Tsukuba Journal of Mathematics Articles (Project Euclid)

Contents for Tsukuba Journal of Mathematics, Vol 33, No. 2

Thu, 05 Aug 2010 15:41 EDT

Source: Tsukuba J. Math., Volume 33, Number 2.

Convergence rates of approximate sums of the areas of surfaces of revolution

Thu, 05 Aug 2010 15:41 EDT

Yuriko Gorai, Hiroyuki Tasaki, Mio Yamakawa

Source: Tsukuba J. Math., Volume 33, Number 2, 281--297.

Abstract:
We represent the convergence rates of approximate sums of the areas of surfaces of revolution as limits of their expanded error terms and estimate them. In the case of convex surfaces of revolution we represent the convergence rates of them by the integral of certain functions.

On some matrix diophantine equations

Thu, 05 Aug 2010 15:41 EDT

Aleksander Grytczuk, Izabela Kurzydlo

Source: Tsukuba J. Math., Volume 33, Number 2, 299--304.

Abstract:
Let $A \in M_n(\mathbf{C})$, $n \ge 2$ be the matrix which has at least one real eigenvalue $\alpha \in (0, 1)$. If the matrix equation \begin{equation} A^x + A^y + A^z = A^w \tag{1} \end{equation} is satisfied in positive integers $x$, $y$, $z$, $w$, then $\max \{x-w, y-w, z-w\} \ge 1$. If suppose that the matrix $A$ has at least one real eigenvalue $\alpha > \sqrt{2}$ and the equation (1) is satisfied in positive integers $x$, $y$, $z$ and $w$, then $\max \{x-w, y-w, z-w\} = -1$. Moveover, we investigate the solvability of the matrix equations (1) and \begin{equation} A^x + A^y = A^z \tag{2} \end{equation} for the non-negative real $n \times n$ matrices, where $|\det A| > 1$, in positive integers $x$, $y$, $z$, $w$ for (1) and $x$, $y$, $z$ for (2). Using the wellknown theorem of Perron-Frobenius we obtain some informations concerning solvability these equations.

On quasi-Einstein spacetimes

Thu, 05 Aug 2010 15:41 EDT

Absos Ali Shaikh, Dae Won Yoon, Shyamal Kumar Hui

Source: Tsukuba J. Math., Volume 33, Number 2, 305--326.

Abstract:
The notion of quasi-Einstein manifolds arose during the study of exact solutions of the Einstein field equations as well as during considerations of quasi-umbilical hypersurfaces. For instance, the Robertson-Walker spacetimes are quasi-Einstein manifolds. The object of the present paper is to study quasi-Einstein spacetimes . Some basic geometric properties of such a spacetime are obtained. The applications of quasi-Einstein spacetimes in general relativity and cosmology are investigated. Finally, the existence of such spacetimes are ensured by several interesting examples.

Dowker spaces revisited

Wed, 08 Sep 2010 13:36 EDT

Lewis D. Ludwig, Peter Nyikos, John E. Porter

Source: Tsukuba J. Math., Volume 34, Number 1, 1--11.

Abstract:
In 1951, Dowker proved that a space $X$ is countably paracompact and normal if and only if $X \times {\bf I}$ is normal. A normal space $X$ is called a Dowker space if $X \times {\bf I}$ is not normal. The main thrust of this article is to extend this work with regards $\alpha$-normality and $\beta$-normality. Characterizations are given for when the product of a space $X$ and $(\omega + 1)$ is $\alpha$-normal or $\beta$-normal. A new definition, $\alpha$- countably paracompact , illustrates what can be said if the product of $X$ with a compact metric space is $\beta$-normal. Several examples demonstrate that the product of a Dowker space and a compact metric space may or may not be $\alpha$-normal or $\beta$-normal. A collectionwise Hausdorff. Moore space constructed by M. Wage is shown to be $\alpha$-normal but not $\beta$-nornal.

A product formula defined by the Beta function and Gauss's hypergeometric function

Wed, 08 Sep 2010 13:36 EDT

Takuma Ogawa, Yasuo Kamata

Source: Tsukuba J. Math., Volume 34, Number 1, 13--30.

Abstract:
Let $c$ be a constant in ${\bf R}^t$. For a plane algebraic curve $r^{2m-n} = 2c^n \cos n\theta$, which depends on $m$ and $n$ in ${\bf N}$, we show that the whole length of the curve are given by a value of a product formula defined by the Beta function and Gauss's hypergeometric function depending $m$ and $n$ in ${\bf N}$. Besides, we point out the fact to be a similar model and an expansion for the complete elliptic integral of the second kind. Last, we give a background for the fact explaining the special case $m = n$.

