Hokkaido Mathematical Journal Articles (Project Euclid)

Projectively flat connections and flat connections on homogeneous spaces

Thu, 05 Aug 2010 15:41 EDT

Hajime URAKAWA

Source: Hokkaido Math. J., Volume 39, Number 2, 139--155.

Abstract:
We show a correspondence between the set of all $G$-invariant projectively flat connections on a homogeneous space $M=G/K$, and the one of all $\widetilde{G}$-invariant flat connections on homogeneous spaces $\widetilde{M}=\widetilde{G}/K$, where $\widetilde{G}$ is a central extension of $G$ (Theorem 3.3).

The abstract Fatou theorem and the signal transmission on Thomson cables

Thu, 05 Aug 2010 15:41 EDT

Hikosaburo KOMATSU

Source: Hokkaido Math. J., Volume 39, Number 2, 157--171.

Abstract:
The Fatou theorem on the Poisson representation of bounded harmonic functions on a half space is generalized to the bounded solutions $u(t)$ of the second order equation $$ u''(t) = A u(t), 0 < t < \infty, $$ in a dual Banach space $X = X_*{'}$, when $A$ is the dual of a non-negative operator $A_*$ with dense domain in $X_*$. Any bounded weak* solution is represented as $u(t) =$ $\exp(-t\sqrt{A})f$ with the weak* initial value $f$. Its prototype is in A.~V. Balakrishnan's paper in 1960 on fractional powers of non-negative operators. This is applied to prove the uniqueness of solutions in the theory of signal transmission on submarine cables by W. Thomson in 1855.

On a theorem of Benard

Thu, 05 Aug 2010 15:41 EDT

Joujuu OHMORI

Source: Hokkaido Math. J., Volume 39, Number 2, 173--209.

Abstract:
We shall give some remarks on a theorem of Benard.

Solvable graphs and Fermat primes

Thu, 05 Aug 2010 15:41 EDT

Nobuo IIYORI

Source: Hokkaido Math. J., Volume 39, Number 2, 211--215.

Abstract:
A solvable graph of a finite group is one of generalized prime graphs of groups which are introduced as generalizations of a prime graph of a finite group in \cite{AI1}. In this paper we will characterize a Fermat prime by a solvable graph of a finite group.

A generalization of antipodal point theorems for set-valued mappings

Thu, 05 Aug 2010 15:41 EDT

Yoshimi SHITANDA

Source: Hokkaido Math. J., Volume 39, Number 2, 217--238.

Abstract:
Let $U$ be a bounded symmetric open neighborhood of the origin of $\R^{m+k} \ (k\geqq 1)$. We shall prove a generalization of the Borsuk's antipodal theorem for an admissible mapping $\varphi:\partial\overline{U}\to \R^m$ and the related topic. We shall generalize the theorem for the case of a bounded symmetric open neighborhood $U$ of the origin of an infinite dimensional normed space $\mathbf{E}$. The Borsuk-Ulam theorem shall be studied for the case of a bounded symmetric open neighborhood $U$ of the origin of an infinite dimensional normed space $\mathbf{E}$.

Limiting absorption principle for the second quantization of self-adjoint operators

Thu, 05 Aug 2010 15:41 EDT

Shoji SHIMIZU

Source: Hokkaido Math. J., Volume 39, Number 2, 239--259.

Abstract:
In this paper we discuss the limiting absorption principle (l.a.p.) of the second quantization of semi-bounded self-adjoint operators. We show that the l.a.p. for a self-adjoint operator on a basic Hilbert space $\mathcal{H}$ is ``inherited'' to the one for its second quantization on a Fock space $\mathcal{F}(\mathcal{H})$. In order to show such a result, we examine the resolvent of $n$-body problem and take the limit of the infinite direct sum of those operators in a suitable subspace of $\mathcal{F}(\mathcal{H})$.

Scaling limit for the Derezi\'nski-G\'erard model

Wed, 15 Dec 2010 09:12 EST

Atsushi OHKUBO

Source: Hokkaido Math. J., Volume 39, Number 3, 261--290.

Abstract:
We consider a scaling limit for the Derezi\'nski-G\'erard model. We derive an effective potential by taking a scaling limit for the total Hamiltonian of the Derezi\'nski-G\'erard model. Our method to derive an effective potential is independent of whether or not the quantum field has a nonnegative mass. As an application of our theory developed in the present paper, we derive an effective potential of the Nelson model.

Time periodic solutions of the Navier-Stokes equations under general outflow condition in a two dimensional symmetric channel

Wed, 15 Dec 2010 09:12 EST

Teppei KOBAYASHI

Source: Hokkaido Math. J., Volume 39, Number 3, 291--316.

