Showing papers in "Journal of The Mathematical Society of Japan in 2005"
TL;DR: In this paper, a new type of limit theorems for the one-dimensional quantum random walk X n ϕ at time n starting from initial qubit state ϕ determined by 2 × 2 unitary matrix U were presented.
Abstract: In this paper we consider the one-dimensional quantum random walk X n ϕ at time n starting from initial qubit state ϕ determined by 2 × 2 unitary matrix U . We give a combinatorial expression for the characteristic function of X n ϕ . The expression clarifies the dependence of it on components of unitary matrix U and initial qubit state ϕ . As a consequence, we present a new type of limit theorems for the quantum random walk. In contrast with the de Moivre-Laplace limit theorem, our symmetric case implies that X n ϕ / n converges weakly to a limit Z ϕ as n → ∞ , where Z ϕ has a density 1 / π ( 1 - x 2 ) 1 - 2 x 2 for x ∈ ( - 1 / 2 , 1 / 2 ) . Moreover we discuss some known simulation results based on our limit theorems.
239 citations
TL;DR: In this article, a theory of local old-and new-forms for representations of GSp(4) over a p-adic field with Iwahori-invariant vectors is developed.
Abstract: A theory of local old- and newforms for representations of GSp(4) over a p-adic field with Iwahori-invariant vectors is developed. The results are applied to Siegel modular forms of degree 2 with square-free level with respect to various congruence subgroups.
80 citations
TL;DR: In this paper, the authors studied various topological properties of generic smooth maps between manifolds whose regular fibers are disjoint unions of homotopy spheres and showed that if a closed 4-manifold admits such a generic map into a surface, then it bounds a 5-Manifold with nice properties.
Abstract: In this paper, we study various topological properties of generic smooth maps between manifolds whose regular fibers are disjoint unions of homotopy spheres. In particular, we show that if a closed 4 -manifold admits such a generic map into a surface,then it bounds a 5 -manifold with nice properties. As a corollary, we show that each regular fiber of such a generic map of the 4 -sphere into the plane is a homotopy ribbon 2 -link and that any spun 2 -knot of a classical knot can be realized as a component of a regular fiber of such a map.
51 citations
TL;DR: In this paper, the de- pendence on the variable x was assumed to be in the class V MO as a function of x, and the continuity of A(x;u;p) with respect to x was not assumed.
Abstract: In this paper we treat the regularity problem for minimizers u(x) : › ‰ R m ! R n of quadratic growth functionals R › A(x;u;Du)dx. About the de- pendence on the variable x we assume only that A(¢;u;p) is in the class V MO as a function of x. Namely, we do not assume the continuity of A(x;u;p) with respect to x. We will prove a partial regularity result for the case m • 4.
37 citations
TL;DR: In this paper, the fundamental group of the complements of some plane irreducible sextics which are not of torus type is shown to be abelian, and it is shown that for all these complements, there exists a fundamental group that is not abelIAN.
Abstract: Recently, Oka-Pho proved that the fundamental group of the complement of any plane irreducible tame torus sextic is not abelian. We compute here the fundamental groups of the complements of some plane irreducible sextics which are not of torus type. For all our examples, we obtain that the fundamental group is abelian.
32 citations
TL;DR: The 3-transposition groups that act on vertex operator algebras in the way described by Miyamoto in [Mi] are classified under the assumption that the group is centerfree and the VOA carries a positive-definite invariant Hermitian form as discussed by the authors.
Abstract: The 3-transposition groups that act on vertex operator algebras in the way described by Miyamoto in [Mi] are classified under the assumption that the group is centerfree and the VOA carries a positive-definite invariant Hermitian form.
27 citations
TL;DR: In this article, the Borel summability of singular vector fields is studied and the existence of a genuine solution u (z ) such that u ( z ) ∼ u ˜ (z) as z → 0 in some sectorial region is proved.
Abstract: Let L = ∑ i = 1 d X i ( z ) ∂ z i be a holomorphic vector field degenerating at z = 0 such that Jacobi matrix ( ( ∂ X i / ∂ z j ) ( 0 ) ) has zero eigenvalues. Consider L u = F ( z , u ) and let u ˜ ( z ) be a formal power series solution. We study the Borel summability of u ˜ ( z ) , which implies the existence of a genuine solution u ( z ) such that u ( z ) ∼ u ˜ ( z ) as z → 0 in some sectorial region. Further we treat singular equations appearing in finding normal forms of singular vector fields and study to simplify L by transformations with Borel summable functions.