On the Cartier duality of certain finite group schemes of type $(p^n, p^n)$

Wed, 08 Sep 2010 13:36 EDT

Nobuhiro Aki, Michio Amano

Source: Tsukuba J. Math., Volume 34, Number 1, 31--46.

Abstract:
In this paper we show that the finite subgroup scheme Spec $A[X, Y]/(X^{p^l}, Y^{p^l})$ of $\mathscr{E}^{\lambda, \mu, D} \in {\rm Ext}^1(\mathscr{G}^{(\lambda)}, \mathscr{G}^{(\mu)})$ is a Cartier dual of a certain finite subgroup scheme of the fiber product $W_{l,A} \times_{{\rm Spec} A} W_{l,A}$ of Witt vectors of length $l$ in positive characteristic $p$. After this, we treat the kernel of the type $F^2 + [a]F + [b]: W_{l,A} \to W_{l,A}$, where $F$ is the Frobenius endomorphism and $[a]$ is the Teichmüller lifting of $a \in A$, respectively.

The construction of the uniformly minimum variance unbiased estimator

Wed, 08 Sep 2010 13:36 EDT

Kim Hyo Gyeong

Source: Tsukuba J. Math., Volume 34, Number 1, 47--58.

Abstract:
For a one-parameter exponential family of distributions, a method to find the uniformly minimum variance unbiased (UMVU) estimator based on the complete sufficient statistic is given in Jani and Dave [1] by change of the expression of the unbiasedness condition. But, it heavily depends on the concrete form of the distribution of the statistic in obtaining indeed the UMVU estimator. In this paper, from the different point of view, the construction of the UMVU estimator for a one-parameter exponential families of distributions and certain two-parameter family of distributions is discussed. Some examples are also given.

Note on Hermitian Jacobi forms

Wed, 08 Sep 2010 13:36 EDT

Soumya Das

Source: Tsukuba J. Math., Volume 34, Number 1, 59--78.

Abstract:
We compare the spaces of Hermitian Jacobi forms (HJF) of weight $k$ and indices 1, 2 with classical Jacobi forms (JF) of weight $k$ and indices 1, 2, 4. Upper bounds for the order of vanishing of HJF at the origin are obtained. We compute the rank of HJF as a module over elliptic modular forms and prove the algebraic independence of the generators in case of index 1. Some related questions are discussed.

Geometric classification of quadratic algebras in two variables

Wed, 08 Sep 2010 13:36 EDT

Kenta Ueyama

Source: Tsukuba J. Math., Volume 34, Number 1, 79--96.

Abstract:
In this paper, we classify quadratic algebras in two variables at two levels: (1) up to isomorphism of graded algebras, (2) up to graded Morita equivalence. In general, it is difficult to classify algebras by looking at generators and relations, so we take a geometric approach, namely, using point schemes defined by Artin, Tate and Van den Bergh, to complete the classification.

Bernoulli-type relations in some noncommutative polynomial ring

Wed, 08 Sep 2010 13:36 EDT

Shunsuke Murata

Source: Tsukuba J. Math., Volume 34, Number 1, 97--116.

Abstract:
We find particular relations which we call “Bernoulli-type” in some noncommutative polynomial ring with a single nontrivial relation. More precisely, our ring is isomorphic to the universal enveloping algebra of a two-dimensional non-abelian Lie algebra. From these Bernoulli-type relations in our ring, we can obtain a representation on a certain left ideal with the Bernoulli numbers as structure constants.

Odd dimensional Riemannian submanifolds admitting the almost contact metric structure in a Euclidean sphere

Wed, 08 Sep 2010 13:36 EDT

Okumura Kazuhiro

Source: Tsukuba J. Math., Volume 34, Number 1, 117--128.

Abstract:
We investigate some odd dimensional Rimannian submanifolds admitting the almost contact metric structure $(\phi, \xi, \eta, \langle , \rangle)$ of a certain Euclidean sphere from the viewpoint of the weakly $\phi$-invariance of the second fundamental form. The family of such submanifolds contains some homogeneous submanifolds of the ambient sphere. In the latter half of this paper, we caluculate the mean curvature and the length of the derivative of the mean curvature vector of these homogeneous submanifolds.

