1.
Homogeneous Reinhardt domains containing no coordinate hyperplanes - Shimizu, Satoru; Kimura, Kouichi
As is well-known, a homogeneous Reinhardt domain in C* coinsides with C*. In this paper, generalizing this fact, we show that a pseudoconvex homogeneous Reinhardt domain in (C*)^{n} coinsides with (C*)^{n} itself.

2.
Convergence of a parametric continuation method - Prashanth, Maroju; Gupta, Dharmendra K.
The aim of this paper is to establish the semilocal convergence of a parameter based continuation method combining the Chebyshev's and the Super-Halley's methods for solving nonlinear equations in Banach spaces. The parameter α $in$ [0,1] be such that for α = 0 it reduces to the Chebyshev's method and for α = 1 to the Super-Halley's method. This convergence is established using recurrence relations under the assumption that the second order Fréchet derivative satisfies the ω-continuity condition. This condition is milder than the Lipschitz and the Hölder continuity conditions used for this purpose. A numerical example is given to...

3.
A note on Fontaine theory using different Lubin-Tate groups - Chiarellotto, Bruno; Esposito, Francesco
The starting point of Fontaine theory is the possibility of translating the study of a p-adic representation of the absolute Galois group of a finite extension K of Q_{p} into the investigation of a (φ, Γ)-module. This is done by decomposing the Galois group along a totally ramified extension of K, via the theory of the field of norms: the extension used is obtained by means of the cyclotomic tower which, in turn, is associated to the multiplicative Lubin-Tate group. It is known that one can insert different Lubin-Tate groups into the "Fontaine theory" machine to obtain equivalences with new...

4.
A Myers theorem via m-Bakry-Émery curvature - Wang, Lin Feng
In this paper, we prove that a complete manifold whose m-Bakry-Émery curvature satisfies ¶ Ric_{f,m}(x) ≥ −(m − 1) $\frac{K_0}{(1+r(x))^2}$ ¶ for some constant K_{0} < $-\frac{1}{4}$ should be compact. We also get an upper bound estimate for the diameter.

5.
Surfaces with inflection points in Euclidean 4-space - Aiyama, Reiko; Akutagawa, Kazuo
For a surface in the Euclidean 4-space, we prove a reduction theorem for the codimension of a surface all whose points are inflection points.

6.
Positive periodic solutions for a nonlinear density-dependent mortality Nicholson's blowflies model - Liu, Bingwen
This paper is concerned with a class of Nicholson's blowflies model with a nonlinear density-dependent mortality term. Under appropriate conditions, we establish some criteria to ensure that the solutions of this model converge globally exponentially to a positive periodic solution. Moreover, we give an example and its numerical simulation to illustrate our main results.

7.
On the number of exceptional points of holomorphic curves and the defect relation for holomorphic curves - Toda, Nobushige
Let X^{n}(2) be a subset of C^{n + 1} $\backslash$ {0} any two elements of which are not propotional. We estimate the number of exceptional points in X^{n}(2) for several holomorphic curves and we consider the defect relation for holomorphic curves. We shall give an example for which the defect relation is extremal and then give some holomorphic curves for which the defect relation is not extremal over X^{n}(2). Another defect relation is also considered.

8.
Properties of meromorphic solutions of some certain difference equations - Peng, Chang-Wen; Chen, Zong-Xuan
This paper considers some properties of meromorphic solutions of the nonlinear difference equation ¶ (f(z + 1) + f(z))(f(z) + f(z − 1)) = $\frac{P(z,f(z))}{Q(z,f(z))}$ , ¶ where P(z, f(z)) and Q(z, f(z)) are polynomials in f having rational coefficients and no common roots.

9.
A construction of a complete bounded null curve in C^{3} - Ferrer, Leonor; Martín, Francisco; Umehara, Masaaki; Yamada, Kotaro
We construct a complete bounded immersed null holomorphic curve in C^{3}, which is a recovery of the previous paper of the last three authors on this subject.

11.
The real hypersurface of type (B) with two distinct principal curvatures in a complex hyperbolic space - Yamashita, Katsufumi; Maeda, Sadahiro
Real hypersurfaces M^{2n−1} of type (B) in CH^{n}(c), n ≥ 2 are known as interesting examples of Hopf hypersurfaces with constant principal curvatures. They are homogeneous in this ambient space. Moreover, the numbers of distinct principal curvatures of all real hypersurfaces of type (B) with radius r ≠ (1/ $\sqrt{|c|}$ ) log_{e}(2 + $\sqrt{3}$ ) are 3. When r = (1/ $\sqrt{|c|}$ ) log_{e}(2 + $\sqrt{3}$ ), the real hypersurface of type (B) has two distinct principal curvatures. The purpose of this paper is to characterize this Hopf hypersurface having two distinct constant principal curvatures.

