Mostrando recursos 1 - 20 de 73

  1. A remark on conditions that a diffusion in the natural scale is a martingale

    Shimizu, Yuuki; Nakano, Fumihiko
    We consider a diffusion processes $\{ X_t \}$ on an interval in the natural scale. Some results are known under which $\{ X_t \}$ is a martingale, and we give simple and analytic proofs for them.

  2. Type numbers of quaternion hermitian forms and supersingular abelian varieties

    Ibukiyama, Tomoyoshi
    The word \textit{type number} of an algebra means classically the number of isomorphism classes of maximal orders in the algebra, but here we consider quaternion hermitian lattices in a fixed genus and their right orders. Instead of inner isomorphism classes of right orders, we consider isomorphism classes realized by similitudes of the quaternion hermitian forms.The number $T$ of such isomorphism classes are called \textit{type number} or \textit{$G$-type number}, where $G$ is the group of quaternion hermitian similitudes. We express $T$ in terms of traces of some special Hecke operators. This is a generalization of the result announced in [5] (I)...

  3. Comparison theorems in pseudo-Hermitian geometry and applications

    Dong, Yuxin; Zhang, Wei
    In this paper, we study the theory of geodesics with respect to the Tanaka-Webster connection in a pseudo-Hermitian manifold, aiming to generalize some comparison results in Riemannian geometry to the case of pseudo-Hermitian geometry. Some Hopf-Rinow type, Cartan-Hadamard type and Bonnet-Myers type results are established.

  4. Biharmonic submanifolds in a Riemannian manifold

    Koiso, Norihito; Urakawa, Hajime
    In this paper, we solve affirmatively B.-Y. Chen's conjecture for hypersurfaces in the Euclidean space, under a generic condition. More precisely, every biharmonic hypersurface of the Euclidean space must be minimal if their principal curvatures are simple, and the associated frame field is irreducible.

  5. On the digital representation of integers with bounded prime factors

    Bugeaud, Yann
    Let $b \ge 2$ be an integer. Not much is known on the representation in base $b$ of prime numbers or of numbers whose prime factors belong to a given, finite set. Among other results, we establish that any sufficiently large integer which is not a multiple of $b$ and has only small (in a suitable sense) prime factors has at least four nonzero digits in its representation in base $b$.

  6. On calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links

    Ishii, Atsushi; Nikkuni, Ryo; Oshiro, Kanako
    There are many studies about twisted Alexander invariants for knots and links, but calculations of twisted Alexander invariants for spatial graphs, handlebody-knots, and surface-links have not been demonstrated well. In this paper, we give some remarks to calculate the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links, and observe their behaviors. For spatial graphs, we calculate the invariants of Suzuki's theta-curves and show that the invariants are nontrivial for Suzuki's theta-curves whose Alexander ideals are trivial. For handlebody-knots, we give a remark on abelianizations and calculate the invariant of the handlebody-knots up to six crossings. For surface-links, we correct...

  7. Galois covers of type $(p,\cdots,p)$, vanishing cycles formula, and the existence of torsor structures

    Saïdi, Mohamed; Williams, Nicholas
    In this article we prove a local Riemman-Hurwitz formula which compares the dimensions of the spaces of vanishing cycles in a finite Galois cover of type $(p,p,\cdots,p)$ between formal germs of $p$-adic curves and which generalises the formula proven in [6] in the case of Galois covers of degree $p$. We also investigate the problem of the existence of a torsor structure for a finite Galois cover of type $(p,p,\cdots,p)$ between $p$-adic schemes.

  8. Étale endomorphisms of 3-folds. I

    Fujimoto, Yoshio
    This paper is the first part of our project towards classifications of smooth projective $3$-folds $X$ with $\kappa(X) = -\infty$ admitting a non-isomorphic étale endomorphism. We can prove that for any extremal ray $R$ of divisorial type, the contraction morphism $\pi_R\colon X\to X'$ associated to $R$ is the blowing-up of a smooth $3$-fold $X'$ along an elliptic curve. The difficulty is that there may exist infinitely many extremal rays on $X$. Thus we introduce the notion of an `ESP' which is an infinite sequence of non-isomorphic finite étale coverings of $3$-folds with constant Picard number. We can run the minimal...

  9. $\delta$-homogeneity in Finsler geometry and the positive curvature problem

    Xu, Ming; Zhang*, Lei
    In this paper, we explore the similarity between normal homogeneity and $\delta$-homogeneity in Finsler geometry. They are both non-negatively curved Finsler spaces. We show that any connected $\delta$-homogeneous Finsler space is $G$-$\delta$-homogeneous, for some suitably chosen connected quasi-compact $G$. So $\delta$-homogeneous Finsler metrics can be defined by a bi-invariant singular metric on $G$ and submersion, just as normal homogeneous metrics, using a bi-invariant Finsler metric on $G$ instead. More careful analysis shows, in the space of all Finsler metrics on $G/H$, the subset of all $G$-$\delta$-homogeneous ones is in fact the closure for the subset of all $G$-normal ones, in...