Similarities involving unbounded normal operators

Wed, 08 Sep 2010 13:36 EDT

Mohammed Hichem Mortad

Source: Tsukuba J. Math., Volume 34, Number 1, 129--136.

Abstract:
We prove and disprove some generalizations of a result about some similarities involving normal operators due to M. R. Embry in 1970. Some interesting consequences are also given.

Hermann type actions on a pseudo-Riemannian symmetric space

Fri, 08 Apr 2011 09:10 EDT

Naoyuki Koike

Source: Tsukuba J. Math., Volume 34, Number 2, 137--172.

Abstract:
In this paper, we first investigate the shape operators of certain kind of orbits of the isotropy action of a semi-simple pseudo-Riemannian symmetric space. The investigation is performed by investigating the complexified action. Next, by using the fact obtained by the investigation, we show that certain kind of principal orbits of a Hermann type action on a semi-simple pseudo-Riemannian symmetric space are curvature-adapted proper complex equifocal submanifolds and that their shape operators are semisimple. It follows from this fact that the principal orbits are isoparametric submanifolds with flat section. Also, we derive an interesting structure of a semi-simple pesudo-Riemannian symmetric space (in particular, the complexification of a Riemannian symmetric space) from two special Hermann type actions on the space.

Comparison of the definitions of abelian 2-categories

Fri, 08 Apr 2011 09:10 EDT

Hiroyuki Nakaoka

Source: Tsukuba J. Math., Volume 34, Number 2, 173--182.

Abstract:
In the efforts to define a 2-categorical analog of an abelian category, two (or three) notions of "abelian 2-categories" are defined in [4] and [2]. One is the relatively exact 2- category defined in [4], and the other(s) is the (2-) abelian Gpd- category defined by Dupont [2]. We compare these notions, using the arguments in [4] and [2]. Since they proceed independently in their own way, in different settings and terminologies, it will be worth while to collect and unify them. In this paper, by comparing their definitions and arguments, we show the relationship among these classes of 2-categories.

On the Cartier duality of certain finite group schemes of type ( p n , ..., p n )

Fri, 08 Apr 2011 09:10 EDT

Nobuhiro Aki

Source: Tsukuba J. Math., Volume 34, Number 2, 183--200.

Abstract:
In this paper, we determine the Cartier dual of certain finite group schemes of type ( p n , ..., p n ), restricting ourselves to positive characteristic p case. They are given by the kernel of certain endomormphisms of the fibre product W l,A × Spec A … × Spec A W l,A of the group scheme of Witt vectors of the length l . Moreover we can treat the kernel of the endomorphism of a type F n + a 1 F n -1 + … + a n : W l,A → W l,A as our special class, where F is the Frobenius endomorphism and a k ( k = 1, ..., n ) are suitable Witt vectors.

On Siegel modular cusp forms of degree two

Fri, 08 Apr 2011 09:10 EDT

Hisashi Kojima

Source: Tsukuba J. Math., Volume 34, Number 2, 201--212.

Abstract:

On some classes of spectral posets

Fri, 08 Apr 2011 09:10 EDT

Tomoo Yokoyama

Source: Tsukuba J. Math., Volume 34, Number 2, 213--219.

Abstract:
This paper deals with sufficient conditions on a poset in order to get it spectral. A motivating question is the following (p. 833 [LO76]): "If X is a height 1 poset such that for all x ≠ y ∈ X , ↑ x ∩ ↑ y and ↓ x ∩ ↓ y are finite, is X spectral?" We obtain the some sufficient conditions for such a poset X to be spectral. In particular, we prove that either if there is a finite subset F ⊆ X such that ↓ F ⊇Min X , or if diam X ≤ 2, then the poset X is spectral.

Behavior of solutions to linear and semilinear parabolic pseudo-differential equations

Fri, 08 Apr 2011 09:10 EDT

Tomoyuki Kakehi, Kensuke Sakai

Source: Tsukuba J. Math., Volume 34, Number 2, 221--253.

Abstract:

Algebraic independence of infinite products generated by Fibonacci numbers

Fri, 08 Apr 2011 09:10 EDT

Takeshi Kurosawa, Yohei Tachiya, Taka-aki Tanaka

Source: Tsukuba J. Math., Volume 34, Number 2, 255--264.

Abstract:
The aim of this paper is to establish necessary and sufficient conditions for certain infinite products generated by Fibonacci numbers and by Lucas numbers to be algebraically independent.