25 citations
TL;DR: The shifted Schur measure as discussed by the authors is a measure on the set of all strict partitions, which is defined by Schur Q -functions, and the main aim of this paper is to calculate the correlation function of this measure, given by a pfaffian.
Abstract: The shifted Schur measure introduced in [TW2] is a measure on the set of all strict partitions, which is defined by Schur Q -functions. The main aim of this paper is to calculate the correlation function of this measure, which is given by a pfaffian. As an application, we prove that a limit distribution of parts of partitions with respect to a shifted version of the Plancherel measure for symmetric groups is identical with the corresponding distribution of the original Plancherel measure. In particular, we obtain a limit distribution of the length of the longest ascent pair for a random permutation. Further we give expressions of the mean value and the variance of the size of partitions with respect to the measure defined by Hall-Littlewood functions.
24 citations
TL;DR: In this paper, essential norms of differences of composition operators on the Banach algebra H ∞ of bounded analytic functions on the unit disk were studied, and they were shown to be equivalent to the norm of the difference of the differences of the composition operators of a function.
Abstract: We study essential norms of differences of composition operators on the Banach algebra H ∞ of bounded analytic functions on the unit disk.
22 citations
TL;DR: In this article, it was shown that one can construct an exponential attractor which depends continuously on a parameter in the dynamical system, which is then applied to the chemotaxis-growth system.
Abstract: We study dependence on a parameter of exponential attractors. As known, exponetial attractors are not uniquely determined from a dissipative dynamical system even if they exist. But we prove in this paper that one can construct an exponential attractor which depends continuously on a parameter in the dynamical system. This result is then applied to the chemotaxis-growth system.
22 citations
TL;DR: In this article, a divisorial contraction of a normal projective 3-fold with only Q-factorial terminal singularities is studied, and the discrepancy of the discrepancy is 1 when P 2 X is a 3-dimensional terminal singularity of type (cD/2) and (cE/2).
Abstract: We study a divisorial contraction … : Y ! X such that … contracts an irreducible divisor E to a point P and that the discrepancy of E is 1 when P 2 X is a 3-dimensional terminal singularity of type (cD/2) and (cE/2). Let Y be a normal projective 3-fold with only Q-factorial terminal singularities. If KY is not nef, then there is an extremal contraction … : Y ! X which is either a birational morphism or of fiber type. Extremal contractions of fiber type are called Mori fiber spaces, and birational extremal contractions are divided into divisorial contractions and flipping contractions. The aim of this article is to study divisorial contractions. Since Mori completed the minimal model program for 3-folds in (10), it has been recognized that one has to know divisorial contractions explicitly for further study of 3-folds. Recent
TL;DR: In this paper, the homogenization of stochastic partial differential equations whose coefficients are rapidly oscillating and are perturbed by a diffusion process is discussed, where the constants are essentially different from the case where the coefficients do not contain perturbed factors.
Abstract: We discuss the homogenization of stochastic partial differential equations whose coefficients are rapidly oscillating and are perturbed by a diffusion process. Such class of equations appear in nonlinear filtering problems with feedback. We specify the constant coefficients of the limit equation. The constants are essentially different from the case where the coefficients do not contain perturbed factors.
TL;DR: In this article, a different proof of strongly amenable subfactors is presented based on Connes and Haagerup's arguments on the uniqueness of the injective factor of type I I I 1.
Abstract: Popa proved that strongly amenable subfactors of type I I I 1 with the same type I I and type I I I principal graphs are completely classified by their standard invariants. In this paper, we present a different proof of this classification theorem based on Connes and Haagerup's arguments on the uniqueness of the injective factor of type I I I 1 .
TL;DR: In this paper, the authors developed reductions for classifications of singularities of orbit closures in module varieties and showed that the orbit closures for representations of Dynkin quivers are regular in codimension two.
Abstract: We develop reductions for classifications of singularities of orbit closures in module varieties. Then we show that the orbit closures for representations of Dynkin quivers are regular in codimension two.
TL;DR: In this paper, the Widder type uniqueness theorem was used to determine Martin boundaries of product domains for elliptic equations in skew product form via Widder types uniqueness theorems for parabolic equations, where the fiber of the Martin boundary at infinity of the base space degenerates into one point if any nonnegative solution to the Dirichlet problem for a corresponding parabolic equation with zero initial and boundary data is identically zero.
Abstract: We give a method to determine Martin boundaries of product domains for elliptic equations in skew product form via Widder type uniqueness theorems for parabolic equations. It is shown that the fiber of the Martin boundary at infinity of the base space degenerates into one point if any nonnegative solution to the Dirichlet problem for a corresponding parabolic equation with zero initial and boundary data is identically zero. We apply it in a unified way to several concrete examples to explicitly determine Martin boundaries for them.
