Hiroshima Mathematical Journal Articles (Project Euclid)
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The latest articles from Hiroshima Mathematical Journal on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTThu, 31 Mar 2011 11:44 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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A new description of convex bases of PBW type for untwisted quantum affine
algebras
http://projecteuclid.org/euclid.hmj/1280754419
<strong>Ken Ito</strong><p><strong>Source: </strong>Hiroshima Math. J., Volume 40, Number 2, 133--183.</p><p><strong>Abstract:</strong><br/>
In [8] we classified all ``convex orders'' on the positive root system $\Delta_+$
of an arbitrary untwisted affine Lie algebra ${\mathfrak g}$ and gave a concrete
method of constructing all convex orders on $\Delta_+$. The aim of this paper is
to give a new description of ``convex bases'' of PBW type of the positive
subalgebra $U^+$ of the quantum affine algebra $U=U_q({\mathfrak g})$ by using
the concrete method of constructing all convex orders on $\Delta_+$. Applying
convexity properties of the convex bases of $U^+$, for each convex order on
$\Delta_+$, we construct a pair of dual bases of $U^+$ and the negative
subalgebra $U^-$ with respect to a $q$-analogue of the Killing form, and then
present the multiplicative formula for the universal $R$-matrix of $U$.
</p>projecteuclid.org/euclid.hmj/1280754419_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTOn the classification of certain ternary codes of length 12http://projecteuclid.org/euclid.hmj/1459525932<strong>Makoto Araya</strong>, <strong>Masaaki Harada</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 1, 87--96.</p><p><strong>Abstract:</strong><br/>
Shimada and Zhang studied the existence of polarizations on some supersingular
$K3$ surfaces by reducing the existence of the polarizations to that of ternary
[12,5] codes satisfying certain conditions. In this note, we give a classification of
ternary [12,5] codes satisfying the conditions. To do this, ternary [10,5] codes are
classified for minimum weights 3 and 4.
</p>projecteuclid.org/euclid.hmj/1459525932_20160401115216Fri, 01 Apr 2016 11:52 EDTBiharmonic hypersurfaces in Riemannian symmetric spaces Ihttp://projecteuclid.org/euclid.hmj/1459525933<strong>Jun-ichi Inoguchi</strong>, <strong>Toru Sasahara</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 1, 97--121.</p><p><strong>Abstract:</strong><br/>
We classify biharmonic geodesic spheres in the Cayley projective plane.
Our results completes the classification of all biharmonic homogeneous hypersurfaces
in simply connected compact Riemannian symmetric spaces of rank 1. In addition we
show that complex Grassmannian manifolds, and exceptional Lie groups $F_4$ and $G_2$
admit proper biharmonic real hypersurfaces.
</p>projecteuclid.org/euclid.hmj/1459525933_20160401115216Fri, 01 Apr 2016 11:52 EDTChow groups of Châtelet surfaces over dyadic fieldshttp://projecteuclid.org/euclid.hmj/1459525934<strong>Takashi Hirotsu</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 1, 123--133.</p>projecteuclid.org/euclid.hmj/1459525934_20160401115216Fri, 01 Apr 2016 11:52 EDTMiscellaneous Frontmatter, Hiroshima Math. J., vol. 46, no. 2 (July 2016)http://projecteuclid.org/euclid.hmj/1471024944<p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 2</p>projecteuclid.org/euclid.hmj/1471024944_20160812140230Fri, 12 Aug 2016 14:02 EDTA note on the value distribution of $f^1(f^{(k)})^n$http://projecteuclid.org/euclid.hmj/1471024945<strong>Yan Jiang</strong>, <strong>Bin Huang</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 2, 135--147.</p><p><strong>Abstract:</strong><br/>
Let $f$ be a transcendental meromorphic function in the complex plane
$\mathbf{C}$, and a be a nonzero complex number. We give quantitative estimates
for the characteristic function $T(r,f)$ in terms of $N(r,1/(
f^1(f^{(k)})^n-a)), for integers $k$, $l$, $n$ greater than 1. We conclude that
$f^1(f^{(k)})^n$ assumes every nonzero finite value infinitely often.
</p>projecteuclid.org/euclid.hmj/1471024945_20160812140230Fri, 12 Aug 2016 14:02 EDTConstruction of spines of two-bridge link complements and upper bounds of their
Matveev complexitieshttp://projecteuclid.org/euclid.hmj/1471024946<strong>Masaharu Ishikawa</strong>, <strong>Keisuke Nemoto</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 2, 149--162.</p><p><strong>Abstract:</strong><br/>
We give upper bounds of the Matveev complexities of two-bridge link complements
by constructing their spines explicitly. In particular, we determine the
complexities for an infinite sequence of two-bridge links corresponding to the
continued fractions of the form [2,1,\dots, 1,2]. We also give upper bounds for
the 3-manifolds obtained as meridian-cyclic branched coverings of the 3-sphere
along two-bridge links.
</p>projecteuclid.org/euclid.hmj/1471024946_20160812140230Fri, 12 Aug 2016 14:02 EDTHigher level representation of the elliptic quantum group
$U_{q,p}(\widehat{\mathfrak{sl}}_2)$ and its integrabilityhttp://projecteuclid.org/euclid.hmj/1471024947<strong>Rasha Mohamed Farghly</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 2, 163--185.</p><p><strong>Abstract:</strong><br/>
By using an elliptic analogue of the Drinfeld coproduct, we construct the
level-$(k+1)$ representation of the elliptic quantum group
$U_{q,p}(\widehat{\mathfrak{sl}}_2)$ from the level-1 highest weight
representation. The quantum Z-algebra of level-$(k+1)$ is realized. We also find
the elliptic analogue of the condition of integrability for higher level modules
constructed by the Drinfeld coproduct. This also enables us to express
$\Delta^k(e(z))\Delta^k(e(zq^2))\dots\Delta^k(e(zq^{2(N-1)}))$ and
$\Delta^k(f(z))\Delta^k(f(zq^2))\Delta^k(f(zq^{-2}))\dots\Delta^k(f(zq^{-2(N-1)}))$
as vertex operators of the level-$(k+1)$ bosons.
