Mostrando recursos 1 - 20 de 23

  1. An inverse spectral uniqueness in exterior transmission problem

    Chen, Lung-Hui
    We consider an inverse spectral theory in a domain with the cavity in a penetrable inhomogeneous medium. An ODE system is constructed piecewise through the ODE eigenfunctions inside and outside the cavity. Then the ODE system is connected to the PDE system via the analytic continuation property of the Helmholtz equation. For each scattered angle, we describe its eigenvalue density in the complex plane, and prove an inverse uniqueness on the inhomogeneity by the measurements in the far-fields. We take advantage of the symmetry near infinity.

  2. Extending functors from the category of strict morphisms of inverse systems to the associated pro-category with applications to the first derived limit

    Mrozik, Peter
    We show that functors on the category of strict morphisms of inverse systems which are indexed by arbitrary cofiltered small categories have at most one extension to the associated procategory and give conditions characterizing the existence of extensions. This is applied to provide a concrete extension of the first derived limit to the category of pro-groups.

  3. On multivalent functions in the unit disc

    Nunokawa, Mamoru; Sokół, Janusz
    Let $\mathcal{A}(p)$ be the class of functions $f(z)$, analytic in $|z| \lt 1$ in the complex plane, of the form $f(z) = z^p + \cdots$. We study the question, that naturally rises, about the relation between the expressions $\frac{zf^{(p)}(z)}{f^{(p-1)}(z)}$ and $\frac{zf^{(p-1)}(z)}{f^{(p-2)}(z)}$, when $f(z) \in \mathcal{A}(p)$. Some relations of this type imply that $f(z)$ is $p$-valent or $p$-valent starlike in $|z| \lt 1$.

  4. Finitely generated semi-cones in product rings

    Kitamura, Yoshimi; Tanaka, Yoshio
    Semi-cones of rings determine the partial orders in the rings. We consider semi-cones in the direct product rings and the product extension rings, inducing finitely generated semi-cones. In particular, we give characterizations for semi-cones of the direct product rings and the basic product extension rings of the ring of integers.

  5. On $T$-coercive interior transmission eigenvalue problems on compact manifolds with smooth boundary

    Shoji, Naotaka
    We consider an interior transmission eigenvalue problem on two compact Riemannian manifolds with common smooth boundary. We assume that this problem is locally anisotropic type. Then we prove that the set of interior transmission eigenvalues forms a discrete subset of complex plane. Moreover, we also mention the interior transmission eigenvalue free region. In order to prove our results, we employ the so-called $T$-coercivity method.

  6. Köhler theory for countable quadruple systems

    Kikyo, Hirotaka; Sawa, Masanori
    From the late 1970s to the early 1980s, Köhler developed a theory for constructing finite quadruple systems with point-transitive Dihedral automorphism groups by introducing a certain algebraic graph, now widely known as the (first) Köhler graph in finite combinatorics. In this paper, we define the countable Köhler graph and discuss countable extensions of a series of Köhler's works, with emphasis on various gaps between the finite and countable cases. We show that there is a simple 2-fold quadruple system over Z with a point-transitive Dihedral automorphism group if the countable Köhler graph has a so-called [1, 2]-factor originally introduced by...

  7. The mean values of the double zeta-function

    Ikeda, Soichi; Kiuchi, Isao; Matsuoka, Kaneaki
    We investigate the mean square formulas of the Euler–Zagier type double zeta-function $\zeta_2(s_1,s_2)$ and provide the $\Omega$ results of the double zeta-function. We also calculate the double integral under certain conditions.

  8. Corrigendum to “On the Cartier duality of certain finite group schemes of order $p^n$, II” [Tsukuba J. Math. 37 (2) (2013) 259-269]

    Amano, Michio
    We correct an error of the proof of Lemma 1 in the author's paper [1]. Also a typographical error is corrected.

  9. Realizations of inner automorphisms of order 4 and fixed points subgroups by them on the connected compact exceptional lie group $E_8$, Part I

    Miyashita, Toshikazu
    The compact simply connected Riemannian 4-symmetric spaces were classified by J. A. Jiménez as the type of Lie algebra. Needless to say, these spaces as homogeneous manifolds are of the form $G/H$, where $G$ is a connected compact simple Lie group with an automorphism $\tilde{\gamma}$ of order 4 on $G$ and $H$ is a fixed points subgroup $G^\gamma$ of $G$. In the present article, as Part I, for the connected compact exceptional Lie group $E_8$, we give the explicit form of automorphism $\tilde{\sigma}'_4$ of order 4 on $E_8$ induced by the $C$-linear transformation $\sigma'_4$ of 248-dimensional vector space $??^{C}_{8}$ and...

  10. On the asymptotic behavior of Bessel-like diffusions

    Shimizu, Yuuki; Nakano, Fumihiko
    We derive the asymptotic behavior of the transition probability density of the Bessel-like diffusions for “dimension” $\rho = 0$.

