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Jun Masamune

Section

Graduate School of Science

Job title

Professor

Degree

博士（情報科学）（東北大学）
修士（数学）（東北大学）

researchmap

https://researchmap.jp/jmas

J-GLOBAL ID

201301037648451980

e-Rad No.

50706538

Research History 5

2022/04 - Present

Tohoku University　Graduate School of Science Department of Mathematics　Professor
2016/09 - 2022/03

Hokkaido University　Hokkaido University
2013/04 - 2016/09

Tohoku University
2009/08 - 2013/03

The Pennsylvania State University
2006/08 - 2009/05

Worcester Polytechnic Institutes　Department of Mathematical Sciences

Professional Memberships 2

一般社団法人日本機械学会
一般社団法人日本数学会

Research Interests 1

global analysis, homogenization theory, Riemannian geometry, Riemannian manifolds, infinite graphs, Laplace-Beltrami operator, Dirichlet forms, non-local operators, heat kernels, Liouville property, Mosco convergence, H-convergence

Research Areas 1

Natural sciences / Geometry /

Awards 3

Paper

2023/07　The Japan Society for Industrial and Applied Mathematics
日本機械学会賞（論文）

2021/03　日本機械学会　幾何学的特徴量に対する偏微分方程式系に基づく幾何学的特徴制約付きトポロジー最適化（積層造形における幾何学的特異点を考慮したオーバーハング制約法）
全学教育貢献賞

2014/01　東北大学

Papers 31

PDE methods for extracting normal vector fields and distance functions of shapes Peer-reviewed

Takahiro Hasebe, Jun Masamune, Hiroshi Teramoto, Takayuki Yamada

Tohoku Series of Mathematical Science, Springer　2026
Essential self-adjointness of the Laplacian on weighted graphs: harmonic functions, stability, characterizations and capacity Peer-reviewed

Atsushi Inoue, Sean Ku, Jun Masamune, Radoslaw K. Wojciechowski

28　(12)　1-43　2025
Construction of signed distance functions with an elliptic equation

Takahiro Hasebe, Jun Masamune, Tomoyuki Oka, Kota Sakai, Takayuki Yamada

arXiv　1-19　2024
Removable sets and L^p-uniqueness on manifolds and metric measure spaces Peer-reviewed

Nonlinear Analysis　234　2023
Intrinsic ultracontractivity for domains in negatively curved manifolds Peer-reviewed

Michiel van den Berg, Hiroaki Aikawa, Jun Masamune

Computational Mathematics and Function Theory　2021/09
Essential self-adjointness and the 𝐿2-Liouville property Peer-reviewed

Bobo Hua, Jun Masamune, Radosław, K. Wojciechowski

Journal of Fourier Analysis and Applications　27　2021/03
Construction of Normal Vector Field Using the Partial Differential Equations Peer-reviewed

Hasebe Takahiro, Kuroda Hirotoshi, Teramoto Hiroshi, Masamune Jun, Yamada Takayuki

Transactions of the Japan Society for Industrial and Applied Mathematics　30　(3)　249-258　2020
Publisher: The Japan Society for Industrial and Applied Mathematics
DOI： 10.11540/jsiamt.30.3_249 　

eISSN： 2424-0982

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Abstract. This article proves that each solution of Yamada’s partial differential equation and thermal equation gives normal vector filed of shapes. First, each problem setting is defined and numerical solutions of the equations are provided using the Finite Element Method. Next, each theorem is given and proved.
A generalized conservation property for the heat semigroup on weighted manifolds Peer-reviewed

Jun Masamune, Marcel Schmidt

Mathematische Annalen　377　1673-1710　2020
H-compactness of elliptic operators on weighted Riemannian manifolds Peer-reviewed

Helmer Hoppe, Jun Masamune, Stefan Neukamm

Interdisciplinary Information Sciences　25　(2)　161-191　2019
Topology optimization with geometrical feature constraints based on the partial differential equation system for geometrical features (Overhang constraints considering geometrical singularities in additive manufacturing) Peer-reviewed

Takayuki YAMADA, Jun MASAMUNE, Hiroshi TERAMOTO, Takahiro HASEBE, Hirotoshi KURODA

