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過去の記録 ～05/22｜本日 05/23 | 今後の予定 05/24～
2013年02月28日(木)
GCOEセミナー
16:00-17:00 数理科学研究科棟(駒場) 270号室
Mourad Choulli 氏 (Univ. Lorraine)
Stability of the determination of the surface impedance of an
obstacle from the scattering amplitude (ENGLISH)
Mourad Choulli 氏 (Univ. Lorraine)
Stability of the determination of the surface impedance of an
obstacle from the scattering amplitude (ENGLISH)
[ 講演概要 ]
In this joint work with Mourad Bellassoued and Aymen Jbalia, we prove a stability estimate of logarithmic type for the inverse problem consisting in the determination of the surface impedance of an obstacle from the scattering amplitude. We present a simple and direct proof which is essentially based on an elliptic Carleman inequality.
In this joint work with Mourad Bellassoued and Aymen Jbalia, we prove a stability estimate of logarithmic type for the inverse problem consisting in the determination of the surface impedance of an obstacle from the scattering amplitude. We present a simple and direct proof which is essentially based on an elliptic Carleman inequality.
GCOEセミナー
17:00-18:00 数理科学研究科棟(駒場) 270号室
Kazufumi Ito 氏 (North Carolina State Univ.)
$L_0$ optimization and Lagrange multiplier (ENGLISH)
Kazufumi Ito 氏 (North Carolina State Univ.)
$L_0$ optimization and Lagrange multiplier (ENGLISH)
[ 講演概要 ]
$L_p$ optimization with $p ¥in[0,1)$ is investigated. The difficulty of natural lack of weak lower-semicontinuity is addressed and the Lagrange multiplier theory is developed. Existence results and necessary optimality conditions are obtained, and the semismooth Newton method using the primal-dual active set is developed. The theory and algorithm are demonstrated for the case of optimal control problems. A maximum principle is derived and existence of controls, in some cases relaxed controls, is proved.
$L_p$ optimization with $p ¥in[0,1)$ is investigated. The difficulty of natural lack of weak lower-semicontinuity is addressed and the Lagrange multiplier theory is developed. Existence results and necessary optimality conditions are obtained, and the semismooth Newton method using the primal-dual active set is developed. The theory and algorithm are demonstrated for the case of optimal control problems. A maximum principle is derived and existence of controls, in some cases relaxed controls, is proved.
2013年02月27日(水)
GCOEセミナー
10:00-11:00 数理科学研究科棟(駒場) 270号室
Dietmar Hoemberg 氏 (Weierstrass Institute)
Sufficient optimality conditions for a semi-linear parabolic system related to multiphase steel production (ENGLISH)
Dietmar Hoemberg 氏 (Weierstrass Institute)
Sufficient optimality conditions for a semi-linear parabolic system related to multiphase steel production (ENGLISH)
[ 講演概要 ]
Multiphase steels combine good formability properties with high strength and have therefore become important construction materials, especially in automotive industry. The standard process route is hot rolling with subsequent controlled cooling to adjust the desired phase mixture. In the first part of the talk a phenomenological model for the austenite ferrite phase transition is developed in terms of a nucleation and growth process, where the growth rate depends on the carbon concentration in austenite. The approach allows for further extensions, e.g., to account for a speed up of nucleation due to deformation of austenite grains. The model is coupled with an energy balance to describe the phase transitions on a run-out table after hot rolling. Here, the most important control parameters are the amount of water flowing per time and the feed velocity of the strip. The spatial flux profile of the water nozzles has been identified from experiments.
Since the process window for the adjustment of the phase composition is very tight the computation of optimal process parameters is an important task also in practice. This is discussed in the second part of the talk using a classical optimal control approach, where a coefficient in the Robin boundary condition acts as the control. I will discuss necessary and sufficient optimality conditions, describe a SQP-approach for its numerical solution and conclude with some numerical results.
(joint work with K. Krumbiegel and N. Togobytska, WIAS)
Multiphase steels combine good formability properties with high strength and have therefore become important construction materials, especially in automotive industry. The standard process route is hot rolling with subsequent controlled cooling to adjust the desired phase mixture. In the first part of the talk a phenomenological model for the austenite ferrite phase transition is developed in terms of a nucleation and growth process, where the growth rate depends on the carbon concentration in austenite. The approach allows for further extensions, e.g., to account for a speed up of nucleation due to deformation of austenite grains. The model is coupled with an energy balance to describe the phase transitions on a run-out table after hot rolling. Here, the most important control parameters are the amount of water flowing per time and the feed velocity of the strip. The spatial flux profile of the water nozzles has been identified from experiments.
