Mostrando recursos 1 - 20 de 21

  1. Elliptic surfaces and contact conics for a 3-nodal quartic

    TUMENBAYAR, Khulan; TOKUNAGA, Hiro-o
    Let ${\mathcal Q}$ be an irreducible $3$-nodal quartic and let ${\mathcal C}$ be a smooth conic such that ${\mathcal C} \cap {\mathcal Q}$ does not contain any node of ${\mathcal Q}$ and the intersection multiplicity at $z \in {\mathcal C} \cap {\mathcal Q}$ is even for each $z$. In this paper, we study geometry of ${\mathcal C} + {\mathcal Q}$ through that of integral sections of a rational elliptic surface which canonically arises from ${\mathcal Q}$ and $z \in {\mathcal C} \cap {\mathcal Q}$. As an application, we construct Zariski pairs $({\mathcal C}_1 + {\mathcal Q}, {\mathcal C}_2 + {\mathcal...

  2. Arithmetic identities for class regular partitions

    MIZUKAWA, Hiroshi; YAMADA, Hiro-Fumi
    Extending the notion of $r$-(class) regular partitions, we define $(r_{1},\dots,r_{m})$-class regular partitions. Partition identities are presented and described by making use of the Glaisher correspondence.

  3. Characteristic function of Cayley projective plane as a harmonic manifold

    EUH, Yunhee; PARK, JeongHyeong; SEKIGAWA, Kouei
    Any locally rank one Riemannian symmetric space is a harmonic manifold. We give the characteristic function of a Cayley projective plane as a harmonic manifold. The aim of this work is to show the explicit form of the characteristic function of the Cayley projective plane.

  4. On the symmetric algebras associated to graphs with loops

    BARBERA, Mariacristina; IMBESI, Maurizio; LA BARBIERA, Monica
    We study the symmetric algebra of monomial ideals that arise from graphs with loops. The notion of $s$-sequence is investigated for such ideals in order to compute standard algebraic invariants of their symmetric algebra in terms of the corresponding invariants of special quotients of the polynomial ring related to the graphs.

  5. An almost complex Castelnuovo de Franchis theorem

    BISWAS, Indranil; MJ, Mahan
    Given a compact almost complex manifold, we prove a Castelnuovo–de Franchis type theorem for it.

  6. Certain bilinear operators on Morrey spaces

    FAN, Dashan; ZHAO, Fayou
    In this paper, we consider that $T(f,g)$ is a bilinear operator satisfying \begin{equation*} |T(f,g)(x)|\preceq \int_{\mathbb{R}^{n}}\frac{|f(x-ty)g(x-y)|}{|y|^{n}}dy \end{equation*} for $x$ such that $0\notin {\rm supp}~(f(x-t\cdot )) \cap {\rm supp}~(g(x+\cdot ))$. We obtain the boundedness of $T(f,g)$ on the Morrey spaces with the assumption of the boundedness of the operator $T(f,g)$ on the Lebesgues spaces. As applications, we yield that many well known bilinear operators, as well as the first Calderón commutator, are bounded from the Morrey spaces $L^{q,\lambda_{1}}\times L^{r,\lambda_{2}}$ to $L^{p,\lambda}$, where $\lambda /p={\lambda_{1}}/{q}+{\lambda_{2}}/{r}$.

  7. The Fermat septic and the Klein quartic as moduli spaces of hypergeometric Jacobians

    KOIKE, Kenji
    We study the Schwarz triangle function with the monodromy group $\Delta(7,7,7)$, and we construct its inverse by theta constants. As consequences, we give uniformizations of the Klein quartic curve and the Fermat septic curve as Shimura curves parametrizing Abelian $6$-folds with endomorphisms $\mathbb{Z}[\zeta_7]$.

  8. Schwarz maps associated with the triangle groups $(2,4,4)$ and $(2,3,6)$

    KOGUCHI, Yuto; MATSUMOTO, Keiji; SETO, Fuko
    We consider the Schwarz maps with monodromy groups isomorphic to the triangle groups $(2,4,4)$ and $(2,3,6)$ and their inverses. We apply our formulas to studies of mean iterations.

  9. Large-time behavior of solutions to a tumor invasion model of Chaplain–Anderson type with quasi-variational structure

    ITO, Akio
    We treat 2D and 3D tumor invasion models with quasi-variational structures, which are composed of two PDEs, one ODE and certain constraint conditions. Although the original model was proposed by M. R. A. Chaplain and A. R. A. Anderson in 2003, the difference between their original model and ours is that the constraint conditions for the distributions of tumor cells and the extracellular matrix are imposed in our model, which give a quasi-variational structure. For 2D and 3D tumor invasion models with quasi-variational structures, we show the existence of global-in-time solutions and consider their large-time behaviors. Especially, for the large-time...

  10. The influence of order and conjugacy class length on the structure of finite groups

    ASBOEI, Alireza Khalili; DARAFSHEH, Mohammad Reza; MOHAMMADYARI, Reza
    Let $2^{n}+1 \gt 5$ be a prime number. In this article, we will show $G\cong C_{n}(2)$ if and only if $|G|=|C_{n}(2)|$ and $G$ has a conjugacy class length ${|C_{n}(2)|}/({2^{n}+1})$. Furthermore, we will show Thompson's conjecture is valid under a weak condition for the symplectic groups $C_{n}(2)$.

  11. Lowerable vector fields for a finitely ${\cal L}$-determined multigerm

    MIZOTA, Yusuke; NISHIMURA, Takashi
    We show that the module of lowerable vector fields for a finitely ${\cal L}$-determined multigerm is finitely generated in a constructive way.

  12. A remark on modified Morrey spaces on metric measure spaces

    SAWANO, Yoshihiro; SHIMOMURA, Tetsu; TANAKA}, Hitoshi
    Morrey norms, which are originally endowed with two parameters, are considered on general metric measure spaces. Volberg, Nazarov and Treil showed that the modified Hardy-Littlewood maximal operator is bounded on Legesgue spaces. The modified Hardy-Littlewood maximal operator is known to be bounded on Morrey spaces on Euclidean spaces, if we introduce the third parameter instead of adopting a natural extension of Morrey spaces. When it comes to geometrically doubling, as long as an auxiliary parameter is introduced suitably, the Morrey norm does not depend on the third parameter and this norm extends naturally the original Morrey norm. If the underlying...

  13. 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...

  14. 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.

  15. 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...

  16. 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.

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

    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...

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

    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...

  19. 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.

  20. 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.

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