Mostrando recursos 1 - 20 de 1.322

  1. On the Moduli Space of Pointed Algebraic Curves of Low Genus III ---Positive Characteristic---

    NAKANO, Tetsuo
    In his classical work, Pinkham discovered a beautiful theorem on the moduli space of pointed algebraic curves with a fixed Weierstrass gap sequence at the marked point. Namely, the complement of a Weierstrass gap sequence in the set of non-negative integers is a numerical semigroup, and he described such a moduli space in terms of the negative part of the miniversal deformation space of the monomial curve of this semigroup. Unfortunately, his theorem holds only in characteristic 0 and does not hold in positive characteristic in general. In this paper, we will study his theorem in positive characteristic, and give a fairly sharp...

  2. A Sufficient Condition for Orbits of Hermann Actions to be Weakly Reflective

    OHNO, Shinji
    In this paper, we give sufficient conditions for orbits of Hermann actions to be weakly reflective in terms of symmetric triads, that is a generalization of irreducible root systems. Using these sufficient conditions, we obtain new examples of weakly reflective submanifolds in compact symmetric spaces.

  3. Asymptotically Unweighted Shifts, Hypercyclicity, and Linear Chaos

    NATSUME, Ayuko; TANIGUCHI, Masahiko
    In this paper, we introduce weighted backward shifts, which are asymptotically unweighted, and give several conditions for such operators on the classical $\ell^p$ spaces to be hypercyclic and chaotic.

  4. Reidemeister Torsion and Dehn Surgery on Twist Knots

    TRAN, Anh T.
    We compute the Reidemeister torsion of the complement of a twist knot in $S^3$ and that of the 3-manifold obtained by a $\frac{1}{q}$-Dehn surgery on a twist knot.

  5. $B_w^u$-function Spaces and Their Interpolation

    NAKAI, Eiichi; SOBUKAWA, Takuya
    We introduce $B_w^u$-function spaces which unify Lebesgue, Morrey-Campanato, Lipschitz, $B^p$, $\mathrm{CMO}$, local Morrey-type spaces, etc., and investigate the interpolation property of $B_w^u$-function spaces. We also apply it to the boundedness of linear and sublinear operators, for example, the Hardy-Littlewood maximal and fractional maximal operators, singular and fractional integral operators with rough kernel, the Littlewood-Paley operator, Marcinkiewicz operator, and so on.

  6. On the Centralizer Algebras of the Primitive Unitary Reflection Group of Order 96

    KOSUDA, Masashi; OURA, Manabu
    Among the unitary reflection groups, the one on the title is singled out by its importance in, for example, coding theory and number theory. In this paper we examine the semi-simple structure of the centralizer algebra in the tensor representation, and show that the dimensions of the centralizers coincide with the numbers of some combinatorial objects.

  7. Remarks on $r$-planes in Complete Intersections

    MIYAZAKI, Chikashi
    This paper investigates the families of smooth complete intersections containing $r$-planes in projective spaces. We are going in a primitive way to shed some light on a point and an $r$-plane containing the point in a complete intersection from the viewpoint of projective geometry.

  8. On Hausdorff Dimension of Certain Sets Arising from Diophantine Approximations for Complex Numbers

    CHEN, Zhengyu
    We discuss the Hausdorff dimension of certain sets related to Diophantine approximations over an imaginary quadratic field $\mathbb{Q}(\sqrt{d})$. We show that, for an infinite subset $\mathcal{A}$ of $\mathbb{Z}[\omega] \backslash \{0\}$, the set of $z \in \mathbb{C}$ with $|z-a/r| < 1 / |r|^{1+\rho}$ having infinitely many solutions of $a \in \mathbb{Z}[\omega]$ and $r \in \mathcal{A}$ with some $\rho > 0$ has Hausdorff dimension $2(1+\gamma) / (1+\rho)$, where $\gamma$ is the sup of $h$ such that $\sum_{r \in \mathcal{A}} 1/(|r|^{2})^{h}$ diverges. This result is a version of a result by G. Harman for complex numbers without the coprime condition. In particular, this result implies a...

  9. Toeplitz Operators and the Roe-Higson Type Index Theorem in Riemannian Surfaces

    SETO, Tatsuki
    Let $M$ be a non-compact complete Riemannian manifold of dimension two and $N$ a circle in $M$. We assume that $M$ is partitioned by $N$. We define a unital $C^{\ast}$-algebra $C_{b}^{\ast}(M)$, which is slightly larger than the Roe algebra of $M$. We also construct $[u_{\phi}]$ in $K_{1}(C_{b}^{\ast}(M))$, which is a counter part of Roe's odd index class. We prove that Connes' pairing of Roe's cyclic one-cocycle with $[u_{\phi}]$ is equal to the Fredholm index of a Toeplitz operator on $N$. It is a part of an extension of the Roe-Higson index theorem to even-dimensional partitioned manifolds.

  10. A Rigidity Theorem for Proper Holomorphic Mappings between Generalized Pseudoellipsoids

    HAYASHIMOTO, Atsushi
    Let $E(\alpha) \subset \mathbb{C}^{m+1}$ and $E(\beta) \subset \mathbb{C}^{n+1}$ be generalized pseudoellipsoids. Assume that the inequality $m

  11. Non-Hopf Hypersurfaces in 2-dimensional Complex Space Forms

    KON, Mayuko
    In this paper we give a geometric characterization of non-Hopf hypersurfaces in the complex space form $M^2(c)$ under a condition on the shape operator. We also classify pseudo-parallel real hypersurfaces of $M^2(c)$.