Since the process window for the adjustment of the phase composition is very tight the computation of optimal process parameters is an important task also in practice. This is discussed in the second part of the talk using a classical optimal control approach, where a coefficient in the Robin boundary condition acts as the control. I will discuss necessary and sufficient optimality conditions, describe a SQP-approach for its numerical solution and conclude with some numerical results.
(joint work with K. Krumbiegel and N. Togobytska, WIAS)
2013年02月23日(土)
保型形式の整数論月例セミナー
13:30-16:00 数理科学研究科棟(駒場) 123号室
平野幹 氏 (愛媛大学) 13:30-14:30
Ramanujan巡回グラフとHardy-Littlewood予想 (JAPANESE)
例外型実リー群$G_2$の一般化ホウィッタカー関数についてのある考察 (JAPANESE)
平野幹 氏 (愛媛大学) 13:30-14:30
Ramanujan巡回グラフとHardy-Littlewood予想 (JAPANESE)
[ 講演概要 ]
TBA
成田宏秋 氏 (熊本大学) 15:00-16:00TBA
例外型実リー群$G_2$の一般化ホウィッタカー関数についてのある考察 (JAPANESE)
[ 講演概要 ]
TBA
TBA
2013年02月22日(金)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 118号室
Stefaan Vaes 氏 (KU Leuven)
II$_1$ factors with a unique Cartan subalgebra (ENGLISH)
Stefaan Vaes 氏 (KU Leuven)
II$_1$ factors with a unique Cartan subalgebra (ENGLISH)
FMSPレクチャーズ
16:30-18:00 数理科学研究科棟(駒場) 118号室
Stefaan Vaes 氏 (KU Leuven)
II_1 factors with a unique Cartan subalgebra (ENGLISH)
Stefaan Vaes 氏 (KU Leuven)
II_1 factors with a unique Cartan subalgebra (ENGLISH)
GCOEセミナー
16:00-17:00 数理科学研究科棟(駒場) 270号室
Fatiha Alabau-Boussouira 氏 (Université de Lorraine)
Exact insensitizing controls for scalar wave equations and control of coupled systems (ENGLISH)
Fatiha Alabau-Boussouira 氏 (Université de Lorraine)
Exact insensitizing controls for scalar wave equations and control of coupled systems (ENGLISH)
[ 講演概要 ]
The control of scalar PDE's such as the wave or heat equation is by now well-understood.
It consists in building a source term which can drive the solution from a given initial state to a final (reachable) desired state.
Exact insensitizing control are exact controls which should satisfy an additional requirement:
they should be robust to small unknown perturbations of the initial data. More precisely, they should, as exact controls, drive the solution to the desired state, but they also should insensitize a given measure of the solution to such perturbations. One can show that the existence of exact insensitizing controls for a scalar wave equation is equivalent to the exact controllability by a single control of a system of two wave equations coupled in cascade.
We shall present in this talk the challenging issues and give some recent results and perspectives for the exact insensitizing control of scalar wave equations. We shall also give some more general results on the controllability of coupled systems by a reduced number of controls.
The control of scalar PDE's such as the wave or heat equation is by now well-understood.
It consists in building a source term which can drive the solution from a given initial state to a final (reachable) desired state.
Exact insensitizing control are exact controls which should satisfy an additional requirement:
they should be robust to small unknown perturbations of the initial data. More precisely, they should, as exact controls, drive the solution to the desired state, but they also should insensitize a given measure of the solution to such perturbations. One can show that the existence of exact insensitizing controls for a scalar wave equation is equivalent to the exact controllability by a single control of a system of two wave equations coupled in cascade.
We shall present in this talk the challenging issues and give some recent results and perspectives for the exact insensitizing control of scalar wave equations. We shall also give some more general results on the controllability of coupled systems by a reduced number of controls.
