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Seminar information archive
Seminar information archive ～03/28｜Today's seminar 03/29 | Future seminars 03/30～
2010/09/03
Lectures
14:30-15:30 Room #370 (Graduate School of Math. Sci. Bldg.)
Luc Robbiano (University of Versailles)
Carleman estimates and boundary problems. (JAPANESE)
Luc Robbiano (University of Versailles)
Carleman estimates and boundary problems. (JAPANESE)
[ Abstract ]
In this presentation, based on joint works with Jerome LeRousseau and Matthieu Leautaud, we consider boundary problems for elliptic/parabolic operators. We prove Carleman estimates in such cases. One of the interest for such an estimate is the implied controllability of (semi-linear) heat equations.
One of the main aspects of the proof is a microlocal decomposition separating high and low tangential frequencies.
If time permits, we will present how such an approach can be used to prove Carleman estimates in the case of non smooth coefficients at an interface, possibly with an additional diffusion process along the interface.
In this presentation, based on joint works with Jerome LeRousseau and Matthieu Leautaud, we consider boundary problems for elliptic/parabolic operators. We prove Carleman estimates in such cases. One of the interest for such an estimate is the implied controllability of (semi-linear) heat equations.
One of the main aspects of the proof is a microlocal decomposition separating high and low tangential frequencies.
If time permits, we will present how such an approach can be used to prove Carleman estimates in the case of non smooth coefficients at an interface, possibly with an additional diffusion process along the interface.
2010/09/01
Lie Groups and Representation Theory
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Bernhard M\"uhlherr (Justus-Liebig-Universit\"at Giessen)
Groups of Kac-Moody type (ENGLISH)
Bernhard M\"uhlherr (Justus-Liebig-Universit\"at Giessen)
Groups of Kac-Moody type (ENGLISH)
[ Abstract ]
Groups of Kac-Moody type are natural generalizations of Kac-Moody groups over fields in the sense that they have an RGD-system. This is a system of subgroups indexed by the roots of a root system and satisfying certain commutation relations.
Roughly speaking, there is a one-to-one correspondence between groups of Kac-Moody type and Moufang twin buildings. This correspondence was used in the last decade to prove several group theoretic results on RGD-systems and in particular on Kac-
Moody groups over fields.
In my talk I will explain RGD-systems and how they provide twin
buildings in a natural way. I will then present some of the group theoretic applications mentioned above and describe how twin buildings are used as a main tool in their proof.
Groups of Kac-Moody type are natural generalizations of Kac-Moody groups over fields in the sense that they have an RGD-system. This is a system of subgroups indexed by the roots of a root system and satisfying certain commutation relations.
Roughly speaking, there is a one-to-one correspondence between groups of Kac-Moody type and Moufang twin buildings. This correspondence was used in the last decade to prove several group theoretic results on RGD-systems and in particular on Kac-
Moody groups over fields.
In my talk I will explain RGD-systems and how they provide twin
buildings in a natural way. I will then present some of the group theoretic applications mentioned above and describe how twin buildings are used as a main tool in their proof.
thesis presentations
16:30-17:45 Room #123 (Graduate School of Math. Sci. Bldg.)
Naoki IMAI (Graduate School of Mathematical Sciences the University of Tokyo )
On the moduli spaces of finite flat models of Galois representations (JAPANESE)
Naoki IMAI (Graduate School of Mathematical Sciences the University of Tokyo )
On the moduli spaces of finite flat models of Galois representations (JAPANESE)
2010/08/06
Lectures
15:30-17:45 Room #370 (Graduate School of Math. Sci. Bldg.)