Transactions of the JSME (in Japanese)　85　(877)　19-00129　2019
Publisher: Japan Society of Mechanical Engineers
DOI： 10.1299/transjsme.19-00129 　

eISSN： 2187-9761

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This paper aims to develop a scheme for geometrical feature constraints in topology optimization for Additive Manufacturing (AM) without support structures based on the Partial Differential Equation (PDE) of geometrical shape features. To begin with, the basic concept of topology optimization and a level set-based topology optimization method are briefly described. Second, the PDE system for geometrical shape features is formulated. Here, aspects of the distribution of state variables are discussed using an analytical solution of the PDE. Based on the discussion, a function indicating the extended normal vector including geometrical singularity points is formulated. Third, geometrical requirements of product shape in AM without support structures – the so-called overhang constraint – are clarified in two-dimensions. A way of extending of the proposed concept to three-dimensional problems is also clarified. Additionally, geometrical singularities in the overhang constraint are discussed. Based on the PDE system and the clarified geometrical requirements, the overhang constraint including geometrical singularities is formulated. A topology optimization problem of the linear elastic problem is formulated considering the overhang constraint. A level set-based topology optimization algorithm is constructed where the Finite Element Method (FEM) is used to solve the governing equation of the linear elastic problem and the PDE, and to update the level set function. Finally, two-dimensional numerical examples are provided to confirm the validity and utility of the proposed method.
Global properties of Dirichlet forms in terms of Green's formula Peer-reviewed

Sebastian Haeseler, Matthias Keller, Daniel Lenz, Jun Masamune, Marcel Schmidt

Calculus of Variations and Partial Differential Equations　56　(5)　2017/10

DOI： 10.1007/s00526-017-1216-7 　

ISSN： 0944-2669

eISSN： 1432-0835
Endothelial monolayer permeability under controlled oxygen tension Peer-reviewed

Kenichi Funamoto, Daisuke Yoshino, Kento Matsubara, Ioannis K. Zervantonakis, Kiyoe Funamoto, Masafumi Nakayama, Jun Masamune, Yoshitaka Kimura, Roger D. Kamm

Integrative Biology　9　(6)　529-538　2017/06

DOI： 10.1039/c7ib00068e 　

ISSN： 1757-9694

eISSN： 1757-9708
Probabilistic characterizations of essential self-adjointness and removability of singularities Peer-reviewed

Michael Hinz, Seunghyun Kang, Jun Masamune

Science Journal of Volgograd State University. Mathematics　2017
Parabolicity and stochastic completeness of manifolds in terms of the Green formula Peer-reviewed

Alexander Grigor'yan, Jun Masamune

Journal de Mathématiques Pures et Appliquées　100　(5)　607-632　2013/11

DOI： 10.1016/j.matpur.2013.01.015 　

ISSN： 0021-7824

eISSN： 1776-3371
A note on self-adjoint extensions of the Laplacian on weighted graphs Peer-reviewed

Xueping Huang, Matthias Keller, Jun Masamune, Radoslaw K. Wojciechowski

Journal of Functional Analysis　265　(8)　1556-1578　2013/10

DOI： 10.1016/j.jfa.2013.06.004 　

ISSN： 0022-1236
On the conservativeness and the recurrence of symmetric jump-diffusions Peer-reviewed

Jun Masamune, Toshihiro Uemura, Jian Wang

Journal of Functional Analysis　263　(12)　3984-4008　2012/12
On stochastic completeness of jump processes Peer-reviewed

Alexander Grigor'yan, Xueping Huang, Jun Masamune

Mathematische Zeitschrift　271　(3-4)　1211-1239　2012/08

DOI： 10.1007/s00209-011-0911-x 　

ISSN： 0025-5874
On an inclusion of the essential spectrum of Laplacians under non-compact change of metric Peer-reviewed

Jun Masamune

Proceedings of the American Mathematical Society　140　(3)　1045-1052　2012/03
Mosco-convergence and Wiener measures for conductive thin boundaries Peer-reviewed

Jun Masamune

Journal of Mathematical Analysis and Applications　384　504-526　2011/12
Lp‐Liouville property for non‐local operators Peer-reviewed

