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 EDTRicci tensors on unit tangent sphere bundles over 4-dimensional Riemannian manifoldshttp://projecteuclid.org/euclid.hmj/1439219704<strong>Jong Taek Cho</strong>, <strong>Sun Hyang Chun</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 45, Number 2, 125--135.</p>projecteuclid.org/euclid.hmj/1439219704_20150810111507Mon, 10 Aug 2015 11:15 EDTOn non-periodic 3-Archimedean tilings with 6-fold rotational symmetryhttp://projecteuclid.org/euclid.hmj/1439219705<strong>Naoko Kinoshita</strong>, <strong>Kazushi Komatsu</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 45, Number 2, 137--146.</p><p><strong>Abstract:</strong><br/>
The purpose of this article is to construct a family of uncountably many
non-periodic 3-Archimedean tilings with 6-fold rotational symmetry, which admit three
types of vertex configurations by regular triangles and squares.
</p>projecteuclid.org/euclid.hmj/1439219705_20150810111507Mon, 10 Aug 2015 11:15 EDTGenerating functions of Box and Ball Systemhttp://projecteuclid.org/euclid.hmj/1439219706<strong>Mami Okiyoshi</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 45, Number 2, 147--163.</p><p><strong>Abstract:</strong><br/>
Generating functions of Box and Ball System (BBS) are defined and
studied. When the number of balls is finite, we show that the generating function
is a rational function. When there are infinitely many balls, we conjecture that the
generating function is rational if and only if the BBS is semi-periodic. We prove the
conjecture in a special case. We also study the generating function of the BBS with
a limited cart, including semi-periodic cases.
</p>projecteuclid.org/euclid.hmj/1439219706_20150810111507Mon, 10 Aug 2015 11:15 EDTTwo-point homogeneous quandles with cardinality of prime powerhttp://projecteuclid.org/euclid.hmj/1439219707<strong>Koshira Wada</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 45, Number 2, 165--174.</p><p><strong>Abstract:</strong><br/>
The main result of this paper classifies two-point homogeneous quandles
with cardinality of prime power. More precisely, such quandles are isomorphic to
Alexander quandles defined by primitive roots over finite fields. This result classifies
all two-point homogeneous finite quandles, by combining with the recent result of
Vendramin.
</p>projecteuclid.org/euclid.hmj/1439219707_20150810111507Mon, 10 Aug 2015 11:15 EDTConsistency of log-likelihood-based information criteria for
selecting variables in high-dimensional canonical correlation
analysis under nonnormalityhttp://projecteuclid.org/euclid.hmj/1439219708<strong>Keisuke Fukui</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 45, Number 2, 175--205.</p><p><strong>Abstract:</strong><br/>
The purpose of this paper is to clarify the conditions for consistency of
the log-likelihood-based information criteria in canonical correlation analysis of q- and
p- dimensional random vectors when the dimension p is large but does not exceed the
sample size. Although the vector of observations is assumed to be normally distributed,
we do not know whether the underlying distribution is actually normal. Therefore,
conditions for consistency are evaluated in a high-dimensional asymptotic framework
when the underlying distribution is not normal.
</p>projecteuclid.org/euclid.hmj/1439219708_20150810111507Mon, 10 Aug 2015 11:15 EDTGalois action on mapping class groupshttp://projecteuclid.org/euclid.hmj/1439219709<strong>Yu Iijima</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 45, Number 2, 207--230.</p><p><strong>Abstract:</strong><br/>
Let l be a prime number. In the paper, we study the outer Galois action
on the profinite and the relative pro- l completions of mapping class groups of pointed
orientable topological surfaces. In the profinite case, we prove that the outer Galois
action is faithful. In the pro- l case, we prove that the kernel of the outer Galois action
has certain stability properties with respect to the genus and the number of punctures.
Also, we prove a variant of the above results for arbitrary families of curves.
</p>projecteuclid.org/euclid.hmj/1439219709_20150810111507Mon, 10 Aug 2015 11:15 EDTGeometric log Hodge structures on the standard log pointhttp://projecteuclid.org/euclid.hmj/1448323766<strong>Taro Fujisawa</strong>, <strong>Chikara Nakayama</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 45, Number 3, 231--266.</p><p><strong>Abstract:</strong><br/>
We construct natural polarized log Hodge structures associated to a projective
log deformation over the standard log point.
</p>projecteuclid.org/euclid.hmj/1448323766_20151123190929Mon, 23 Nov 2015 19:09 ESTNonautonomous differential equations and Lipschitz evolution operators in Banach spaceshttp://projecteuclid.org/euclid.hmj/1448323767<strong>Yoshikazu Kobayashi</strong>, <strong>Naoki Tanaka</strong>, <strong>Yukino Tomizawa</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 45, Number 3, 267--307.</p><p><strong>Abstract:</strong><br/>
A new class of Lipschitz evolution operators is introduced and a characterization
of continuous infinitesimal generators of such evolution operators is given.
