{"title":"Characterisations of $V$-sufficiency and $C^0$-sufficiency of relative jets","authors":"K. Bekka, Satoshi Koike","doi":"10.14492/hokmj/2022-606","DOIUrl":"https://doi.org/10.14492/hokmj/2022-606","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139815211","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}
{"title":"Characterisations of $V$-sufficiency and $C^0$-sufficiency of relative jets","authors":"K. Bekka, Satoshi Koike","doi":"10.14492/hokmj/2022-606","DOIUrl":"https://doi.org/10.14492/hokmj/2022-606","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139875021","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}
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.
{"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":null,"pages":null},"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}
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.
{"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":null,"pages":null},"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}
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.
{"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":null,"pages":null},"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}
{"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":null,"pages":null},"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}
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.
{"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":null,"pages":null},"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}
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).
{"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":null,"pages":null},"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}
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