Mostrando recursos 1 - 20 de 1.320

  1. Finiteness of the Moderate Rational Points of Once-punctured Elliptic Curves

    HOSHI, Yuichiro
    In the present paper, we prove the {\it finiteness} of the set of {\it moderate} rational points of a once-punctured elliptic curve over a number field. This {\it finiteness} may be regarded as an analogue for a once-punctured elliptic curve of the well-known {\it finiteness} of the set of torsion rational points of an abelian variety over a number field. In order to obtain the {\it finiteness}, we discuss the {\it center} of the image of the pro-$l$ outer Galois action associated to a hyperbolic curve. In particular, we give, under the assumption that $l$ is {\it odd}, a {\it...

  2. Absence of zero resonances of massless Dirac operators

    AIBA, Daisuke
    We consider the massless Dirac operator $H = \alpha \cdot D + Q(x)$ on the Hilbert space $L^{2}( \mathbb{R}^{3}, \mathbb{C}^{4} )$, where $Q(x)$ is a $4 \times 4$ Hermitian matrix valued function which decays suitably at infinity. We show that the the zero resonance is absent for $H$, extending recent results of Sait\={o}-Umeda [6] and Zhong-Gao [7].

  3. A tower condition characterizing normality

    KADISON, Lars
    We define left relative H-separable tower of rings and continue a study of these begun by Sugano. It is proven that a progenerator extension has right depth 2 if and only if the ring extension together with its right endomorphism ring is a left relative H-separable tower. In particular, this applies to twisted or ordinary Frobenius extensions with surjective Frobenius homomorphism. For example, normality for Hopf subalgebras of finite-dimensional Hopf algebras is also characterized in terms of this tower condition.

  4. On the Separated Bumps Conjecture for Calderón-Zygmund Operators

    LACEY, Michael T.
    Let $\sigma (dx) = \sigma (x)dx$ and $w (dx)= w (x)dx$ be two weights with non-negative locally finite densities on $\mathbb R^{d}$, and let $1 \lt p \lt \infty$. A sufficient condition for the norm estimate \begin{equation*} \int \lvert T (\sigma f)\rvert^{p} \, w (dx) \le C_{T, \sigma ,w}^{p} \int \lvert f\rvert^{p}\, \sigma (dx) , \end{equation*} valid for all Calder\'on-Zygmund operators $T$ is that the condition below holds. \begin{equation*} \sup_{\textup{$Q$ a cube}} \lVert \sigma^{1/{p'}}\rVert_{L^{A} (Q, {dx}/{\lvert Q\rvert})} \varepsilon \big(\lVert \sigma^{1/{p'}}\rVert_{L^{A} (Q, {dx}/{\lvert Q\rvert})}/ \sigma (Q)^{1/{p'}}\big) \bigg[\frac{w (Q)}{\lvert Q\rvert} \bigg]^{1/{p}} \lt \infty \end{equation*} Here $A$ is Young function, with dual in the P{\'e}rez class $B_{p}$, and the function $\varepsilon (t)$ is...

  5. Removable sets for subcaloric functions and solutions of semilinear heat equations with absorption

    HIRATA, Kentaro
    We investigate removable sets for subcaloric functions satisfying either a growth condition or an integrability condition by defining suitably upper Minkowski content with respect to the parabolic distance. Results are also applied to obtain removability theorems for nonnegative solutions of a semilinear heat equation with an absorption term.

  6. Integral Homology of the Moduli Space of Tropical Curves of Genus 1 with Marked Points

    LIU, Ye
    Kozlov has studied the topological properties of the moduli space of tropical curves of genus 1 with marked points, such as its mod 2 homology, while the integral homology remained a conjecture. In this paper, we present a complete proof of Kozlov's conjecture concerning the integral homology of this moduli space.