Jun Masamune, Toshihiro Uemura

Mathematische Nachrichten　284　(17-18)　2249-2267　2011/12
Conservation property of symmetric jump processes Peer-reviewed

Jun Masamune, Toshihiro Uemura

Annales de l’Institut Henri Poincaré　47　(3)　650-662　2011/04
A Liouville property and its application to the Laplacian of an infinite graph Peer-reviewed

Jun Masamune

Contemporary Mathematics　484　103-115　2009
Vanishing and conservativeness of harmonic forms of a non-compact CR manifold Peer-reviewed

Jun Masamune

Rendiconti Lincei Matematica e Applicazioni　19　(2)　79-102　2008/06
The Serre duality theorem for a non-compact weighted CR Manifold Peer-reviewed

Mitsuhiro Itoh, Jun Masamune, Takanari Saotome

Proceedings of the American Mathematical Society　136　(10)　3539-3548　2008
The Liouville property of unbounded fractal layers Peer-reviewed

Maria Rosaria Lancia, Jun Masamune

Complex Variables and Elliptic Equations　53　(4)　297-306　2008
Conservative principle for differential forms Peer-reviewed

Jun Masamune

Rendiconti Lincei Matematica e Applicazioni　18　351-358　2007
Analysis of the Laplacian of an incomplete manifold with almost polar boundary Peer-reviewed

Rendiconti di Matematica e delle sue Applicazioni　25　109-125　2005
Essential self-adjointness of a sublaplacian via heat equation Peer-reviewed

Jun Masamune

Communications in Partial Differential Equations　30　(11)　1595-1609　2005

DOI： 10.1080/03605300500299935 　

ISSN： 0360-5302
Discrete spectrum and Weyl's asymptotic formula for incomplete manifolds

Jun Masamune, Wayne Rossman

Advanced Studies in Pure Mathematics　34　2002
Publisher: Mathematical Society of Japan
DOI： 10.2969/aspm/03410219 　

ISSN： 0920-1971
Cauchy-Riemann orbifolds Peer-reviewed

Sorin Dragomir, Jun Masamune

Tsukuba journal of mathematics　26　(2)　351-386　2002
Essential self adjointness of Laplacians on Riemannian manifolds with fractal boundary Peer-reviewed

Jun Masamune

Communications in Partial Differential Equations　24　(3-4)　749-757　1999

ISSN： 0360-5302

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Misc. 4

2D34 Investigation of Permeability of Endothelial Cell Monolayer by Using Microfluidic Device with Controllability of Oxygen Tension

MATSUBARA Kento, FUNAMOTO Kenichi, ZERVANTONAKIS Ioannis K., FUNAMOTO Kiyoe, ITO Takuya, MASAMUNE Jun, KIMURA Yoshitaka, HAYASE Toshiyuki, KAMM Roger D.

The Proceedings of the Bioengineering Conference Annual Meeting of BED/JSME　2016.28　_2D34-1_-_2D34-5_　2016
Publisher: The Japan Society of Mechanical Engineers
DOI： 10.1299/jsmebio.2016.28._2d34-1_ 　

eISSN： 2424-2829

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Permeability changes of an endothelial cell (EC) monolayer are related to many diseases. This study evaluated permeability of the EC monolayer under normoxia and hypoxia by using fluorescent dextrans of two different molecular weights in a microfluidic device with controllability of oxygen tension. As the results, permeability of the EC monolayer increased by hypoxic exposure, and the increase of the permeability measured by fluorescent dextran of 10 kDa was smaller than that measured by fluorescent dextran of 70 kDa. The results indicated that the size-selectivity of EC monolayer became weaken under hypoxia.
Dependency of polarity on the drift of Brownian motion of a compact manifold (Regularity and Singularity for Partial Differential Equations with Conservation Laws)

Masamune Jun

(1962)　45-49　2015/08

ISSN： 1880-2818
1C34 Evaluation of permeability of endothelial monolayer by using hypoxia microfluidic device

MATSUBARA Kento, FUNAMOTO Kenichi, Zervantonakis Ioannis, FUNAMOTO Kiyoe, ITO Takuya, MASAMUNE Jun, KIMURA Yoshitaka, HAYASE Toshiyuki, KAMM Roger