</p>projecteuclid.org/euclid.hmj/1471024947_20160812140230Fri, 12 Aug 2016 14:02 EDTnew example of the dissipative wave equations with the total energy decayhttp://projecteuclid.org/euclid.hmj/1471024948<strong>Hideo Ueda</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 2, 187--193.</p><p><strong>Abstract:</strong><br/>
This note gives a new sufficient condition of the total energy decay for the
solutions of the initial-boundary value problems to the dissipative wave
equations in exterior domains with non-compactly supported initial data. That
condition provides an example of the damping terms of the dissipative wave
equations with the total energy decay which has a smaller amplitude than those
of all examples derived from a sufficient condition in Mochizuki and Nakazawa
[Publ. Res. Inst. Math. Sci. 32 (1996), 401–414].
</p>projecteuclid.org/euclid.hmj/1471024948_20160812140230Fri, 12 Aug 2016 14:02 EDTDegeneration of Fermat hypersurfaces in positive characteristichttp://projecteuclid.org/euclid.hmj/1471024949<strong>Thanh Hoai Hoang</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 2, 195--215.</p><p><strong>Abstract:</strong><br/>
We work over an algebraically closed field $k$ of positive characteristic $p$.
Let $q$ be a power of $p$. Let $A$ be an $(n+1)\times(n+1)$ matrix with
coefficients $a_{ij}$ in $k$, and let $X_A$ be a hypersurface of degree $q + 1$
in the projective space $\mathbf{P}^n$ defined by $\sum a_{ij}x_i x^q_j=0$. It
is well-known that if the rank of $A$ is $n + 1$, the hypersurface $X_A$ is
projectively isomorphic to the Fermat hypersuface of degree $q + 1$. We
investigate the hypersurfaces $X_A$ when the rank of $A$ is $n$, and determine
their projective isomorphism classes.
</p>projecteuclid.org/euclid.hmj/1471024949_20160812140230Fri, 12 Aug 2016 14:02 EDTCommensurability between once-punctured torus groups and once-punctured Klein
bottle groupshttp://projecteuclid.org/euclid.hmj/1471024950<strong>Mikio Furokawa</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 2, 217--253.</p><p><strong>Abstract:</strong><br/>
The once-punctured torus and the once-punctured Klein bottle are topologically
commensurable, in the sense that both of them are doubly covered by the
twice-punctured torus. In this paper, we give a condition for a faithful
type-preserving $\mathrm{PSL}(2,\mathbf{C})$-representation of the fundamental
group of the once-punctured Klein bottle to be ‘‘commensurable’’ with that of
the once-punctured torus. We also show that such a pair of
$\mathrm{PSL}(2,\mathbf{C})$-representations extend to a representation of the
fundamental group of a common quotient orbifold. Finally, we give an application
to the study of the Ford domains.
</p>projecteuclid.org/euclid.hmj/1471024950_20160812140230Fri, 12 Aug 2016 14:02 EDTFree involutions on torus semi-bundles and the Borsuk-Ulam Theorem for maps into
$\mathbf{R}^n$http://projecteuclid.org/euclid.hmj/1487991621<strong>Alexandre Paiva Barreto</strong>, <strong>Daciberg Lima Gonçalves</strong>, <strong>Daniel Vendrúscolo</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 3, 255--270.</p><p><strong>Abstract:</strong><br/>
In this article we classify the free involutions of every torus semi-bundle Sol
3-manifold. Moreover, we classify all the triples $M, \tau, \mathbf{R}^n$, where
$M$ is as above, $\tau$ is a free involution on $M$, and $n$ is a positive
integer, for which the Borsuk-Ulam Property holds.
</p>projecteuclid.org/euclid.hmj/1487991621_20170224220050Fri, 24 Feb 2017 22:00 ESTThe boundary of a fibered face of the magic 3-manifold and the asymptotic
behavior of minimal pseudo-Anosov dilatationshttp://projecteuclid.org/euclid.hmj/1487991622<strong>Eiko Kin</strong>, <strong>Mitsuhiko Takasawa</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 3, 271--287.</p><p><strong>Abstract:</strong><br/>
Let $\delta_{g,n}$ be the minimal dilation of pseudo-Anosovs defined on an
orientable surface of genus $g$ with $n$ punctures. It is proved by Tsai that
for any fixed $g\ge2$, there exists a constant $c_g$ depending on $g$ such that
\[ \frac{1}{c_g}\cdot \frac{\log n}{n} \lt \log \delta_{g,n} \lt c_g \cdot
\frac{\log n}{n} \qquad \text{for any }n\ge3 \] This means that the logarithm of
the minimal dilatation $\log \delta_{g, n}$ is on the order of $\log n/n$. We
prove that if $2g + 1$ is relatively prime to $s$ or $s + 1$ for each $0\le s\le
g$, then \[ \limsup_{n\to\infty}\frac{n(\log \delta_{g,n})}{\log n}\le 2 \]
holds. In particular, if $2g + 1$ is prime, then the above inequality on
$\delta_{g,n}$ holds. Our examples of pseudo-Anosovs $\phi$’s which provide the
upper bound above have the following property: The mapping torus $M_\phi$ of
$\phi$ is a single hyperbolic 3-manifold $N$ called the magic manifold, or the
fibration of $M_\phi$ comes from a fibration of $N$ by Dehn filling cusps along
the boundary slopes of a fiber.
</p>projecteuclid.org/euclid.hmj/1487991622_20170224220050Fri, 24 Feb 2017 22:00 ESTConfluence of general Schlesinger systems and Twistor theoryhttp://projecteuclid.org/euclid.hmj/1487991623<strong>Hironobu Kimura</strong>, <strong>Damiran Tseveennamjil</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 3, 289--309.</p><p><strong>Abstract:</strong><br/>
We give a description of confluence for the general Schlesinger systems (GSS)
from the view point of twistor theory. GSS is a system of nonlinear di¤erential
equations on the Grassmannian manifold $G_{2,N}(\mathbf{C}$ which is obtained,
for any partition $\lambda$ of $N$, as the integrability condition of a
connection $\nabla_\lambda$ on $\mathbf{P}^1\times G_{2,N}$ constructed using
the twistor-theoretic point of view and is known to describe isomonodromic
deformation of linear differential equations on the projective space
$\mathbf{P}^1$. For a pair of partitions $\lambda, \mu$ of $N$ such that m is
obtained from $\lambda$ by making two parts into on parts and leaving other
parts unchanged, we construct the limit process $\nabla_\lambda\to \nabla_\mu$
and as a result the confluence for GSS.
