1.
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.

2.
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 +...

3.
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.

4.
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.

5.
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}.

6.
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.

8.
The Dixmier-Douady class in the simplicial de Rham complex - Suzuki, Naoya
On the basis of A. L. Carey, D. Crowley, M. K. Murray's work, we exhibit a cocycle in the simplicial de Rham complex which represents the Dixmier-Douady class.

9.
Stability of F-stationary maps of a class of functionals related to conformal maps - Han, Yingbo; Feng, Shuxiang; Pan, Hong
In this paper, we study a generalized functional Φ_{F} related to the conformality of maps between Riemannian manifolds. We derive the first variation formula and the second variation formula of Φ_{F}, then we study the stability of F-stationary map from or into the standard sphere. We also introduce the F-stress energy tensor associated to Φ_{F} which is naturally linked to conservation law.

11.
On triangles in the universal Teichmüller space - Zhou, Zemin; Liu, Lixin
Let $\mathcal{T}$ (Δ) be the universal Teichmüller space, viewed as the set of all Teichmüller equivalent classes [f] of quasiconformal mappings f of Δ onto itself. The notion of completing triangles was introduced by F. P. Gardiner. Three points [f], [g] and [h] are called to form a completing triangle if each pair of them has a unique geodesic segment joining them. Otherwise, they form a non-completing triangle. In this paper, we construct two Strebel points [f] and [g] such that [f], [g] and [id] form a non-completing triangle. A sufficient condition for points [f], [g] and [id] to form...

12.
Functional central limit theorem for tagged particle dynamics in stochastic ranking process - Nagahata, Yukio
In this paper we consider "parabolically" scaled centered tagged particle dynamics for a stochastic ranking process (regarded as a particle system), which is driven according to an algorithm for self-organizing linear list of a finite number of items. We let the number of items to infinity and show that the scaled tagged particle weakly converges to a "diffusion" processes with occasional jumps, in which the particle jumps to 0 when its own Poisson clock rings and behaves as a "diffusion" process otherwise. The "diffusion" is decomposed into a sum of independent continuous Markov Gaussian processes with a random covariance. Intuitively,...

13.
Tagged particle dynamics in stochastic ranking process - Nagahata, Yukio
We consider a stochastic ranking process, which is a mathematical model of the ranking in the web page of online bookstores or posting web pages. We give a scaling limit of tagged particle dynamics. In this limit the scaled tagged particles jumps to the top of the list when its own Poisson clock rings and moves deterministically along a curve otherwise. This curve is characteristic curve of a system of quasi linear PDE, which is mentioned in [11, 14]. We also give a scaling limit of multi-tagged particle dynamics, in which the motion of the particles are independent.

15.
The generator and quantum Markov semigroup for quantum walks - Ko, Chul Ki; Yoo, Hyun Jae
The quantum walks in the lattice spaces are represented as unitary evolutions. We find a generator for the evolution and apply it to further understand the walks. We first extend the discrete time quantum walks to continuous time walks. Then we construct the quantum Markov semigroup for quantum walks and characterize it in an invariant subalgebra. In the meanwhile, we obtain the limit distributions of the quantum walks in one-dimension with a proper scaling, which was obtained by Konno by a different method.

16.
Relative injectivity and flatness of complexes - Lu, Bo; Liu, Zhongkui
A complex C is said to be FR-injective (resp., FR-flat) if Ext^{1}(D,C) = 0 (resp., $\overline{\mathrm{Tor}}_1$ (C,D) = 0) for any finitely represented complex D. We prove that a complex C is FR-injective (resp., FR-flat) if and only if C is exact and Z_{m}(C) is FR-injective (resp., FR-flat) in R-Mod for all m $in$ Z. We show that the class of FR-injective complexes is closed under direct limits and the class of FR-flat complexes is closed under direct products over any ring R. We use this result to prove that every complex have FR-flat preenvelopes and FR-injective covers.

17.
Crossed products of Hopf group-coalgebras - Guo, Shuang-jian; Wang, Shuan-hong
The main aim of this paper is to study Hopf group-crossed products and Hopf group-cleft extensions in the setting of Hopf group-coalgebras.

18.
Area integral means, Hardy and weighted Bergman spaces of planar harmonic mappings - Chen, Shaolin; Ponnusamy, Saminathan; Wang, Xiantao
In this paper, we investigate some properties of planar harmonic mappings. First, we generalize the main results in [2] and [10], and then discuss the relationship between area integral means and harmonic Hardy spaces or harmonic weighted Bergman spaces. At the end, coefficient estimates of mappings in weighted Bergman spaces are obtained.

19.
Diffeomorphisms between Siegel domains of the first kind preserving the holomorphic automorphism groups and applications - Kodama, Akio; Shimizu, Satoru
This is a continuation of our previous paper [4]. In the class of hyperbolic manifolds in the sense of S. Kobayashi [3], we obtained in [4] an intrinsic characterization of bounded symmetric domains in C^{n} from the viewpoint of the holomorphic automorphism group. In connection with this, we give in this paper a structure theorem on diffeomorphisms between Siegel domains of the first kind that preserve the holomorphic automorphism groups. As an application, we obtain a well-known fact [2] that two Siegel domains of the first kind are biholomorphically equivalent if and only if they are linearly equivalent.

20.
A note on the geometricity of open homomorphisms between the absolute Galois groups of p-adic local fields - Hoshi, Yuichiro
In the present paper, we prove that an open continuous homomorphism between the absolute Galois groups of p-adic local fields is geometric [i.e., roughly speaking, arises from an embedding of fields] if and only if the homomorphism is HT-preserving [i.e., roughly speaking, satisfies the condition that the pull-back by the homomorphism of every Hodge-Tate representation is Hodge-Tate].