  12. The Uniqueness Theorem for the Heat Equation on the Heisenberg Group

    OKA, Yasuyuki
    The aim of this paper is to establish the uniqueness theorem for the Cauchy problem for the heat equation with the Tikhonov condition on the Heisenberg group. To do this, we give Green's formula and show the existence of a Lipschitz cut-off function on the Heisenberg group in accordance with the idea in [7].

  13. The Capitulation Problem for Certain Cyclic Quartic Number Fields

    AZIZI, Abdelmalek; JERRARI, Idriss; TALBI, Mohammed
    Let $K$ be a cyclic quartic number field such that its 2-class group is of type $(2,4)$, $K_2^{(1)}$ be the Hilbert 2-class field of $K$, $K_2^{(2)}$ be the Hilbert 2-class field of $K_2^{(1)}$ and $G=\text{Gal}(K_2^{(2)}/K)$ be the Galois group of $K_2^{(2)}/K$. Our goal is to study the capitulation problem of 2-ideal classes of $K$ and to determine the structure of $G$.

  14. New Trigonometric Identities and Reciprocity Laws of Generalized Dedekind Sums

    SHIBUKAWA, Genki
    In this paper, we prove new trigonometric identities, which are product-to-sum type formulas for the higher derivatives of the cotangent and cosecant functions. Furthermore, from specializations of our formulas, we derive various known and new reciprocity laws of generalized Dedekind sums.

  15. Trace Operator for 2-microlocal Besov Spaces with Variable Exponents

    NOI, Takahiro
    Moura, Neves and Schneider proved the trace theorem for 2-microlocal Besov spaces with variable integrability and smoothness, where the summability parameter was constant (Math.\,Nachr.,286 (2013) 1240--1254). In this paper, we extend the trace theorem for the case that the summability parameter is also a variable exponent.

  16. Asymptotic Behavior of Solutions for Semilinear Volterra Diffusion Equations with Spatial Inhomogeneity and Advection

    YOSHIDA, Yusuke; YAMADA, Yoshio
    This paper is concerned with semilinear Volterra diffusion equations with spatial inhomogeneity and advection. We intend to study the effects of interaction among diffusion, advection and Volterra integral under spatially inhomogeneous environments. Since the existence and uniqueness result of global-in-time solutions can be proved in the standard manner, our main interest is to study their asymptotic behavior as $t\to \infty$. For this purpose, we study the related stationary problem by the monotone method and establish some sufficient conditions on the existence of a unique positive solution. Its global attractivity is also studied with use of a suitable Lyapunov functional.

  17. Nested Square Roots and Poincaré Functions

    AOKI, Noboru; KOJIMA, Shota
    We are concerned with finitely nested square roots which are roots of iterations of a real quadratic polynomial $x^2-c$ with $c\geq 2$, and the limits of such nested square roots. We investigate how they are related to a Poincaré function $f(x)$ satisfying the functional equation $f(sx)=f(x)^2-c$, where $s=1+\sqrt{1+4c}$. Our main theorems can be viewed as a natural generalization of the work of Wiernsberger and Lebesgue for the case $c=2$. The key ingredients of the proof are some analytic properties of $F(x)$, which have been intensively studied by the second author using infinite compositions.

  18. Higher-order Convolution Identities for Cauchy Numbers

    KOMATSU, Takao
    Euler's famous formula written in symbolic notation as $(B_0+B_0)^n=-n B_{n-1}-(n-1)B_n$ was extended to $(B_{l_1}+\cdots+B_{l_m})^n$ for $m\ge 2$ and arbitrary fixed integers $l_1,\dots,l_m\ge 0$. In this paper, we consider the higher-order recurrences for Cauchy numbers $(c_{l_1}+\cdots+c_{l_m})^n$, where the $n$-th Cauchy number $c_n$ ($n\ge 0$) is defined by the generating function $x/\ln(1+x)=\sum_{n=0}^\infty c_n x^n/n!$. In special, we give an explicit expression in the case $l_1=\cdots=l_m=0$ for any integers $n\ge 1$ and $m\ge 2$. We also discuss the case for Cauchy numbers of the second kind $\widehat c_n$ in similar ways.

  19. On the $C^\alpha$-convergence of the Solution of the Chern-Ricci Flow on Elliptic Surfaces

    KAWAMURA, Masaya
    We will study the Chern-Ricci flow on non-Kähler properly elliptic surfaces. These surfaces are compact complex surfaces whose first Betti number is odd, Kodaira dimension is equal to 1 and admit an elliptic fibration to a smooth compact curve. We will show that a solution of the Chern-Ricci flow converges in $C^\alpha$-topology on these elliptic surfaces by choosing a special initial metric.

  20. Uniform Blow-up Rate for Nonlocal Diffusion-like Equations with Nonlocal Nonlinear Source

    ZHENG, Jiashan
    We present new blow-up results for nonlocal reaction-diffusion equations with nonlocal nonlinearities. The nonlocal source terms we consider are of several types, and are relevant to various models in physics and engineering. They may involve an integral of an unknown function, either in space, in time, or both in space and time, or they may depend on localized values of the solution. We first show the existence and uniqueness of the solution to problem relying on contraction mapping fixed point theorem. Then, the comparison principles for problem are established through a standard method. Finally, for the radially symmetric and non-increasing initial data, we give a...

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