GCOEセミナー
17:00-18:00 数理科学研究科棟(駒場) 270号室
Piermarco Cannarsa 氏 (Univ. Roma II)
Carleman estimates and Lipschitz stability for Grushin-type operators (ENGLISH)
Piermarco Cannarsa 氏 (Univ. Roma II)
Carleman estimates and Lipschitz stability for Grushin-type operators (ENGLISH)
[ 講演概要 ]
The Baouendi-Grushin operator is an important example of a degenerate elliptic operator that has strong connections with almost-riemannian structures. It is also the infinitesimal generator of a strongly continuous semigroup on Lebesgue spaces with very interesting properties from the point of view of control theory. Such properties will be discussed in this lecture, starting with approximate and null controllability.
We will then address the inverse source problem for these operators deriving a Lipschitz stability result.
The Baouendi-Grushin operator is an important example of a degenerate elliptic operator that has strong connections with almost-riemannian structures. It is also the infinitesimal generator of a strongly continuous semigroup on Lebesgue spaces with very interesting properties from the point of view of control theory. Such properties will be discussed in this lecture, starting with approximate and null controllability.
We will then address the inverse source problem for these operators deriving a Lipschitz stability result.
2013年02月21日(木)
FMSPレクチャーズ
15:00-16:00 数理科学研究科棟(駒場) 056号室
Michael Mascagni 氏 (Florida State University
)
Monte Carlo Methods for Partial Differential Equations: Computing Permeability
(ENGLISH)
Michael Mascagni 氏 (Florida State University
)
Monte Carlo Methods for Partial Differential Equations: Computing Permeability
(ENGLISH)
[ 講演概要 ]
We present a brief overview of Monte Carlo methods for the solution of elliptic and parabolic partial differential equations (PDEs). We begin with a review of the Feynman-Kac formula, and its use in the probabilistic representation of the solutions of elliptic and parabolic PDEs. We then consider some specific Monte Carlo methods used for obtaining the solution of simple elliptic partial differential equations (PDEs) as part of exterior boundary value problems that arise in electrostatics and flow through porous media. These Monte Carlo methods use Feynman-Kac to represent the solution of the elliptic PDE at a point as the expected value of functionals of Brownian motion trajectories started at the point of interest. We discuss the rapid solution of these equations, in complex exterior geometries, using both the "walk on spheres" and "Greens function first-passage" algorithms. We then concentrate on methods for quickly computing the isotropic permeability using the "unit
capacitance" and "penetration depth'' methods. The first of these methods, requires computing a linear functional of the solution to an exterior elliptic PDE. Both these methods for computing permeability are simple, and provide accurate solutions in a few seconds on laptop-scale computers. We then conclude with a brief look at other Monte Carlo methods and problems that arise on related application areas.
We present a brief overview of Monte Carlo methods for the solution of elliptic and parabolic partial differential equations (PDEs). We begin with a review of the Feynman-Kac formula, and its use in the probabilistic representation of the solutions of elliptic and parabolic PDEs. We then consider some specific Monte Carlo methods used for obtaining the solution of simple elliptic partial differential equations (PDEs) as part of exterior boundary value problems that arise in electrostatics and flow through porous media. These Monte Carlo methods use Feynman-Kac to represent the solution of the elliptic PDE at a point as the expected value of functionals of Brownian motion trajectories started at the point of interest. We discuss the rapid solution of these equations, in complex exterior geometries, using both the "walk on spheres" and "Greens function first-passage" algorithms. We then concentrate on methods for quickly computing the isotropic permeability using the "unit
capacitance" and "penetration depth'' methods. The first of these methods, requires computing a linear functional of the solution to an exterior elliptic PDE. Both these methods for computing permeability are simple, and provide accurate solutions in a few seconds on laptop-scale computers. We then conclude with a brief look at other Monte Carlo methods and problems that arise on related application areas.
2013年02月19日(火)
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
畠中 英里 氏 (東京農工大学)
On the ring of Fricke characters of free groups (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
畠中 英里 氏 (東京農工大学)
On the ring of Fricke characters of free groups (JAPANESE)
[ 講演概要 ]
This is a joint work with Takao Satoh (Tokyo University of Science). We study a descending filtration of the ring of Fricke characters of a free group consisting of ideals on which the automorphism group of the free group naturally acts. Then by using it, we define a descending filtration of the automorphism group of a free group, and investigate a relation between it and the Andreadakis-Johnson filtration.