The Proceedings of the Bioengineering Conference Annual Meeting of BED/JSME　2015.27　121-122　2015
Publisher: The Japan Society of Mechanical Engineers
DOI： 10.1299/jsmebio.2015.27.121 　

eISSN： 2424-2829
B106 Measurement of permeability of endothelial monolayer under hypoxia by using microfluidic device

MATSUBARA Kento, FUNAMOTO Kenichi, ZERVANTONAKIS Ioannis K., FUNAMOTO Kiyoe, ITO Takuya, MASAMUNE Jun, KIMURA Yoshitaka, HAYASE Toshiyuki, KAMM Roger D.

The Proceedings of the JSME Conference on Frontiers in Bioengineering　2015.26　35-36　2015
Publisher: The Japan Society of Mechanical Engineers
DOI： 10.1299/jsmebiofro.2015.26.35 　

eISSN： 2424-2810

Books and Other Publications 1

感じる数学〜ガリレイからポアンカレまで〜

数学みえる化プロジェクト

共立出版　2022/08

ISBN: 9784320114784

Presentations 8

Construction of Signed Distance Functions with an Elliptic Equation Invited

Jun Masamune

The 3rd Taiwan-Japan International Workshop on Applied Mathematics　2025/05/02
Recent progress on the essential selfadjointness of the Laplacians on Riemannian manifolds and weighted graphs Invited

HeKKSaGOn Mathematics Meeting 2024　2024/11/25
Capacities and essential self adjointness of the Laplacian Invited

正宗淳

Geometry and Probability　2023/02/14
On convergence of elliptic operators on a Riemannian manifold

正宗淳

The 14th SNU-HU Symposium of Mathematics 2020　2022/11/14
A generalized conservation property for the heat semigroup on weighted manifolds Invited

正宗淳

Analysis Seminar, ドレスデン工科大学　2019/06/16
A conservation property of Brownian motion with killing of a Riemannian manifold International-presentation Invited

Jun Masamune

Analysis and PDEs on Manifolds　2017/09/21
Generalized conservation property International-presentation Invited

Jun Masamune

Japanese-German Open Conference on Stochastic Analysis 2017　2017/09/04
H-convergence on Riemannian manifolds International-presentation Invited

Jun Masamune

Analysis and Geometry on Graphs and Manifolds　2017/07/31

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Research Projects 8

Modelings of Shape Design Based on the Mathematics

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Transformative Research Areas (B)

2023/04 - 2026/03
数学に基づいた構造最適化における基礎理論の構築とボトムアップ型展開

正宗淳

Offer Organization: 日本学術振興会

System: 科学研究費助成事業学術変革領域研究(B)

Category: 学術変革領域研究(B)

Institution: 東北大学

2023/04 - 2026/03
一般のリーマン多様体のラプラシアンの自己共役性ならびにリュービル性

正宗淳

Offer Organization: 日本学術振興会

System: 科学研究費助成事業基盤研究(C)

Category: 基盤研究(C)

Institution: 北海道大学

2018/04 - 2024/03

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多様体のラプラシアンの本質的自己共役性が局所的性質をもつことを明らかにした．本研究課題の前々年度の研究成果により，ある状況下では本質的自己共役性は特異集合の容量で特徴付されることが分かった．その容量を決定する1-調和関数は空間全体の情報を持っており局所性を持たないため，多様体のラプラシアンの本質的自己共役性が局所的性質をもつことは不明であった．そこで部分積分の境界項が消えるという本質的自己共役性の特徴付を用いて，多様体のラプラシアンの本質的自己共役性が局所的性質であることを証明した．この結果を具体的に述べると「リーマン多様体がそれらの共通部分がその境界になるように二つの境界付き多様体に分解され，また，その境界がコンパクトであるならば，全体の多様体のラプラシアンが本質的自己共役であることと，それら部分多様体のノイマン境界条件をもつラプラシアンが共に本質的自己共役であることは同値である」である．この研究とは別に，リーマン多様体にレイリッヒの埋め込み定理が成立するような多様体を付け加えても，もしくはリーマン多様体からレイリッヒの埋め込み定理が成立する部分多様体を取り除いてもラプラシアンの本質的スペクトルが変わらないことを証明した．これは本質的スペクトルに関する新たな不変量の発見である．コンパクト作用素の摂動について本質的スペクトルは不変量になっていることはよく知られているが，今回の研究成果により空間自体が変形しても同様なことが成立することが分かった．これと先に述べた本質的自己共役性を組み合わせることで，本質的自己共役性をL^2リュービル性を用いて証明するレシピが完成した．この研究成果については既にいくつかのセミナーで報告をした．
Consistent method for optimal design and manufacturing based on the unified geometrical feature evaluation by the partial differential equation