Abstract:
In this paper we will prove that there exists a time periodic solution of the Navier-Stokes equations with the inhomogeneous boundary condition for infinite symmetric channels in $\R^2$. In two and three dimensional more generalized infinite channels (than treated in this paper) H.~Beir\~ao~da Veiga \cite{Beirao} proved that there exists time periodic solutions of the Navier-Stokes equations with the homogeneous boundary condition under a small time periodic flux. G.~P.~Galdi and A.~M.~Robertson \cite{GalRob} obtained time-periodic Poiseuille flow in a straight channel with a smooth cross section. C.~J.~Amick \cite{Amick2} proved that in two and three dimensional unbounded channels there exists solutions of the stationary Navier-Stokes equations with the nonhomogenous boundary condition. H.~Morimoto and H.~Fujita \cite{Morimoto1} and H.~Morimoto \cite{Morimoto2} proved that in a two dimensional certain unbounded symmetric channel there exists symmetric solutions of the stationary Navier-Stokes equations with a special symmetric Dirichlet boundary condition. T-P.~Kobayashi \cite{Kobayashi3} demonstrated that for two and three dimensional infinite channels time periodic solutions of the Navier-Stokes equations exist under the same condition as C.~J.~Amick \cite{Amick2}. In this paper using the condition of H.~Morimoto and H.~Fujita \cite{Morimoto1} and H.~Morimoto \cite{Morimoto2}, we obtain time priodic solutions.

On generalized spin-boson models with singular perturbations

Wed, 15 Dec 2010 09:12 EST

Toshimitsu TAKAESU

Source: Hokkaido Math. J., Volume 39, Number 3, 317--349.

Abstract:
In this paper we consider generalized spin-boson models with singular perturbations. It is proven that under the infrared regularity condition Hamiltonians have the unique ground state for sufficiently small values of coupling constants. In addition it is shown that the asymptotic creation and annihilation operators of massless boson field exist.

Orthogonal almost complex structures of hypersurfaces of purely imaginary octonions

Wed, 15 Dec 2010 09:12 EST

Hideya HASHIMOT, Misa OHASHI

Source: Hokkaido Math. J., Volume 39, Number 3, 351--387.

Abstract:
First we give the new elementary proof of the structure equations of $G_2$ and the congruence theorem of hypersurfaces of the purely imaginary octonions $\ImO$ under the action of $G_2$. Next, we classify almost complex structures of homogeneous hypersurfaces of $\ImO$ into 4-types.

The unique ergodicity of equicontinuous laminations

Wed, 15 Dec 2010 09:12 EST

Shigenori MATSUMOTO

Source: Hokkaido Math. J., Volume 39, Number 3, 389--403.

Abstract:
We prove that a transversely equicontinuous minimal lamination on a locally compact metric space $Z$ has a transversely invariant nontrivial Radon measure. Moreover if the space $Z$ is compact, then the tranversely invariant Radon measure is shown to be unique up to a scaling.

On the boundedness of a class of rough maximal operators on product spaces

Mon, 14 Mar 2011 09:13 EDT

Hussain M. AL-QASSEM, Leslie C. CHENG, Yibiao PAN

Source: Hokkaido Math. J., Volume 40, Number 1, 1--32.

Abstract:
In this paper, we study the L p boundedness of a class of maximal operators T {Ω j } (γ) and a related class of rough singular integrals on product spaces. We obtain appropriate L p estimates for such maximal operators and singular integrals. These estimates are used in an extrapolation argument and allow us to obtain some new and improved results for certain maximal integral operators and singular integrals on product spaces under certain sharp conditions on the kernel functions. Also, one of our main results in this paper is a corrigendum of a result obtained by Ding-Lin.

A removable singularity theorem of J -holomorphic mappings for strongly pseudo-convex manifolds

Mon, 14 Mar 2011 09:13 EDT

Takanari SAOTOME

Source: Hokkaido Math. J., Volume 40, Number 1, 33--49.

Abstract:
We investigate a removable singularity theorem and other some basic properties of a J -holomorphic mapping for strongly pseudo-convex manifolds, which are necessary for constructing the moduli space of J -holomorphic mappings.

Finite p -groups with a fixed-point-free automorphisms of order seven

Mon, 14 Mar 2011 09:13 EDT

Shousaku ABE

Source: Hokkaido Math. J., Volume 40, Number 1, 51--66.

Abstract:
We prove several properties of finite p -groups which are generated by two elements of prime order p and which have a fixed-point-free automorphism of order seven.

Riesz transforms on generalized Hardy spaces and a uniqueness theorem for the Navier-Stokes equations

Mon, 14 Mar 2011 09:13 EDT

Eiichi NAKAI, Tsuyoshi YONEDA

Source: Hokkaido Math. J., Volume 40, Number 1, 67--88.

Abstract:
The purpose of this paper is twofold. Let R j ( j = 1,2, …, n ) be Riesz transforms on $\mathbb{R}$ n . First we prove the convergence of truncated operators of R i R j in generalized Hardy spaces. Our first result is an extension of the convergence in L p ($\mathbb{R}$^ n ) (1 < p < ∞). Secondly, as an application of the first result, we show a uniqueness theorem for the Navier-Stokes equation. J. Kato (2003) established the uniqueness of solutions of the Navier-Stokes equations in the whole space when the velocity field is bounded and the pressure field is a BMO-valued locally integrable-in-time function for bounded initial data. We extend the part “BMO-valued” in his result to “generalized Campanato space valued”. The generalized Campanato spaces include L 1 , BMO and homogeneous Lipschitz spaces of order α (0 < α < 1).

On the Riesz bases, frames and minimal exponential systems in L 2 [-π,π]

Mon, 14 Mar 2011 09:13 EDT

Akihiro Nakamura

Source: Hokkaido Math. J., Volume 40, Number 1, 89--102.

