Mostrando recursos 1 - 20 de 124

  1. A small remark on the filtered $\varphi$-module of Fermat varieties and Stickelberger's theorem

    Yamashita, Go
    We show that the weakly admissibility of the filtered $\varphi$-module with coefficients of Fermat varieties in the sense of Fontaine essentially expresses Stickelberger's theorem in Iwasawa theory. In particular, it gives us a simple re-proof of the weakly admissibility of it.

  2. Weakly UU rings

    Danchev, Peter V.
    We introduce and give a comprehensive study of weakly UU rings, calling them WUU rings. This notion is a natural generalization of the so-called UU rings, defined by Calugareanu (Carpath. J. Math., 2015) and investigated in details by Danchev-Lam (Publicat. Math. Debrecen, 2016). It also demarcates the strength of recent results about these kind of rings by giving a strong barrier between some of their crucial properties.

  3. Analytic properties of generalized Mordell-Tornheim type of multiple zeta-functions and $L$-functions

    Miyagawa, Takashi
    Analytic properties of three types of multiple zeta functions, that is, the Euler-Zagier type, the Mordell-Tornheim type and the Apostol-Vu type have been studied by a lot of authors. In particular, in the study of multiple zeta functions of the Apostol-Vu type, a generalized multiple zeta function, including both the Euler-Zagier type and the Apostol-Vu type, was introduced. In this paper, similarly we consider generalized multiple zeta-functions and $L$-functions, which include both the Euler-Zagier type and the Mordell-Tornheim type as special cases. We prove the meromorphic continuation to the multi-dimensional complex space, and give the results on possible singularities.

  4. Tails of the first hitting times of linear diffusions

    Kasahara, Yuji
    The tail probability of the first hitting time is discussed for linear diffusions. We obtain the decay rates in terms of the spectral functions and the scale functions. The result is a generalization of recent results of Hamana-Matsumoto for Bessel processes.

  5. Abstract incomplete degenerate differential equations

    Kostić, Marko
    In this paper, we investigate the abstract incomplete degenerate di.erential equations in locally convex spaces, associated with use of the modified Liuoville right-sided fractional derivatives ([21]). The existence of solutions of abstract incomplete degenerate di.erential equations of second order is proved by considering the corresponding incomplete degenerate differential equations of order $1 / \gamma\;(0 \lt \gamma \lt 1/2$) and using an approximation process when $\gamma \rightarrow 1/2\:-$.

  6. A probabilistic approach to the zero-mass limit problem for three magnetic relativistic Schrödinger heat semigroups

    Murayama, Taro
    We consider three magnetic relativistic Schrödinger operators which correspond to the same classical symbol $\sqrt{(\xi - A(x))^2 + m^2} + V(x)$ and whose heat semigroups admit the Feynman-Kac-Itô type path integral representation $E[e^{ - S^m (x,\,t;\,X)} g(x + X(t))]$. Using these representations, we prove the convergence of these heat semigroups when the mass-parameter $m$ goes to zero. Its proof reduces to the convergence of $e^{- S^m (x,\,t;\,X)}$, which yields a limit theorem for exponentials of semimartingales as functionals of Lévy processes $X$.

  7. Erratum

    Miyashita, Toshikazu

  8. Quotients and Hopf images of a smash coproduct

    Bichon, Julien
    We describe the Hopf algebra quotients and Hopf images of the smash coproduct of a group algebra by the algebra of functions on a finite group.

  9. Spacelike constant mean curvature and maximal surfaces in 3-dimensional de Sitter space via Iwasawa splitting

    Ogata, Yuta
    We study the construction of spacelike constant mean curvature (CMC) surfaces with mean curvature $0 \le H \lt 1$ in 3-dimensional de Sitter space $\mathbf{S}^{2, 1}$, by using Iwasawa splitting. We also study their singularities and create some criteria for them.

  10. Autonomous equations of Mahler type and transcendence

    Nishioka, Kumiko; Nishioka, Seiji
    In this paper, we study transcendence of values of Mahler functions satisfying first-order rational difference equations of Mahler type with constant coefficients.

  11. Certain nonlinear differential polynomial sharing a nonzero polynomial IM

    Banerjee, Abhijit; Majumder, Sujoy
    We study the uniqueness of meromorphic functions when certain nonlinear differential polynomial sharing a nonzero polynomial having common poles and thus radically improve and extend some recent results due to of Wang-Lu-Chen [17], Sahoo [16] and Liu and Yang [14].