Yamada Takayuki

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

Category: Grant-in-Aid for Scientific Research (B)

2019/04/01 - 2022/03/31

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In this study, the geometric constraints required from the manufacturing process are formulated by using partial differential equations. These partial differential equations are called fictitious physical model because it is a fictitious field introduced to represent manufacturability. We also integrated it with the topology optimization method to create a new design method that integrates design and production. Furthermore, by considering assemblability, we proposed a method that also allows topology optimization of mechanical structures composed of multiple parts.
複雑領域のポテンシャル解析の深化―非線形PDEと理想境界への応用

相川弘明, 志賀啓成, 倉田和浩, 須川敏幸, 平田賢太郎, 鈴木紀明, 正宗淳, 利根川吉廣, 木上淳, 加須栄篤, 堀田一敬, 野瀬敏洋

Offer Organization: 日本学術振興会

System: 科学研究費助成事業基盤研究(A)

Category: 基盤研究(A)

2017/04/01 - 2021/03/31

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Intrinsic ultracontractivity を応用して，Lipschitz領域やJohn領域をベースにするシリンダー上の熱方程式の優解の可積分性を与え，正値優調和関数の可積分性を放物型に拡張した．境界条件付きの一般化された平均曲率流であるBrakke流の時間大域解存在を証明した．非線形無限ネットワークのラプラシアンを研究し，リウヴィユ性，カシミンスキー条件，Omori-Yauタイプの弱最大値原理などの同値性や正値優調和関数の最小増大度，具体的判定条件について成果を得た．パターン形成に関わるFitzHugh反応拡散系のヘテロクリニック定常解の構成とエネルギー漸近展開を行なった. 3波相互作用を持つ非線形シュレディンガー方程式系に現れる変分問題のエネルギー最小解の存在とその漸近挙動に関する知見を得た.領域の境界の一様完全性や領域の一様性の新しいポテンシャル論的特徴づけを得た．有界Lipschitz領域において，半線形楕円型方程式の正値解に対する境界Harnack原理を，Greenポテンシャルの評価と反復法を用いて示した．孤立境界特異点をもつ正値解の漸近挙動および除去可能性について考察した．自己相似集合の Ahlfors regular conformal dimension と対応する無限グラフの parabolic index の関係および自己相似集合上への p-energy の構成について研究し，parabolic index とAhlfors regular conformal dimension の間の不等式などを示した．ポテンシャル付きの二階楕円型作用素の保存則を定式化して，対応するカシミンスキー・テストを証明した．均質化法のH収束理論を多様体に拡張し，作用素の収束を実現するリーマン計量ならびに複雑な空間への収束する多様体の族の変形理論を構築した．
Stochastic homogenization for uncertainty quantification in multiscale analysis

Masamune Jun

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

Category: Grant-in-Aid for Scientific Research (C)

Institution: Hokkaido University

2016/07/19 - 2019/03/31

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We established a homogenization theory, more precisely, the H-convergence theory on general Riemannian manifolds. The main theoretical result in the project was to show a compactness result for a family of diffusion coefficients and that H-convergence implies Mosco convergence. As a consequence, there is a weak converging sequence of Brownian motions provided the tightness. As applications of homogenization theory, we constructed a mathematical model for micro-fibers and analyzed it, and, discussed the results obtain by the averaging methods and homogenization theory. We also studied the Carbon Fiber Reinforced Polymer Composites (CFRP) using the homogenization theory and numerical analysis. In particular, we proposed several new methods to evaluate the strengths of CFRP and conducted tests using numerical methods combined with homogenization theory.
Global properties and the theory of convergences of diffusion processes of measure spaces

