Mostrando recursos 1 - 20 de 3.873

  1. Positive ground state solutions for some non-autonomous Kirchhoff type problems

    Xie, Qilin; Ma, Shiwang
    In this paper, we study the existence of positive ground state solutions for non-autonomous Kirchhoff type problems: $$ -\Big (1+b\int _{\mathbb R^3} |\nabla u|^2\Big ) \Delta u+u=a(x)|u|^{p-1}u \quad \mbox {in } \mathbb {R}^3, $$ where $b>0$, $3\lt p\lt 5$ and $a:\mathbb R^3\rightarrow \mathbb R$ is such that $$ \lim _{|x|\rightarrow \infty } a(x)=a_\infty >0, $$ but no symmetry property on $a(x)$ is required.

  2. The differential structure of an orbifold

    Watts, Jordan
    We prove that the underlying set of an orbifold equipped with the ring of smooth real-valued functions completely determines the orbifold atlas. Consequently, we obtain an essentially injective functor from orbifolds to differential spaces.

  3. On the Sobolev orthogonality of classical orthogonal polynomials for non standard parameters

    Sánchez-Lara, J.F.
    The discrete part of the discrete-continuous orthogonality \[ \mathscr {B}(f,g)=\mathscr {B}_d( f,g)+\mathscr {B}_c(f^{(N)},g^{(N)}), \] is studied for families of classical orthogonal polynomials such that the associated three-term recurrence relation \[ xp_n=p_{n+1}+\beta _np_n+ \gamma _n p_{n-1}, \] presents one vanishing coefficient $\gamma _n$, as in the case of Laguerre polynomials $L_n^{(-N)}$, Jacobi polynomials $P_n^{(-N,\beta )}$ and Gegenbauer polynomials $C_n^{(-N+1/2)}$ with $N\in \mathbb {N}$. It is shown that the discrete bilinear functional $\mathscr {B}_d$ can be replaced by a linear functional, $\mathscr {L}$, or by another bilinear functional related with $\mathscr {L}$, which allows us to reformulate the orthogonality in a much...

  4. Sharp bounds for the general Randić index $R_-1$ of a graph

    Milovanović, E.I.; Bekakos, M.P.
    Let $G$ be an undirected simple, connected graph with $n \geq 3$ vertices and $m$ edges, with vertex degree sequence $d_1\ge d_2 \ge \cdots \ge d_n$. The general Randi\'c index is defined by \[ R_{-1}=\sum _{(i,j)\in E}\frac {1}{d_id_j}. \] Lower and upper bounds for $R_{-1}$ are obtained in this paper.

  5. Weighted Bergman kernel functions associated to meromorphic functions

    Jacobson, Robert
    We present a technique for computing explicit, concrete formulas for the weighted Bergman kernel on a planar domain with modulus squared weight of a meromorphic function in the case that the meromorphic function has a finite number of zeros on the domain and a concrete formula for the unweighted kernel is known. We apply this theory to the study of the Lu Qi-keng problem.

  6. Tate cohomology of Gorenstein flat modules with respect to semidualizing modules

    Hu, Jiangsheng; Geng, Yuxian; Ding, Nanqing
    We study Tate cohomology of modules over a commutative Noetherian ring with respect to semidualizing modules. First, we show that the class of modules admitting a Tate $\mathcal{F}_C $-resolution is exactly the class of modules in $\mathcal{B}_{C} $ with finite $\mathcal{GF}_{C} $-projective dimension. Then, the interaction between the corresponding relative and Tate cohomologies of modules is given. Finally, we give some new characterizations of modules with finite $\mathcal{F}_C $-projective dimension.

  7. Quasiconformal extendability of integral transforms of Noshiro-Warschawski functions

    Hotta, Ikkei; Wang, Li-Mei
    Since the nonlinear integral transforms $$ J_{\alpha }[f](z) = \int _{0}^{z}(f'(u))^{\alpha } du $$ and $$ \ \ I_{\alpha }[f](z) =\int _0^z (f(u)/u)^{\alpha } du $$ with a complex number $\alpha $ were introduced, a great number of studies have been dedicated to deriving sufficient conditions for univalence on the unit disk. However, little is known about the conditions where $J_{\alpha }[f]$ or $I_{\alpha }[f]$ produce a holomorphic univalent function in the unit disk which extends to a quasiconformal map on the complex plane. In this paper, we discuss quasiconformal extendability of the integral transforms $J_{\alpha }[f]$ and $I_{\alpha }[f]$...

  8. Blaschke's rolling ball property and conformal metric ratios

    Herron, David A.; Julian, Poranee K.
    We characterize the closed sets in Euclidean space that satisfy a two-sided rolling ball property. As an application we show that certain conformal metric ratios have boundary value~1.

  9. Inverse semigroup actions on groupoids

    Buss, Alcides; Meyer, Ralf
    We define inverse semigroup actions on topological groupoids by partial equivalences. From such actions, we construct saturated Fell bundles over inverse semigroups and non-Hausdorff \'etale groupoids. We interpret these as actions on $C^*$\nobreakdash -algebras by Hilbert bimodules and describe the section algebras of these Fell bundles. ¶ Our constructions give saturated Fell bundles over non-Hausdorff \'etale groupoids that model actions on locally Hausdorff spaces. We show that these Fell bundles are usually not Morita equivalent to an action by automorphisms, that is, the Packer-Raeburn stabilization trick does not generalize to non-Hausdorff groupoids.