  12. Essential m-sectoriality and essential spectrum of the Schrödinger operators with rapidly oscillating complex-valued potentials

    Oshime, Yorimasa
    Schrödinger operators $T_0 = -\Delta + q(x)$ with rapidly oscillating complex-valued potentials $q(x)$ are considered. Each of such operators is sectorial and hence has Friedrichs extension. We prove that $T_0$ is essentially m-sectorial in the sense that the closure of $T_0$ coincides with its Friedrichs extension $T$. In particular, $T_0$ is essentially self-adjoint if the rapidly oscillating potential $q(x)$ is realvalued. Further, we prove $\sigma_{ess} (T) = [0, \infty)$ under somewhat stricter condition on the potentials $q(x)$.

  13. Embedding products in symmetric products of continua

    Castañeda-Alvarado, Enrique; Sánchez-Martínez, Javier
    Let $X$ be a continuum. For each natural number $n, F_n(X)$ is the $n^{th}$-symmetric product of $X$ and $X^n$ is the product of $X$ with itself $n$ times. In this paper we consider the problem of determining the continua $X$ such that $X^n$ can be embedded in $F_n(X)$. Moreover, we characterize finite graphs $X$ for which $X^2$ is embeddable in $F_2(X)$.

  14. Partially ordered rings II

    Kitamura, Yoshimi; Tanaka, Yoshio
    This paper is a continuation of [6]. We study partially ordered rings in terms of non-negative semi-cones and convex ideals, considering order-preserving homomorphisms, residue class rings, and certain product rings, etc.

  15. An asymptotic extension of Moran construction in metric measure spaces

    Wu, Daruhan
    In this paper, we define asymptotically generalized Cantor sets in metric measure spaces by generalizing the notion of $\lambda$-similarity maps. We define the notion of $(\lambda, c, \nu)$-similarity maps, and extend the Moran theorem about the generalized Cantor set in $\mathbf{R}^d$ to this general setting. As an example, we construct generalized Cantor sets in Riemannian manifolds by using $(\lambda, c, \nu)$-similarity maps.

  16. Erratum to "Asymptotic dimension and boundary dimension of proper CAT(0) spaces"

    Chinen, Naotsugu; Hosaka, Tetsuya
    The review on [1] in Mathematical Reviews points out that the proof of its main result is incorrect. The aim of this paper is to correct the previous paper's argument and clarify the statement.

  17. On the Cauchy problem for a class of hyperbolic operators whose coefficients depend only on the time variable

    Wakabayashi, Seiichiro
    In this paper we investigate the Cauchy problem for hyperbolic operators with double characteristics and hyperbolic operators of third order whose coefficients depend only on the time variable. And we give sufficient conditions for $C^{\infty}$ well-posedness.

  18. A characterization of the tempered distributions supported by a regular closed set in the Heisenberg group

    Oka, Yasuyuki
    The aim of this paper is to give a characterization of the tempered distributions supported by a (Whitney's) regular closed set in the Euclidean space and the Heisenberg group by means of the heat kernel method. The heat kernel method, introduced by T. Matsuzawa, is the method to characterize the generalized functions on the Euclidean space by the initial value of the solutions of the heat equation.

  19. Structural properties of ideals over $\mathscr P_{\kappa}\lambda$ I

    Abe, Yoshihiro
    We try to take a first step to a theory of the structural properties of ideals over $\mathscr P_{\kappa}\lambda$, that was studied in detail by Baumgartner, Taylor and Wagon [1] for $\kappa$;. In defining the basic notions, P-points, Q-points, and selective ideals, we put importance on the behavior of the function on $\mathscr P_{\kappa}\lambda$ to the bounded ideal and Rudin-Keisler ordering. ¶ Several facts hold similarly as on $\kappa$;, for instance, the bounded ideal is a nowhere Q-point. However some differences exist such as the bounded ideal is isomorphic to another ideal. We state the sufficient condition for ideals to be Q-points and the weakly normal ideals...

  20. On certain conformally invariant systems of differential equations II: Further study of type A systems

    Kable, Anthony C.
    Previously, several families of systems of differential equations that generalize the Heisenberg Laplacian equations were introduced. The study of one of these families is continued here. It is shown that the systems in this family are free of integrability conditions provided that a parameter appearing in the system avoids a certain set of bad values, which is explicitly determined. Properties of polynomial solutions to the systems are investigated and special polynomial solutions involving terminating Lauricella hypergeometric series are given in some cases.

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