  11. Convex functions and $p$-barycenter on CAT(1)-spaces of small radii

    Yokota, Takumi
    We establish unique existence of $p$-barycenter of any probability measure for $p \ge 2$ on CAT(1)-spaces of small radii. In our proof, we employ Kendall's convex function on a ball of CAT(1)-spaces instead of the convexity of distance function. Various properties of $p$-barycenter on those spaces are also presented. They extend the author's previous work [Yo].

  12. On the groups of isometries of simple para-Hermitian symmetric spaces

    Shimokawa, Takuya; Sugimoto, Kyoji
    The main purpose in this paper is to completely determine the groups of isometries of simple para-Hermitian symmetric spaces. That enables us to also determine the groups of affine transformations of these spaces, with respect to the canonical affine connections.

  13. Selections and deleted symmetric products

    Buhagiar, David; Gutev, Valentin
    We give a very simple example of a connected second countable space $X$ whose hyperspace $[X]^{n+1}$ of unordered $(n + 1)$-tuples of points has a continuous selection, but $[X]^n$ has none. This settles an open question posed by Michael Hrušák and Ivan Martánez-Ruiz. The substantial part of the paper sheds some light on this phenomenon by showing that in the presence of connectedness this is essentially the only possible example of such spaces.

  14. Periodicity of Certain Piecewise Affine Planar Maps

    Akiyama, Shigeki; Brunotte, Horst; Pethö, Attila; Steiner, Wolfgang
    We determine periodic and aperiodic points of certain piecewise affine maps in the Euclidean plane. Using these maps, we prove for $\lambda \in \left\{ \frac{\pm 1 \pm \sqrt{5}}{2}, \pm \sqrt{2}, \pm{\sqrt{3}} \right \}$ that all integer sequences $(a_{k})_{k \in \mathbb{Z}}$ satisfying $0 \leq a_{k-1}+\lambda a_{k} + a_{k+1} \lt 1$ are periodic.

  15. On $p$-Maps and $M$-Maps

    Bai, Yun-Feng; Miwa, Takuo
    We introduce new notions of $p$-maps and $M$-maps, and investigate some of their basic properties, which are extensions of corresponding properties of $p$-spaces and $M$-spaces.

  16. Spaces with a d-Point-Discrete Weak Base

    Liu, Chuan; Lin, Shou; Ludwig, Lewis D.
    In this paper $\sigma$-point-discrete weak bases are considered. Three necessary conditions that individually ensure that a space with a $\sigma$-point-discrete weak base has a s-compact-finite weak base are given. We show that $\sigma$-compact-finite weak bases are preserved by closed sequence-covering maps. It is shown that a space $X$ is metrizable if and only if $X^{\omega}$ has a $\sigma$-point-discrete weak base. Conditions are given to ensure when a paratopological group with $\sigma$-point-discrete weak base is metrizable. Several open questions are posed.

  17. A Note on the Fusion of Two Vertices in a Fuzzy Graph

    Ramakrishnan, P. V.; Lakshmi, T.
    The concept of fuzzy sets was introduced by L. A. Zadeh in 1965. The concept of fuzzy graph was introduced by A. Rosenfeld [5] in 1975. Many of the crisp graph concepts have been extended to fuzzy graph theory. Here we define the fusion of two vertices in a fuzzy graph and investigate some properties and also give fusion algorithm for effective connectedness and for adjacency matrix.

  18. Submetacompactness and Weak Submetacompactness in Countable Products, Ⅱ

    Tanaka, Hidenori
    In this paper, we shall discuss submetacompactness and weak submetacompactness in countable products of Čech-scattered spaces and prove the following: (1) If $\{ X_{n} : n \in \omega \}$ is a countable collection of submetacompact Čech-scattered spaces, then the product $\Prod_{n\in \omega} X_{n}$ is submetacompact. (2) If $Y$ is a hereditarily weakly submetacompact space and $\{X_{n} : n \in \omega \}$ is a countable collection of weakly submetacompact Čech-scattered spaces, then the product $Y \times \Prod_{n\in \omega}X_{n}$ is weakly submetacompact.

  19. Introduction to Boundary Value Problems of Nonlinear Elastostatics

    Taira, Kazuaki
    This paper provides a careful and accessible exposition of an $L^p$ approach to boundary value problems of nonlinear elastostatics in the case where solutions of the linearized problem correspond faithfully to those of the nonlinear problem, that is, in the case where there is no bifurcation. We prove that if the linearized problem has unique solutions, then so does the nonlinear one, nearby. This is done by using the linear $L^p$ theory and the inverse mapping theorem. The main theorem can be applied to the Saint Venant-Kirchhoff elastic material and the Hencky-Nadai elastoplastic material in a unified theory. The approach...

  20. On The Mean, Gauss, The Second Gaussian and The Second Mean Curvature of The Helicoidal Surfaces with Light-Like Axis in $\mathbb{R}^{3}$

    Güler, Erhan; Vanli, Aysel Turght
    In this paper, the second Gaussian and the second mean curvature of the helicoidal surfaces with light-like axis of type $IV^{+}$ is obtained in Minkowski 3-space. In addition, some relations between the mean, Gauss, the second Gaussian and the second mean curvature of the helicoidal surfaces with light-like axis of type $IV^{+}$ are given in Minkowski 3-space.

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