Recursos de colección
Project Euclid (Hosted at Cornell University Library) (192.977 recursos)
Hiroshima Mathematical Journal
Hiroshima Mathematical Journal
Güneş Aktaş, Çisem
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.
Noda, Takahiro
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.
Tonda, Tetsuji; Nakagawa, Tomoyuki; Wakaki, Hirofumi
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.
Sakamoto, Takuro; Yonezawa, Yasuyoshi
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.
Ando, Masanori; Yamada, Hiro-Fumi
A $q$-analogue of a partition identity is presented.
Oger, Francis
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...
Kubo, Akira; Onda, Kensuke; Taketomi, Yuichiro; Tamaru, Hiroshi
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...
Kuno, Erika
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.
Hemmi, Yutaka; Kobayashi, Teiichi
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.
Liu, Xiaojing; Horiuchi, Toshio
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 $\Omega$.
Kimura, Hironobu; Tseveennamjil, Damiran
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...
Kin, Eiko; Takasawa, Mitsuhiko
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...
Paiva Barreto, Alexandre; Lima Gonçalves, Daciberg; Vendrúscolo, Daniel
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.
Furokawa, Mikio
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.
Hoai Hoang, Thanh
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.
Ueda, Hideo
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].
Mohamed Farghly, Rasha
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.
Ishikawa, Masaharu; Nemoto, Keisuke
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.
Jiang, Yan; Huang, Bin
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.