Showing papers in "Tohoku Mathematical Journal in 2006"
TL;DR: In this paper, the authors provide a characterization of the compressed lattice polytopes in terms of their facet defining inequalities and prove that every compressed polytope is affinely isomorphic to a 0/1-polytope.
Abstract: We provide a characterization of the compressed lattice polytopes in terms of their facet defining inequalities and prove that every compressed lattice polytope is affinely isomorphic to a 0/1-polytope. As an application, we characterize those graphs whose cut polytopes are compressed and discuss consequences for studying linear programming relaxations in statistical disclosure limitation.
105 citations
TL;DR: In this article, the authors consider the problem of time-periodic strong solutions of the Stokes and Navier-Stokes system modelling viscous incompressible fluid flow past or around a rotating obstacle in Euclidean three-space.
Abstract: Consider the problem of time-periodic strong solutions of the Stokes and Navier-Stokes system modelling viscous incompressible fluid flow past or around a rotating obstacle in Euclidean three-space. Introducing a rotating coordinate system attached to the body, a linearization yields a system of partial differential equations of second order involving an angular derivative not subordinate to the Laplacian. In this paper we find an explicit solution for the linear whole space problem when the axis of rotation is parallel to the velocity of the fluid at infinity. For the analysis of this solution in $L^q$-spaces, $1
77 citations
TL;DR: In this paper, a suitably established local version of the Calderon-Zygmund operator theory was used to obtain weighted norm inequalities with weights more general than previously considered power weights.
Abstract: The Hankel transform transplantation operator is investigated by means of a suitably established local version of the Calderon-Zygmund operator theory. This approach produces weighted norm inequalities with weights more general than previously considered power weights. Moreover, it also allows to obtain weighted weak type $(1,1)$ inequalities, which seem to be new even in the unweighted setting. As a typical application of the transplantation, multiplier results in weighted $L^p$ spaces with general weights are obtained for the Hankel transform of any order $\alpha > -1$ greater than $-1$ by transplanting cosine transform multiplier results.
52 citations
TL;DR: In this article, the authors classified all toric Fano 3-folds with terminal singularities by solving the equivalent combinatoric problem; that of finding, up to the action of GL(3,Z), all convex polytopes in Z^3 which contain the origin as the only non-vertex lattice point.
Abstract: This paper classifies all toric Fano 3-folds with terminal singularities. This is achieved by solving the equivalent combinatoric problem; that of finding, up to the action of GL(3,Z), all convex polytopes in Z^3 which contain the origin as the only non-vertex lattice point.
43 citations
TL;DR: In this article, the authors classify singularities of light-like hypersurfaces in Minkowski 4-space via the contact invariants for corresponding spacelike surfaces and lightcones.
Abstract: We classify singularities of lightlike hypersurfaces in Minkowski 4-space via the contact invariants for the corresponding spacelike surfaces and lightcones.
40 citations
TL;DR: In this paper, the question of deformability of Legendre surfaces with respect to the symmetry group of Lie sphere contact transformations is addressed from the point of view of the deformation theory of submanifolds in homogeneous spaces.
Abstract: The theory of surfaces in Euclidean space can be naturally formulated in the more general context of Legendre surfaces into the space of contact elements. We address the question of deformability of Legendre surfaces with respect to the symmetry group of Lie sphere contact transformations from the point of view of the deformation theory of submanifolds in homogeneous spaces. Necessary and sufficient conditions are provided for a Legendre surface to admit non-trivial deformations, and the corresponding existence problem is discussed.
30 citations
TL;DR: In this paper, a large family of Lagrangian surfaces in complex Euclidean plane was constructed by using Legendre curves in the 3-sphere and in the anti de Sitter 3-space.
Abstract: We present a method to construct a large family of Lagrangian surfaces in complex Euclidean plane $\boldsymbol{C}^2$ by using Legendre curves in the 3-sphere and in the anti de Sitter 3-space or, equivalently, by using spherical and hyperbolic curves, respectively. Among this family, we characterize minimal, constant mean curvature, Hamiltonian-minimal and Willmore surfaces in terms of simple properties of the curvature of the generating curves. As applications, we provide explicitly conformal parametrizations of known and new examples of minimal, constant mean curvature, Hamiltonian-minimal and Willmore surfaces in $\boldsymbol{C}^2$.
29 citations
29 citations
TL;DR: In this paper, the complex Coxeter group associated with a proper complex equifocal submanifold in a symmetric space of non-compact type was defined and proved to be decomposable.
