We investigate the relation between the level set approach and the varifold approach for the mean curvature flow with Neumann boundary conditions. With an appropriate initial data, we prove that the almost all level sets of the unique viscosity level set solution satisfy Brakke's inequality and a generalized Neumann boundary condition.
{"title":"Level set mean curvature flow, with Neumann boundary conditions","authors":"Satoru Aimi","doi":"10.14492/hokmj/2020-426","DOIUrl":"https://doi.org/10.14492/hokmj/2020-426","url":null,"abstract":"We investigate the relation between the level set approach and the varifold approach for the mean curvature flow with Neumann boundary conditions. With an appropriate initial data, we prove that the almost all level sets of the unique viscosity level set solution satisfy Brakke's inequality and a generalized Neumann boundary condition.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44525976","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 present a precise discussion of Golubitsky and Schaeffer's treatment on bifurcation of Euler buckling problem. We discuss smoothness of the problem and derive equations describing the bifurcation set $B$ and the hysteresis set $H$ up to order 3, which enable us to draw their figures approximately under suitable assumptions.
{"title":"Bifurcation of Euler buckling problem, revisited","authors":"Atia Afroz, Toshizumi Fukui","doi":"10.14492/hokmj/2018-910","DOIUrl":"https://doi.org/10.14492/hokmj/2018-910","url":null,"abstract":"We present a precise discussion of Golubitsky and Schaeffer's treatment on bifurcation of Euler buckling problem. We discuss smoothness of the problem and derive equations describing the bifurcation set $B$ and the hysteresis set $H$ up to order 3, which enable us to draw their figures approximately under suitable assumptions.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49002750","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 study the fourth order nonlinear Schrodinger equation begin{equation*} i{partial }_{t}u-frac{1}{4}partial _{x}^{4}u=f(u) ,quad (t,x)in mathbb{R}times mathbb{R}, end{equation*} where $f(u) $ is the power nonlinearity of order $p>5.$ The scattering operator is constructed in a neighborhood of the origin in a sutable weighted Sobolev space.
{"title":"Scattering operator for the fourth order nonlinear Schrüdinger equation","authors":"N. Hayashi, Yuichiro Kawahara, P. Naumkin","doi":"10.14492/hokmj/2018-907","DOIUrl":"https://doi.org/10.14492/hokmj/2018-907","url":null,"abstract":"We study the fourth order nonlinear Schrodinger equation begin{equation*} i{partial }_{t}u-frac{1}{4}partial _{x}^{4}u=f(u) ,quad (t,x)in mathbb{R}times mathbb{R}, end{equation*} where $f(u) $ is the power nonlinearity of order $p>5.$ The scattering operator is constructed in a neighborhood of the origin in a sutable weighted Sobolev space.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44702146","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}
Let $(R,frak{m})$ be a Noetherian local ring, $frak{a}$ an ideal of $R$ and $M$ a finitely generated $R$-module. In this paper, we study Colocalization of formal local cohomology modules. Here, similar to the local global Principle in local cohomology theory, we investigate artinianness and minimaxness of formal local cohomology modules in terms of their colocalizations. Among other things, we will prove that, for any integer $n$, $mathfrak{F}_{frak{a}}^i(M)$ is artinian $R$-module for all $i lt n$, if and only if $_{frak{p}}(mathfrak{F}_{frak{a}}^i(M)) $ is representable $R_{frak{p}}$-module for all $i lt n$ and all $frak{p} in operatorname{Spec}(R)$. Also, $ mathfrak{F}_{frak{a}}^i(M) $ is minimax $R$-module for all $i lt n$, if and only if $ _{frak{p}}(mathfrak{F}_{frak{a}}^i(M)) $ is representable $R_{frak{p}}$-module for all $i lt n$ and all $frak{p} in operatorname{Spec}(R)setminuslbrace frak{m}rbrace$.