</p>projecteuclid.org/euclid.hmj/1487991623_20170224220050Fri, 24 Feb 2017 22:00 ESTRemarks on the strong maximum principle involving $p$-Laplacianhttp://projecteuclid.org/euclid.hmj/1487991624<strong>Xiaojing Liu</strong>, <strong>Toshio Horiuchi</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 3, 311--331.</p><p><strong>Abstract:</strong><br/>
Let $N\ge 1, 1 \lt p \lt \infty$ and $p^*=\max(1,p-1)$. Let $\Omega$ be a bounded
domain of $\mathbf{R}^N$. We establish the strong maximum principle for the
$p$-Laplace operator with a nonlinear potential term. More precisely, we show
that every super-solution $u \in \Omega^{1, p^*}_{\mathrm{loc}}(\Omega)$
vanishes identically in $\Omega$, if $u$ is admissible and $u = 0$ a.e on a set
of positive $p$-capacity relative to $\Omega$.
</p>projecteuclid.org/euclid.hmj/1487991624_20170224220050Fri, 24 Feb 2017 22:00 ESTStable extendibility of some complex vector bundles over lens
spaces and Schwarzenberger’s theoremhttp://projecteuclid.org/euclid.hmj/1487991625<strong>Yutaka Hemmi</strong>, <strong>Teiichi Kobayashi</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 3, 333--341.</p><p><strong>Abstract:</strong><br/>
We obtain conditions for stable extendibility of some complex vector
bundles over the $(2n + 1)$-dimensional standard lens space $L^n(p) \operatorname{mod} p$, where $p$ is
a prime. Furthermore, we study stable extendibility of the bundle $\pi^*_n (\tau(\mathbf{C}P^n))$ induced
by the natural projection $\pi_n : L^n(p)\to \mathbf{C}P^n$ from the complex tangent bundle $\tau(\mathbf{C}P^n)$ of
the complex projective $n$-space $\mathbf{C}P^n$. As an application, we have a result on stable
extendibility of $\tau(\mathbf{C}P^n)$ which gives another proof of Schwarzenberger’s theorem.
</p>projecteuclid.org/euclid.hmj/1487991625_20170224220050Fri, 24 Feb 2017 22:00 ESTUniform hyperbolicity for curve graphs of non-orientable surfaceshttp://projecteuclid.org/euclid.hmj/1487991626<strong>Erika Kuno</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 3, 343--355.</p><p><strong>Abstract:</strong><br/>
Hensel-Przytycki-Webb proved that the curve graphs of all orientable
surfaces are 17-hyperbolic. In this paper, we show that the curve graphs of nonorientable
surfaces are 17-hyperbolic by applying Hensel-Przytycki-Webb’s argument.
We also show that the arc graphs of non-orientable surfaces are 7-hyperbolic, and arccurve
graphs of (non-)orientable surfaces are 9-hyperbolic.
</p>projecteuclid.org/euclid.hmj/1487991626_20170224220050Fri, 24 Feb 2017 22:00 ESTOn the moduli spaces of left-invariant pseudo-Riemannian
metrics on Lie groupshttp://projecteuclid.org/euclid.hmj/1487991627<strong>Akira Kubo</strong>, <strong>Kensuke Onda</strong>, <strong>Yuichiro Taketomi</strong>, <strong>Hiroshi Tamaru</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 3, 357--374.</p><p><strong>Abstract:</strong><br/>
The moduli space of left-invariant pseudo-Riemannian metrics on a given
Lie group is defined as the orbit space of a certain isometric action on some pseudo-
Riemannian symmetric space. In terms of the moduli space, we formulate a procedure
to obtain a generalization of Milnor frames for left-invariant pseudo-Riemannian
metrics on a given Lie group. This procedure is an analogue of the recent studies
on left-invariant Riemannian metrics. In this paper, we describe the orbit space of the
action of a particular parabolic subgroup, and then apply it to obtain a generalization
of Milnor frames for so-called the Lie groups of real hyperbolic spaces, and also for the
three-dimensional Heisenberg group. As a corollary we show that all left-invariant
pseudo-Riemannian metrics of arbitrary signature on the Lie groups of real hyperbolic
spaces have constant sectional curvatures.
</p>projecteuclid.org/euclid.hmj/1487991627_20170224220050Fri, 24 Feb 2017 22:00 ESTThe number of paperfolding curves in a covering of the planehttp://projecteuclid.org/euclid.hmj/1492048844<strong>Francis Oger</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 47, Number 1, 1--14.</p><p><strong>Abstract:</strong><br/>
This paper completes our previous one in the same journal (vol. 42, pp. 37–
75). Let $\mathscr{C}$ be a covering of the plane by disjoint complete folding curves which
satisfies the local isomorphism property. We show that $\mathscr{C}$ is locally isomorphic to
an essentially unique covering generated by an $\infty$-folding curve. We prove that $\mathscr{C}$
necessarily consists of 1, 2, 3, 4 or 6 curves. We give examples for each case; the last
one is realized if and only if $\mathscr{C}$ is generated by the alternating folding curve or one
of its successive antiderivatives. We also extend the results of our previous paper to
another class of paperfolding curves introduced by M. Dekking.
</p>projecteuclid.org/euclid.hmj/1492048844_20170412220103Wed, 12 Apr 2017 22:01 EDTProducts of parts in class regular partitionshttp://projecteuclid.org/euclid.hmj/1492048845<strong>Masanori Ando</strong>, <strong>Hiro-Fumi Yamada</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 47, Number 1, 15--18.</p><p><strong>Abstract:</strong><br/>
A $q$-analogue of a partition identity is presented.
</p>projecteuclid.org/euclid.hmj/1492048845_20170412220103Wed, 12 Apr 2017 22:01 EDTLink invariant and $G_2$ web spacehttp://projecteuclid.org/euclid.hmj/1492048846<strong>Takuro Sakamoto</strong>, <strong>Yasuyoshi Yonezawa</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 47, Number 1, 19--41.</p><p><strong>Abstract:</strong><br/>
In this paper, we reconstruct Kuperberg’s $G_2$ web space [5, 6]. We
introduce a new web diagram (a trivalent graph with only double edges) and new
relations between Kuperberg’s web diagrams and the new web diagram. Using the web
diagrams, we give crossing formulas for the $R$-matrices associated to some irreducible
representations of $U_q(G_2)$ and calculate $G_2$ quantum link invariants for generalized twist
links.