Abstract:
P. G. Casazza, O. Christensen, S. Li, and A. Lindner proved in [3] that some families of complex exponentials were either Riesz bases or not frames in L 2 [-π,π]. First, we shall advance their results in this note. Sedletskii constructed in [9] an exponential system which is complete, minimal and not uniformly minimal with separable spectrum in L 2 [-π,π]. Next, we shall construct a similar example with nonseparable spectrum in L 2 [-π,π].

The structure of δ-stable minimal hypersurfaces in $\mathbb{R}$ n+1

Mon, 14 Mar 2011 09:13 EDT

Hai-Ping FU

Source: Hokkaido Math. J., Volume 40, Number 1, 103--110.

Abstract:
Let M n ( n ≥ 3) be a complete δ (> $\frac{(n-1)^2}{n^2}$)-stable minimal hypersurface in an ( n + 1)-dimensional Euclidean space $\mathbb{R}$ n +1 . We prove that there are no nontrivial L 2 harmonic 1-forms on M and the first de Rham's cohomology group with compact support of M is trivial. As corollaries, M has only one end. This implies that if M has finite total curvature, then M is a hyperplane.

A new generalization of Besov-type and Triebel-Lizorkin-type spaces and wavelets

Mon, 14 Mar 2011 09:13 EDT

Koichi SAKA

Source: Hokkaido Math. J., Volume 40, Number 1, 111--147.

Abstract:
In this paper we introduce a new function space which unifies and generalizes the Besov-type and the Triebel-Lizorkin-type function spaces introduced by S. Jaffard and D. Yang- W. Yuan. This new function space covers the Besov spaces and the Triebel-Lizorkin spaces in the homogeneous case, and further the Morrey spaces. We define the new function space through wavelet expansions. We establish characterizations of the new function space such as the ϕ-transform characterization in the sense of Frazier-Jawerth, the atomic and molecular decomposition characterization. Moreover, in the inhomogeneous case, we give a characterization by local polynomial approximation. As application, we investigate the boundedness of the Calderòn-Zygmund operator and the trace theorem on the new function space.

An inverse scattering problem for the Klein-Gordon equation with a classical source in quantum field theory

Thu, 07 Jul 2011 08:47 EDT

Hironobu SASAKI, Akito SUZUKI

Source: Hokkaido Math. J., Volume 40, Number 2, 149--186.

Abstract:
An inverse scattering problem for a quantized scalar field ${\bm \phi}$ obeying a linear Klein-Gordon equation $$ (\square + m^2 + V) {\bm \phi} = J \quad\mbox{in $\mathbb{R} \times \mathbb{R}^3$} $$ is considered, where $V$ is a repulsive external potential and $J$ an external source. We prove that the scattering operator $\mathscr{S}= \mathscr{S}(V,J)$ associated with ${\bm \phi}$ uniquely determines $V$. Assuming that $J$ is of the form $J(t,x)=j(t)\rho(x)$, $(t,x) \in \mathbb{R} \times \mathbb{R}^3$, we represent $\rho$ (resp. $j$) in terms of $j$ (resp. $\rho$) and $\mathscr{S}$.

Hardy's inequality in Orlicz-Sobolev spaces of variable exponent

Thu, 07 Jul 2011 08:47 EDT

Yoshihiro MIZUTA, Eiichi NAKAI, Takao OHNO, Tetsu SHIMOMURA

Source: Hokkaido Math. J., Volume 40, Number 2, 187--203.

Abstract:
Our aim in this paper is to deal with a norm version of Hardy's inequality for Orlicz-Sobolev functions with $|\nabla u| \in L^{p(\cdot)}\log L^{p(\cdot)q(\cdot)}(\Omega)$ for an open set $\Omega \subset \R^n$. Here $p(\cdot)$ and $q(\cdot)$ are variable exponents satisfying log-H\"older and loglog-H\"older conditions, respectively. We are also concerned with the case when $p$ attains the value 1 in some parts of the domain is included in the results.

Real hypersurfaces which are contact in a nonflat complex space form

Thu, 07 Jul 2011 08:47 EDT

Toshiaki ADACHI, Masumi KAMEDA, Sadahiro MAEDA

Source: Hokkaido Math. J., Volume 40, Number 2, 205--217.

Abstract:
In an $n$ $(\geqq2)$-dimensional nonflat complex space form $\widetilde{M}_n(c)(=\mathbb{C}P^n(c)$ or $\mathbb{C}H^n(c)$), we classify real hypersurfaces $M^{2n-1}$ which are contact with respect to the almost contact metric structure $(\phi,\xi,\eta,g)$ induced from the K\"ahler structure $J$ and the standard metric $g$ of the ambient space $\widetilde{M}_n(c)$. Our theorems show that this contact manifold $M^{2n-1}$ is congruent to a homogeneous real hypersurface of $\widetilde{M}_n(c)$.

Null Darboux developable and pseudo-spherical Darboux image of null Cartan curve in Minkowski 3-space

Thu, 07 Jul 2011 08:47 EDT

Zhigang WANG, Donghe PEI

Source: Hokkaido Math. J., Volume 40, Number 2, 219--240.