Abstract: In this paper, we define the notion of the complex Coxeter group associated with a proper complex equifocal submanifold in a symmetric space of non-compact type. We prove that a proper complex equifocal submanifold is decomposed into a non-trivial (extrinsic) product of two such submanifolds if and only if its associated complex Coxeter group is decomposable. Its proof is performed by showing a splitting theorem for an infinite-dimensional proper anti-Kaehlerian isoparametric submanifold.
27 citations
TL;DR: In this paper, a complete classification of all immersed hypersurfaces in the unit sphere with parallel Blaschke tensors is given, and two kinds of new examples are constructed.
Abstract: In this paper, we give a complete classification of all immersed hypersurfaces in the unit sphere with parallel Blaschke tensors. For this classification, two kinds of new examples are constructed.
25 citations
TL;DR: In this article, a self-contained combinatorial approach to Fujita's conjectures in the toric case is presented, where the main result is a generalization of the very ampleness conjecture for toric varieties with arbitrary singularities.
Abstract: We present a self-contained combinatorial approach to Fujita's conjectures in the toric case. Our main new result is a generalization of Fujita's very ampleness conjecture for toric varieties with arbitrary singularities. In an appendix, we use similar methods to give a new proof of an analogous toric generalization of Fujita's freeness conjecture due to Fujino.
TL;DR: In this paper, the uniqueness problem of meromorphic functions in the whole plane was studied under some conditions in an angular domain instead of the whole planes. And the authors showed that those conditions are necessary and sufficient.
Abstract: There are many papers on the uniqueness theory of meromorphic functions in the whole plane $\boldsymbol{C}$. However, the uniqueness theory concerned with shared sets in an angular domain does not yet seem widely investigated. In this paper, we deal with the problem of uniqueness for meromorphic functions in $\boldsymbol{C}$ under some conditions in an angular domain instead of the whole plane. Moreover, examples show that those conditions are necessary.
TL;DR: In this paper, the authors generalize and complete some of Maxim's recent results on Alexan- der invariants of a polynomial transversal to the hyperplane at infinity.
Abstract: We generalize and complete some of Maxim's recent results on Alexan- der invariants of a polynomial transversal to the hyperplane at infinity. Roughly speaking, and surprisingly, such a polynomial behaves both topologically and al- gebraically (e.g. in terms of the variation of MHS on the cohomology of its smooth fibers), like a homogeneous polynomial.
TL;DR: In this article, a characterisation of semi-stable stochastic processes on local fields such as epochs, spans, and indices is given, and differences in nature from the corresponding objects for Euclidean spaces are clarified.
Abstract: Some characters of semi-stable stochastic processes on local fields such as epochs, spans, and indices are given, and differences in nature from the corresponding objects for Euclidean spaces are clarified. Criteria for the recurrence and for the polarity of one point sets are given, and it is shown that semi-stable processes are characterized as limits of suitably scaled sums of independent identically distributed random variables.
TL;DR: The Catanese-Ciliberto surface of as mentioned in this paper is a minimal algebraic surface of general type with pg = q = 1, K2 S = 3 and k2 S 2 = 3.
Abstract: In this paper, we study a minimal surface of general type with pg = q = 1, K2 S = 3 which we call a Catanese-Ciliberto surface. The Albanese map of this surface gives a fibration of curves over an elliptic curve. For an arbitrary elliptic curve E, we obtain the Catanese-Ciliberto surface which satisfies Alb(S) ∼= E, has no (−2)-curves and has a unique singular fiber. Furthermore, we show that the number of the isomorphism classes satisfying these conditions is four if E has no automorphism of complex multiplication type. 0. Introduction. Let S be a minimal algebraic surface of general type over C. A proper surjective morphism f : S → C from an algebraic surface S to a non-singular algebraic curve C is called a fibration of curves of genus g if fibers of f are connected and the genus of the generic fiber is g . It is important to study the structures of the fibrations for surfaces of general type. For instance, Horikawa studied surfaces with fibrations of curves of genus two [5, 6]. We set pg (S) = dimH 2(S,OS) and q(S) = dimH 1(S,OS). Let K2 S be the self intersection number of the canonical divisor KS of S. In this paper, we are interested in the case pg (S) = q(S) = 1 and K2 S = 3. If q(S) = 1, then the Albanese map a : S → Alb(S) gives a fibration of curves over the elliptic curve E = Alb(S). Let g be the genus of a general fiber of a. Catanese and Ciliberto studied this surface in [2, 3] and showed that the genus g is two or three. DEFINITION. Let S be a minimal algebraic surface of general type over C. S is called a Catanese-Ciliberto surface if S satisfies pg = q = 1 and K2 S = 3. We also denote by KS the invertible sheaf associated to the divisor KS . In the case g = 3, Catanese and Ciliberto showed that the direct image V = a∗KS/E of the relative canonical sheaf KS/E = KS ⊗OS (a∗Ω1 E)∨ ∼= KS is an indecomposable vector bundle of rank three and degree one over the elliptic curve E. Therefore, there exists a point P ∈ E such that detV ∼= OE(P ). Let p : PE(a∗KS) → E be the P2-bundle associated with a∗KS and ω : S → PE(a∗KS) the relative canonical map. They obtained the following theorem. THEOREM 0.1 (Catanese-Ciliberto [3, Theorem 3.1]). Let S, a,E, g, P, p and ω be as above, and H the tautological divisor of PE(a∗KS), i.e., it satisfies p∗OPE(a∗KS)(H) ∼= a∗KS . If g = 3, then we have: 2000 Mathematics Subject Classification. Primary 14D05; Secondary 14J29, 14D06.