</p>projecteuclid.org/euclid.hmj/1492048846_20170412220103Wed, 12 Apr 2017 22:01 EDTEPMC estimation in discriminant analysis when the dimension
and sample sizes are largehttp://projecteuclid.org/euclid.hmj/1492048847<strong>Tetsuji Tonda</strong>, <strong>Tomoyuki Nakagawa</strong>, <strong>Hirofumi Wakaki</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 47, Number 1, 43--62.</p><p><strong>Abstract:</strong><br/>
In this paper we obtain a higher order asymptotic unbiased estimator for
the expected probability of misclassification (EPMC) of the linear discriminant function
when both the dimension and the sample size are large. Moreover, we evaluate the
mean squared error of our estimator. We also present a numerical comparison between
the performance of our estimator and that of the other estimators based on Okamoto
(1963, 1968) and Fujikoshi and Seo (1998). It is shown that the bias and the mean
squared error of our estimator are less than those of the other estimators.
</p>projecteuclid.org/euclid.hmj/1492048847_20170412220103Wed, 12 Apr 2017 22:01 EDTOn prolongations of second-order regular overdetermined systems
with two independent and one dependent variableshttp://projecteuclid.org/euclid.hmj/1492048848<strong>Takahiro Noda</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 47, Number 1, 63--86.</p><p><strong>Abstract:</strong><br/>
The purpose of this paper is to investigate the geometric structure of
regular overdetermined systems of second order with two independent and one dependent
variables from the point of view of the rank two prolongation. Utilizing this
prolongation, we characterize the type of overdetermined systems and clarify the
specificity for each type. We also give systematic methods for constructing the
geometric singular solutions by analyzing a decomposition of this prolongation. As
an application, we determine the geometric singular solutions of Cartan’s overdetermined
system.
</p>projecteuclid.org/euclid.hmj/1492048848_20170412220103Wed, 12 Apr 2017 22:01 EDTClassification of simple quartics up to equisingular deformationhttp://projecteuclid.org/euclid.hmj/1492048849<strong>Çisem Güneş Aktaş</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 47, Number 1, 87--112.</p><p><strong>Abstract:</strong><br/>
We study complex spatial quartic surfaces with simple singularities up to
equisingular deformations; as a first step, give a complete equisingular deformation
classification of non-special simple quartic surfaces.
</p>projecteuclid.org/euclid.hmj/1492048849_20170412220103Wed, 12 Apr 2017 22:01 EDTExtremality of quaternionic Jørgensen inequalityhttp://projecteuclid.org/euclid.hmj/1499392822<strong>Krishnendu Gongopadhyay</strong>, <strong>Abhishek Mukherjee</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 47, Number 2, 113--137.</p><p><strong>Abstract:</strong><br/>
Let $\mathrm{SL}(2,\mathbb{H})$ be the group of $2 × 2$ quaternionic matrices with
Dieudonné determinant one. The group $\mathrm{SL}(2,\mathbb{H})$ acts on the five
dimensional hyperbolic space by isometries. We investigate extremality of Jørgensen type
inequalities in $\mathrm{SL}(2,\mathbb{H})$. Along the way, we derive Jørgensen type
inequalities for quaternionic Möbius transformations which extend earlier inequalities
obtained by Waterman and Kellerhals.
</p>projecteuclid.org/euclid.hmj/1499392822_20170706220047Thu, 06 Jul 2017 22:00 EDTA fixed contact angle condition for varifoldshttp://projecteuclid.org/euclid.hmj/1499392823<strong>Takashi Kagaya</strong>, <strong>Yoshihiro Tonegawa</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 47, Number 2, 139--153.</p><p><strong>Abstract:</strong><br/>
We define a generalized fixed contact angle condition for $n$-varifold and establish a
boundary monotonicity formula. The results are natural generalizations of those for the
Neumann boundary condition considered by Grüter-Jost [7].
</p>projecteuclid.org/euclid.hmj/1499392823_20170706220047Thu, 06 Jul 2017 22:00 EDTBounds on Walsh coefficients by dyadic difference and a new
Koksma-Hlawka type inequality for Quasi-Monte Carlo integrationhttp://projecteuclid.org/euclid.hmj/1499392824<strong>Takehito Yoshiki</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 47, Number 2, 155--179.</p><p><strong>Abstract:</strong><br/>
In this paper we give a new Koksma-Hlawka type inequality for Quasi-Monte Carlo (QMC)
integration. QMC integration of a function $f\colon[0,1)^s\rightarrow\mathbb{R}$ by a
finite point set $\mathcal{P}\subset[0,1)^s$ is the approximation of the integral
$I(f):=\int_{[0,1)^s}f(\mathbf{x})\,d\mathbf{x}$ by the average
$I_{\mathcal{P}}(f):=\frac{1}{|\mathcal{P}|}\sum_{\mathbf{x} \in
\mathcal{P}}f(\mathbf{x})$. We treat a certain class of point sets $\mathcal{P}$ called
digital nets. A Koksma-Hlawka type inequality is an inequality providing an upper bound on
the integration error $\text{Err}(f;\mathcal{P}):=I(f)-I_{\mathcal{P}}(f)$ of the form
$|\text{Err}(f;\mathcal{P})|\le C\cdot \|f\|\cdot D(\mathcal{P})$. We can obtain a
Koksma-Hlawka type inequality by estimating bounds on $|\hat{f}(\mathbf{k})|$, where
$\hat{f}(\mathbf{k})$ is a generalized Fourier coefficient with respect to the Walsh
system. In this paper we prove bounds on the Walsh coefficients $\hat{f}(\mathbf{k})$ by
introducing an operator called ‘dyadic difference’ $\partial_{i,n}$. By converting dyadic
differences $\partial_{i,n}$ to derivatives $\frac{\partial }{\partial x_i}$, we get a new
bound on $|\hat{f}(\mathbf{k})|$ for a function $f$ whose mixed partial derivatives up to
order $\alpha$ in each variable are continuous. This new bound is smaller than the known
bound on $|\hat{f}(\mathbf{k})|$ under some instances. The new Koksma-Hlawka type
inequality is derived using this new bound on the Walsh coefficients.