Leevan Ling (Hong Kong Baptist University) 15:30-16:30
A Spectral Method for Space--
Time Fractional Diffusion Equation (ENGLISH)
Mourad Choulli (University of Metz) 16:45-17:45
A multidimensional Borg-Levinson theorem (ENGLISH)
Leevan Ling (Hong Kong Baptist University) 15:30-16:30
A Spectral Method for Space--
Time Fractional Diffusion Equation (ENGLISH)
Mourad Choulli (University of Metz) 16:45-17:45
A multidimensional Borg-Levinson theorem (ENGLISH)
GCOE Seminars
15:00-16:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Matthieu Alfaro (University Montpellier 2)
Motion by mean curvature and Allen-Cahn equations (ENGLISH)
Matthieu Alfaro (University Montpellier 2)
Motion by mean curvature and Allen-Cahn equations (ENGLISH)
[ Abstract ]
After introducing the classical and the generalized motion by mean curvature, we give some connections with the singular limit of Allen-Cahn equations in both framework. New results and estimates shall be provided.
After introducing the classical and the generalized motion by mean curvature, we give some connections with the singular limit of Allen-Cahn equations in both framework. New results and estimates shall be provided.
2010/08/05
Lectures
16:30-17:30 Room #370 (Graduate School of Math. Sci. Bldg.)
Yongzhi Steve Xu (University of Louisville, USA)
Radiation Conditions for Wave in Stratified Medium and Related Inverse
Problems (ENGLISH)
Yongzhi Steve Xu (University of Louisville, USA)
Radiation Conditions for Wave in Stratified Medium and Related Inverse
Problems (ENGLISH)
Lectures
16:30-17:30 Room #370 (Graduate School of Math. Sci. Bldg.)
Yongzhi Steve Xu (University of Louisville, USA)
Radiation Conditions for Wave in Stratified Medium and Related Inverse Problems (ENGLISH)
Yongzhi Steve Xu (University of Louisville, USA)
Radiation Conditions for Wave in Stratified Medium and Related Inverse Problems (ENGLISH)
2010/07/30
GCOE Seminars
16:30-17:30 Room #370 (Graduate School of Math. Sci. Bldg.)
Oleg Emanouilov (Colorado State University)
Global uniqueness in determining a coefficient by boundary data on small subboundaries (ENGLISH)
Oleg Emanouilov (Colorado State University)
Global uniqueness in determining a coefficient by boundary data on small subboundaries (ENGLISH)
[ Abstract ]
We consider the Dirichlet problem for the stationary two-dimensional Schroedinger equation. We discuss an inverse boundary value problem of determining the potential from a pair of all Dirichlet data supported in a subboundary S+ and all the corresponding Neumann data taken only on a subboundary S-. In the case where S+ = S- are the whole boundary, the data are the classical Dirichlet to Neumann map and there are many uniqueness results, while in the case where S+=S- is an arbitrary subboundary, Imanuvilov-Uhlmann-Yamamoto (2010) proves the uniqueness. In this talk, for the case where S+ and S- are not same, we prove the global uniqueness for this inverse problem under a condition only on the locations of S+, S-. We note that within the condition, S+ and S- can be arbitrarily small. The key of the proof is the construction of suitable complex geometrical optics solutions by a Carleman estimate with singular weight function.
We consider the Dirichlet problem for the stationary two-dimensional Schroedinger equation. We discuss an inverse boundary value problem of determining the potential from a pair of all Dirichlet data supported in a subboundary S+ and all the corresponding Neumann data taken only on a subboundary S-. In the case where S+ = S- are the whole boundary, the data are the classical Dirichlet to Neumann map and there are many uniqueness results, while in the case where S+=S- is an arbitrary subboundary, Imanuvilov-Uhlmann-Yamamoto (2010) proves the uniqueness. In this talk, for the case where S+ and S- are not same, we prove the global uniqueness for this inverse problem under a condition only on the locations of S+, S-. We note that within the condition, S+ and S- can be arbitrarily small. The key of the proof is the construction of suitable complex geometrical optics solutions by a Carleman estimate with singular weight function.