This is a joint work with Takao Satoh (Tokyo University of Science). We study a descending filtration of the ring of Fricke characters of a free group consisting of ideals on which the automorphism group of the free group naturally acts. Then by using it, we define a descending filtration of the automorphism group of a free group, and investigate a relation between it and the Andreadakis-Johnson filtration.
2013年02月18日(月)
GCOEセミナー
17:00-18:00 数理科学研究科棟(駒場) 270号室
Larisa A. Nazarova 氏 (Department
Institute of Mining Siberian Branch of Russian Academy of Sciences)
INVERSE PROBLEMS OF GEOMECHANICS AND ITS APPLICATION IN MINING AND GEOPHYSICS (ENGLISH)
Larisa A. Nazarova 氏 (Department
Institute of Mining Siberian Branch of Russian Academy of Sciences)
INVERSE PROBLEMS OF GEOMECHANICS AND ITS APPLICATION IN MINING AND GEOPHYSICS (ENGLISH)
[ 講演概要 ]
The communication devotes to the boundary, coefficient and mixed inverse problems in modeling solid mineral mining processes.
Direct and indirect methods for estimation of natural stress field components were compared.
Based on GPS data (South Siberia, 2000-2003) interpretation the possible indicator (sharp increase of horizontal strains increment in epicenter vicinity) of future strong seismic event was established.
The theoretical approach for evaluation of future earthquake focal parameters (hypocentre depth and fractal dimension of fault anomalous zone) was proposed. The approach is found on inverse problem solution by variation of daylight surface strains.
Using a viscoelastic model, a method is proposed to evaluating the equation-of-state parameters that describe deformation of structural units of the room-and-pillar implementation in bedded deposits composed of rocks developing rheological properties. The method is based on the inverse coefficient problem solution with the data on roof and floor convergence in stopes.
A method of day-to-day qualitative assessment of elastic and strength properties of backfill in flat bedded deposits has been developed on the basis of the solution of the coefficient inverse problem for a set of equations (quasi-static formulation) which describe deformation and failure of filling mass. Uniqueness of the solution only requires simultaneous minimization of two objective functions.
The communication devotes to the boundary, coefficient and mixed inverse problems in modeling solid mineral mining processes.
Direct and indirect methods for estimation of natural stress field components were compared.
Based on GPS data (South Siberia, 2000-2003) interpretation the possible indicator (sharp increase of horizontal strains increment in epicenter vicinity) of future strong seismic event was established.
The theoretical approach for evaluation of future earthquake focal parameters (hypocentre depth and fractal dimension of fault anomalous zone) was proposed. The approach is found on inverse problem solution by variation of daylight surface strains.
Using a viscoelastic model, a method is proposed to evaluating the equation-of-state parameters that describe deformation of structural units of the room-and-pillar implementation in bedded deposits composed of rocks developing rheological properties. The method is based on the inverse coefficient problem solution with the data on roof and floor convergence in stopes.
A method of day-to-day qualitative assessment of elastic and strength properties of backfill in flat bedded deposits has been developed on the basis of the solution of the coefficient inverse problem for a set of equations (quasi-static formulation) which describe deformation and failure of filling mass. Uniqueness of the solution only requires simultaneous minimization of two objective functions.
2013年02月16日(土)
東京無限可積分系セミナー
13:30-15:00 数理科学研究科棟(駒場) 117号室
Alexey Silantyev 氏 (Tokyo. Univ.)
Generalized Calogero-Moser type systems and Cherednik Algebras (ENGLISH)
Alexey Silantyev 氏 (Tokyo. Univ.)
Generalized Calogero-Moser type systems and Cherednik Algebras (ENGLISH)
[ 講演概要 ]
Calogero-Moser systems can be obtained using Dunkl operators, which
define the polynomial representation of the corresponding rational
Cherednik algebra. Parabolic ideals invariant under the action of the
Dunkl operators give submodules of Cherednik algebra. Considering the
corresponding quotient-modules one yields the generalized (or deformed)
Calogero-Moser systems. In the same way we construct the generalized
elliptic Calogero-Moser systems using the elliptic Dunkl operators
obtained by Buchstaber, Felder and Veselov. The Macdonald-Ruijsenaars
systems (difference (relativistic) Calogero-Moser type systems) can be
considered in terms of Double Affine Hecke Algebra (DAHA). We construct
appropriate submodules in the polynomial representation of DAHA, which
were obtained by Kasatani for some affine root systems. Considering the
corresponding quotient representation we derive the generalized
(deformed) Macdonald-Ruijsenaars systems for any affine root system,
which where obtained by Sergeev and Veselov for the A series. This is
joint work with Misha Feigin.