</p>projecteuclid.org/euclid.hmj/1499392824_20170706220047Thu, 06 Jul 2017 22:00 EDTAn unbiased $C_{p}$ type criterion for ANOVA model with a tree
order restrictionhttp://projecteuclid.org/euclid.hmj/1499392825<strong>Yu Inatsu</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 47, Number 2, 181--216.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider a $C_{p}$ type criterion for ANOVA model with a tree ordering
($\mathrm{TO}$) $\theta_{1}\leq\theta_{j}, (j=2,\ldots,l)$ where $\theta_{1},\ldots\theta_{l}$
are population means. In general, under ANOVA model with the $\mathrm{TO}$, the usual
$C_{p}$ criterion has a bias to a risk function, and the bias depends on unknown
parameters. In order to solve this problem, we calculate a value of the bias, and we
derive its unbiased estimator. By using this estimator, we provide an unbiased $C_{p}$
type criterion for ANOVA model with the $\mathrm{TO}$, called $\mathrm{TO}C_{p}$. A
penalty term of the $\mathrm{TO}C_{p}$ is simply defined as a function of an indicator
function and maximum likelihood estimators. Furthermore, we show that the
$\mathrm{TO}C_{p}$ is the uniformly minimum-variance unbiased estimator (UMVUE) of a risk
function.
</p>projecteuclid.org/euclid.hmj/1499392825_20170706220047Thu, 06 Jul 2017 22:00 EDTBifurcation analysis of a diffusion-ODE model with
Turing instability and hysteresishttp://projecteuclid.org/euclid.hmj/1499392826<strong>Ying Li</strong>, <strong>Anna Marciniak-Czochra</strong>, <strong>Izumi Takagi</strong>, <strong>Boying Wu</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 47, Number 2, 217--247.</p><p><strong>Abstract:</strong><br/>
This paper is devoted to the existence and (in)stability of nonconstant
steady-states in a system of a semilinear parabolic equation coupled to an ODE, which
is a simplified version of a receptor-ligand model of pattern formation. In the neighborhood
of a constant steady-state, we construct spatially heterogeneous steady-states
by applying the bifurcation theory. We also study the structure of the spectrum of
the linearized operator and show that bifurcating steady-states are unstable against
high wave number disturbances. In addition, we consider the global behavior of the
bifurcating branches of nonconstant steady-states. These are quite different from
classical reaction-diffusion systems where all species diffuse.
</p>projecteuclid.org/euclid.hmj/1499392826_20170706220047Thu, 06 Jul 2017 22:00 EDTHigh-dimensional asymptotic distributions of characteristic roots in multivariate linear models and canonical correlation analysishttps://projecteuclid.org/euclid.hmj/1509674447<strong>Yasunori Fujikoshi</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 47, Number 3, 249--271.</p><p><strong>Abstract:</strong><br/>
In this paper, we derive the asymptotic distributions of the characteristic roots in multivariate linear models when the dimension $p$ and the sample size $n$ are large. The results are given for the case that the population characteristic roots have multiplicities greater than unity, and their orders are $\mathrm{O}(np)$ or $\mathrm{O}(n)$. Next, similar results are given for the asymptotic distributions of the canonical correlations when one of the dimensions and the sample size are large, assuming that the order of the population canonical correlations is $\mathrm{O}(\sqrt{p})$ or $\mathrm{O}(1)$.
</p>projecteuclid.org/euclid.hmj/1509674447_20171102220114Thu, 02 Nov 2017 22:01 EDTA two-sample test for high-dimension, low-sample-size data under the strongly spiked eigenvalue modelhttps://projecteuclid.org/euclid.hmj/1509674448<strong>Aki Ishii</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 47, Number 3, 273--288.</p><p><strong>Abstract:</strong><br/>
A common feature of high-dimensional data is that the data dimension is high, however, the sample size is relatively low. We call such data HDLSS data. In this paper, we consider a new two-sample test for high-dimensional data under the strongly spiked eigenvalue (SSE) model. We consider the distance-based two-sample test under the SSE model. We introduce the noise-reduction (NR) methodology and apply that to the two-sample test. Finally, we give simulation studies and demonstrate the new test procedure by using microarray data sets.
</p>projecteuclid.org/euclid.hmj/1509674448_20171102220114Thu, 02 Nov 2017 22:01 EDTThe skew growth functions for the monoid of type $\mathrm{B_{ii}}$ and othershttps://projecteuclid.org/euclid.hmj/1509674449<strong>Tadashi Ishibe</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 47, Number 3, 289--317.</p><p><strong>Abstract:</strong><br/>
For a class of positive homogeneously presented cancellative monoids whose heights are greater than or equal to 2, we will present several explicit calculations of the skew growth functions for them. By the inversion formula, the spherical growth functions for them can be determined. For most of them, the direct calculations are not known. The datum of certain lemmas for proving the cancellativity of the monoids are indispensable to the calculations of the skew growth functions. By improving the technique to show the lemmas, we succeed in the calculations.
</p>projecteuclid.org/euclid.hmj/1509674449_20171102220114Thu, 02 Nov 2017 22:01 EDTAsymptotic cut-off point in linear discriminant rule to adjust the misclassification probability for large dimensionshttps://projecteuclid.org/euclid.hmj/1509674450<strong>Takayuki Yamada</strong>, <strong>Tetsuto Himeno</strong>, <strong>Tetsuro Sakurai</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 47, Number 3, 319--348.</p><p><strong>Abstract:</strong><br/>
This paper is concerned with the problem of classifying an observation vector into one of two populations $\mathit{\Pi}_{1} : N_{p}(\mu_{1},\Sigma)$ and $\mathit{\Pi}_{2} : N_{p}(\mu_{2},\Sigma)$. Anderson (1973, Ann. Statist.) provided an asymptotic expansion of the distribution for a Studentized linear discriminant function, and proposed a cut-off point in the linear discriminant rule to control one of the two misclassification probabilities. However, as dimension $p$ becomes larger, the precision worsens, which is checked by simulation. Therefore, in this paper we derive an asymptotic expansion of the distribution of a linear discriminant function up to the order $p^{-1}$ as $N_1$, $N_2$, and $p$ tend to infinity together under the condition that $p/(N_{1}+N_{2}-2)$ converges to a constant in $(0, 1)$, and $N_{1}/N_{2}$ converges to a constant in $(0, \infty)$, where $N_i$ means the size of sample drown from $\mathit{\Pi}_i(i=1, 2)$. Using the expansion, we provide a cut-off point. A small-scale simulation revealed that our proposed cut-off point has good accuracy.
</p>projecteuclid.org/euclid.hmj/1509674450_20171102220114Thu, 02 Nov 2017 22:01 EDTBiharmonic hypersurfaces in Riemannian symmetric spaces IIhttps://projecteuclid.org/euclid.hmj/1509674451<strong>Jun-ichi Inoguchi</strong>, <strong>Toru Sasahara</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 47, Number 3, 349--378.</p><p><strong>Abstract:</strong><br/>
We study biharmonic homogeneous hypersurfaces in Riemannian symmetric spaces associated to the exceptional Lie groups $\mathrm{E}_6$ and $\mathrm{G}_2$ as well as real, complex and quaternion Grassmannian manifolds.