2010/07/29
Algebraic Geometry Seminar
14:30-16:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Masahiro Futaki (The University of Tokyo)
Homological Mirror Symmetry for 2-dimensional toric Fano stacks (JAPANESE)
Masahiro Futaki (The University of Tokyo)
Homological Mirror Symmetry for 2-dimensional toric Fano stacks (JAPANESE)
[ Abstract ]
Homological Mirror Symmetry (HMS for short) is a conjectural
duality between complex and symplectic geometry, originally proposed
for mirror pairs of Calabi-Yau manifolds and later extended to
Fano/Landau-Ginzburg mirrors (both due to Kontsevich, 1994 and 1998).
We explain how HMS is established in the case of 2-dimensional smooth
toric Fano stack X as an equivalence between the derived category of X
and the derived directed Fukaya category of its mirror Lefschetz
fibration W. This is related to Kontsevich-Soibelman's construction of
3d CY category from the quiver with potential.
We also obtain a local mirror extension following Seidel's suspension
theorem, that is, the local HMS for the canonical bundle K_X and the
double suspension W+uv. This talk is joint with Kazushi Ueda (Osaka
U.).
Homological Mirror Symmetry (HMS for short) is a conjectural
duality between complex and symplectic geometry, originally proposed
for mirror pairs of Calabi-Yau manifolds and later extended to
Fano/Landau-Ginzburg mirrors (both due to Kontsevich, 1994 and 1998).
We explain how HMS is established in the case of 2-dimensional smooth
toric Fano stack X as an equivalence between the derived category of X
and the derived directed Fukaya category of its mirror Lefschetz
fibration W. This is related to Kontsevich-Soibelman's construction of
3d CY category from the quiver with potential.
We also obtain a local mirror extension following Seidel's suspension
theorem, that is, the local HMS for the canonical bundle K_X and the
double suspension W+uv. This talk is joint with Kazushi Ueda (Osaka
U.).
2010/07/28
GCOE Seminars
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
及川 一誠 (東京大学大学院数理科学研究科)
定常移流拡散方程式に対するハイブリッド型不連続Galerkin法 (JAPANESE)
http://www.infsup.jp/utnas/
及川 一誠 (東京大学大学院数理科学研究科)
定常移流拡散方程式に対するハイブリッド型不連続Galerkin法 (JAPANESE)
[ Abstract ]
本講演では,ハイブリッド型不連続Galerkin(HDG)法による,定常移流拡散方程式の新しい数値計算スキームを紹介し,定式化や誤差評価,安定性等について述べる.新スキームの有効性を確認するために,数値計算例もいくつか示す.なお,講演前半は準備として,Poisson方程式に対するHDG法について解説する.
[ Reference URL ]本講演では,ハイブリッド型不連続Galerkin(HDG)法による,定常移流拡散方程式の新しい数値計算スキームを紹介し,定式化や誤差評価,安定性等について述べる.新スキームの有効性を確認するために,数値計算例もいくつか示す.なお,講演前半は準備として,Poisson方程式に対するHDG法について解説する.
http://www.infsup.jp/utnas/
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Issei Oikawa (University of Tokyo)
Hybridized discontinuous Galerkin method for a convection-diffusion equation (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Issei Oikawa (University of Tokyo)
Hybridized discontinuous Galerkin method for a convection-diffusion equation (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
2010/07/27
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ayumu Inoue (Tokyo Institute of Technology)
Quandle homology and complex volume
(Joint work with Yuichi Kabaya) (JAPANESE)
Ayumu Inoue (Tokyo Institute of Technology)
Quandle homology and complex volume
(Joint work with Yuichi Kabaya) (JAPANESE)
[ Abstract ]
For a hyperbolic 3-manifold M, the complex value (Vol(M) + i CS(M)) is called the complex volume of M. Here, Vol(M) denotes the volume of M, and CS(M) the Chern-Simons invariant of M.
In 2004, Neumann defined the extended Bloch group, and showed that there is an element of the extended Bloch group corresponding to a hyperbolic 3-manifold.
He further showed that we can compute the complex volume of the manifold by evaluating the element of the extended Bloch group.
To obtain an element of the extended Bloch group corresponding to a hyperbolic 3-manifold, we have to find an ideal triangulation of the manifold and to solve several equations.