TL;DR: In this article, a Zariski ϕ ( q ) -ple, distinguished by the Alexander polynomial, whose curves are tame torus curves of type (p, q ), with q smooth irreducible components of degree p, and one single singular point topologically equivalent to the Brieskorn-Pham singularity v q + u q p 2 = 0.
Abstract: Let p and q be integers such that p > q ≥ 2 and q divides p . Let ϕ ( q ) be the Euler number of q . We exhibit a Zariski ϕ ( q ) -ple, distinguished by the Alexander polynomial, whose curves are tame torus curves of type ( p , q ) , with q smooth irreducible components of degree p ,and one single singular point topologically equivalent to the Brieskorn-Pham singularity v q + u q p 2 = 0 .
TL;DR: In this article, a method was presented to construct all harmonic maps via loop group splittings into a compact symmetric space, where G is an arbitrary Lie group (semisimple or not) and K is the fixpoint group of some involution of G.
Abstract: In [19] a method was presented, which constructs via loop group splittings all harmonic maps into a compact symmetric space The present paper generalizes this method to all spaces G / K , where G is an arbitrary Lie group (semisimple or not) and K is the fixpoint group of some involution of G The method is illustrated by a number of examples
TL;DR: In this paper, the authors generalize Prudnikov's method of using a double integral to deduce relations between the Riemann zeta-values, so as to prove intriguing relations between double zeta values of depth 2.
Abstract: In this note we are going to generalize Prudnikov's method of using a double integral to deduce relations between the Riemann zeta-values, so as to prove intriguing relations between double zeta-values of depth 2. Prior to this, we shall deduce the most well-known relation that expresses the sum ∑ j = 1 m - 2 ζ ( j + 1 ) ζ ( m - j ) in terms of ζ 2 ( 1 , m ) .
TL;DR: In this paper, the authors consider a simply connected Lie group and consider a Lie G foliation on a closed manifold M whose leaves are all dense in M and show that the space of ends of a leaf F of the foliation is either a singleton, a two points set, or a Cantor set.
Abstract: Let G be a simply connected Lie group and consider a Lie G foliation ℱ on a closed manifold M whose leaves are all dense in M . Then the space of ends ℰ ( F ) of a leaf F of ℱ is shown to be either a singleton, a two points set, or a Cantor set. Further if G is solvable, or if G has no cocompact discrete normal subgroup and ℱ admits a transverse Riemannian foliation of the complementary dimension, then ℰ ( F ) consists of one or two points. On the contrary there exists a Lie S L ˜ ( 2 , R ) foliation on a closed 5-manifold whose leaf is diffeomorphic to a 2-sphere minus a Cantor set.
TL;DR: In this paper, a necessary and sufficient condition for a totally bounded metric space X = (X, d ) is given for a uniform ANR in order that each component of C l d H (X ) is a uniform AR.
Abstract: For a metric space X = ( X , d ) ,let C l d H ( X ) be the space of all nonempty closed sets in X with the topology induced by the Hausdorff extended metric: d H ( A , B ) = max sup x ∈ B d ( x , A ) , sup x ∈ A d ( x , B ) ∈ [ 0 , ∞ ] . On each component of C l d H ( X ) , d H is a metric (i.e., d H ( A , B ) < ∞ ). In this paper, we give a condition on X such that each component of C l d H ( X ) is a uniform AR (in the sense of E. Michael). For a totally bounded metric space X , in order that C l d H ( X ) is a uniform ANR,a necessary and sufficient condition is also given. Moreover, we discuss the subspace D i s H ( X ) of C l d H ( X ) consisting of all discrete sets in X and give a condition on X such that each component of D i s H ( X ) is a uniform AR and D i s H ( X ) is homotopy dense in C l d H ( X ) .
TL;DR: In this paper, the boundedness of the Hardy-Littlewood operator on Dirichlet spaces of harmonic functions on the open unit ball in R n has been investigated and a -Bloch, Hardy, Bergman, B M O p and Dirichlets spaces of the harmonic functions were investigated.
Abstract: In this paper we investigate a -Bloch, Hardy, Bergman, B M O p and Dirichlet spaces of harmonic functions on the open unit ball in R n , and the boundedness of the Hardy-Littlewood operator on these spaces.
TL;DR: In this article, a graphical method, called the chart description, is introduced to describe the monodromy representation of a genus one Lefschetz fibration and a new and purely combinatorial proof of the classification theorem of genus one lefschechetz fibrations is given.
