Mostrando recursos 1 - 20 de 1.651

  1. 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...

  2. 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.

  3. 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.

  4. 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 $\Omega$.

  5. 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...

  6. 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...

  7. 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.

  8. 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.

  9. 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.

  10. 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].

  11. 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.

  12. 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.

  13. 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.

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

  15. Chow groups of Châtelet surfaces over dyadic fields

    Hirotsu, Takashi

  16. Biharmonic hypersurfaces in Riemannian symmetric spaces I

    Inoguchi, Jun-ichi; Sasahara, Toru
    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.

  17. On the classification of certain ternary codes of length 12

    Araya, Makoto; Harada, Masaaki
    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.

  18. A note on a result of Lanteri about the class of a polarized surface

    Fukuma, Yoshiaki

  19. Almost universality of a sum of norms

    Park, Jeongho
    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.

  20. On the average of some arithmetical functions under a constraint on the sum of digits of squares

    Aloui, Karam

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