12.
Remarks on space-time behavior in the Cauchy problems of the heat equation and the curvature flow equation with mildly oscillating initial values - Yagisita, Hiroki
We study two initial value problems of the linear diffusion equation u_{t} = u_{xx} and the nonlinear diffusion equation u_{t} = (1 + u_{x}^{2})^{−1}u_{xx}, when Cauchy data u(x,0) = u_{0}(x) are bounded and oscillate mildly. The latter nonlinear heat equation is the equation of the curvature flow, when the moving curves are represented by graphs. In the case of lim_{|x|→+∞}|xu′_{0}(x)|= 0, by using an elementary scaling technique, we show ¶ lim_{t→+∞}|u( $\sqrt{t}$ x,t) − (F(−x)u_{0}(− $\sqrt{t}$ ) + F(+ x)u_{0}(+ $\sqrt{t}$ ))| = 0 ¶ for the linear heat equation u_{t} = u_{xx}, where x $in$ R and F(z): =...

13.
Uniqueness of L^{1} harmonic functions on rotationally symmetric Riemannian manifolds - Murata, Minoru; Tsuchida, Tetsuo
We show that any rotationally symmetric Riemannian manifold has the L^{1}-Liouville property for harmonic functions, i.e., any integrable harmonic function on it must be identically constant. We also give a characterization of a manifold which carries a non-constant L^{1} nonnegative subharmonic function.

14.
Certain holomorphic sections relating to 2-pointed Weierstrass gap sets on a compact Riemann surface - Gotoh, Tohru
For a compact Riemann surface X of genus g, we will construct a holomorphic section of the line bundle π_{1}^{*}K_{X}^{g(g+1)(g+2)/6} $\otimes$ π_{2}^{*}K_{X}^{g(g+1)(g+2)/6} over X × X whose zero set consists exactly of the points (P,Q) with the cardinalities of the Weierstrass gap sets G(P,Q) greater than the minimal value (g^{2} + 3g)/2.

15.
Some extensions of the four values theorem of Nevanlinna-Gundersen - Si, Duc Quang
Nevanlinna showed that two distinct non-constant meromorphic functions on C must be linked by a Möbius transformation if they have the same inverse images counted with multiplicities for four distinct values. Later on, Gundersen generalized the result of Nevanlinna to the case where two meromorphic functions share two values ignoring multiplicity and share other two values with counting multiplicities. In this paper, we will extend the results of Nevanlinna-Gundersen to the case of two holomorphic mappings into P^{n}(C) sharing (n + 1) hyperplanes ignoring multiplicity and other (n + 1) hyperplanes with multiplicities counted to level 2 or (n +...

16.
Functional analysis on two-dimensional local fields - Cámara, Alberto
We establish how a two-dimensional local field can be described as a locally convex space once an embedding of a local field into it has been fixed. We study the resulting spaces from a functional analytic point of view: in particular we study bounded, c-compact and compactoid submodules of two-dimensional local fields.

17.
Precise large deviations for Ornstein-Uhlenbeck processes - Yang, Xiangfeng
For a family of Ornstein-Uhlenbeck processes having an infinitesimal size of noise, we prove precise asymptotics for large deviations of an integral form over the continuous path space. The main ingredients in the proof are an exponential change of measures and subtle Taylor expansions with suitable estimates. An application of these precise integral large deviations to partial differential equations is included.

18.
Partial generalizations of some conjectures in Lorentzian manifolds - Sun, Zhongyang
In this paper, we mainly investigate complete or compact spacelike hypersurfaces with constant mean curvature or constant scalar curvature in Lorentzian manifolds L_{1}^{n+1}. We give a new estimate of the Laplacian ΔS of the squared length S of the second fundamental form of such spacelike hypersurfaces. Finally, we give partial generalizations of some Conjectures in Lorentzian manifolds L_{1}^{n+1}.

19.
Explicit estimates on distance estimator method for Julia sets of polynomials - Fujimura, Masayo; Gotoh, Yasuhiro; Yoshida, Satoshi
The distance estimator method is well-known as an iterative method which estimates the Euclidean distance between a given point and Julia set. Although it brings a remarkable effect in drawing Julia set, it seems to be not known about how accurate this method is. In the present paper, we give explicit estimates on this method.