Abstract: We introduce a graphical method, called the chart description, to describe the monodromy representation of a genus one Lefschetz fibration. Using this method, we give a new and purely combinatorial proof of the classification theorem of genus one Lefschetz fibrations.
TL;DR: In this paper, the authors characterize symmetric cones among homogeneous convex cones by the condition that the corresponding tube domains are mapped onto the dual tube domains under pseudoinverse maps with parameter.
Abstract: In this paper we characterize symmetric cones among homogeneous convex cones by the condition that the corresponding tube domains are mapped onto the dual tube domains under pseudoinverse maps with parameter. The condition also restricts the parameter to specific ones.
TL;DR: In this paper, it was shown that each arithmetic progressions contains only finitely many prime numbers l for which the l -class group of F is nontrivial, which implies that the set of prime numbers L for which F is trivial has natural density 1 in the whole set of all prime numbers.
Abstract: Let S be a non-empty finite set of prime numbers and, for each p in S , let Z p denote the ring of p -adic integers. Let F be an abelian extension over the rational field such that the Galois group of F over some subfield of F with finite degree is topologically isomorphic to the additive group of the direct product of Z p for all p in S . We shall prove that each of certain arithmetic progressions contains only finitely many prime numbers l for which the l -class group of F is nontrivial. This result implies our conjecture in [3] that the set of prime numbers l for which the l -class group of F is trivial has natural density 1 in the set of all prime numbers.
TL;DR: In this article, the authors pose a variational problem for surfaces whose solutions are a geometric model for thin films with gravity which is partially supported by a given contour, and determine the stability or instability of each solution.
Abstract: We pose a variational problem for surfaces whose solutions are a geometric model for thin films with gravity which is partially supported by a given contour. The energy functional contains surface tension, a gravitational energy and a wetting energy, and the Euler-Lagrange equation can be expressed in terms of the mean curvature of the surface, the curvatures of the free boundary and a few other geometric quantities. Especially, we study in detail a simple case where the solutions are vertical planar surfaces bounded by two vertical lines. We determine the stability or instability of each solution.
TL;DR: In this paper, it was shown that the asymptotic cone of every complete, connected, non-compact Riemannian manifold of roughly non-negative radial curvature exists, and it is isometric to the Euclidean cone over their Tits ideal boundaries.
Abstract: We prove that the asymptotic cone of every complete, connected, non-compact Riemannian manifold of roughly non-negative radial curvature exists, and it is isometric to the Euclidean cone over their Tits ideal boundaries.
TL;DR: In this article, it was shown that if a non-degenerate algebraic function field in n variables over C admits an algebraic addition theorem, then any f ∈ K is a rational function of some coordinate functions and abelian functions of other variables.
Abstract: A statement of Weierstrass is known for meromorphic functions which admit an algebraic addition theorem. We give its precise formulation and prove it complex analytically. In fact, we show that if K is a non-degenerate algebraic function field in n variables over C which admits an algebraic addition theorem, then any f ∈ K is a rational function of some coordinate functions and abelian functions of other variables.
TL;DR: In this paper, a new system consisting of differential equations as a mathematical model for shape memory alloy materials occupying the three dimensional domain was proposed. But the key of the modelling is the characterization for the generalized stop operators by using the ordinary differential equations including the subdifferential of the indicator function for the closed interval.
Abstract: It is a crucial step how to describe the relationship between the strain, the stress and the temperature field, when we consider the mathematical modelling for shape memory alloy materials. From the experimental results we know that the relationship can be described by the hysteresis operators. In this paper we propose a new system consisting of differential equations as a mathematical model for shape memory alloy materials occupying the three dimensional domain. The key of the modelling is the characterization for the generalized stop operators by using the ordinary differential equations including the subdifferential of the indicator function for the closed interval. Also, we give a proof of the well-posedness of the system.
TL;DR: In this article, the classification of all one-parametric selfinjective algebras over algebraically closed fields which admit simply connected Galois coverings is complete.
Abstract: In continuation of our papers [5], [6] we complete the classification of all one-parametric selfinjective algebras over algebraically closed fields which admit simply connected Galois coverings.
TL;DR: In this paper, it was shown that any generic graph satisfying some property * is strictly stable or ω -stable and as a corollary, any generic pseudoplane is also strictly stable.
Abstract: We show that any saturated generic graph satisfying some property (*) is strictly stable or ω -stable. As a corollary, we obtain that any saturated generic pseudoplane is strictly stable or ω -stable.