On the other hand, we show that the element of the extended Bloch group corresponding to the exterior of a hyperbolic link is obtained from a quandle shadow coloring.
It means that we can compute the complex volume combinatorially from a link diagram.
For a hyperbolic 3-manifold M, the complex value (Vol(M) + i CS(M)) is called the complex volume of M. Here, Vol(M) denotes the volume of M, and CS(M) the Chern-Simons invariant of M.
In 2004, Neumann defined the extended Bloch group, and showed that there is an element of the extended Bloch group corresponding to a hyperbolic 3-manifold.
He further showed that we can compute the complex volume of the manifold by evaluating the element of the extended Bloch group.
To obtain an element of the extended Bloch group corresponding to a hyperbolic 3-manifold, we have to find an ideal triangulation of the manifold and to solve several equations.
On the other hand, we show that the element of the extended Bloch group corresponding to the exterior of a hyperbolic link is obtained from a quandle shadow coloring.
It means that we can compute the complex volume combinatorially from a link diagram.
thesis presentations
16:00-17:15 Room #123 (Graduate School of Math. Sci. Bldg.)
Ryoko TOMIYASU (graduate school of Mathematical Sciences)
On some algebraic properties of CM-types of CM-fields and their reflexes (JAPANESE)
Ryoko TOMIYASU (graduate school of Mathematical Sciences)
On some algebraic properties of CM-types of CM-fields and their reflexes (JAPANESE)
2010/07/22
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Owen Sizemore (UCLA)
$W^*$ Rigidity for actions of wreath product groups (ENGLISH)
Owen Sizemore (UCLA)
$W^*$ Rigidity for actions of wreath product groups (ENGLISH)
[ Abstract ]
The past 8 years have seen much progress in the classification of
actions of groups on measure spaces. Much of this is due to new powerful
techniques in operator algebras. We will survey some of these results
as well as the new operator algebra techniques. We will then give new
results concerning the classification of actions of wreath product groups.
The past 8 years have seen much progress in the classification of
actions of groups on measure spaces. Much of this is due to new powerful
techniques in operator algebras. We will survey some of these results
as well as the new operator algebra techniques. We will then give new
results concerning the classification of actions of wreath product groups.
2010/07/20
Tuesday Seminar on Topology
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Keiko Kawamuro (University of Iowa)
A polynomial invariant of pseudo-Anosov maps (JAPANESE)
Keiko Kawamuro (University of Iowa)
A polynomial invariant of pseudo-Anosov maps (JAPANESE)
[ Abstract ]
Thurston-Nielsen classified surface homomorphism into three classes. Among them, the pseudo-Anosov class is the most interesting since there is strong connection to the hyperbolic manifolds. As an invariant, the dilatation number has been known. In this talk, I will introduce a new invariant of pseudo-Anosov maps. It is an integer coefficient polynomial, which contains the dilatation as the largest real root and is often reducible. I will show properties of the polynomials, examples, and some application to knot theory. (This is a joint work with Joan Birman and Peter Brinkmann.)
Thurston-Nielsen classified surface homomorphism into three classes. Among them, the pseudo-Anosov class is the most interesting since there is strong connection to the hyperbolic manifolds. As an invariant, the dilatation number has been known. In this talk, I will introduce a new invariant of pseudo-Anosov maps. It is an integer coefficient polynomial, which contains the dilatation as the largest real root and is often reducible. I will show properties of the polynomials, examples, and some application to knot theory. (This is a joint work with Joan Birman and Peter Brinkmann.)
2010/07/15
Lie Groups and Representation Theory
14:30-16:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Soo Teck Lee (Singapore National University)
Pieri rule and Pieri algebras for the orthogonal groups (ENGLISH)
Soo Teck Lee (Singapore National University)
Pieri rule and Pieri algebras for the orthogonal groups (ENGLISH)
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Narutaka Ozawa (Univ. Tokyo)
Type II$_1$ von Neumann representations for Hecke operators on Maass forms (after F. Radulescu) (ENGLISH)
Narutaka Ozawa (Univ. Tokyo)
Type II$_1$ von Neumann representations for Hecke operators on Maass forms (after F. Radulescu) (ENGLISH)
Seminar on Probability and Statistics
15:00-16:10 Room #000 (Graduate School of Math. Sci. Bldg.)