TL;DR: In this article, the normality of the closure of the set of vectors which are conjugate to a vector in a simply connected semisimple algebraic group was studied.
Abstract: Let $G$ be a simply connected semisimple algebraic group and let $K$ be the subgroup of points fixed by an involution of $G$ For certain representations containing a line $r$ preserved by $K$, we study the normality of the closure of the set of vectors which are $G$ conjugate to a vector in $r$ Some applications of our result to the normality of certain classical varieties are given
TL;DR: In this paper, a wavelet transform of Moritoh has been used to characterize wave front sets in the sense of Hormander in the case of dimensions n = 1, 2, 4, 8.
Abstract: We consider a special wavelet transform of Moritoh and give new definitions of wave front sets of tempered distributions via that wavelet transform. The major result is that these wave front sets are equal to the wave front sets in the sense of Hormander in the cases $n=1, 2, 4, 8$. If $n\in \boldsymbol{N} \setminus \{1, 2, 4, 8\}$, then we combine results for dimensions $n=1, 2, 4, 8$ and characterize wave front sets in $\xi$-directions, where $\xi$ are presented as products of non-zero points of $\boldsymbol{R}^{n_1}, \dotsc, \boldsymbol{R}^{n_s}$, $n_1+ \dotsb +n_s=n, n_i \in \{1, 2, 4, 8\}$, $i=1, \dotsc, s$. In particular, the case $n=3$ is discussed through the fourth-dimensional wavelet transform.
TL;DR: In this paper, the authors extend the well-known results about the process of confluence for the Gauss hypergeometric differential equation to the case of general hyper-geometric systems.
Abstract: We extend the well-known results about the process of confluence for the Gauss hypergeometric differential equation to the case of general hypergeometric systems. We see that the process of confluence comes from the geometry of the set of regular elements of the Lie algebra of complex general linear group. As a consequence, we give a geometric and group-theoretic view on the process of confluence for classical special functions.
TL;DR: In this paper, a two-parameter family of coupled Painleve II systems in dimension four, which can be obtained by a degeneration from the systems of type $A_4^{(1)}$, were studied.
Abstract: We find and study a two-parameter family of coupled Painleve II systems in dimension four, which can be obtained by a degeneration from the systems of type $A_4^{(1)}$. These systems are compared with other types of coupled Painleve II systems from the viewpoint of the local index. We also give the phase spaces for these systems.
TL;DR: In this article, the authors established the law of large numbers for the range of simple symmetric random walks under the conditional probability given the event that the last point is the origin.
Abstract: The range of random walks means the number of distinct sites visited at least once by the random walk. In two-or-more-dimensional cases, we established the law of large numbers for the range of simple symmetric random walks under the conditional probability given the event that the last point is the origin. Moreover we studied the large deviations in the upward direction and obtained similar results to the original random walk.
TL;DR: In this article, equivariant completions of toric contraction morphisms are treated as an ap-plication of the toric Mori theory for non-Q-factorial toric varieties.
Abstract: We treat equivariant completions of toric contraction morphisms as an ap- plication of the toric Mori theory. For this purpose, we generalize the toric Mori theory for non-Q-factorial toric varieties. So, our theory seems to be quite different from Reid's original combinatorial toric Mori theory. We also explain various examples of non-Q-factorial con- tractions, which imply that the Q-factoriality plays an important role in the Minimal Model Program. Thus, this paper completes the foundation of the toric Mori theory and shows us a new aspect of the Minimal Model Program.