Calogero-Moser systems can be obtained using Dunkl operators, which
define the polynomial representation of the corresponding rational
Cherednik algebra. Parabolic ideals invariant under the action of the
Dunkl operators give submodules of Cherednik algebra. Considering the
corresponding quotient-modules one yields the generalized (or deformed)
Calogero-Moser systems. In the same way we construct the generalized
elliptic Calogero-Moser systems using the elliptic Dunkl operators
obtained by Buchstaber, Felder and Veselov. The Macdonald-Ruijsenaars
systems (difference (relativistic) Calogero-Moser type systems) can be
considered in terms of Double Affine Hecke Algebra (DAHA). We construct
appropriate submodules in the polynomial representation of DAHA, which
were obtained by Kasatani for some affine root systems. Considering the
corresponding quotient representation we derive the generalized
(deformed) Macdonald-Ruijsenaars systems for any affine root system,
which where obtained by Sergeev and Veselov for the A series. This is
joint work with Misha Feigin.
2013年02月08日(金)
講演会
10:30-11:30 数理科学研究科棟(駒場) 370号室
Zdzislaw Brzezniak 氏 (University of York)
Strong and weak solutions to stochastic Landau-Lifshitz equations (ENGLISH)
Zdzislaw Brzezniak 氏 (University of York)
Strong and weak solutions to stochastic Landau-Lifshitz equations (ENGLISH)
[ 講演概要 ]
I will speak about the existence of weak solutions (and the existence and uniqueness of strong solutions) to the stochastic Landau-Lifshitz equations for multi (and one)-dimensional spatial domains. I will also describe the corresponding Large Deviations principle and it's applications to a ferromagnetic wire.
The talk is based on a joint work with B. Goldys and T. Jegaraj.
I will speak about the existence of weak solutions (and the existence and uniqueness of strong solutions) to the stochastic Landau-Lifshitz equations for multi (and one)-dimensional spatial domains. I will also describe the corresponding Large Deviations principle and it's applications to a ferromagnetic wire.
The talk is based on a joint work with B. Goldys and T. Jegaraj.
博士論文発表会
09:45-11:00 数理科学研究科棟(駒場) 118号室
古場 一 氏 (東京大学大学院数理科学研究科)
Stability of Navier-Stokes-Boussinesq Type Systems（ナヴィエ・ストークス・ブジネスク型方程式の安定性） (JAPANESE)
古場 一 氏 (東京大学大学院数理科学研究科)
Stability of Navier-Stokes-Boussinesq Type Systems（ナヴィエ・ストークス・ブジネスク型方程式の安定性） (JAPANESE)
博士論文発表会
11:00-12:15 数理科学研究科棟(駒場) 118号室
大島 芳樹 氏 (東京大学大学院数理科学研究科)
Discrete branching laws of Zuckerman\\'s derived functor modulesZuckerman（導来関手加群の離散的分岐則） (JAPANESE)
大島 芳樹 氏 (東京大学大学院数理科学研究科)
Discrete branching laws of Zuckerman\\'s derived functor modulesZuckerman（導来関手加群の離散的分岐則） (JAPANESE)
博士論文発表会
11:00-12:15 数理科学研究科棟(駒場) 118号室
大島 芳樹 氏 (東京大学大学院数理科学研究科)
Discrete branching laws of Zuckerman\\'s derived functor modulesZuckerman（導来関手加群の離散的分岐則） (JAPANESE)
大島 芳樹 氏 (東京大学大学院数理科学研究科)