</p>projecteuclid.org/euclid.hmj/1509674451_20171102220114Thu, 02 Nov 2017 22:01 EDTOn a Riemannian submanifold whose slice representation has no nonzero fixed pointshttps://projecteuclid.org/euclid.hmj/1520478020<strong>Yuichiro Taketomi</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 1, 1--20.</p><p><strong>Abstract:</strong><br/>
In this paper, we define a new class of Riemannian submanifolds which we call arid submanifolds. A Riemannian submanifold is called an arid submanifold if no nonzero normal vectors are invariant under the full slice representation. We see that arid submanifolds are a generalization of weakly reflective submanifolds, and arid submanifolds are minimal submanifolds. We also introduce an application of arid submanifolds to the study of left-invariant metrics on Lie groups. We give a suffcient condition for a left-invariant metric on an arbitrary Lie group to be a Ricci soliton.
</p>projecteuclid.org/euclid.hmj/1520478020_20180307220026Wed, 07 Mar 2018 22:00 ESTCosmetic surgery and the $SL(2,\mathbb{C})$ Casson invariant for two-bridge knotshttps://projecteuclid.org/euclid.hmj/1520478021<strong>Kazuhiro Ichihara</strong>, <strong>Toshio Saito</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 1, 21--37.</p><p><strong>Abstract:</strong><br/>
We consider the cosmetic surgery problem for two-bridge knots in the 3-sphere. We first verify by using previously known results that all the two-bridge knots of at most $9$ crossings admit no purely cosmetic surgery pairs except for the knot $9_{27}$. Then we show that any two-bridge knot corresponding to the continued fraction $[0, 2x, 2, -2x, 2x, 2, -2x]$ for a positive integer $x$ admits no cosmetic surgery pairs yielding homology 3-spheres, where $9_{27}$ appears when $x = 1$. Our advantage to prove this is using the $SL(2,\mathbb{C})$ Casson invariant.
</p>projecteuclid.org/euclid.hmj/1520478021_20180307220026Wed, 07 Mar 2018 22:00 ESTLCM-stability and formal power serieshttps://projecteuclid.org/euclid.hmj/1520478022<strong>Walid Maaref</strong>, <strong>Ali Benhissi</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 1, 39--55.</p><p><strong>Abstract:</strong><br/>
In this paper we study the LCM-stability property and other related concepts, and their universality in the case of polynomial and formal power series extensions.
</p>projecteuclid.org/euclid.hmj/1520478022_20180307220026Wed, 07 Mar 2018 22:00 ESTStable extendibility and extendibility of vector bundles over lens spaceshttps://projecteuclid.org/euclid.hmj/1520478023<strong>Mitsunori Imaoka</strong>, <strong>Teiichi Kobayashi</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 1, 57--66.</p><p><strong>Abstract:</strong><br/>
Firstly, we obtain conditions for stable extendibility and extendibility of complex vector bundles over the $(2n+1)$-dimensional standard lens space $L^n(p)$ mod $p$, where $p$ is a prime. Secondly, we prove that the complexification $c(\tau_n(p))$ of the tangent bundle $\tau_n(p) (=\tau(L^n(p)))$ of $L^n(p)$ is extendible to $L^{2n+1}(p)$ if $p$ is a prime, and is not stably extendible to $L^{2n+2}(p)$ if $p$ is an odd prime and $n \ge 2p-2$. Thirdly, we show, for some odd prime $p$ and positive integers $n$ and $m$ with $m > n$, that $\tau(L^n(p))$ is stably extendible to $L^m(p)$ but is not extendible to $L^m(p)$.
</p>projecteuclid.org/euclid.hmj/1520478023_20180307220026Wed, 07 Mar 2018 22:00 ESTExistence of supersingular reduction for families of $K3$ surfaces with large Picard number in positive characteristichttps://projecteuclid.org/euclid.hmj/1520478024<strong>Kazuhiro Ito</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 1, 67--79.</p><p><strong>Abstract:</strong><br/>
We study non-isotrivial families of $K3$ surfaces in positive characteristic $p$ whose geometric generic fibers satisfy $\rho \ge 21 - 2h$ and $h \ge 3$, where $\rho$ is the Picard number and $h$ is the height of the formal Brauer group. We show that, under a mild assumption on the characteristic of the base field, they have potential supersingular reduction. Our methods rely on Maulik’s results on moduli spaces of $K3$ surfaces and the construction of sections of powers of Hodge bundles due to van der Geer and Katsura. For large $p$ and each $2 \le h \le 10$, using deformation theory and Taelman’s methods, we construct non-isotrivial families of $K3$ surfaces satisfying $\rho = 22 - 2h$.
</p>projecteuclid.org/euclid.hmj/1520478024_20180307220026Wed, 07 Mar 2018 22:00 ESTA small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twistshttps://projecteuclid.org/euclid.hmj/1520478025<strong>Genki Omori</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 1, 81--88.</p><p><strong>Abstract:</strong><br/>
We give a small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twists. The di¤erence between the number of the generators and a lower bound of numbers of generators for the twist subgroup by Dehn twists is one. The lower bounds is obtained from an argument of Hirose [5].
</p>projecteuclid.org/euclid.hmj/1520478025_20180307220026Wed, 07 Mar 2018 22:00 ESTA multiple conjugation biquandle and handlebody-linkshttps://projecteuclid.org/euclid.hmj/1520478026<strong>Atsushi Ishii</strong>, <strong>Masahide Iwakiri</strong>, <strong>Seiichi Kamada</strong>, <strong>Jieon Kim</strong>, <strong>Shosaku Matsuzaki</strong>, <strong>Kanako Oshiro</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 1, 89--117.</p><p><strong>Abstract:</strong><br/>
We introduce a multiple conjugation biquandle, and show that it is the universal algebra for defining a semi-arc coloring invariant for handlebody-links. A multiple conjugation biquandle is a generalization of a multiple conjugation quandle. We extend the notion of $n$-parallel biquandle operations for any integer $n$, and show that any biquandle gives a multiple conjugation biquandle with them.
