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Maximum and minimum of support functions 支持功能的最大值和最小值
4区 数学
Hokkaido Mathematical Journal Pub Date : 2023-10-01 DOI: 10.14492/hokmj/2021-557
Huhe HAN
{"title":"Maximum and minimum of support functions","authors":"Huhe HAN","doi":"10.14492/hokmj/2021-557","DOIUrl":"https://doi.org/10.14492/hokmj/2021-557","url":null,"abstract":"For given continuous functions $gamma_{{}_{i}}: S^{n}to mathbb{R}_{+}$ ($i=1, 2$), the functions $gamma_{{}_{max}}$ and $gamma_{{}_{min}}$ can be defined naturally. In this paper, by applying the spherical method, we first show that the Wulff shape associated to $gamma_{{}_{max}}$ is the convex hull of the union of Wulff shapes associated to $gamma_{{}_1}$ and $gamma_{{}_2}$, if $gamma_{{}_1}$ and $gamma_{{}_2}$ are convex integrands. Next, we show that the Wulff shape associated to $gamma_{{}_{min}}$ is the intersection of Wulff shapes associated to $gamma_{{}_1}$ and $gamma_{{}_2}$. Moreover, relationships between their dual Wulff shapes are given.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136204782","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
Improvements of $A$-numerical radius bounds $A$数值半径界的改进
4区 数学
Hokkaido Mathematical Journal Pub Date : 2023-10-01 DOI: 10.14492/hokmj/2022-603
Raj Kumar NAYAK, Pintu BHUNIA, Kallol PAUL
{"title":"Improvements of $A$-numerical radius bounds","authors":"Raj Kumar NAYAK, Pintu BHUNIA, Kallol PAUL","doi":"10.14492/hokmj/2022-603","DOIUrl":"https://doi.org/10.14492/hokmj/2022-603","url":null,"abstract":"We obtain upper and lower bounds for the $A$-numerical radius inequalities of operators and operator matrices which generalize and improve on the existing ones. We present new upper bounds for the $A$-numerical radius of the product of two operators. We also develop various inequalities for the $A$-numerical radius of $2 times 2 $ operator matrices.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136204784","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
Upper bounds of local electronic densities in molecules 分子中局部电子密度的上界
4区 数学
Hokkaido Mathematical Journal Pub Date : 2023-10-01 DOI: 10.14492/hokmj/2021-577
Sohei ASHIDA
{"title":"Upper bounds of local electronic densities in molecules","authors":"Sohei ASHIDA","doi":"10.14492/hokmj/2021-577","DOIUrl":"https://doi.org/10.14492/hokmj/2021-577","url":null,"abstract":"The eigenfunctions of electronic Hamiltonians determine the stable structures and dynamics of molecules through the local distributions of their densities. In this paper an a priori upper bound for such local distributions of the densities is given. The bound means that concentration of electrons is prohibited due to the repulsion between the electrons. A relation between one-electron and two-electron densities resulting from the antisymmetry of the eigenfunctions plays a crucial role in the proof.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":"137 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136204466","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
The artin braid group actions on the set of spin structures on a surface 编织基团作用于表面上的自旋结构集
4区 数学
Hokkaido Mathematical Journal Pub Date : 2023-10-01 DOI: 10.14492/hokmj/2021-570
Gefei WANG
{"title":"The artin braid group actions on the set of spin structures on a surface","authors":"Gefei WANG","doi":"10.14492/hokmj/2021-570","DOIUrl":"https://doi.org/10.14492/hokmj/2021-570","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136204785","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
An analogy of Jacobi's formula and its applications 雅可比公式的类比及其应用
4区 数学
Hokkaido Mathematical Journal Pub Date : 2023-10-01 DOI: 10.14492/hokmj/2021-572
Jun CHIBA, Keiji MATSUMOTO
{"title":"An analogy of Jacobi's formula and its applications","authors":"Jun CHIBA, Keiji MATSUMOTO","doi":"10.14492/hokmj/2021-572","DOIUrl":"https://doi.org/10.14492/hokmj/2021-572","url":null,"abstract":"We give an analogy of Jacobi's formula, which relates the hypergeometric function with parameters $(1/4,1/4,1)$ and theta constants. By using this analogy and twice formulas of theta constants, we obtain a transformation formula for this hypergeometric function. As its application, we express the limit of a pair of sequences defined by a mean iteration by this hypergeometric function.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136204780","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
