisynski (1963) from the viewpoint of the energy method. Next we derive a more precise asymptotic profile as $varepsilon to +0$ of the solution itself depending on $varepsilon$ under rather high regularity assumptions on the initial data.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44002475","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
The differential equations associated with Calogero-Moser-Sutherland particle models in the freezing regime 冻结状态下与Calogero-Moser-Sutherland粒子模型相关的微分方程
IF 0.5 4区 数学
Hokkaido Mathematical Journal Pub Date : 2019-10-17 DOI: 10.14492/hokmj/2020-307
M. Voit, Jeannette H. C. Woerner
{"title":"The differential equations associated with Calogero-Moser-Sutherland particle models in the freezing regime","authors":"M. Voit, Jeannette H. C. Woerner","doi":"10.14492/hokmj/2020-307","DOIUrl":"https://doi.org/10.14492/hokmj/2020-307","url":null,"abstract":"Multivariate Bessel processes describe Calogero-Moser-Sutherland particle models and are related with $beta$-Hermite and $beta$-Laguerre ensembles. They depend on a root system and a multiplicity $k$. Recently, several limit theorems for $ktoinfty$ were derived where the limits depend on the solutions of associated ODEs in these freezing regimes. In this paper we study the solutions of these ODEs which are are singular on the boundaries of their domains. In particular we prove that for a start in arbitrary boundary points, the ODEs always admit unique solutions in their domains for $t>0$.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46615706","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: 8
The decompositional structure of certain fractional integral operators 一类分数阶积分算子的分解结构
IF 0.5 4区 数学
Hokkaido Mathematical Journal Pub Date : 2019-10-01 DOI: 10.14492/hokmj/1573722020
M. Luo, R. K. Raina
{"title":"The decompositional structure of certain fractional integral operators","authors":"M. Luo, R. K. Raina","doi":"10.14492/hokmj/1573722020","DOIUrl":"https://doi.org/10.14492/hokmj/1573722020","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48078381","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
Truncated Euler-Carlitz numbers 截断Euler-Carlitz数
IF 0.5 4区 数学
Hokkaido Mathematical Journal Pub Date : 2019-10-01 DOI: 10.14492/hokmj/1573722018
T. Komatsu, V. Laohakosol, Pinthira Tangsupphathawat
{"title":"Truncated Euler-Carlitz numbers","authors":"T. Komatsu, V. Laohakosol, Pinthira Tangsupphathawat","doi":"10.14492/hokmj/1573722018","DOIUrl":"https://doi.org/10.14492/hokmj/1573722018","url":null,"abstract":"In this paper, we introduce the truncated Euler-Carlitz numbers as analogues of hypergeometric Euler numbers. In a special case, Euler-Carlitz numbers are defined, which is an analogue of the classical Euler numbers. We give several interesting properties for these numbers. We also show some determinant expressions of Euler-Carlitz numbers.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49209043","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
Adic sheaves over weighted projective lines and elliptic curves 加权投影线和椭圆曲线上的矢束
IF 0.5 4区 数学
Hokkaido Mathematical Journal Pub Date : 2019-10-01 DOI: 10.14492/hokmj/1573722014
Jinjing Chen, Jianmin Chen, Yanan Lin
{"title":"Adic sheaves over weighted projective lines and elliptic curves","authors":"Jinjing Chen, Jianmin Chen, Yanan Lin","doi":"10.14492/hokmj/1573722014","DOIUrl":"https://doi.org/10.14492/hokmj/1573722014","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44291225","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
Integral curves of the characteristic vector field of minimal ruled real hypersurfaces in non-flat complex space forms 非平坦复空间形式中极小规则实超曲面特征向量场的积分曲线
IF 0.5 4区 数学
Hokkaido Mathematical Journal Pub Date : 2019-10-01 DOI: 10.14492/hokmj/1573722019
M. Kimura, S. Maeda, H. Tanabe
{"title":"Integral curves of the characteristic vector field of minimal ruled real hypersurfaces in non-flat complex space forms","authors":"M. Kimura, S. Maeda, H. Tanabe","doi":"10.14492/hokmj/1573722019","DOIUrl":"https://doi.org/10.14492/hokmj/1573722019","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46113508","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
Degree formulas for the Euler characteristic of semialgebraic sets 半代数集欧拉特征的度公式
IF 0.5 4区 数学
Hokkaido Mathematical Journal Pub Date : 2019-10-01 DOI: 10.14492/hokmj/1573722013
J. Lapébie
{"title":"Degree formulas for the Euler characteristic of semialgebraic sets","authors":"J. Lapébie","doi":"10.14492/hokmj/1573722013","DOIUrl":"https://doi.org/10.14492/hokmj/1573722013","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42436122","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
Matching complexes of polygonal line tilings 多边形线条拼接的匹配复合体
IF 0.5 4区 数学
Hokkaido Mathematical Journal Pub Date : 2019-10-01 DOI: 10.14492/hokmj/2019-213
Takahiro Matsushita
{"title":"Matching complexes of polygonal line tilings","authors":"Takahiro Matsushita","doi":"10.14492/hokmj/2019-213","DOIUrl":"https://doi.org/10.14492/hokmj/2019-213","url":null,"abstract":"The matching complex of a simple graph $G$ is a simplicial complex consisting of the matchings on $G$. Jelic Milutinovic et al. studied the matching complexes of the polygonal line tilings, and they gave a lower bound for the connectivity of the matching complexes of polygonal line tilings. In this paper, we determine the homotopy types of the matching complexes of polygonal line tilings recursively, and determine their connectivities.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45125674","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: 6
Global existence for null-form wave equations with data in a Sobolev space of lower regularity and weight 具有较低正则性和权重的Sobolev空间中数据的零型波动方程的全局存在性
IF 0.5 4区 数学
Hokkaido Mathematical Journal Pub Date : 2019-09-11 DOI: 10.14492/hokmj/2021-523
K. Hidano, K. Yokoyama
{"title":"Global existence for null-form wave equations with data in a Sobolev space of lower regularity and weight","authors":"K. Hidano, K. Yokoyama","doi":"10.14492/hokmj/2021-523","DOIUrl":"https://doi.org/10.14492/hokmj/2021-523","url":null,"abstract":"Assuming initial data have small weighted $H^4times H^3$ norm, we prove global existence of solutions to the Cauchy problem for systems of quasi-linear wave equations in three space dimensions satisfying the null condition of Klainerman. Compared with the work of Christodoulou, our result assumes smallness of data with respect to $H^4times H^3$ norm having a lower weight. Our proof uses the space-time $L^2$ estimate due to Alinhac for some special derivatives of solutions to variable-coefficient wave equations. It also uses the conformal energy estimate for inhomogeneous wave equation $Box u=F$. A new observation made in this paper is that, in comparison with the proofs of Klainerman and Hormander, we can limit the number of occurrences of the generators of hyperbolic rotations or dilations in the course of a priori estimates of solutions. This limitation allows us to obtain global solutions for radially symmetric data, when a certain norm with considerably low weight is small enough.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49074522","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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