On the group of extensions Ext 1 ($\mathscr{G}$ (λ 0 ) , $\mathscr{E}$ (λ 1 , ..., λ n ) ) over a discrete valuation ring

Fri, 08 Apr 2011 09:10 EDT

Takashi Kondo

Source: Tsukuba J. Math., Volume 34, Number 2, 265--294.

Abstract:
For given group schemes $\mathscr{G}$ (λ i ) ( i = 1, 2, ...) deforming the additive group scheme G a to the multiplicative group scheme G m , T. Sekiguchi and N. Suwa constructed extensions: 0 → $\mathscr{G}$ (λ 2 ) → $\mathscr{E}$ (λ 1 , λ 2 ) → $\mathscr{G}$ (λ 1 ) → 0, … 0 → $\mathscr{G}$ (λ n ) → $\mathscr{E}$ (λ 1 , ..., λ n ) → $\mathscr{E}$ (λ 1 , ..., λ n -1 ) → 0, … inductively, by calculating the group of extensions Ext 1 ($\mathscr{E}$ (λ 1 , ..., λ n -1 ) , $\mathscr{G}$ (λ n ) ). Here changing the group schemes, we treat the group Ext 1 ($\mathscr{G}$ (λ 0 ) , $\mathscr{E}$ (λ 1 , ..., λ n ) ) of extensions for any positive integers n . The case of n = 2, 3 were studied by D. Horikawa and T. Kondo.

The Gromov-Hausdorff distances between Alexandrov spaces of curvature bounded below by 1 and the standard spheres

Tue, 19 Jul 2011 09:17 EDT

Ayato Mitsuishi

Source: Tsukuba J. Math., Volume 35, Number 1, 1--12.

Abstract:
Main result in the present paper is the following: If an n -dimensional Alexandrov spaces X n of curvature ≥ 1 has radius greater than Π - ε, then the Gromov-Hausdor. distance between X n and the standard sphere S n is less than τ(ε). Here, τ(ε) is an explicit positive function depending only on ε such that lim ε→0 τ(ε) = 0. We prove this by using quasigeodesics on Alexandrov spaces.

Propagation of analyticity in the C ∞ solutions of quasi-linear weakly hyperbolic wave equations

Tue, 19 Jul 2011 09:17 EDT

R. Manfrin

Source: Tsukuba J. Math., Volume 35, Number 1, 13--52.

Abstract:
We study the propagation of the analytic regularity of the C ∞ solutions of the quasi-linear, weakly hyperbolic wave equation u tt - a ( u ) u xx = 0, where a ( u ) is a bounded, nonnegative analytic function.

The structure Jacobi operator for real hypersurfaces in the complex projective plane and the complex hyperbolic plane

Tue, 19 Jul 2011 09:17 EDT

Hiroyuki Kurihara

Source: Tsukuba J. Math., Volume 35, Number 1, 53--66.

Abstract:
Recently, we investigated real hypersurfaces in a n -dimentional complex projective space and complex hyperbolic space with respect to various structure Jacobi operator conditions. However these results necessitates dimension assumption n ≥ 3. The purpose of this paper is to study such real hypersurfaces in the complex projective plane and the complex hyperbolic plane.

Chain mixing endomorphisms are approximated by subshifts on the Cantor set

Tue, 19 Jul 2011 09:17 EDT

Takashi Shimomura

Source: Tsukuba J. Math., Volume 35, Number 1, 67--77.

Abstract:
Let f be a chain mixing continuous onto mapping from the Cantor set onto itself. Let g be a homeomorphism on the Cantor set that is topologically conjugate to a subshift. Then, homeomorphisms that are topologically conjugate to g approximate f in the topology of uniform convergence if a trivial necessary condition on the periodic points holds. In particular, if f is a chain mixing continuous onto mapping from the Cantor set onto itself with a fixed point, then homeomorphisms on the Cantor set that are topologically conjugate to a subshift approximate f in the topology of uniform convergence. In addition, homeomorphisms on the Cantor set that are topologically conjugate to a subshift without periodic points approximate any chain mixing continuous onto mappings from the Cantor set onto itself. In particular, let f be a homeomorphism on the Cantor set that is topologically conjugate to a full shift. Let g be a homeomorphism on the Cantor set that is topologically conjugate to a subshift. Then, a sequence of homeomorphisms that is topologically conjugate to g approximates f .

Metric spheres in the projective spaces with constant holomorphic sectional curvature

Tue, 19 Jul 2011 09:17 EDT

Nobuhiro Innami, Yukihiro Mashiko, Katsuhiro Shiohama

Source: Tsukuba J. Math., Volume 35, Number 1, 79--90.