Masamune Jun

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

Category: Grant-in-Aid for Scientific Research (C)

2014/04/01 - 2018/03/31

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In this research project, we aim to develop the global analysis of diffusion processes on measure spaces associated with some Markov processes. The main results in this projects are (1) conservation property and recurrence of general Markov processes in terms of Green's formula (2) Characterizations of Liouville type problems of Riemannian manifolds and graphs (3) Generalized conservation property of Brownian motion with killing inside and its characterizations (4) Probabilisitic characterization of the essential selfadjointness of the Laplacian of Euclidean space removed a compact set.
測度空間における拡散現象の大域解析

正宗淳

Offer Organization: 日本学術振興会

System: 科学研究費助成事業研究活動スタート支援

Category: 研究活動スタート支援

Institution: 東北大学

2013/08/30 - 2015/03/31

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本年度は，以下の１，２，３の研究を行った．１．測度空間上で，ディリクレ形式に対してグリーンの公式を定式化し，さらに，マルコフ過程の保存性と再帰性をグリーンの公式による特徴付けを行った．これらの性質は空間の無限遠の大きさと密接な関係があることが知られている．そこで，本研究では，無限遠が小さければ，ある関数のクラスに対してはグリーンの公式の境界項が消えると考え，保存性と再帰性に対応する，それぞれの関数のクラスを完全に決定した．さらに，これらの関数のクラスを多様体，グラフ，量子グラフの場合に詳しく調べた．本研究は，D. Lenz（イエナ・ドイツ）との共同研究であり，現在執筆中である．２．測度空間の作用素の拡張の問題を，特に重要な例である，離散シュレディンガー作用素に対して調べた．とりわけ，Colin de Verdiereらによる最近の重要な結果を拡張した．また，離散シュレディンガー作用素の基底状態変換公式を一般の局所有限な無限グラフに拡張し，両方の符号を持つポテンシャルを持つ離散シュレディンガー作用素の正定値性を得た．３．境界付きコンパクト・リーマン多様体上で定義された，ドリフトとポテンシャルを持つ二階の微分作用素の解の挙動を調べた．解の一意性と正則性を示し，さらに，正定値性とマルコフ性が成立する為のポテンシャルおよび第三種境界条件を特徴付けた．本研究は，M. Bordoni（ローマ・イタリア）とS. Gallot（グレノーブル・フランス）の共同研究であり，現在執筆中である．

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Social Activities 2

NPO 数学みえる化プロジェクト

2023/04 - Present
数学展「感じる数学 Tangible Math 〜ガリレイからポアンカレまで〜」

2022/07/30 - 2022/09/25

Academic Activities 8

Journal of Tohoku Mathematical Journal（編集委員）

2023 - Present

Activity type: Scientific advice/Review
Journal of Theoretical Probability（編集委員）

2023 - Present

Activity type: Scientific advice/Review
ブラソフ方程式とマックスウェル方程式、プラズマの数理 III（組織委員）

東北大学理学研究科数学専攻

2025/06/03 - 2025/06/03

Activity type: Academic society, research group, etc.
2024 Open German-Japanese Conference on Stochastic Analysis and Applications（Scientific Committee）

2024/09/09 - 2024/09/13

Activity type: Academic society, research group, etc.
ブラソフ方程式とマックスウェル方程式、プラズマの数理 II（組織委員）

東北大学理学研究科数学専攻

2024/06/28 - 2024/06/29

Activity type: Academic society, research group, etc.
ブラソフ方程式とマックスウェル方程式、プラズマの数理（組織委員）

東京大学

2024/03/27 - 2024/03/29

Activity type: Academic society, research group, etc.
RIMS合宿型セミナー「均質化法と非局所型作用素」（代表）

北海道、ニセコ

2023/08/07 - 2023/08/11

Activity type: Academic society, research group, etc.
離散微分型式と均質化法の融合による異方性を持つ場の数値計算手法の開発と産業への応用

九州大学マス・フォア・インダストリ研究所

2023/05/12 - 2023/05/14

Activity type: Academic society, research group, etc.

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