Mostrando recursos 1 - 20 de 27

  1. Computational methods for set-relation-based scalarizing functions

    Yu, Hui; Ike, Koichiro; Ogata, Yuto; Saito, Yutaka; Tanaka, Tamaki
    In this research, we propose computational methods to evaluate scalarizing functions, which are defined via set-relations. In recent years, many theoretical results of the scalarizing functions for sets have been published. The aim of this paper is to show that each value of the scalarizing functions can be computed and to introduce computational algorithms of them for convex polytopes in a finite dimensional space.

  2. The von Neumann-Jordan constant of $\pi/2$-rotation invariant norms on $\mathbb{R}^2$

    Tomizawa, Yukino
    In this paper, we study the von Neumann-Jordan constant of $\pi/2$-rotation invariant norms on $\mathbb{R}^2$. We give some estimations of the constant and have a relationship between the constant and a ratio of two certain functions. These results are an extension of existing results of a unitary version of the von Neumann-Jordan constant.

  3. Cyclic vectors in Fock-type spaces of single variable

    Huang, Hansong; Izuchi, Kou Hei
    This paper mainly considers cyclic vectors in the Fock-type spaces $ L_{a,\alpha}^{p,s }(\mathbb{C} )$ $(\alpha>0,p\geq 1, s>0)$ which consists of all entire functions $f$ such that $|f|^p$ is integrable with respect to the measure $\exp(-\alpha |z|^s) dA(z).$ The case of $s$ not being an integer was done in [9], where cyclic vectors are exactly those non-vanishing entire functions in $ L_{a,\alpha}^{p,s }(\mathbb{C} )$. In this paper it is shown that for each positive integer $s$, a function $f$ is cyclic in $ L_{a,\alpha}^{p,s }(\mathbb{C} )$ if and only if $f$ is non-vanishing and $f \mathcal{C} \subseteq L_{a,\alpha}^{p,s }(\mathbb{C} )$, where...

  4. Comments on some recent existence theorems of best proximity points for Kannan-type and Chatterjea-type mappings

    Suzuki, Tomonari
    In 2013, Basha, Shahzad and Jeyaraj proved two existence theorems of best proximity points for Kannan-type and Chatterjea-type mappings. In this paper, in order to clarify the mathematical structure of these theorems, we improve these theorems in the aspects of both statements and proofs. Indeed, we give very simple proofs of these theorems. We also discuss the best possibility on the numbers that appear in these theorems.

  5. A note on Galois embedding and its application to $\mathbb P^n$

    Yoshihara, Hisao
    We show a condition that a Galois covering $\pi : V \longrightarrow \mathbb P^n$ is induced by a Galois embedding. Then we consider the Galois embedding for $\mathbb P^n$. If the Galois group $G$ is abelian, then $G \cong \bigoplus\limits^{n} Z_d$ and the projection $\pi$ can be expressed as $\pi(X_0:X_1: \cdots :X_n)=({X_0}^d:{X_1}^d:\cdots:{X_n}^d)$.

  6. The squared chain length function of 5 or 6-membered straight-chains with the tetrahedral bond angle

    Komatsu, Kazushi
    We provide straight-chains with the tetrahedral bond angle $\cos^{-1}(-1/3)$ as a mathematical model of $n$-membered straight-chain hydrocarbon molecules. We study the squared chain length function on the configuration space of the model and determine the critical points with planar configurations when $n = 5, 6$.

  7. Integral Representations of Positive Definite Functions on Convex Sets of Certain Semigroups of Rational Numbers

    Furuta, Koji
    H. Glöckner proved that an operator-valued positive definite function on an open convex subset of $\boldsymbol Q^N$ is a restriction of the Laplace transform of an operator-valued measure on $\boldsymbol R^N$. We generalize this result to a function on an open convex subset of a certain subsemigroup of $\boldsymbol Q^2$.

  8. The equivalence of gyrocommutative gyrogroups and K-loops

    Abe, Toshikazu
    It is known that gyrocommutative gyrogroups and K-loops are equivalent. This is a self-contained paper that presents the equivalence.

  9. The automorphism theorem and additive group actions on the affine plane

    Kuroda, Shigeru
    Due to Rentschler, Miyanishi and Kojima, the invariant ring for a $\mathrm{G}_a$-action on the affine plane over an arbitrary field is generated by one coordinate. In this note, we give a new short proof for this result using the automorphism theorem of Jung and van der Kulk.

  10. Real hypersufraces of non-flat complex hyperbolic planes whose Jacobi structure operator satisfies a generalized commutative condition

    Theofanidis, Theoharis
    Real hypersurfaces satisfying the condition $\phi l = l \phi$, $(l = R( . , \xi)\xi)$, have been studied by many authors under at least one more condition, since the class of these hypersurfaces is quite tough to be classified. The aim of the present paper is the classification of real hypersurfaces in complex hyperbolic plane $\mathbb{C}H^{2}$ satisfying a generalization of $\phi l = l \phi$ under an additional restriction on a specific function.