Abstract:
We discuss codimension one isometric immersions of complete Riemannian manifolds into the projective spaces with constant holomorphic sectional curvature. Here, the shape operator and the curvature transformation with respect to the normal unit have the same eigenspaces. We then characterize the metric spheres in terms of the shape operator.

On weakly s -quasinormally embedded and ss -quasinormal subgroups of finite groups

Tue, 19 Jul 2011 09:17 EDT

Changwen Li

Source: Tsukuba J. Math., Volume 35, Number 1, 91--102.

Abstract:
Suppose G is a finite group and H is a subgroup of G . H is called weakly s -quasinormally embedded in G if there are a subnormal subgroup T of G and an s -quasinormally embedded subgroup H se of G contained in H such that G = HT and H ∩ T ≤ H se ; H is called ss -quasinormal in G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B . We investigate the influence of weakly s -quasinormally embedded and ss -quasinormal subgroups on the structure of finite groups. Some recent results are generalized.

An asymptotic expansion for the distribution of the supremum of a Markov-modulated random walk

Tue, 19 Jul 2011 09:17 EDT

Mikhail Sgibnev

Source: Tsukuba J. Math., Volume 35, Number 1, 103--113.

Abstract:
We obtain an asymptotic expansion for the distribution of the supremum of a Markov-modulated random walk, which takes into account the influence of the roots of the characteristic equation. An estimate is given for the remainder term by means of submultiplicative weight functions.

On the quasi-irreducibility and complete quasi-reducibility of some reductive prehomogeneous vector spaces

Tue, 19 Jul 2011 09:17 EDT

Michio Hamada

Source: Tsukuba J. Math., Volume 35, Number 1, 115--130.

Abstract:
In this paper, we investigate the Q-irreducibility and complete Q-reducibility of prehomogeneous vector spaces and classify such prehomogeneous vector spaces in some cases.

The quandle coloring invariant of a reducible handlebody-knot

Tue, 19 Jul 2011 09:17 EDT

Atsushi Ishii, Kengo Kishimoto

Source: Tsukuba J. Math., Volume 35, Number 1, 131--141.

Abstract:
A handlebody-knot is a handlebody embedded in the 3-sphere. We provide methods to detect the irreducibility of a handlebody-knot by using the quandle coloring invariant.

Random graphs with a random bijection

Tue, 19 Jul 2011 09:17 EDT

Yuki Anbo

Source: Tsukuba J. Math., Volume 35, Number 1, 143--151.

Abstract:
We show that the theory of random graphs with a bijection between the binary Cartesian product of the universe and the universe has a model companion which is complete, simple, and unsupersimple.

On boundaries of coxeter groups and topological fractal structures

Tue, 13 Mar 2012 13:11 EDT

Tetsuya Hosaka

Source: Tsukuba J. Math., Volume 35, Number 2, 153--160.

Abstract:
In this paper, based on research on rank-one isometries by W. Ballmann and M. Brin and recent research on rank-one isometries of Coxeter groups by P. Caprace and K. Fujiwara, we study a topological fractal structure of boundaries of Coxeter groups. We also show that the limit-point set is dense in a boundary of a Coxeter group and introduce some observations on boundaries of CAT(0) groups with rank-one isometries.

On p -harmonic maps into spheres

Tue, 13 Mar 2012 13:11 EDT

Sorin Dragomir, Andrea Tommasoli

Source: Tsukuba J. Math., Volume 35, Number 2, 161--167.

Abstract:
We study the topology of p -harmonic maps ϕ : M → S ν from a compact Riemannian manifold M into a sphere S ν . We also show that any p -energy minimizing map ϕ : M → S ν omitting a totally geodesic submanifold of codimension two Ε S ν is of class C 1 . This extends results by B. Solomon, [13], from harmonic to p -harmonic maps.

Metrizability of ordered additive groups

Tue, 13 Mar 2012 13:11 EDT

Chuan Liu, Yoshio Tanaka

Source: Tsukuba J. Math., Volume 35, Number 2, 169--183.

Abstract:
In terms of General Topology, we consider ordered additive groups having the order topology, including ordered fields. Namely, we investigate metrizability of these groups or fields, and topological properties of ordered fields in terms of Archimedes' axiom or the axiom of continuity. Also, we give a negative answer to a question in [9]. Finally, we revise the proof of [2, Theorem 2.6], and give some related results.