MASUDA, Hiroki (Graduate School of Mathematics, Kyushu University)
Mighty convergence in LAD type estimation (JAPANESE)
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/04.html
MASUDA, Hiroki (Graduate School of Mathematics, Kyushu University)
Mighty convergence in LAD type estimation (JAPANESE)
[ Abstract ]
We propose a LAD (least absolute deviation) type contrast function for estimating Levy driven Ornstein-Uhlenbeck processes sampled at high frequency. The asymptotic behavior and polynomial-type large deviation inequality concerning the statistical random fields in question are derived, entailing an asymptotic normality and convergence of moments of the LAD estimator. Also, we will mention some numerical experiments done by the R software and some possible extensions of the framework.
[ Reference URL ]We propose a LAD (least absolute deviation) type contrast function for estimating Levy driven Ornstein-Uhlenbeck processes sampled at high frequency. The asymptotic behavior and polynomial-type large deviation inequality concerning the statistical random fields in question are derived, entailing an asymptotic normality and convergence of moments of the LAD estimator. Also, we will mention some numerical experiments done by the R software and some possible extensions of the framework.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/04.html
2010/07/13
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Marion Moore (University of California, Davis)
High Distance Knots in closed 3-manifolds (ENGLISH)
Marion Moore (University of California, Davis)
High Distance Knots in closed 3-manifolds (ENGLISH)
[ Abstract ]
Let M be a closed 3-manifold with a given Heegaard splitting.
We show that after a single stabilization, some core of the
stabilized splitting has arbitrarily high distance with respect
to the splitting surface. This generalizes a result of Minsky,
Moriah, and Schleimer for knots in S^3. We also show that in the
complex of curves, handlebody sets are either coarsely distinct
or identical. We define the coarse mapping class group of a
Heeegaard splitting, and show that if (S,V,W) is a Heegaard
splitting of genus greater than or equal to 2, then the coarse
mapping class group of (S,V,W) is isomorphic to the mapping class
group of (S, V, W). This is joint work with Matt Rathbun.
Let M be a closed 3-manifold with a given Heegaard splitting.
We show that after a single stabilization, some core of the
stabilized splitting has arbitrarily high distance with respect
to the splitting surface. This generalizes a result of Minsky,
Moriah, and Schleimer for knots in S^3. We also show that in the
complex of curves, handlebody sets are either coarsely distinct
or identical. We define the coarse mapping class group of a
Heeegaard splitting, and show that if (S,V,W) is a Heegaard
splitting of genus greater than or equal to 2, then the coarse
mapping class group of (S,V,W) is isomorphic to the mapping class
group of (S, V, W). This is joint work with Matt Rathbun.
Tuesday Seminar of Analysis
17:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Carlos Villegas Blas (Universidad Nacional Autonoma de Mexico)
On a limiting eigenvalue distribution theorem for perturbations of the hydrogen atom (JAPANESE)
Carlos Villegas Blas (Universidad Nacional Autonoma de Mexico)
On a limiting eigenvalue distribution theorem for perturbations of the hydrogen atom (JAPANESE)
[ Abstract ]
Let H be the hydrogen atom Hamiltonian. We will show that
the operator H+P can have well defined clusters of eigenvalues
for a suitable perturbation P=f(h)Q where Q is a pseudo-differential
operator of order zero and f(h) is a small quantity depending of
the Planck's parameter h. We will show that the distribution of
eigenvalues in those clusters has a semi-classical limit involving
the averages of the principal symbol of Q along the classical orbits
of the Kepler problem.
Let H be the hydrogen atom Hamiltonian. We will show that
the operator H+P can have well defined clusters of eigenvalues
for a suitable perturbation P=f(h)Q where Q is a pseudo-differential
operator of order zero and f(h) is a small quantity depending of
the Planck's parameter h. We will show that the distribution of
eigenvalues in those clusters has a semi-classical limit involving
the averages of the principal symbol of Q along the classical orbits
of the Kepler problem.