</p>projecteuclid.org/euclid.hmj/1520478026_20180307220026Wed, 07 Mar 2018 22:00 ESTA mixed formulation of the Stokes equations with slip conditions in exterior domains and in the half-spacehttps://projecteuclid.org/euclid.hmj/1533088823<strong>Nabil Kerdid</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 2, 119--131.</p><p><strong>Abstract:</strong><br/>
We are concerned with Stokes equations in the half-space or in an exterior domain of $\mathbb{R}^n$ when slip conditions are imposed on the boundary. We present a mixed velocity-pressure formulation and we show its well posedness. A weighted variant of Korn’s inequality in unbounded domains is the cornerstone of our approach.
</p>projecteuclid.org/euclid.hmj/1533088823_20180731220100Tue, 31 Jul 2018 22:01 EDTStrongly nonperiodic hyperbolic tilings using single vertex configurationhttps://projecteuclid.org/euclid.hmj/1533088825<strong>Kazushi Ahara</strong>, <strong>Shigeki Akiyama</strong>, <strong>Hiroko Hayashi</strong>, <strong>Kazushi Komatsu</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 2, 133--140.</p><p><strong>Abstract:</strong><br/>
A strongly nonperiodic tiling is defined as a tiling that does not admit infinite cyclic symmetry. The purpose of this article is to construct, up to isomorphism, uncountably many strongly nonperiodic hyperbolic tilings with a single vertex configuration by a hyperbolic rhombus tile. We use a tile found by Margulis and Mozes [5], which admits tilings, but no tiling with a compact fundamental domain.
</p>projecteuclid.org/euclid.hmj/1533088825_20180731220100Tue, 31 Jul 2018 22:01 EDTBesov and Triebel–Lizorkin space estimates for fractional diffusionhttps://projecteuclid.org/euclid.hmj/1533088828<strong>Kôzô Yabuta</strong>, <strong>Minsuk Yang</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 2, 141--158.</p><p><strong>Abstract:</strong><br/>
We study Besov and Triebel–Lizorkin space estimates for fractional diffusion. We measure the smoothing effect of the fractional heat flow in terms of the Besov and Triebel–Lizorkin scale. These estimates have many applications to various partial differential equations.
</p>projecteuclid.org/euclid.hmj/1533088828_20180731220100Tue, 31 Jul 2018 22:01 EDTClassification of bi-polarized 3-folds $(X, L_{1}, L_{2})$ with $h^{0}(K_{X}+L_{1}+L_{2})=1$https://projecteuclid.org/euclid.hmj/1533088829<strong>Yoshiaki Fukuma</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 2, 159--170.</p><p><strong>Abstract:</strong><br/>
Let $X$ be a complex smooth projective variety of dimension 3, and let $L_1$ and $L_2$ be ample line bundles on $X$. In this paper we classify $(X, L_{1}, L_{2})$ with $h^{0}(K_{X}+L_{1}+L_{2})=1$.
</p>projecteuclid.org/euclid.hmj/1533088829_20180731220100Tue, 31 Jul 2018 22:01 EDTA localization principle for biholomorphic mappings between the Fock-Bargmann-Hartogs domainshttps://projecteuclid.org/euclid.hmj/1533088831<strong>Akio Kodama</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 2, 171--187.</p><p><strong>Abstract:</strong><br/>
In this paper, we prove that a localization principle for biholomorphic mappings between equidimensional Fock-Bargmann-Hartogs domains holds. As an application of this, we show that any proper holomorphic mapping between two equidimensional Fock-Bargmann-Hartogs domains satisfying some condition is necessarily a biholomorphic mapping.
</p>projecteuclid.org/euclid.hmj/1533088831_20180731220100Tue, 31 Jul 2018 22:01 EDTPolynomial argument for $q$-binomial cubic sums*https://projecteuclid.org/euclid.hmj/1533088834<strong>Xiaoyuan Wang</strong>, <strong>Wenchang Chu</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 2, 189--202.</p><p><strong>Abstract:</strong><br/>
By means of the polynomial argument, a class of cubic sums of $q$-binomial coefficients are evaluated in closed forms.
</p>projecteuclid.org/euclid.hmj/1533088834_20180731220100Tue, 31 Jul 2018 22:01 EDTExplicit solution to the minimization problem of generalized cross-validation criterion for selecting ridge parameters in generalized ridge regressionhttps://projecteuclid.org/euclid.hmj/1533088835<strong>Hirokazu Yanagihara</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 2, 203--222.</p><p><strong>Abstract:</strong><br/>
This paper considers optimization of the ridge parameters in generalized ridge regression (GRR) by minimizing a model selection criterion. GRR has a major advantage over ridge regression (RR) in that a solution to the minimization problem for one model selection criterion, i.e., Mallows’ $C_p$ criterion, can be obtained explicitly with GRR, but such a solution for any model selection criteria, e.g., $C_p$ criterion, cross-validation (CV) criterion, or generalized CV (GCV) criterion, cannot be obtained explicitly with RR. On the other hand, $C_p$ criterion is at a disadvantage compared to CV and GCV criteria because a good estimate of the error variance is required in order for $C_p$ criterion to work well. In this paper, we show that ridge parameters optimized by minimizing GCV criterion can also be obtained by closed forms in GRR. We can overcome one disadvantage of GRR by using GCV criterion for the optimization of ridge parameters. By using the result, we propose a principle component regression hybridized with the GRR that is a new method for a linear regression with highdimensional explanatory variables.
</p>projecteuclid.org/euclid.hmj/1533088835_20180731220100Tue, 31 Jul 2018 22:01 EDTOn a good reduction criterion for proper polycurves with sectionshttps://projecteuclid.org/euclid.hmj/1533088836<strong>Ippei Nagamachi</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 2, 223--251.</p><p><strong>Abstract:</strong><br/>
We give a good reduction criterion for proper polycurves with sections, i.e., successive extensions of family of curves with section, under a mild assumption. This criterion is a higher dimensional version of the good reduction criterion for hyperbolic curves given by Oda and Tamagawa.
</p>projecteuclid.org/euclid.hmj/1533088836_20180731220100Tue, 31 Jul 2018 22:01 EDTTwo categorical characterizations of local fieldshttps://projecteuclid.org/euclid.hmj/1544238027<strong>Yuichiro Hoshi</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 3, 253--277.</p><p><strong>Abstract:</strong><br/>
In the present paper, we discuss two categorical characterizations of local fields. We first prove that a certain full subcategory of the category of finite flat coverings of the spectrum of the ring of integers of a local field equipped with coherent modules completely determines the isomorphism class of the local field. Next, we also prove that a certain full subcategory of the category of irreducible schemes which are finite over the spectrum of the ring of integers of a local field completely determines the isomorphism class of the local field.