Necessary and sufficient conditions for the solvability and maximal regularity of abstract differential equations of mixed type in UMD spaces

Tue, 13 Mar 2012 13:11 EDT

Fatima Zohra Mezeghrani

Source: Tsukuba J. Math., Volume 35, Number 2, 185--202.

Abstract:
In this paper we give some results on some abstract second order differential elliptic equations with mixed type boundary conditions. The study is performed in UMD spaces. The main purpose of this paper is the study of necessary and sufficient conditions on the data for obtaining existence, uniqueness and maximal regulariy properties of the strict solution. On the other hand, we give some new examples related to traces results.

A generalization of Shelah's omitting types theorem

Tue, 13 Mar 2012 13:11 EDT

Kota Takeuchi

Source: Tsukuba J. Math., Volume 35, Number 2, 203--213.

Abstract:
This note gives generalizations of Shelah's omitting types theorem and Lopez-Escobar's Theorem.

Lorentzian stationary surfaces in 4-dimensional space forms of index 2

Tue, 13 Mar 2012 13:11 EDT

Makoto Sakaki

Source: Tsukuba J. Math., Volume 35, Number 2, 215--229.

Abstract:
We discuss the necessary and sufficient conditions for the existence of Lorentzian stationary surfaces in 4-dimensional space forms of index 2, and isometric stationary deformations preserving normal curvature.

A second limit formula for higher rank twisted Epstein zeta functions and some applications

Tue, 13 Mar 2012 13:11 EDT

Keiju Sono

Source: Tsukuba J. Math., Volume 35, Number 2, 231--251.

Abstract:
In this paper, we give the second limit formula and an analogue of the Chowla-Selberg formula for the twisted Epstein zeta functions of rank n > 2. As an application, we compute the determinant of the Euclidean Laplacian on the space of asymmetrically automorphic functions on R n by using our second limit formula.

On killing fields preserving minimal foliations of polynomial growth at most 2

Tue, 13 Mar 2012 13:11 EDT

Gen-ichi Oshikiri

Source: Tsukuba J. Math., Volume 35, Number 2, 253--258.

Abstract:
Let $\mathscr{F}$ be a minimal foliation of a complete Riemannian manifold ( M , g ). Assume that the orthogonal distribution to $\mathscr{F}$ is also integrable. We show that if the growth of $\mathscr{F}$ is at most 2 then any Killing field with bounded length preserves the foliation $mathscr{F}$.

Fractional powers and interpolation theory for multivalued linear operators and applications to degenerate differential equations

Tue, 13 Mar 2012 13:11 EDT

Alberto Favaron, Angelo Favini

Source: Tsukuba J. Math., Volume 35, Number 2, 259--323.

Abstract:
We provide intermediate properties for the domains of the fractional powers of an abstract multivalued linear operator A of weak parabolic type. In particular, our results exhibit the special role played by the linear subspace A 0, which reduces to {0} if and only if A is single-valued. The behaviour of the singular semigroup generated by A with respect to the domains of the fractional powers is then studied, and applications of this behaviour to questions of maximal time and space regularity for abstract multivalued evolution equations are given. As a concrete case we consider a class of degenerate partial differential evolution equations which may be rewritten in a multivalued evolution form.

Asymptotic behaviors for multidimensional Kirchhoff equations

Tue, 10 Jul 2012 16:22 EDT

Kunihiko Kajitani

Source: Tsukuba J. Math., Volume 36, Number 1, 1--42.

The construction of rotation surfaces of constant mean curvature and the corresponding Lagrangians

Tue, 10 Jul 2012 16:22 EDT

Keiichi Kikuchi

Source: Tsukuba J. Math., Volume 36, Number 1, 43--52.

Abstract:
A family of S 1 -equivariant hypersurfaces of constant mean curvature can be obtained by using the Lagrangians with suitable potentials in the unit 3-sphere equipped with a certain parameterized metric. The conservation law is e.ectively applied to the construction of S 1 -equivariant hypersurfaces of constant mean curvature.

Galois-Tukey connection involving sets of metrics

Tue, 10 Jul 2012 16:22 EDT

Masaru Kada, Yasuo Yoshinobu

Source: Tsukuba J. Math., Volume 36, Number 1, 53--66.

Abstract:
Kada proved in a previous paper (Topology Appl., 2009) that the collection of compatible metrics on a locally compact separable metrizable space has the same cofinal type, in the sense of Tukey relation, as the set of functions from ω to ω with respect to eventually dominating order. By generalizing this result, we characterize the order structure of the collection of compatible metrics on a separable metrizable space in terms of generalized Galois-Tukey connection.