TL;DR: Recently, this article proved that Schubert varieties are globally F -regular and gave another simpler proof simpler than the original one, which is based on the same algorithm as the one presented here.
Abstract: Recently, Lauritzen, Raben-Pedersen and Thomsen proved that Schubert varieties are globally F -regular. We give another proof simpler than the original one.
TL;DR: In this article, the authors obtained several characterizations of the relatively weakly compact subsets of the predual of a JBW*-triple, and described the relative compactness of these subsets.
Abstract: We obtain several characterizations of the relatively weakly compact subsets of the predual of a JBW*-triple. As a consequence we describe the relatively weakly compact subsets of the predual of a JBW*-algebra.
TL;DR: In this article, it was shown that the complex projective 3-space of a harmonic Riemann sphere into the unit 4-dimensional sphere has area 4 pi d for some positive integer d. When d is less than or equal to 2, the subspace consisting of those maps which are linearly full is empty.
Abstract: A harmonic map of the Riemann sphere into the unit 4-dimensional sphere has area 4 pi d for some positive integer d, and it is well-known that the space of such maps may be given the structure of a complex algebraic variety of dimension 2d+4. When d is less than or equal to 2, the subspace consisting of those maps which are linearly full is empty. We use the twistor fibration from complex projective 3-space to the 4-sphere to show that, if d is equal to 3,4 or 5, this subspace is a complex manifold.
TL;DR: In this paper, the Alexandrov-Toponogov comparison theorem was generalized to the case of complete Riemannian manifolds referred to warped product models, and the maximal diameter theorem and the rigidity theorem were proved.
Abstract: We generalize the Alexandrov-Toponogov comparison theorem to the case of complete Riemannian manifolds referred to warped product models. We prove the maximal diameter theorem and the rigidity theorem. In particular, we discuss collapsing phenomena where the curvature explosion may occur.
TL;DR: In this paper, the authors studied Hankel operators on the harmonic Bergman spaces on bounded smooth domains and obtained a necessary and sufficient condition for them to be bounded or compact on both the harmonic space and its dual space.
Abstract: We study Hankel operators on the harmonic Bergman spaces on bounded smooth domains, and obtain a necessary and sufficient condition for Hankel operators to be bounded or compact on both harmonic Bergman space and its dual space.
TL;DR: In this paper, the authors studied the Borel summability of divergent solutions for singularly perturbed inhomogeneous first-order linear ordinary differential equations which have a regularity at the origin.
Abstract: This paper is concerned with the study of the Borel summability of divergent solutions for singularly perturbed inhomogeneous first-order linear ordinary differential equations which have a regularity at the origin. In order to assure the Borel summability of divergent solutions, global analytic continuation properties for coefficients are required despite the fact that the domain of the Borel sum is local.
TL;DR: In this paper, the structure of local cohomology modules of the Fourier transform of A-hypergeometric systems is studied, with respect to the orbit of a certain action on the toric variety determined by A. The purpose is to describe their structure by using a certain combinatorial object.
Abstract: We study the structure of the local cohomologymodules of the Fourier transform of A-hypergeometric systems. In particular, we are interested in local cohomology modules with respect to the orbit of a certain action on the toric variety determined by A. The purpose in this paper is to describe their structure by using a certain combinatorial object.
TL;DR: In this article, the von Neumann rho-invariant of surface bundles over the circle S 1 is described. And a relation among the von-Neumann rHO-Invariant, the first Morita-Mumford class and the Rochlin invariant in a framework of bounded cohomology is given.
Abstract: In this short note, we give a formula for the von Neumann rho-invariant of surface bundles over the circle S1. As a corollary, we describe a relation among the von Neumann rho-invariant, the first Morita-Mumford class and the Rochlin invariant in a framework of the bounded cohomology.
TL;DR: In this article, it was shown that the flow generated by a generalized cooperative and irreducible system is strongly monotone and an analogue of the Poincare-Bendixon theorem holds for three dimensional generalized competitive and dissipative systems.
Abstract: In this paper, we are concerned with $n$-dimensional generalized competitive or cooperative systems of ordinary differential equations. A result is established to show that the flow generated by a generalized cooperative and irreducible system is strongly monotone. Also, it is shown that an analogue of the Poincare-Bendixon theorem holds for three dimensional generalized competitive and dissipative systems. Finally, we provide a generalized Smale's construction.