2010/07/12
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yu KAWAKAMI (Kyushu Univ.)
The value distribution of the Gauss map of wave fronts and its applications (JAPANESE)
Yu KAWAKAMI (Kyushu Univ.)
The value distribution of the Gauss map of wave fronts and its applications (JAPANESE)
Algebraic Geometry Seminar
16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)
Ryo Ohkawa (Tokyo Institute of Technology)
Flips of moduli of stable torsion free sheaves with $c_1=1$ on
$\\mathbb{P}^2$ (JAPANESE)
Ryo Ohkawa (Tokyo Institute of Technology)
Flips of moduli of stable torsion free sheaves with $c_1=1$ on
$\\mathbb{P}^2$ (JAPANESE)
[ Abstract ]
We study flips of moduli schemes of stable torsion free sheaves
on the projective plane via wall-crossing phenomena of Bridgeland stability.
They are described as stratified Grassmann bundles by variation of
stability of modules over certain finite dimensional algebra.
We study flips of moduli schemes of stable torsion free sheaves
on the projective plane via wall-crossing phenomena of Bridgeland stability.
They are described as stratified Grassmann bundles by variation of
stability of modules over certain finite dimensional algebra.
2010/07/08
Applied Analysis
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Anna Vainchtein (University of Pittsburgh, Department of Mathematics)
Effect of nonlinearity on the steady motion of a twinning dislocation (ENGLISH)
Anna Vainchtein (University of Pittsburgh, Department of Mathematics)
Effect of nonlinearity on the steady motion of a twinning dislocation (ENGLISH)
[ Abstract ]
We consider the steady motion of a twinning dislocation in a Frenkel-Kontorova lattice with a double-well substrate potential that has a non-degenerate spinodal region. Semi-analytical traveling wave solutions are constructed for the piecewise quadratic potential, and their stability and further effects of nonlinearity are investigated numerically. We show that the width of the spinodal region and the nonlinearity of the potential have a significant effect on the dislocation kinetics, resulting in stable steady motion in some low-velocity intervals and lower propagation stress. We also conjecture that a stable steady propagation must correspond to an increasing portion of the kinetic relation between the applied stress and dislocation velocity.
We consider the steady motion of a twinning dislocation in a Frenkel-Kontorova lattice with a double-well substrate potential that has a non-degenerate spinodal region. Semi-analytical traveling wave solutions are constructed for the piecewise quadratic potential, and their stability and further effects of nonlinearity are investigated numerically. We show that the width of the spinodal region and the nonlinearity of the potential have a significant effect on the dislocation kinetics, resulting in stable steady motion in some low-velocity intervals and lower propagation stress. We also conjecture that a stable steady propagation must correspond to an increasing portion of the kinetic relation between the applied stress and dislocation velocity.
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Dave Penneys (UC Berkeley)
Killing weeds with annular multiplicities $*10$ via quadratic tangles (ENGLISH)
Dave Penneys (UC Berkeley)
Killing weeds with annular multiplicities $*10$ via quadratic tangles (ENGLISH)
[ Abstract ]
In recent work with Morrison, Peters, and Snyder, we eliminate two
families of possible principal graphs with graph norms less than 5 using
techniques derived from Jones' work on quadratic tangles.
In recent work with Morrison, Peters, and Snyder, we eliminate two
families of possible principal graphs with graph norms less than 5 using
techniques derived from Jones' work on quadratic tangles.
2010/07/07
Seminar on Mathematics for various disciplines
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Masahide Sato (Information Media Center, Kanazawa University)
Instabilities of steps on a vicinal face induced by the
asymmetry of diffusion field. (JAPANESE)
Masahide Sato (Information Media Center, Kanazawa University)
Instabilities of steps on a vicinal face induced by the
asymmetry of diffusion field. (JAPANESE)
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