Sublinear Higson corona of Euclidean cone

Tue, 10 Jul 2012 16:22 EDT

Tomohiro Fukaya

Source: Tsukuba J. Math., Volume 36, Number 1, 67--77.

Abstract:
Let X be a proper metric space. The sublinear Higson compactification h L X is a variant of the Higson compactification. Its boundary h L X \ X is denoted ν L X , and is called the sublinear Higson corona of X . The sublinear Higson corona is a functor from the category of coarse spaces to that of compact Hausdorff spaces. Let P be a compact metric space and X be an unbounded proper metric space. We show that the sublinear Higson corona of a product space P × X equipped with a cone metric is homeomorphic to a product P × ν L X . Especially, the sublinear Higson corona of the n -dimensional Euclidean space is homeomorphic to the product of an ( n − 1)-dimensional sphere and the sublinear Higson corona of natural numbers.

Loop groups SL 2 ( F [ X ; X −1 ]), universal central extensions and additive Steinberg symbols

Tue, 10 Jul 2012 16:22 EDT

Yasutomo Asai

Source: Tsukuba J. Math., Volume 36, Number 1, 79--97.

Abstract:
We determine the group presentations of universal central extensions derived from loop groups, where loop groups are Chevalley groups over Laurent polynomial rings. We also show that the universal central extensions have Tits systems. For our purpose, we introduce additive Steinberg symbols.

Pseudo-parallel CR submanifolds of a complex space form

Tue, 10 Jul 2012 16:22 EDT

Mayuko Kon

Source: Tsukuba J. Math., Volume 36, Number 1, 99--110.

Abstract:
We classify pseudo-parallel proper CR submanifolds of a non-flat complex space form with semi-flat normal connection under the condition that the dimension of the holomorphic tangent space is greater than 2.

Hochschild cohomology ring of a maximal order of the quaternion algebra

Tue, 10 Jul 2012 16:22 EDT

Takao Hayami

Source: Tsukuba J. Math., Volume 36, Number 1, 111--120.

Abstract:
We give an efficient bimodule projective resolution of a maximal Z -order Λ of the ordinary quaternion algebra over Q , and therefore we determine the ring structure of the Hochschild cohomology of Λ by calculating the Yoneda products using this resolution.

Gaps of F -Yang-Mills fields on submanifolds

Tue, 10 Jul 2012 16:22 EDT

Gao-Yang Jia, Zhen-Rong Zhou

Source: Tsukuba J. Math., Volume 36, Number 1, 121--134.

Abstract:
Replacing the integrand of the Yang-Mills functional by F (|| R ∇ || 2 /2), we define an F -Yang-Mills functional, and hence F -Yang-Mills fields, where F is a non-negative function. The gaps of F -Yang-Mills fields on some submanifolds of the Euclidean spaces and the spheres are investegated in this paper.

On a classification of 3-simple prehomogeneous vector spaces with two irreducible components

Tue, 10 Jul 2012 16:22 EDT

Yoshiteru Kurosawa

Source: Tsukuba J. Math., Volume 36, Number 1, 135--172.

Abstract:
In this paper, we give some results about a classification of reductive prehomogeneous vector spaces with two irreducible components. In particular, we give the complete classification of 3-simple prehomogeneous vector spaces with two irreducible components. We consider everything over the complex number field C .

Aperiodic homeomorphisms approximate chain mixing endomorphisms on the Cantor set

Mon, 21 Jan 2013 09:03 EST

Takashi Shimomura

Source: Tsukuba J. Math., Volume 36, Number 2, 173--183.

Abstract:
Let f be a chain mixing continuous onto mapping from the Cantor set onto itself. Let g be an aperiodic homeomorphism on the Cantor set. We show that homeomorphisms that are topologically conjugate to g approximate f in the topology of uniform convergence if a trivial necessary condition on periodic points is satisfied. In particular, let f be a chain mixing continuous onto mapping from the Cantor set onto itself with a fixed point and g , an aperiodic homeomorphism on the Cantor set. Then, homeomorphisms that are topologically conjugate to g approximate f .

Asymptotic dimension and boundary dimension of proper CAT(0) spaces

Mon, 21 Jan 2013 09:03 EST

Naotsugu Chinen, Tetsuya Hosaka

Source: Tsukuba J. Math., Volume 36, Number 2, 185--191.