Abstract:
Singularities of null Darboux developable, Gaussian surfaces and pseudo-spherical Darboux images associated with a null Cartan curve will be investigated in Minkowski 3-space. The relationships will be revealed between singularities of the above three subjects and differential geometric invariants of null Cartan curves, these invariants are deeply related to the order of contact of null Cartan curves with null helices.

A remark on radial $\bm{A_p}$ weights

Thu, 07 Jul 2011 08:47 EDT

Kôzô YABUTA

Source: Hokkaido Math. J., Volume 40, Number 2, 241--249.

Abstract:
We show that a class of radial weights $\tilde A_p(\R_+)$, introduced by Duoandikoetxea, is contained in the weight class $A_p^I(\Rn)$ defined by using all $n$-dimensional rectangles with sides parallel to the coordinate axes.

A study on the dimension of global sections of adjoint bundles for polarized manifolds, II

Thu, 07 Jul 2011 08:47 EDT

Yoshiaki FUKUMA

Source: Hokkaido Math. J., Volume 40, Number 2, 251--277.

Abstract:
Let $X$ be a smooth complex projective variety of dimension $n$ and let $L$ be an ample line bundle on $X$. In our previous paper, in order to investigate the dimension of $H^{0}(K_{X}+tL)$ more systematically, we introduced the invariant $A_{i}(X,L)$ for every integer $i$ with $0\leq i\leq n$. Main purposes of this paper are (1) to study a lower bound of $A_{i}(X,L)$ for the following two cases: (1.a) the case where $L$ is merely ample and $i\leq 3$, (1.b) the case of $h^{0}(L)>0$, and (2) to evaluate a lower bound for the dimension of $H^{0}(K_{X}+tL)$ by using $A_{i}(X,L)$.

Invariant measures for subshifts arising from substitutions of some primitive components

Thu, 07 Jul 2011 08:47 EDT

Masaki HAMA, Hisatoshi YUASA

Source: Hokkaido Math. J., Volume 40, Number 2, 279--312.

Abstract:
The notion of substitutions of some primitive components is introduced. A bilateral subshift arising from a substitution of some primitive components is decomposed into pairwise disjoint, locally compact, shift-invariant sets, on each of which an invariant Radon measure is unique up to scaling. In terms of eigenvalues of an incidence matrix associated with the substitution, it is completely characterized when the unique invariant measure is finite.

Equivalence problem of second order PDE for scale transformations

Tue, 25 Oct 2011 22:24 EDT

Takahiro NODA

Source: Hokkaido Math. J., Volume 40, Number 3, 313--335.

Abstract:
The purpose of the paper is to consider an equivalence problem of second order partial differential equations for one unknown function of two independent variables under scale transformations. For this equivalence problem, explicit forms of invariant functions are given. In particular, if all of these invariant functions vanish, then PDEs are equivalent to the flat equation.

Bishop's property (β) and an elementary operator

Tue, 25 Oct 2011 22:24 EDT

Muneo CHŌ, Slavisa DJORDJEVIĆ, Bhaggy DUGGAL

Source: Hokkaido Math. J., Volume 40, Number 3, 337--356.

Abstract:
A Banach space operator T ∈ B (¥cal{X}) is hereditarily polaroid, T ∈ (¥cal{HP}), if the isolated points of the spectrum of every part T p of the operator are poles of the resolvent of T p ; T is hereditarly normaloid, T ∈ (¥cal{HN}), if every part T p of T is normaloid. Let (¥cal{HNP}) denote the class of operators T ∈ B (¥cal{X}) such that T ∈ (¥cal{HP}) ∩ (¥cal{HN}). (¥cal{HNP}) operators such that the Berberian-Quigley extension T ° of T is also in (¥cal{HNP}) satisfy Bishop's property (β). Given Hilbert space operators A , B * ∈ B (¥cal{H}), let d AB ∈ B ( B (¥cal{H})) stands for either of the elementary operators δ AB ( X ) = AX - XB and Δ AB ( X ) = AXB - X . If A , B * ∈ (¥cal{HP}) satisfy property (β), and the eigenspaces corresponding to distinct eigenvalues of A (resp., B * ) are orthogonal, then f ( d AB ) satisfies Weyl's theorem and f ( d AB ) * satisfies a -Weyl's theorem for every function f which is analytic on a neighbourhood of σ( d AB ). Finally, we characterize perturbations of d AB by quasinilpotent and algebraic operators A , B ∈ B (¥cal{H}).

An elementary semi-ampleness result for log canonical divisors

Tue, 25 Oct 2011 22:24 EDT

Shigetaka FUKUDA

Source: Hokkaido Math. J., Volume 40, Number 3, 357--360.

Abstract:
If the log canonical divisor on a projective variety with only Kawamata log terminal singularities is numerically equivalent to some semi-ample Q -divisor, then it is semi-ample.

View from inside

Tue, 25 Oct 2011 22:24 EDT

Takashi NISHIMURA, Yu SAKEMI

Source: Hokkaido Math. J., Volume 40, Number 3, 361--373.

