Mostrando recursos 1 - 20 de 1.328

  1. Local symmetry on almost Kenmotsu three-manifolds

    CHO, Jong Taek
    We prove that a locally symmetric almost Kenmotsu three-manifold is locally isometric to either the hyperbolic space $\mathrm{\Bbb{H}^3(-1)}$ or a product space $\Bbb{H}^2(-4)\times \Bbb{R}$.

  2. A Note on Vertex-transitive K\"ahler graphs

    TUERXUNMAIMAITI, Yaermaimaiti; ADACHI, Toshiaki
    In this paper we construct finite vertex-transitive K\"ahler graphs, which may be considered as discrete models of Hermitian symmetric spaces admitting K\"ahler magnetic fields. We give a condition on cardinality of the set of vertices and the principal and the auxiliary degrees for a vertex-transitive K\"ahler graphs. Also we give some examples of K\"ahler graphs corresponding typical vertex-transitive ordinary graphs.

  3. The metric growth of the discrete Laplacian

    KURATA, Hisayasu; YAMASAKI, Maretsugu
    Networks play important roles in the theory of discrete potentials. Especially, the theory of Dirichlet spaces on networks has become one of the most important tools for the study of potentials on networks. In this paper, first we study some relations between the Dirichlet sums of a function and of its Laplacian. We introduce some conditions to investigate properties of several functional spaces related to Dirichlet potentials and to biharmonic functions. Our goal is to study the growth of the Laplacian related to biharmonic functions on an infinite network. As an application, we prove a Riesz Decomposition theorem for Dirichlet...

  4. Curve diagrams for Artin groups of type B

    ITO, Tetsuya
    We develop a theory of curve diagrams for Artin groups of type $B$. We define the winding number labeling and the wall crossing labeling of curve diagrams, and show that these labelings detect the classical and the dual Garside length, respectively. A remarkable point is that our argument does not require Garside theory machinery like normal forms, and is more geometric in nature.

  5. Screen Semi-Slant Lightlike Submanifolds of Indefinite Sasakian Manifolds

    SHUKLA, S. S.; YADAV, Akhilesh
    In this paper, we introduce the notion of screen semi-slant lightlike submanifolds of indefinite Sasakian manifolds giving characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions D1, D2 and RadTM on screen semi-slant lightlike submanifolds of indefinite Sasakian manifolds have been obtained. Further we obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic. We also study mixed geodesic screen semi-slant lightlike submanifolds of indefinite Sasakian manifolds and obtain a necessary and sufficient condition for induced connection to be metric connection.

  6. A New Characterization of Some Simple Groups by Order and Degree Pattern of Solvable Graph

    The solvable graph of a finite group $G$, denoted by ${\Gamma}_{\rm s}(G)$, is a simple graph whose vertices are the prime divisors of $|G|$ and two distinct primes $p$ and $q$ are joined by an edge if and only if there exists a solvable subgroup of $G$ such that its order is divisible by $pq$. Let $p_1

  7. Estimates of operator convex and operator monotone functions on bounded intervals

    NAJAFI, Hamed; MOSLEHIAN, Mohammad Sal; FUJII, Masatoshi; NAKAMOTO, Ritsuo
    Recently the behavior of operator monotone functions on unbounded intervals with respect to the relation of strictly positivity has been investigated. In this paper we deeply study such behavior not only for operator monotone functions but also for operator convex functions on bounded intervals. More precisely, we prove that if $f$ is a nonlinear operator convex function on a bounded interval $(a,b)$ and $A, B$ are bounded linear operators acting on a Hilbert space with spectra in $(a,b)$ and $A-B$ is invertible, then $sf(A)+(1-s)f(B)>f(sA+(1-s)B)$. A short proof for a similar known result concerning a nonconstant operator monotone function on $[0,\infty)$...

  8. $S^1$-equivariant Rabinowitz--Floer homology

    We define the $S^1$-equivariant Rabinowitz--Floer homology of a bounding contact hypersurface $\Sigma$ in an exact symplectic manifold, and show by a geometric argument that it vanishes if $\Sigma$ is displaceable.

  9. 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...

  10. 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].

  11. 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.

  12. 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...

  13. 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.

  14. 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.

  15. 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...

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

    MASUDA, Kyûya

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

    IKAWA, Mitsuru

  18. Weierstrass's function and chaos

    YAMAGUTI, Masaya; HATA, Masayoshi

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

    UKAI, Seiji; ASANO, Kiyoshi

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

    MIZOHATA, Sigeru

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