  11. An $L^1$-theory for scalar conservation laws with multiplicative noise on a periodic domain

    Noboriguchi, Dai
    We study the Cauchy problem for a multi-dimensional scalar conservation law with a multiplicative noise. Our aim is to give the well-posedness of an $L^1$-solution characterized by a kinetic formulation under appropriate assumptions. In particular, we focus on the existence of such a solution.

  12. One dimensional perturbation of invariant subspaces in the Hardy space over the bidisk II

    Izuchi, Kei Ji; Izuchi, Kou Hei; Izuchi, Yuko
    This paper is a continuation of the previous paper [9]. Let $M_1$ be an invariant subspace of $H^2$ over the bidisk. Then there exists a nonzero $f_0$ in $M_1$ such that $M_2:=M_1\ominus \mathbb{C} \cdot f_0$ is also an invariant subspace. A relationship is given the ranks of the cross commutators $[R^*_z,R_w]$ on $M_1$ and $M_2$. We also give a relationship of the ranks of the cross commutators $[S_w,S^*_z]$ on $H^2\ominus M_1$ and $H^2\ominus M_2$.

  13. One dimensional perturbation of invariant subspaces in the Hardy space over the bidisk I

    Izuchi, Kei Ji; Izuchi, Kou Hei; Izuchi, Yuko
    For an invariant subspace $M_1$ of the Hardy space $H^2$ over the bidisk $\mathbb{D}^2$, write $N_1=H^2 \ominus M_1$. Let $\Omega(M_1)=M_1\ominus(z M_1+w M_1)$ and $\widetilde\Omega(N_1)=\{f\in N_1: z f, w f\in M_1\}$. Then $\Omega(M_1)\not=\{0\}$, and $\Omega(M_1), \widetilde\Omega(N_1)$ are key spaces to study the structure of $M_1$. It is known that there is a nonzero $f_0\in M_1$ such that $M_2=M_1\ominus \mathbb{C} \cdot f_0$ is an invariant subspace. It is described the structures of $\Omega(M_2), \widetilde\Omega(N_2)$ using the words of $\Omega(M_1), \widetilde\Omega(N_1)$ and $f_0$. To do so, it occur many cases. We shall give examples for each cases.

  14. Viscosity approximation method for quasinonexpansive mappings with contraction-like mappings

    Aoyama, Koji
    We study the viscosity approximation method for a sequence of quasinonexpansive mappings with contraction-like mappings. We establish a strong convergence theorem and then we apply our result to approximate a solution of a split feasibility problem and a fixed point of a Lipschitz continuous pseudo-contraction.

  15. The boundary of the Q-numerical range of some Toeplitz nilpotent matrix

    Huang, Peng-Ruei; Nakazato, Hiroshi
    In this note we compute the boundary of some generalized numerical range $W_q(A)$ of a $4 \times 4$ Toeplitz nilpotent matrix $A$. We also provide a program to plot $W_q(A)$ by using ``Mathematica".

  16. Topological linear subspace of $L_0(\Omega, \mu)$ for the infinite measure $\mu$

    Okazaki, Yoshiaki
    Let $(\Omega, \mathcal{A}, \mu)$ be a measure space. We shall characterize the maximal topological linear subspace $M_{\infty}$ of $L_0(\Omega, \mathcal{A}, \mu)$ in the case where $\mu(\Omega)=+\infty$. $M_{\infty}$ is the truncated $L_{\infty}$ space which is open and closed in $L_0(\Omega, \mathcal{A}, \mu)$. In the case where $\Omega=\textbf{N}$(natural numbers), $\mu(A)=\sharp A=$ the cardinal number of $A$, the maximal linear subspace of $L_0(\textbf{N}, \mu)$ is $\ell_{\infty}$.

  17. Pointwise multipliers on Musielak-Orlicz spaces

    Nakai, Eiichi
    We consider the pointwise multipliers on Musielak-Orlicz spaces. We treat a wide class of Musielak-Orlicz spaces with generalized Young functions which include quasi-normed spaces.

  18. Note On Dunkl-Williams inequality with $n$ elements

    Mitani, Ken-Ichi; Tabiraki, Noriyuki; Ohwada, Tomoyoshi
    Recently, Pečarić and Rajić established a generalization of the Dunkl-Williams inequality for $n$ elements in a Banach space. In this note we show a refinement of this inequality.

  19. A refinement of the grand Furuta inequality

    Fujii, Masatoshi; Nakamoto, Ritsuo
    A refinement of the Löwner--Heinz inequality has been discussed by Moslehian--Najafi. In the preceding paper, we improved it and extended to the Furuta inequality. In this note, we give a further extension for the grand Furuta inequality. We also discuss it for operator means. A refinement of the arithmetic-geometric mean inequality is obtained.

  20. A confirmation by hand calculation that the Möbius ball is a gyrovector space

    Watanabe, Keiichi
    We give a confirmation that the Möbius ball of any real inner product space is a gyrovector space by using only elementary hand calculation. Some remarks to [2] will also be made.

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