Abstract:
In this paper, we define a perspective projection of a given immersed n -dimensional hypersurface as a C ∞ map via a C ∞ immersion from the given n -manifold to S n +1 , and characterize when and only when such a perspective projection is non-singular. In order to obtain such characterizations, we consider an immersion from an n -dimensional manifold to S n +1 . We first obtain equivalent conditions for a given point P of S n +1 to be outside the union of tangent great hyperspheres of a given immersed n -dimensional manifold r ( N ) in S n +1 (Theorem 2.4). It turns out that if such a point P exists then the given manifold N must be diffeomorphic to S n and in the case that n ≥ 2 the given immersion r : N → S n +1 must be an embedding. Then, we obtain characterizations of a perspective projection of a given immersed n -dimensional manifold to be non-singular. Next, we obtain one more equivalent condition in terms of hedgehogs when the given N is S n and the given immersion is an embedding (Theorem 3.3). We also explain why we consider these equivalent conditions for an embedding r : S n → S n +1 instead of an embedding ¥widetilde{ r }: S n → ¥mathbb{R} n +1 in terms of hedgehogs.

Bases for the derivation modules of two-dimensional ~multi-Coxeter arrangements and universal derivations

Tue, 25 Oct 2011 22:24 EDT

Atsushi WAKAMIKO

Source: Hokkaido Math. J., Volume 40, Number 3, 375--392.

Abstract:
Let ¥cal{A} be an irreducible Coxeter arrangement and k be a multiplicity of ¥cal{A}. We study the derivation module D (¥cal{A}, k ). Any two-dimensional irreducible Coxeter arrangement with even number of lines is decomposed into two orbits under the action of the Coxeter group. In this paper, we will explicitly construct a basis for D (¥cal{A}, k ) assuming k is constant on each orbit. Consequently we will determine the exponents of (¥cal{A}, k ) under this assumption. For this purpose we develop a theory of universal derivations and introduce a map to deal with our exceptional cases.

Reverse Cauchy-Schwarz type inequalities in pre-inner product C * -modules

Tue, 25 Oct 2011 22:24 EDT

Jun-Ichi FUJII, Masatoshi FUJII, Mohammad Sal MOSLEHIAN, Josip E. PEČARIĆ, Yuki SEO

Source: Hokkaido Math. J., Volume 40, Number 3, 393--409.

Abstract:
In the framework of a pre-inner product C * -module over a unital C * -algebra, we show several reverse Cauchy-Schwarz type inequalities of additive and multiplicative types, by using some ideas in N. Elezović et al. [Math. Inequal. Appl., 8 (2005), no.2, 223-231]. We apply our results to give Klamkin-Mclenaghan, Shisha-Mond and Cassels type inequalities. We also present a Grüss type inequality.

Grassmann geometry on the 3-dimensional unimodular Lie groups II

Tue, 25 Oct 2011 22:24 EDT

Jun-ichi INOGUCHI, Hiroo NAITOH

Source: Hokkaido Math. J., Volume 40, Number 3, 411--429.

Abstract:
We study the Grassmann geometry of surfaces in the special real linear group SL (2,¥mathbb{R}).

A characterization of 42 ovoids with a certain property in PG (3,2)

Tue, 25 Oct 2011 22:24 EDT

Koichi INOUE

Source: Hokkaido Math. J., Volume 40, Number 3, 431--447.

Abstract:
In this paper, we characterize 42 ovoids with a certain property in a projective space PG (3,2) described in Yucas [6]. As a corollary, we construct the Steiner 4-wise balanced design S (4,{5,6},17) with 252 blocks which is an extension of the point-plane design A of an affine space AG (4,2). The construction leads to not only the uniqueness of such an extension, but also a (usual) extension of the 2-repeated design 2. A .

Motivic interpretation of Milnor K -groups attached to Jacobian varieties

Mon, 27 Feb 2012 09:02 EST

Satoshi MOCHIZUKI

Source: Hokkaido Math. J., Volume 41, Number 1, 1--10.

Abstract:
In the paper [Som90], Somekawa conjectures that his Milnor K -group K ( k , G 1 ,…, G r ) attached to semi-abelian varieties G 1 ,…, G r over a field k is isomorphic to Ext $¥mathcal{M}$ k r ($¥mathbb{Z}$, G 1 [-1] ⊗ … ⊗ G r [-1]) where $¥mathcal{M}$ k is a certain category of motives over k . The purpose of this note is to prove this conjecture, when the varieties G i are Jacobians of smooth curves over a perfect field and we take $¥mathcal{M}$ k as Voevodsky's category of motives DM - eff ( k ).

Finite p -groups which determine p -nilpotency locally

Mon, 27 Feb 2012 09:02 EST

Thomas S. WEIGEL

Source: Hokkaido Math. J., Volume 41, Number 1, 11--29.

Abstract:
Let G be a finite group, and let p be a prime number. It might happen that the p -Sylow normalizer N G ( P ), P ∈ Syl p ( G ), of G is p -nilpotent, but G will not be p -nilpotent (see Example 1.1). However, under certain hypothesis on the structure of the Sylow p -subgroup P of G , this phenomenon cannot occur, e.g., by J. Tate's p -nilpotency criterion this is the case if P is a Swan group in the sense of H-W. Henn and S. Priddy. In this note we show that if P does not contain subgroups of a certain isomorphism type Y p ( m ) in which case we call the p -group P slim the previously mentioned phenomenon will not occur provided p is odd. For p = 2 the same remains true if P is D 8 -free (see Main Theorem).

