Mostrando recursos 1 - 9 de 9

  1. Growth of meromorphic solutions of some linear differential equations

    BEDDANI, Hamid; HAMANI, Karima
    In this paper, we investigate the order and the hyper-order of meromorphic solutions of the linear differential equation \begin{equation*} f^{(k)}+\sum^{k-1}_{j=1}(D_{j}+B_{j}e^{P_{j}(z) })f^{(j)}+( D_{0}+A_{1}e^{Q_{1}( z)}+A_{2}e^{Q_{2}( z) }) f=0, \end{equation*} where $k\geq 2$ is an integer, $Q_{1}(z),Q_{2}(z)$, $P_{j}(z) $ $(j=1, \dots ,k-1)$ are nonconstant polynomials and $A_{s}(z)$ $(\not\equiv 0)$ $(s=1,2)$, $B_{j}( z)$ $(\not\equiv 0)$ $(j=1, \dots ,k-1)$, $D_{m}(z)$ $(m=0,1, \dots ,k-1)$ are meromorphic functions. Under some conditions, we prove that every meromorphic solution $f$ $(\not\equiv 0)$ of the above equation is of infinite order and we give an estimate of its hyper-order. Furthermore, we obtain a result about the exponent of convergence and...

  2. Kinematic expansive suspensions of irrational rotations on the circle

    MATSUMOTO, Shigenori
    We shall show that the rotation of some irrational rotation number on the circle admits suspensions which are kinematic expansive.

  3. Spectral analysis of a massless charged scalar field with cutoffs

    WADA, Kazuyuki
    A quantum system of a massless charged scalar field with a self-interaction is investigated. By introducing a spacial cut-off function, a Hamiltonian of the quantum system is realized as a linear operator on a boson Fock space. Under certain conditions, it is proven that the Hamiltonian is bounded below, self-adjoint and has a ground state for an arbitrary coupling constant. Moreover the Hamiltonian strongly commutes with the total charge operator. This fact implies that the state space of the charged scalar field is decomposed into the infinite direct sum of fixed total charge spaces. A total charge of an eigenstate...

  4. On the class of projective surfaces of general type

    FUKUMA, Yoshiaki; ITO, Kazuhisa
    Let $S$ be a smooth complex projective surface of general type, $H$ be a very ample divisor on $S$ and $m(S,H)$ be the class of $(S,H)$. In this paper, we study a lower bound for $m(S,H)-3H^2$ and we improve an inequality obtained by Lanteri. We also study $(S,H)$ with each value of $m(S,H)-3H^2$ and exhibit some examples.

  5. The extended zero-divisor graph of a commutative ring II

    BAKHTYIARI, M.; NIKMEHR, M. J.; NIKANDISH, R.
    Let $R$ be a commutative ring with identity, and let $Z(R)$ be the set of zero-divisors of $R$. The extended zero-divisor graph of $R$ is the undirected (simple) graph $\Gamma'(R)$ with the vertex set $Z(R)^*=Z(R)\setminus\{0\}$, and two distinct vertices $x$ and $y$ are adjacent if and only if either $Rx\cap \mathrm{Ann}(y)\neq (0)$ or $Ry\cap \mathrm{Ann}(x)\neq (0)$. In this paper, we continue our study of the extended zero-divisor graph of a commutative ring that was introduced in [4]. We show that the extended zero-divisor graph associated with an Artinian ring is weakly perfect, i.e., its vertex chromatic number equals its clique...

  6. The extended zero-divisor graph of a commutative ring I

    BAKHTYIARI, M.; NIKMEHR, M. J.; NIKANDISH, R.
    Let $R$ be a commutative ring with identity, and let $Z(R)$ be the set of zero-divisors of $R$. The extended zero-divisor graph of $R$ is the undirected (simple) graph $\Gamma'(R)$ with the vertex set $Z(R)^*=Z(R)\setminus\{0\}$, and two distinct vertices $x$ and $y$ are adjacent if and only if either $Rx\cap \mathrm{Ann}(y)\neq (0)$ or $Ry\cap \mathrm{Ann}(x)\neq (0)$. It follows that the zero-divisor graph $\Gamma(R)$ is a subgraph of $\Gamma'(R)$. It is proved that $\Gamma'(R)$ is connected with diameter at most two and with girth at most four, if $\Gamma'(R)$ contains a cycle. Moreover, we characterize all rings whose extended zero-divisor graphs...

  7. A vector-valued estimate of multilinear Calderón-Zygmund operators in Herz-Morrey spaces with variable exponents

    SHEN, Conghui; XU, Jingshi
    In this paper, we obtain a vector valued inequality of multilinear Calderón-Zygmund operators on products of Herz-Morrey spaces with variable exponents.

  8. The DPW method for constant mean curvature surfaces in 3-dimensional Lorentzian spaceforms, with applications to Smyth type surfaces

    OGATA, Yuta
    We give criteria for singularities of spacelike constant mean curvature surfaces in 3-dimensional de Sitter and anti-de Sitter spaces constructed by the DPW method, which is a generalized Weierstrass representation. We also construct some examples of spacelike CMC surfaces, including analogs of Smyth surfaces with singularities, using appropriate models to visualize them.

  9. Sufficient conditions for decay estimates of the local energy and a behavior of the total energy of dissipative wave equations in exterior domains

    KAWASHITA, Mishio
    Decaying properties of the local energy for the dissipative wave equations with the Dirichlet boundary conditions in exterior domains are discussed. For the dissipation coefficient, natural conditions ensuring that waves trapped by obstacles may lose their energy are considered. Under this setting, two sufficient conditions for getting the decay estimates for the energy in bounded regions (i.e. the local energy) are given. These conditions bring some relaxation on classes of the dissipation coefficient which uniformly decaying estimates for the local energy hold. Further, decaying properties of the total energy are also discussed.

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