  10. A rigidity of equivariant holomorphic maps into a complex Grassmannian induced from orthogonal direct sums of holomorphic line bundles

    Koga, Isami
    In the present paper, we study holomorphic maps induced from orthogonal direct sums of holomorphic line bundles over a compact simply connected homogeneous Kähler manifold into a complex Grassmannian. Then we show if such maps are equivariant, then they are unique up to complex isometry.

  11. Asymptotic behavior of the solutions for the Laplace equation with a large spectral parameter and the inhomogeneous Robin type conditions

    Ikehata*, Masaru; Kawashita**, Mishio
    Reduced problems are elliptic problems with a large parameter (as the spectral parameter) given by the Laplace transform of time dependent problems. In this paper, asymptotic behavior of the solutions of the reduced problem for the classical heat equation in bounded domains with the inhomogeneous Robin type conditions is discussed. The boundary of the domain consists of two disjoint surfaces, outside one and inside one. When there are inhomogeneous Robin type data at both boundaries, it is shown that asymptotics of the value of the solution with respect to the large parameter at a given point inside the domain is...

  12. Representations of quantized coordinate algebras via PBW-type elements

    Oya, Hironori
    Inspired by the work of Kuniba-Okado-Yamada, we study some tensor product representations of quantized coordinate algebras of symmetrizable Kac-Moody Lie algebras in terms of quantized enveloping algebras. As a consequence, we describe structures and properties of certain reducible representations of quantized coordinate algebras. This paper includes alternative proofs of Soibelman's tensor product theorem and Kuniba-Okado-Yamada's common structure theorem based on our direct calculation method using global bases.

  13. Global existence of solutions to an $n$-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth and superlinear production

    Nakaguchi, Etsushi; Osaki, Koichi
    We study the global existence of solutions to an $n$-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth. We introduce superlinear production of a chemoattractant. We then show the global existence of solutions in $L_p$ space $( p > n )$ under certain relations between the degradation and production orders.

  14. On five dimensional Sasakian Lie algebras with trivial center

    Loiudice, E.; Lotta, A.
    We show that every five-dimensional Sasakian Lie algebra with trivial center is $\varphi$-symmetric. Moreover starting from a particular Sasakian structure on the Lie group $SL(2,\mathbb{R})\times\text{Aff}(\mathbb{R})$ we obtain a family of contact metric $(k,\mu)$ structures whose Boeckx invariants assume all values less than $-1$.

  15. The arc metric on Teichmüller spaces of surfaces of infinite type with boundary

    Chen, Qiyu; Liu, Lixin
    Let $X_{0}$ be a complete hyperbolic surface of infinite type with geodesic boundary which admits a countable pair of pants decomposition. As an application of the Basmajian identity for complete bordered hyperbolic surfaces of infinite type with limit sets of 1-dimensional measure zero, we define an asymmetric metric (which is called arc metric) on the quasiconformal Teichmüller space $\mathcal{T}(X_{0})$ provided that $X_{0}$ satisfies a geometric condition. Furthermore, we construct several examples of hyperbolic surfaces of infinite type satisfying the geometric condition and discuss the relation between the Shiga's condition and the geometric condition.

  16. Groups of automorphisms of bordered orientable Klein surfaces of topological genus 2

    Bujalance, E.; Etayo, J.J.; Martínez, E.
    In this paper, we obtain the groups of automorphisms of orientable bordered Klein surfaces of topological genus $2$. For each of those groups $G$ we determine the values of $k$ such that $G$ acts on a surface with $k$ boundary components. Besides, for each given $k$ we exhibit the groups acting on a surface with $k$ boundary components.

  17. Groups of automorphisms of bordered orientable Klein surfaces of topological genus 2

    Bujalance, E.; Etayo, J.J.; Martínez, E.
    In this paper, we obtain the groups of automorphisms of orientable bordered Klein surfaces of topological genus $2$. For each of those groups $G$ we determine the values of $k$ such that $G$ acts on a surface with $k$ boundary components. Besides, for each given $k$ we exhibit the groups acting on a surface with $k$ boundary components.

  18. Groups of automorphisms of bordered orientable Klein surfaces of topological genus 2

    Bujalance, E.; Etayo, J.J.; Martínez, E.
    In this paper, we obtain the groups of automorphisms of orientable bordered Klein surfaces of topological genus $2$. For each of those groups $G$ we determine the values of $k$ such that $G$ acts on a surface with $k$ boundary components. Besides, for each given $k$ we exhibit the groups acting on a surface with $k$ boundary components.

  19. Groups of automorphisms of bordered orientable Klein surfaces of topological genus 2

    Bujalance, E.; Etayo, J.J.; Martínez, E.
    In this paper, we obtain the groups of automorphisms of orientable bordered Klein surfaces of topological genus $2$. For each of those groups $G$ we determine the values of $k$ such that $G$ acts on a surface with $k$ boundary components. Besides, for each given $k$ we exhibit the groups acting on a surface with $k$ boundary components.

  20. Realizing homology classes up to cobordism

    Grant, Mark; SZŰCS, András; Terpai, Tamás
    It is known that neither immersions nor maps with a fixed finite set of multisingularities are enough to realize all mod $2$ homology classes in manifolds. In this paper we define the notion of realizing a homology class up to cobordism; it is shown that for realization in this weaker sense immersions are sufficient, but maps with a fixed finite set of multisingularities are still insufficient.

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