It is shown that a continuous mapping $A$ from a subset $omega$ of $[a,b) x X into X$, where
$[a,b)$ is a real half-open interval and $X$ is a real Banach space, is the infinitesimal
generator of a Lipschitz evolution operator if and only if it satisfies a sub-tangential
condition, a general type of quasi-dissipative condition with respect to a metric-like
functional and a connectedness condition. An application of the results to the initial
value problem for the quasilinear wave equation with dissipation is also given.
</p>projecteuclid.org/euclid.hmj/1448323767_20151123190929Mon, 23 Nov 2015 19:09 ESTAnisohedral spherical triangles and classification of spherical tilings by congruent kites, darts and rhombihttp://projecteuclid.org/euclid.hmj/1448323768<strong>Yudai Sakano</strong>, <strong>Yohji Akama</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 45, Number 3, 309--339.</p><p><strong>Abstract:</strong><br/>
We classify all spherical monohedral (kite/dart/rhombus)-faced tilings, as
follows: The set of spherical monohedral rhombus-faced tilings consists of (1) the
central projection of the rhombic dodecahedron, (2) the central projection of the
rhombic triacontahedron, (3) a series of non-isohedral tilings, and (4) a series of tilings
which are topologically trapezohedra (here a trapezohedron is the dual of an antiprism.).
The set of spherical tilings by congruent kites consists of (1) the central projection
$T$ of the tetragonal icosikaitetrahedron, (2) the central projection of the tetragonal
hexacontahedron, (3) a non-isohedral tiling obtained from $T$ by gliding a hemisphere
of $T$ with $pi/4$ radian, and (4) a continuously deformable series of tilings which are
topologically trapezohedra. The set of spherical tilings by congruent darts is a continuously
deformable series of tilings which are topologically trapezohedra. In the above
explanation, unless otherwise stated, the tilings we have enumerated are isohedral and
admit no continuous deformation. We prove that if a spherical (kite/dart/rhombus)
admits an edge-to-edge spherical monohedral tiling, then it also does a spherical
isohedral tiling. We also prove that the set of anisohedral, spherical triangles (i.e.,
spherical triangles admitting spherical monohedral triangular tilings but not any
spherical isohedral triangular tilings) consists of a certain, infinite series of isosceles
triangles $I$ , and an infinite series of right scalene triangles which are the bisections
of $I$ .
</p>projecteuclid.org/euclid.hmj/1448323768_20151123190929Mon, 23 Nov 2015 19:09 ESTWAFOM over abelian groups for quasi-Monte Carlo point setshttp://projecteuclid.org/euclid.hmj/1448323769<strong>Kosuke Suzuki</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 45, Number 3, 341--364.</p>projecteuclid.org/euclid.hmj/1448323769_20151123190929Mon, 23 Nov 2015 19:09 ESTTable of Contents, Hiroshima Math. J., Volume 45, (2014)http://projecteuclid.org/euclid.hmj/1448323770<p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 45, Number 3, --.</p>projecteuclid.org/euclid.hmj/1448323770_20151123190929Mon, 23 Nov 2015 19:09 ESTThe space of geometric limits of abelian subgroups of $\mathrm{PSL}_2(\mathbb{C})$http://projecteuclid.org/euclid.hmj/1459525928<strong>Hyungryul Baik</strong>, <strong>Lucien Clavier</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 1, 1--36.</p>projecteuclid.org/euclid.hmj/1459525928_20160401115216Fri, 01 Apr 2016 11:52 EDTOn the average of some arithmetical functions under a constraint on the sum of digits of squareshttp://projecteuclid.org/euclid.hmj/1459525929<strong>Karan Aloui</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 1, 37--54.</p>projecteuclid.org/euclid.hmj/1459525929_20160401115216Fri, 01 Apr 2016 11:52 EDTAlmost universality of a sum of normshttp://projecteuclid.org/euclid.hmj/1459525930<strong>Jeongho Park</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 1, 55--77.</p><p><strong>Abstract:</strong><br/>
In this paper the author considers a particular type of polynomials with
integer coefficients, consisting of a perfect power and two norm forms of abelian number
fields with coprime discriminants. It is shown that such a polynomial represents every
natural number with only finitely many exceptions. The circle method is used, and the
local class field theory played a central role in estimating the singular series.
</p>projecteuclid.org/euclid.hmj/1459525930_20160401115216Fri, 01 Apr 2016 11:52 EDTA note on a result of Lanteri about the class of a polarized surfacehttp://projecteuclid.org/euclid.hmj/1459525931<strong>Yoskiaki Fukuma</strong>. <p><strong>Source: </strong>Hiroshima Mathematical Journal, Volume 46, Number 1, 79--85.</p>projecteuclid.org/euclid.hmj/1459525931_20160401115216Fri, 01 Apr 2016 11:52 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 EST