  7. Low energy spectral and scattering theory for relativistic Schroedinger operators

    RICHARD, Serge; UMEDA, Tomio
    Spectral and scattering theory at low energy for the relativistic Schr\"odinger operator are investigated. Some striking properties at thresholds of this operator are exhibited, as for example the absence of 0-energy resonance. Low energy behavior of the wave operators and of the scattering operator are studied, and stationary expressions in terms of generalized eigenfunctions are proved for the former operators. Under slightly stronger conditions on the perturbation the absolute continuity of the spectrum on the positive semi axis is demonstrated. Finally, an explicit formula for the action of the free evolution group is derived. Such a formula, which is well...

  8. On the global existence and asymptotic behavior of solutions of reaction-diffusion equations

    MASUDA, Kyûya

  9. On the distribution of the poles of the scattering matrix for two strictly convex obstacles

    IKAWA, Mitsuru

  10. Weierstrass's function and chaos

    YAMAGUTI, Masaya; HATA, Masayoshi

  11. The Euler limit and initial layer of the nonlinear Boltzmann equation

    UKAI, Seiji; ASANO, Kiyoshi

  12. On the hyperbolicity in the domain of real analytic functions and Gevrey classes

    MIZOHATA, Sigeru

  13. An example of a globally hypo-elliptic operator

    FUJIWARA, Daisuke; OMORI, Hideki

  14. Aberrant CR Structures

    JACOBOWITZ, Howard; TREVES, Francois

  15. Linear Volterra integral equations of parabolic type

    TANABE, Hiroki

  16. Period-additivity and multistability in piecewise smooth systems

    KANG, Hunseok; LEE, Ah Reum
    Piecewise smooth systems have been consistently considered and investigated in nonlinear dynamics due to their practical applications. In this paper, we study a generic type of piecewise smooth dynamical system to deal with period-additivity and multistability in the system; an arithmetic sequence of periodic attractors appearing in the period-adding bifurcation and the coexistence of multiple attractors in the system. We state a physical observation of the phenomena and then provide rigorous mathematical arguments and numerical simulations.

  17. Periodic solutions for a class of nonlinear difference equations

    SHI, Haiping; LIU, Xia; ZHANG, Yuanbiao
    By using the critical point theory, some new criteria are obtained for the existence and multiplicity of periodic solutions to a class of nonlinear difference equations. The proof is based on the Linking Theorem in combination with variational technique. Our results successfully generalize and improve some existing results in the literature.

  18. Degenerate and dihedral Heun functions with parameters

    VIDŪNAS, Raimundas
    Just as with the Gauss hypergeometric function, particular cases of the local Heun function can be Liouvillian (that is, ``elementary'') functions. One way to obtain these functions is by pull-back transformations of Gauss hypergeometric equations with Liouvillian solutions. This paper presents the Liouvillian solutions of Heun's equations that are pull-backs of the parametric hypergeometric equations with cyclic or dihedral monodromy groups.

  19. Zeta functions of adjacency algebras of association schemes of prime order or rank two

    HANAKI, Akihide; HIRASAKA, Mitsugu
    For a module $L$ which has only finitely many submodules with a given finite index we define the zeta function of $L$ to be a formal Dirichlet series $\zeta_L(s)=\sum_{n\geq 1}a_nn^{-s}$ where $a_n$ is the number of submodules of $L$ with index $n$. For a commutative ring $R$ and an association scheme $(X,S)$ we denote the adjacency algebra of $(X,S)$ over $R$ by $RS$. In this article we aim to compute $\zeta_{\mathbb{Z}S}(s)$, where $\mathbb{Z}S$ is viewed as a regular $\mathbb{Z}S$-module, under the assumption that $|X|$ is a prime or $|S|=2$.

  20. A projective characterization of a class of abelian groups

    KEEF, Patrick W.
    This paper considers the class of abelian groups that are extensions of subgroups that are direct sums of cyclic groups by factor groups that are also of this form. This class is shown to be the projectives with respect to a natural collection of short exact sequences, and that the corresponding class of injectives consists of those groups whose first Ulm subgroup is pure-injective. This class of projectives is quite extensive, but satisfactory descriptions are given for the countable groups in the class that are either torsion-free, or else mixed groups of torsion-free rank one. Particular attention is paid to...

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