  10. The discriminant of abelian number fields

    Bautista-Ancona, Victor; Uc-Kuk, Jose
    For an abelian number field $K$, the discriminant can be obtained from the conductor~$m$ of~$K$, the degree of~$K$ over $\mathbb {Q}$, and the degrees of extensions $K\cdot \mathbb {Q}(\zeta _{m/p^{\alpha }})/\mathbb {Q}(\zeta _{m/p^{\alpha }})$, where $p$ runs through the set of primes that divide $m$, and $p^{\alpha }$ is the greatest power that divides~$m$. In this paper, we give a formula for computing the discriminant of any abelian number field.

  11. Almost multiplicative linear functionals and entire functions

    Anjidani, Ehsan
    Let $T$ be a unital, continuous linear functional defined on complex Banach algebra $A$. First, we prove an approximate version of the Gleason-Kahane-\.Zelazko theorem: given $\epsilon >0$, there exists an $M>0$ such that, if $$ T(\exp x)\neq 0,\quad x\in A,\ \|x\|\leq M, $$ then $T$ is $\epsilon $-almost multiplicative. Then, we show that this result remains true if the exponential function is replaced by a nonsurjective entire function~$F$ with $F'(0)\neq 0$.

  12. A sign-changing solution for the Schrödinger-Poisson equation in $\mathbb R^3$

    Alves, Claudianor O.; Souto, Marco A.S.; Soares, Sérgio H.M.
    We find a sign-changing solution for a class of Schr\"odinger-Poisson systems in $\mathbb {R}^3$ as an existence result by minimization in a closed subset containing all the sign-changing solutions of the equation. The proof is based on variational methods in association with the deformation lemma and Miranda's theorem.

  13. Volume Index for Volume 46

  14. Content formulas for power series and Krull domains

    Yin, Huayu; Chen, Youhua; Zhu, Xiaosheng
    Let $R$ be an integral domain with quotient field $K$, and let $X$ be an indeterminate over $R$. In this paper, we consider content formulae for power series in terms of $*$-operations for PVMDs, Krull domains and Dedekind domains, where $*$ is the star-operation, $d$, $w$, $t$, or $v$. We prove that $R$ is a Krull domain if and only if $c(f/g)_w=(c(f)c(g)^{-1})_w$ for all $f,g\in R[[X]]^*$ with $c(f/g)$ a fractional ideal if and only if $c(f/g)_t=(c(f)c(g)^{-1})_t$ for all $f,g\in R[[X]]^*$ with $c(f/g)$ a fractional ideal, and $R$ is a Dedekind domain if and only if for all $f,g\in R[[X]]^*$ with...

  15. Arithmetic and geometry of rational elliptic surfaces

    Salgado, Cec[! \' i!]lia
    Let $\mathscr {E}$ be a rational elliptic surface over a number field~$k$. We study the interplay between a geometric property, the configuration of its singular fibers, and arithmetic features such as its Mordell-Weil rank over the base field and its possible minimal models over~$k$.

  16. On Schauder basis properties of multiply generated Gabor systems

    Nielsen, Morten
    Let $\mathcal{A} $ be a finite subset of $L^2(\mathbb{R} )$ and $p,q\in \mathbb{N} $. We characterize the Schauder basis properties in $L^2(\mathbb{R} )$ of the Gabor system \[ G(1,p/q,\mathcal{A} )=\{e^{2\pi i m x}g(x-np/q) : m,n\in \mathbb{Z} , g\in \mathcal{A} \}, \] with a specific ordering on $\mathbb{Z} \times \mathbb{Z} \times \mathcal{A} $. The characterization is given in terms of a Muckenhoupt matrix $A_2$ condition on an associated Zibulski-Zeevi type matrix.

  17. Strongly copure projective, injective and flat complexes

    Ma, Xin; Liu, Zhongkui
    In this paper, we extend the notions of strongly copure projective, injective and flat modules to that of complexes and characterize these complexes. We show that the strongly copure projective precover of any finitely presented complex exists over $n$-FC rings, and a strongly copure injective envelope exists over left Noetherian rings. We prove that strongly copure flat covers exist over arbitrary rings and that $(\mathcal {SCF},\mathcal {SCF}^\bot )$ is a perfect hereditary cotorsion theory where $\mathcal {SCF}$ is the class of strongly copure flat complexes.

  18. A functional equation and degenerate principal series

    Lee, Juhyung
    A functional equation between the $\zeta $ distributions can be obtained from the theory of prehomogeneous vector spaces. We show that the functional equation can be extended from the Schwartz space to certain degenerate principal series.

  19. Substitution Markov chains and Martin boundaries

    Koslicki, David; Denker, Manfred
    Substitution Markov chains have been introduced \cite {KoslickiThesis2012} as a new model to describe molecular evolution. In this note, we study the associated Martin boundaries from a probabilistic and topological viewpoint. An example is given that, although having a boundary homeomorphic to the well-known coin tossing process, has a metric description that differs significantly.

  20. Smooth center manifolds for random dynamical systems

    Guo, Peng; Shen, Jun
    In this paper, we will prove the existence and H\"{o}lder continuity of smooth center-unstable and center-stable manifolds for random dynamical systems based on their Lyapunov exponents. Furthermore, we obtain the existence and H\"{o}lder continuity of smooth center manifolds.

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