Discrete branching laws of Zuckerman\\'s derived functor modulesZuckerman（導来関手加群の離散的分岐則） (JAPANESE)
博士論文発表会
11:00-12:15 数理科学研究科棟(駒場) 118号室
大島 芳樹 氏 (東京大学大学院数理科学研究科)
Discrete branching laws of Zuckerman’s derived functor modules（Zuckerman導来関手加群の離散的分岐則） (JAPANESE)
大島 芳樹 氏 (東京大学大学院数理科学研究科)
Discrete branching laws of Zuckerman’s derived functor modules（Zuckerman導来関手加群の離散的分岐則） (JAPANESE)
博士論文発表会
13:00-14:15 数理科学研究科棟(駒場) 118号室
Uzun Mecit Kerem 氏 (東京大学大学院数理科学研究科)
Motivic Homology and Class Field Theory over p-adic Fields（p-進数体の上モチフィックホモロジーと類体論） (JAPANESE)
Uzun Mecit Kerem 氏 (東京大学大学院数理科学研究科)
Motivic Homology and Class Field Theory over p-adic Fields（p-進数体の上モチフィックホモロジーと類体論） (JAPANESE)
博士論文発表会
14:15-15:30 数理科学研究科棟(駒場) 118号室
植松 哲也 氏 (東京大学大学院数理科学研究科)
Uniform Representability of the Brauer Group of Diagonal Cubic Surfaces（対角的3次曲面のBrauer群の統一的な表示可能性について） (JAPANESE)
植松 哲也 氏 (東京大学大学院数理科学研究科)
Uniform Representability of the Brauer Group of Diagonal Cubic Surfaces（対角的3次曲面のBrauer群の統一的な表示可能性について） (JAPANESE)
博士論文発表会
09:30-10:45 数理科学研究科棟(駒場) 128号室
Li Qinglong 氏 (東京大学大学院数理科学研究科)
Nuclearity of reduced free product C*-algebras（既約自由積C*環の核型性について） (JAPANESE)
Li Qinglong 氏 (東京大学大学院数理科学研究科)
Nuclearity of reduced free product C*-algebras（既約自由積C*環の核型性について） (JAPANESE)
博士論文発表会
11:00-12:15 数理科学研究科棟(駒場) 128号室
Suthichitranont Noppakhun 氏 (東京大学大学院数理科学研究科)
Construction of holomorphic local conformal framed nets（局所共形正則枠付きネットの構成） (JAPANESE)
Suthichitranont Noppakhun 氏 (東京大学大学院数理科学研究科)
Construction of holomorphic local conformal framed nets（局所共形正則枠付きネットの構成） (JAPANESE)
博士論文発表会
13:00-14:15 数理科学研究科棟(駒場) 128号室
糟谷 久矢 氏 (東京大学大学院数理科学研究科)
Topology, symplectic geometry and complex geometry of solvmanifolds -From nilpotent to solvable-（可解多様体のトポロジー、シンプレクティック幾何学および複素幾何学 -冪零から可解へ-） (JAPANESE)
糟谷 久矢 氏 (東京大学大学院数理科学研究科)
Topology, symplectic geometry and complex geometry of solvmanifolds -From nilpotent to solvable-（可解多様体のトポロジー、シンプレクティック幾何学および複素幾何学 -冪零から可解へ-） (JAPANESE)
博士論文発表会
14:15-15:30 数理科学研究科棟(駒場) 128号室
松家 敬介 氏 (東京大学大学院数理科学研究科)
Discretization and ultradiscretization of differential equations preserving characters of their solutions（微分方程式の解の特徴を保った離散化及び超離散化） (JAPANESE)
松家 敬介 氏 (東京大学大学院数理科学研究科)
Discretization and ultradiscretization of differential equations preserving characters of their solutions（微分方程式の解の特徴を保った離散化及び超離散化） (JAPANESE)
2013年02月07日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
David Kerr 氏 (東大数理/Texas A&M Univ.)
Combinatorial independence, amenability, and sofic entropy (ENGLISH)
David Kerr 氏 (東大数理/Texas A&M Univ.)
Combinatorial independence, amenability, and sofic entropy (ENGLISH)
博士論文発表会
09:45-11:00 数理科学研究科棟(駒場) 118号室
加藤 直樹 氏 (東京大学大学院数理科学研究科)
Lie foliations transversely modeled on nilpotent Lie algebras（ベキ零リー環を横断構造に持つリー葉層構造について） (JAPANESE)
加藤 直樹 氏 (東京大学大学院数理科学研究科)
Lie foliations transversely modeled on nilpotent Lie algebras（ベキ零リー環を横断構造に持つリー葉層構造について） (JAPANESE)
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