Harmonic maps and biharmonic maps for double fibrations of compact Lie groups 紧李群双颤振的调和映射和双调和映射
4区 数学
Hokkaido Mathematical Journal Pub Date : 2023-10-01 DOI: 10.14492/hokmj/2021-558
Hajime URAKAWA
{"title":"Harmonic maps and biharmonic maps for double fibrations of compact Lie groups","authors":"Hajime URAKAWA","doi":"10.14492/hokmj/2021-558","DOIUrl":"https://doi.org/10.14492/hokmj/2021-558","url":null,"abstract":"This work is motivated by the works of W.Y. Hsiang and H.B. Lawson [7], Pages $12$ and $13$. In this paper, we deal with the following double fibration: [ xymatrix@R-0.5cm @C-0.5cm{ & (G,g) ar[ld]_{pi_1} ar[rd]^{pi_2} & (G/H,h_1) && (Kbackslash G,h_2) } ] We will show that every $K$-invariant minimal or biharmonic hypersurface $M$ in $(G/H,h_1)$ induces an $H$-invariant minimal or biharmonic hypersurface $widetilde{M}$ in $(Kbackslash G,h_2)$ by means of $widetilde{M}:=pi_2(pi_1{}^{-1}(M))$ (cf. Theorems 3.2 and 4.1). We give a one to one correspondence between the class of all the $K$-invariant minimal or biharmonic hypersurfaces in $G/H$ and the one of all the $H$-invariant minimal or biharmonic hypersurfaces in $Kbackslash G$ (cf. Theorem 4.2).","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":"152 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136204783","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
Accessibility and stabilization by infinite horizon optimal control with negative discounting 负折现无限视界最优控制的可达性与镇定性
4区 数学
Hokkaido Mathematical Journal Pub Date : 2023-10-01 DOI: 10.14492/hokmj/2021-551
Fumihiko NAKAMURA
{"title":"Accessibility and stabilization by infinite horizon optimal control with negative discounting","authors":"Fumihiko NAKAMURA","doi":"10.14492/hokmj/2021-551","DOIUrl":"https://doi.org/10.14492/hokmj/2021-551","url":null,"abstract":"The present paper investigates systems exhibiting two attractors, and we discuss the problem of steering the state from one attractor to the other attractor by our idea of associating with the stabilization problem an optimal control problem. We first formulate the steering problem and give partial answers for the problem in a two-dimensional case by using the ordinary differential equation based on the infinite horizon optimal control model with negative discounts. Furthermore, under some conditions, we verify that the phase space can be separated into some openly connected components depending on the asymptotic behavior of the orbit starting from initial points in their components. This classification of initial points suggests that the system enables robust stabilizable control. Moreover, we illustrate some numerical results for the control obtained by applying our focused system for the Bonhoeffer–Van der Pol model.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136204781","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
Certain Convexity Properties of Hurwitz-Lerch Zeta and Mittag-Leffler Functions Hurwitz-Lerch-Zeta和Mittag-Leffler函数的某些凸性
IF 0.5 4区 数学
Hokkaido Mathematical Journal Pub Date : 2023-06-01 DOI: 10.14492/hokmj/2021-543
D. Bansal, R. K. Raina
{"title":"Certain Convexity Properties of Hurwitz-Lerch Zeta and Mittag-Leffler Functions","authors":"D. Bansal, R. K. Raina","doi":"10.14492/hokmj/2021-543","DOIUrl":"https://doi.org/10.14492/hokmj/2021-543","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48225472","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
Hardy-Sobolev inequalities for double phase functionals 双相泛函的Hardy-Sobolev不等式
IF 0.5 4区 数学
Hokkaido Mathematical Journal Pub Date : 2023-06-01 DOI: 10.14492/hokmj/2021-544
Y. Mizuta, T. Shimomura
{"title":"Hardy-Sobolev inequalities for double phase functionals","authors":"Y. Mizuta, T. Shimomura","doi":"10.14492/hokmj/2021-544","DOIUrl":"https://doi.org/10.14492/hokmj/2021-544","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46301054","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
On surjective homomorphisms from a configuration space group to a surface group 构形空间群到平面群的满射同态
IF 0.5 4区 数学
Hokkaido Mathematical Journal Pub Date : 2023-06-01 DOI: 10.14492/hokmj/2021-526
K. Sawada
{"title":"On surjective homomorphisms from a configuration space group to a surface group","authors":"K. Sawada","doi":"10.14492/hokmj/2021-526","DOIUrl":"https://doi.org/10.14492/hokmj/2021-526","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42608374","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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