Lie group-Lie algebra correspondences of unitary groups in finite von Neumann algebras

Mon, 27 Feb 2012 09:02 EST

Hiroshi ANDO, Yasumichi MATSUZAWA

Source: Hokkaido Math. J., Volume 41, Number 1, 31--99.

Abstract:
We give an affirmative answer to the question whether there exist Lie algebras for suitable closed subgroups of the unitary group U ($¥mathcal{H}$) in a Hilbert space $¥mathcal{H}$ with U ($¥mathcal{H}$) equipped with the strong operator topology. More precisely, for any strongly closed subgroup G of the unitary group U ($¥mathfrak{M}$) in a finite von Neumann algebra $¥mathfrak{M}$, we show that the set of all generators of strongly continuous one-parameter subgroups of G forms a complete topological Lie algebra with respect to the strong resolvent topology. We also characterize the algebra $¥overline{¥mathfrak{M}}$ of all densely defined closed operators affiliated with $¥mathfrak{M}$ from the viewpoint of a tensor category.

Analysis of strongly commuting self-adjoint operators with applications to a spin-$¥frac{1}{2}$ neutral particle with anomalous magnetic moment

Mon, 27 Feb 2012 09:02 EST

Norio TOMINAGA, Yasuhiko FURIHATA

Source: Hokkaido Math. J., Volume 41, Number 1, 101--134.

Abstract:
Using strong commuting self-adjoint operators in the Minkowski space, we showed that the operator concerning a neutral particle with an anomalous magnetic moment is related to that of a free particle by a non-unitary transformation.

Limits of iterations of complex maps and hypergeometric functions

Mon, 27 Feb 2012 09:02 EST

Keiji MATSUMOTO, Takashi OIKAWA

Source: Hokkaido Math. J., Volume 41, Number 1, 135--155.

Abstract:
We consider the limit of the iteration of a map z ↦ m ( z ) from a complex domain D to D . For two kinds of maps m , we show that each iteration m n ( z ) of m ( z ) converges for any z ∈ D as n → ∞ and that this limit is expressed by the hypergeometric function. These are analogs of the expression of the arithmetic-geometric mean by the Gauss hypergeometric function.

Prediction of fractional processes with long-range dependence

Tue, 26 Jun 2012 08:40 EDT

Akihiko INOUE, Vo V. ANH

Source: Hokkaido Math. J., Volume 41, Number 2, 157--183.

Abstract:
We introduce a class of Gaussian processes with stationary increments which exhibit long-range dependence. The class includes fractional Brownian motion with Hurst parameter H > 1/2 as a typical example. We establish infinite and finite past prediction formulas for the processes in which the predictor coefficients are given explicitly in terms of the MA(∞) and AR(∞) coefficients.

Extensions of cyclic p -groups which preserve the irreducibilities of induced characters

Tue, 26 Jun 2012 08:40 EDT

Katsusuke SEKIGUCHI

Source: Hokkaido Math. J., Volume 41, Number 2, 185--208.

Abstract:
For a prime p , we denote by B n the cyclic group of order p n . Let ϕ be a faithful irreducible character of B n , where p is an odd prime. We study the p -group G containing B n such that the induced character ϕ G is also irreducible. Set [ N G ( B n ): B n ] = p m and [ G : B n ] = p M . The purpose of this paper is to determine the structure of G under the hypothesis [ N G ( B n ): B n ] 2 d ≤ p n , where d is the smallest integer not less than M/m .

Local existence and uniqueness for the n -dimensional Helfrich flow as a projected gradient flow

Tue, 26 Jun 2012 08:40 EDT

Takeyuki NAGASAWA, Taekyung YI

Source: Hokkaido Math. J., Volume 41, Number 2, 209--226.

Abstract:
The gradient flow associated to the Helfrich variational problem, called the Helfrich flow is considered. Here the n -dimensional Helfrich flow is investigated for any n , as a projected gradient flow. A result of local existence is proved. The uniqueness is shown for the cases (i) for the initial hypersurface with non-zero Gramian when n ≥ 2, (ii) for every initial curve when n = 1.

Rational solutions of the Sasano system of type A 1 (1)

Tue, 26 Jun 2012 08:40 EDT

Kazuhide MATSUDA

Source: Hokkaido Math. J., Volume 41, Number 2, 227--255.

Abstract:
In this paper, we completely classify the rational solutions of the Sasano system of type A 1 (1) , which is a degeneration of the Sasano system of type A 4 (2) . These systems of differential equations are both expressed as coupled Painlevé II systems. The Sasano system of type A 1 (1) is a higher order version of the second Painlevé equation, P II , with the same affine Weyl group symmetry of type A 1 (1) as P II .

Positive Toeplitz operators on the Bergman space of a minimal bounded homogeneous domain

Tue, 26 Jun 2012 08:40 EDT

Satoshi YAMAJI

Source: Hokkaido Math. J., Volume 41, Number 2, 257--274.

Abstract:
Necessary and sufficient conditions for positive Toeplitz operators on the Bergman space of a minimal bounded homogeneous domain to be bounded or compact are described in terms of the Berezin transform, the averaging function and the Carleson property

Algebraic BP -theory and norm varieties

Tue, 26 Jun 2012 08:40 EDT

Nobuaki YAGITA

Source: Hokkaido Math. J., Volume 41, Number 2, 275--316.