</p>projecteuclid.org/euclid.hmj/1544238027_20181207220057Fri, 07 Dec 2018 22:00 ESTThe Besicovitch covering theorem for parabolic balls in Euclidean spacehttps://projecteuclid.org/euclid.hmj/1544238028<strong>Tsubasa Itoh</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 3, 279--289.</p><p><strong>Abstract:</strong><br/>
The Besicovitch covering theorem is well known to be the useful tools in many fields of analysis. Federer extended the result of Besicovitch to a directionally limited metric space. In this paper, we prove the Besicovitch covering theorem for parabolic balls in Euclidean space, although the parabolic metric is not directionally limited.
</p>projecteuclid.org/euclid.hmj/1544238028_20181207220057Fri, 07 Dec 2018 22:00 ESTInformation geometry in a global settinghttps://projecteuclid.org/euclid.hmj/1544238029<strong>Atsuhide Mori</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 3, 291--305.</p><p><strong>Abstract:</strong><br/>
We begin a global study of information geometry. In this article, we describe the geometry of normal distributions by means of positive and negative contact structures associated to the suspension Anosov flows on $Sol^3$-manifolds.
</p>projecteuclid.org/euclid.hmj/1544238029_20181207220057Fri, 07 Dec 2018 22:00 ESTModel selection criterion based on the prediction mean squared error in generalized estimating equationshttps://projecteuclid.org/euclid.hmj/1544238030<strong>Yu Inatsu</strong>, <strong>Shinpei Imori</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 3, 307--334.</p><p><strong>Abstract:</strong><br/>
The present paper considers a model selection criterion in regression models using generalized estimating equation (GEE). Using the prediction mean squared error (PMSE) normalized by the covariance matrix, we propose a new model selection criterion called PMSEG that reflects the correlation between responses. Numerical studies reveal that the PMSEG has better performance than previous other criteria for model selection.
</p>projecteuclid.org/euclid.hmj/1544238030_20181207220057Fri, 07 Dec 2018 22:00 ESTInterpolation of an analytic family of operators on variable exponent Morrey spaceshttps://projecteuclid.org/euclid.hmj/1544238031<strong>Alexander Meskhi</strong>, <strong>Humberto Rafeiro</strong>, <strong>Muhammad Asad Zaighum</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 3, 335--346.</p><p><strong>Abstract:</strong><br/>
In this paper we show the validity of Stein’s interpolation theorem on variable exponent Morrey spaces.
</p>projecteuclid.org/euclid.hmj/1544238031_20181207220057Fri, 07 Dec 2018 22:00 ESTUniqueness of some di¤erential polynomials of meromorphic functionshttps://projecteuclid.org/euclid.hmj/1544238032<strong>Kuldeep Singh Charak</strong>, <strong>Banarsi Lal</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 3, 347--361.</p><p><strong>Abstract:</strong><br/>
In this paper, we prove some uniqueness results which improve and generalize several earlier works. Also, we prove a value distribution result concerning $f^{(k)}$ which is related to a conjecture of Fang and Wang [A note on the conjectures of Hayman, Mues and Gol’dberg, Comp. Methods, Funct. Theory (2013) 13, 533–543].
</p>projecteuclid.org/euclid.hmj/1544238032_20181207220057Fri, 07 Dec 2018 22:00 ESTTwo existence results between an affine resolvable SRGD design and a difference schemehttps://projecteuclid.org/euclid.hmj/1544238033<strong>Satoru Kadowaki</strong>, <strong>Sanpei Kageyama</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 3, 363--371.</p><p><strong>Abstract:</strong><br/>
The existence of affine resolvable block designs has been discussed since 1942 in the literature (cf. Bose (1942), Clatworthy (1973), Raghavarao (1988)). Kadowaki and Kageyama (2009, 2010, 2012) obtained a number of results on combinatorics for the existence of an affine resolvable SRGD design. In this paper, a new existence result is shown as a generalization of Theorem 3.3.3 given in Kadowaki and Kageyama (2009, 2010). Furthermore, another existence result is shown as a conditional converse of Theorem 3.3.3 and also a generalization of Theorem 3.3.4, both theorems given in Kadowaki and Kageyama (2009, 2010).
</p>projecteuclid.org/euclid.hmj/1544238033_20181207220057Fri, 07 Dec 2018 22:00 ESTEstimating the probabilities of misclassification using CV when the dimension and the sample sizes are largehttps://projecteuclid.org/euclid.hmj/1544238034<strong>Tomoyuki Nakagawa</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 3, 373--411.</p><p><strong>Abstract:</strong><br/>
In this paper, we study about estimating the probabilities of misclassification in the high-dimensional data. In many cases, the cross-validation (CV) is often used for estimations of the probabilities of misclassification. CV provides a nearly unbiased estimate, using the original data when the sample sizes are large. On the other hand, the properties of CV are not well-known when the dimension is large as compared to the sample sizes. Therefore, we investigate asymptotic properties of CV when the dimension and the sample sizes tend to be large. Furthermore, we suggest the three methods for correcting the bias by using CV which is usable in the high-dimensional data. We show performances of the estimators in the simulation studies.
</p>projecteuclid.org/euclid.hmj/1544238034_20181207220057Fri, 07 Dec 2018 22:00 ESTPseudo-Einstein unit tangent sphere bundleshttps://projecteuclid.org/euclid.hmj/1544238035<strong>Jong Taek Cho</strong>, <strong>Sun Hyang Chun</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 3, 413--427.</p><p><strong>Abstract:</strong><br/>
In the present paper, we study the pseudo-Hermitian almost CR structure of unit tangent sphere bundle $T_{1}M$ over a Riemannian manifold $M$. Then we prove that if the unit tangent sphere bundle $T_{1}M$ is pseudo-Einstein, that is, the pseudo- Hermitian Ricci tensor is proportional to the Levi form, then the base manifold $M$ is Einstein. Moreover, when $\dim M = 3$ or $4$, we prove that $T_{1}M$ is pseudo-Einstein if and only if $M$ is of constant curvature 1.
</p>projecteuclid.org/euclid.hmj/1544238035_20181207220057Fri, 07 Dec 2018 22:00 ESTTable of Contents, Hiroshima Math. J., Volume 48, (2018)https://projecteuclid.org/euclid.hmj/1544238036<p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 48, Number 3</p>projecteuclid.org/euclid.hmj/1544238036_20181207220057Fri, 07 Dec 2018 22:00 EST