Abstract:
In this paper, we investigate asymptotic dimension of proper CAT(0) spaces and we show that for a proper cocompact CAT(0) space ( X , d ), the asymptotic dimension asdim( X , d ) is greater than the covering dimension dim ∂ X of the boundary of X .

On the Gauss map of surfaces of revolution in the three-dimensional Minkowski space

Mon, 21 Jan 2013 09:03 EST

Chahrazede Baba-Hamed, Mohammed Bekkar

Source: Tsukuba J. Math., Volume 36, Number 2, 193--215.

Abstract:
In this paper, we study surfaces of revolution without parabolic points in the 3-dimensional Lorentz-Minkowski space whose Gauss map N satisfies the condition Δ II N = A N, where Δ II is the Laplace operator with respect to the second fundamental form and A is a real 3 × 3 matrix. More precisely we prove that such surfaces are either pseudo-Riemannian spheres S 2 1 or pseudohyperbolic spaces H 2 0 .

Weierstrass gap sequences at points of curves on some rational surfaces

Mon, 21 Jan 2013 09:03 EST

Jiryo Komeda, Akira Ohbuchi

Source: Tsukuba J. Math., Volume 36, Number 2, 217--233.

Abstract:
Let $\tilde{C}$ be a non-singular plane curve of degree d ≥ 8 with an involution σ over an algebraically closed field of characteristic 0 and $\tilde{P}$ a point of $\tilde{C}$ fixed by σ. Let π : $\tilde{C}$ → C = $\tilde{C}$/$/\langle\sigma\rangle $be the double covering. We set P = π($\tilde{P}$). When the intersection multiplicity at $\tilde{P}$ of the curve $\tilde{C}$ and the tangent line at $\tilde{P}$ is equal to d − 3 or d − 4, we determine the Weierstrass gap sequence at P on C using blowing-ups and blowing-downs of some rational surfaces.

On finite factors of centralizers of parabolic subgroups in Coxeter groups

Mon, 21 Jan 2013 09:03 EST

Koji Nuida

Source: Tsukuba J. Math., Volume 36, Number 2, 235--294.

Abstract:
It has been known that the centralizer Z W ( W I ) of a parabolic subgroup W I of a Coxeter group W is a split extension of a naturally defined reflection subgroup by a subgroup defined by a 2-cell complex $\mathscr{Y}$. In this paper, we study the structure of Z W ( W I ) further and show that, if I has no irreducible components of type A n with 2 ≤ n < ∞, then every element of finite irreducible components of the inner factor is fixed by a natural action of the fundamental group of $\mathscr{Y}$. This property has an application to the isomorphism problem in Coxeter groups.

The box topology of infinite simplicial complexes

Mon, 21 Jan 2013 09:03 EST

Katsuro Sakai, Hanbiao Yang

Source: Tsukuba J. Math., Volume 36, Number 2, 295--309.

Abstract:
In this paper, realizing an infinite simplicial complex K in the linear space R K (0) naturally, we investigate the box topology on | K | inherited from R K (0) that is finer than the metric topology and coarser than the Whitehead (weak) topology.

Semilinear degenerate elliptic boundary value problems via critical point theory

Mon, 21 Jan 2013 09:03 EST

Kazuaki Taira

Source: Tsukuba J. Math., Volume 36, Number 2, 311--365.

Abstract:
The purpose of this paper is to study a class of semilinear elliptic boundary value problems with degenerate boundary conditions which include as particular cases the Dirichlet and Robin problems. The approach here is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in the theory of partial differential equations. By making use of a variant of the Ljusternik-Schnirelman theory of critical points, we prove very exact results on the number of solutions of our problem. The results here extend earlier theorems due to Castro-Lazer to the degenerate case.

Dense chaos and densely chaotic operators

Mon, 21 Jan 2013 09:03 EST

Xinxing Wu, Peiyong Zhu

Source: Tsukuba J. Math., Volume 36, Number 2, 367--375.

Abstract:
The aim of this paper is to study dense chaos and densely chaotic operators on Banach spaces. First, we prove that a dynamical system is densely δ-chaotic for some δ > 0 if and only if it is densely chaotic and sensitive. Meanwhile, we also show that for general dynamical systems, Devaney chaos and dense chaos do not imply each other. Then, by using these results, we have that for a operator defined on a Banach space, dense chaos, dense δ-chaos, generic chaos and generic δ-chaos are equivalent and they are all strictly stronger than Li-Yorke chaos.