Abstract:
Let p be an odd prime and BP * ( pt ) ≅ $¥mathbb Z$ ( p ) [ v 1 , v 2 ,…] the coefficient ring of the Brown-Peterson cohomology theory BP * (−) with | v i | = −2 p i + 2. We study ABP *,*' (−) theory, which is the counter part in algebraic geometry of the BP * (−) theory. Let k be a field with k ⊂ $¥mathbb C$ and K * M ( k ) the Milnor K -theory. For a nonzero symbol a ∈ K n +1 M ( k )/ p , a norm variety V a is a smooth variety such that a | k ( V a ) = 0 ∈ K n +1 M ( k ( V a ))/ p and V a ($¥mathbb C$) = v n . In particular, we compute ABP *,*' ( M a ) for the Rost motive M a which is a direct summand of the motive M ( V a ) of some norm variety V a .

Equinormalizable theory for plane curve singularities with embedded points and the theory of equisingularity

Wed, 24 Oct 2012 09:43 EDT

Công-Trình LÊ

Source: Hokkaido Math. J., Volume 41, Number 3, 317--334.

Abstract:
In this paper we give some criteria for a family of generically reduced plane curve singularities to be equinormalizable. The first criterion is based on the δ-invariant of a (non-reduced) curve singularity which is introduced by Brücker-Greuel ([BG]). The second criterion is based on the I-equisingularity of a k -parametric family ( k ≥ 1) of generically reduced plane curve singularities, which is introduced by Nobile ([No]) for one-parametric families. The equivalence of some kinds of equisingularities of a family of generically reduced plane curve singularities is also studied.

Representing and interpolating sequences on parabolic Bloch type spaces

Wed, 24 Oct 2012 09:43 EDT

Yôsuke HISHIKAWA, Masahiro YAMADA

Source: Hokkaido Math. J., Volume 41, Number 3, 335--364.

Abstract:
Let H be the upper half-space of the Euclidean space. The α-parabolic Bloch type space $¥cal B$ α (σ) on H is the set of all solutions u of the parabolic equation (∂/∂ t + (−Δ x ) α ) u = 0 with 0 < α ≤ 1 which belong to C 1 ( H ) and have finite Bloch norm with weight t σ . In this paper, we study representing and interpolating sequences on parabolic Bloch type spaces. In our previous paper [8], the reproducing formula on $¥cal B$ α (σ) is given. A representing sequence gives a discrete version of the reproducing formula on $¥cal B$ α (σ). Interpolating sequences are closely related to representing sequences, and such sequences are very interesting in their own right.

Some elliptic fibrations arising from free rigid body dynamics

Wed, 24 Oct 2012 09:43 EDT

Isao NARUKI, Daisuke TARAMA

Source: Hokkaido Math. J., Volume 41, Number 3, 365--407.

Abstract:
An elliptic fibration over P 3 ($¥mathbb{C}$), naively arising from the Euler equation for free rigid body dynamics, is studied from the viewpoint of complex algebraic geometry. With this elliptic fibration, associated is an elliptic fibration in Weierstraß normal form, whose generic fibres are isomorphic to those of the original fibration. This normal form is desingularized in a canonical manner. It is shown that there is a four-to-one meromorphic mapping from the naive elliptic fibration to the Weierstraß mormal form. The latter fibration is also shown to be bimeromorphic to the family of spectral curves arising from the corresponding Manakov equation.

Geometric characterization of Monge-Ampère equations

Wed, 24 Oct 2012 09:43 EDT

Atsushi YANO

Source: Hokkaido Math. J., Volume 41, Number 3, 409--440.

Abstract:
It is well known that a Monge-Ampère equation can be expressed in terms of exterior differential system—Monge-Ampère system, which is the ideal generated algebraically by a contact form and a 2-form and its exterior derivatives on a 5-dimensional contact manifold, and the system is independent of the choice of coordinate system. On the other hand, a single second order partial differential equation of one unknown function with two independent variables corresponds to the differential system on a hypersurface of Lagrange-Grassmann bundle over a 5-dimensional contact manifold obtained by restricting its canonical system to the hypersurface. We observe relations between Monge characteristic systems of Monge-Ampère equation and those of Monge-Ampère system and particularly analyze structure equations of those systems. This observation leads to the result—to characterize Monge-Ampère equation by the property that the certain differential system defined from the Monge characteristic system drops down to the contact manifold.

Generalized Mannheim curves in Minkowski space-time E 1 4

Wed, 24 Oct 2012 09:43 EDT

Soley ERSOY, Murat TOSUN, Hiroo MATSUDA

Source: Hokkaido Math. J., Volume 41, Number 3, 441--461.

Abstract:
In this paper, the definition of generalized spacelike Mannheim curve in Minkowski space-time E 1 4 is given. The necessary and sufficient conditions for the generalized spacelike Mannheim curve are obtained. Also, some characterizations of Mannheim curve are given.

A note on extreme norms on $\mathbb R$ 2

Mon, 04 Mar 2013 09:17 EST

Kichi-Suke SAITO, Ken-Ichi MITANI, Naoto KOMURO

Source: Hokkaido Math. J., Volume 42, Number 1, 1--9.

