Mostrando recursos 1 - 20 de 1.657

  1. Classification of simple quartics up to equisingular deformation

    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.

  2. On prolongations of second-order regular overdetermined systems with two independent and one dependent variables

    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.

  3. EPMC estimation in discriminant analysis when the dimension and sample sizes are large

    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.

  4. Link invariant and $G_2$ web space

    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.

  5. Products of parts in class regular partitions

    Ando, Masanori; Yamada, Hiro-Fumi
    A $q$-analogue of a partition identity is presented.

  6. The number of paperfolding curves in a covering of the plane

    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...

  7. On the moduli spaces of left-invariant pseudo-Riemannian metrics on Lie groups

    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...

  8. Uniform hyperbolicity for curve graphs of non-orientable surfaces

    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.

  9. Stable extendibility of some complex vector bundles over lens spaces and Schwarzenberger’s theorem

    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.

  10. Remarks on the strong maximum principle involving $p$-Laplacian

    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 $\Omega$.

  11. Confluence of general Schlesinger systems and Twistor theory

    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...

  12. The boundary of a fibered face of the magic 3-manifold and the asymptotic behavior of minimal pseudo-Anosov dilatations

    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...

  13. Free involutions on torus semi-bundles and the Borsuk-Ulam Theorem for maps into $\mathbf{R}^n$

    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.

  14. Commensurability between once-punctured torus groups and once-punctured Klein bottle groups

    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.

  15. Degeneration of Fermat hypersurfaces in positive characteristic

    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.

  16. A new example of the dissipative wave equations with the total energy decay

    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].

  17. Higher level representation of the elliptic quantum group $U_{q,p}(\widehat{\mathfrak{sl}}_2)$ and its integrability

    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.

  18. Construction of spines of two-bridge link complements and upper bounds of their Matveev complexities

    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.

  19. A note on the value distribution of $f^1(f^{(k)})^n$

    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.

  20. Miscellaneous Frontmatter, Hiroshima Math. J., vol. 46, no. 2 (July 2016)

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