{"title":"Colocalization of formal local cohomology modules","authors":"S. Rezaei","doi":"10.14492/hokmj/2018-906","DOIUrl":"https://doi.org/10.14492/hokmj/2018-906","url":null,"abstract":"Let $(R,frak{m})$ be a Noetherian local ring, $frak{a}$ an ideal of $R$ and $M$ a finitely generated $R$-module. In this paper, we study Colocalization of formal local cohomology modules. Here, similar to the local global Principle in local cohomology theory, we investigate artinianness and minimaxness of formal local cohomology modules in terms of their colocalizations. Among other things, we will prove that, for any integer $n$, $mathfrak{F}_{frak{a}}^i(M)$ is artinian $R$-module for all $i lt n$, if and only if $_{frak{p}}(mathfrak{F}_{frak{a}}^i(M)) $ is representable $R_{frak{p}}$-module for all $i lt n$ and all $frak{p} in operatorname{Spec}(R)$. Also, $ mathfrak{F}_{frak{a}}^i(M) $ is minimax $R$-module for all $i lt n$, if and only if $ _{frak{p}}(mathfrak{F}_{frak{a}}^i(M)) $ is representable $R_{frak{p}}$-module for all $i lt n$ and all $frak{p} in operatorname{Spec}(R)setminuslbrace frak{m}rbrace$.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48503351","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}
Pub Date : 2020-10-01DOI: 10.14492/hokmj/1607936538
M. Shirali, E. Momtahan, S. Safaeeyan
{"title":"Perpendicular graph of modules","authors":"M. Shirali, E. Momtahan, S. Safaeeyan","doi":"10.14492/hokmj/1607936538","DOIUrl":"https://doi.org/10.14492/hokmj/1607936538","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":"49 1","pages":"463-479"},"PeriodicalIF":0.5,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49089918","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}
Pub Date : 2020-10-01DOI: 10.14492/hokmj/1607936536
Masaya Kawamura
{"title":"On Kähler-like almost Hermitian metrics and the almost Hermitian curvature flow","authors":"Masaya Kawamura","doi":"10.14492/hokmj/1607936536","DOIUrl":"https://doi.org/10.14492/hokmj/1607936536","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":"49 1","pages":"431-450"},"PeriodicalIF":0.5,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43183094","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}
Pub Date : 2020-10-01DOI: 10.14492/hokmj/1607936535
Yuichiro Hoshi
— In the present paper, we study profinite groups of PIPSC-type, i.e., abstract profinite groups isomorphic to the extensions determined by outer representations of PIPSCtype. In particular, we establish a “group-theoretic” algorithm for constructing, from a profinite group of PIPSC-type that is noncuspidal, a certain profinite graph.
{"title":"Reconstruction of profinite graphs from profinite groups of PIPSC-type","authors":"Yuichiro Hoshi","doi":"10.14492/hokmj/1607936535","DOIUrl":"https://doi.org/10.14492/hokmj/1607936535","url":null,"abstract":"— In the present paper, we study profinite groups of PIPSC-type, i.e., abstract profinite groups isomorphic to the extensions determined by outer representations of PIPSCtype. In particular, we establish a “group-theoretic” algorithm for constructing, from a profinite group of PIPSC-type that is noncuspidal, a certain profinite graph.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":"49 1","pages":"399-430"},"PeriodicalIF":0.5,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41566458","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}
Pub Date : 2020-10-01DOI: 10.14492/hokmj/1607936539
Makoto Nakamura, Yuya Sato
{"title":"Remarks on global solutions for the semilinear diffusion equation in the de Sitter spacetime","authors":"Makoto Nakamura, Yuya Sato","doi":"10.14492/hokmj/1607936539","DOIUrl":"https://doi.org/10.14492/hokmj/1607936539","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":"49 1","pages":"481-508"},"PeriodicalIF":0.5,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44856196","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}
Pub Date : 2020-10-01DOI: 10.14492/hokmj/1607936533
Gopal Datt, Shesh Kumar Pandey
{"title":"Slant Toeplitz operators on the Lebesgue space of $n$-dimensional torus","authors":"Gopal Datt, Shesh Kumar Pandey","doi":"10.14492/hokmj/1607936533","DOIUrl":"https://doi.org/10.14492/hokmj/1607936533","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":"49 1","pages":"363-389"},"PeriodicalIF":0.5,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47252674","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 consider the Pauli--Fierz model, which describes a particle (an electron) coupled to the quantized electromagnetic field and limit the number of photons to less than 2. By computing red{the resolvent explicitly}, we located the spectrum of the Hamiltonian mass. Our results do not depend on the coupling constant $e$ nor on the infrared cutoff parameter $R$.
{"title":"Non-relativistic Pauli–Fierz Hamiltonian for less than two photons","authors":"D. Dayantsolmon, A. Galtbayar","doi":"10.14492/hokmj/2019-164","DOIUrl":"https://doi.org/10.14492/hokmj/2019-164","url":null,"abstract":"We consider the Pauli--Fierz model, which describes a particle (an electron) coupled to the quantized electromagnetic field and limit the number of photons to less than 2. By computing red{the resolvent explicitly}, we located the spectrum of the Hamiltonian mass. Our results do not depend on the coupling constant $e$ nor on the infrared cutoff parameter $R$.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46813977","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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