Abstract:
We denote by AN 2 the set of all absolute normalized norms on $\mathbb R$ 2 . It is known that the set AN 2 and the set of all continuous convex functions ψ on [0,1] with max{1−t,t} ≤ ψ( t ) ≤ 1 for t ∈ [0,1] (denoted by Ψ 2 ) are in a one to one correspondence under the equation ψ( t ) = ||(1− t , t )||. Recently, we characterized extreme points of AN 2 by considering Ψ 2 . In this paper we give another proof of this result.

Linearized stability analysis of surface diffusion for hypersurfaces with triple lines

Mon, 04 Mar 2013 09:17 EST

Daniel DEPNER, Harald GARCKE

Source: Hokkaido Math. J., Volume 42, Number 1, 11--52.

Abstract:
The linearized stability of stationary solutions for surface diffusion is studied. We consider three hypersurfaces that lie inside a fixed domain and touch its boundary with a right angle and fulfill a non-flux condition. Additionally they meet at a triple line with prescribed angle conditions and further boundary conditions resulting from the continuity of chemical potentials and a flux balance have to hold at the triple line. We introduce a new specific parametrization with two parameters corresponding to a movement in tangential and normal direction to formulate the geometric evolution law as a system of partial differential equations. For the linearized stability analysis we identify the problem as an H −1 -gradient flow, which will be crucial to show self-adjointness of the linearized operator. Finally we study the linearized stability of some examples.

On generalizations of separable polynomials over rings

Mon, 04 Mar 2013 09:17 EST

Naoki HAMAGUCHI, Atsushi NAKAJIMA

Source: Hokkaido Math. J., Volume 42, Number 1, 53--68.

Abstract:
We define that a ring extension S/R is weakly separable or weakly quasi-separable by using R -derivations of S , and give the necessary and sufficient condition that the extension R [ X ]/( X n − aX − b ) of a commutative ring R is weakly separable. Since the notions of weakly separability and weakly quasi-separability coincide for commutative ring extensions, we treat a quotient ring R [ x ; *] = R [ X ; *]/ f ( X ) R [ X ; *] of a skew polynomial ring R [ X ; *], and show that if R is a commutative domain, then the extension R [ x ; *]/ R is always weakly quasi-separable, where * is either a ring automorphism or a derivation of R . We also treat the weakly separability of R [ x ; *]/ R and give various types of examples of these extensions.

A characterization of the standard Reeb flow

Mon, 04 Mar 2013 09:17 EST

Shigenori MATSUMOTO

Source: Hokkaido Math. J., Volume 42, Number 1, 69--80.

Abstract:
Among the topological conjugacy classes of the continuous flows {ϕ t } whose orbit foliations are the planar Reeb foliation, there is one special class called the standard Reeb flow. We show that {ϕ t } is conjugate to the standard Reeb flow if and only if {ϕ t } is conjugate to {ϕ λ t } for any λ > 0.

Generalized wave operators for a system of semilinear wave equations in three space dimensions

Mon, 04 Mar 2013 09:17 EST

Hideo KUBO, Kôji KUBOTA

Source: Hokkaido Math. J., Volume 42, Number 1, 81--111.

Abstract:
This paper is concerned with the final value problem for a system of semilinear wave equations. The main issue is to solve the problem when the nonlinearity is of a long-range type. By assuming that the solution is spherically symmetric, we shall show global solvability of the final value problem around a suitable final state, and hence, the generalized wave operator and long range-scattering operator can be constructed.

Takeshita's examples for Leray's Inequality

Mon, 04 Mar 2013 09:17 EST

Teppei KOBAYASHI

Source: Hokkaido Math. J., Volume 42, Number 1, 113--120.

Abstract:
It is well known that Leray's Inequality holds under stringent outflow condition ( SOC ). But Leray's Inequality does not hold under general outflow condition ( GOC ). This fact has been proved by Takeshita [8]. But, Takeshita's argument is very complicated. The author succeeds in giving an alternative proof which is simpler than Takeshita's. Moreover, the result is an improvement of Takeshita's result.

On the existence of local frames of CR vector bundles

Mon, 04 Mar 2013 09:17 EST

Tomonori KAJISA

Source: Hokkaido Math. J., Volume 42, Number 1, 121--130.

Abstract:
Given a CR manifold D , we shall show that existence of a CR local frame of a certain CR vector bundle over D is equivalent to the local imbeddability of D . This will imply that there exists a CR vector bundle which doesn't have CR local frames. Using this bundle, we shall construct CR line bundles over 3-dimensional non-imbeddable CR manifolds which don't have CR local frames.

Atomic decompositions of weighted Hardy-Morrey spaces

Mon, 04 Mar 2013 09:17 EST

Kwok-Pun HO

Source: Hokkaido Math. J., Volume 42, Number 1, 131--157.

Abstract:
We obtain the Fefferman-Stein vector-valued maximal inequalities on Morrey spaces generated by weighted Lebesgue spaces. Using these inequalities, we introduce and define the weighted Hardy-Morrey spaces by using the Littlewood-Paley functions. We also establish the non-smooth atomic decompositions for the weighted Hardy-Morrey spaces and, as an application of the decompositions, we obtain the boundedness of a class of singular integral operators on the weighted Hardy-Morrey spaces.