1.
The existence of quasiconformal homeomorphism between planes with countable marked points - Fujino, Hiroki
We consider quasiconformal deformations of C $\backslash$ Z. We give some criteria for infinitely often punctured planes to be quasiconformally equivalent to C $\backslash$ Z. In particular, we characterize the closed subsets of R whose compliments are quasiconformally equivalent to C $\backslash$ Z.

2.
Nilpotent admissible indigenous bundles via Cartier operators in characteristic three - Hoshi, Yuichiro
In the present paper, we study the p-adic Teichmüller theory in the case where p = 3. In particular, we discuss nilpotent admissible/ordinary indigenous bundles over a projective smooth curve in characteristic three. The main result of the present paper is a characterization of the supersingular divisors of nilpotent admissible/ordinary indigenous bundles in characteristic three by means of various Cartier operators. By means of this characterization, we prove that, for every nilpotent ordinary indigenous bundle over a projective smooth curve in characteristic three, there exists a connected finite étale covering of the curve on which the indigenous bundle is not...

4.
Two normality criteria and counterexamples to the converse of Bloch's principle - Charak, Kuldeep Singh; Singh, Virender
In this paper, we prove two normality criteria for a family of meromorphic functions. The first criterion extends a result of Fang and Zalcman [Normal families and shared values of meromorphic functions II, Comput. Methods Funct. Theory, 1 (2001), 289-299] to a bigger class of differential polynomials whereas the second one leads to some counterexamples to the converse of the Bloch's principle.

5.
Some inverse fractional legendre transforms of gamma function form - Ansari, Alireza
In this paper, using the asymptotic expansion of the ratio of gamma functions, we obtain new inversion formulas for the fractional Legendre transforms. These formulas are given in terms of some integral representations of the inverse Mellin transforms. Also, the closed forms of solutions of the fractional Laplace and Helmholtz equations are obtained by these inversion formulas.

6.
Equinormalizability and topologically triviality of deformations of isolated curve singularities over smooth base spaces - Lê, Công-Trình
We give a δ-constant criterion for equinormalizability of deformations of isolated (not necessarily reduced) curve singularities over smooth base spaces of dimension ≥ 1. For one-parametric families of isolated curve singularities, we show that their topologically triviality is equivalent to the admission of weak simultaneous resolutions.

8.
Sectional curvatures of geodesic spheres in a complex hyperbolic space - Kajiwara, Tetsuo; Maeda, Sadahiro
We characterize geodesic spheres with sufficiently small radii in a complex hyperbolic space of constant holomorphic sectional curvature c(<0) by using their geometric three properties. These properties are based on their contact forms, geodesics and shape operators. These geodesic spheres are the only examples of hypersurfaces of type (A) which are of nonnegative sectional curvature in this ambient space. Moreover, in particular, when −1 ≤ c < 0, the class of these geodesic spheres has just one example of Sasakian space forms.

9.
On Milnor fibrations of mixed functions, a_{
f
}-condition and boundary stability - Oka, Mutsuo
Convenient mixed functions with strongly non-degenerate Newton boundaries have a Milnor fibration ([9]), as the isolatedness of the singularity follows from the convenience. In this paper, we consider the Milnor fibration for non-convenient mixed functions. We also study geometric properties such as Thom's a_{f}-condition, the transversality of the nearby fibers and stable boundary property of the Milnor fibration and their relations.

10.
Isospectral Kähler graphs - Tuerxunmaimaiti, Yaermaimaiti; Adachi, Toshiaki
We give some basic ways to construct Kähler graphs which are compound graphs having principal and auxiliary graphs. By use of these methods we give some examples of isospectral pairs of Kähler graphs.

11.
A finite presentation of the level 2 principal congruence subgroup of GL(n; Z) - Kobayashi, Ryoma
It is known that the level 2 principal congruence subgroup of GL(n; Z) has a finite generating set (see [7]). In this paper, we give a finite presentation of the level 2 principal congruence subgroup of GL(n; Z).

12.
Existence and multiple solutions for nonautonomous second order systems with nonsmooth potentials - Ning, Yan; An, Tianqing
This paper is concerned with the nonautonomous second order Hamiltonian systems with nondifferetiable potentials. By using the nonsmooth least action principle and the nonsmooth local linking theorem, we obtain some new existence and multiplicity results for the periodic solutions.

13.
Hyers-Ulam stability of a class of fractional linear differential equations - Wang, Chun; Xu, Tian-Zhou
In this paper, we investigate the Hyers-Ulam stability of a class of fractional linear differential equations. Applying the Laplace transform method, we prove that a class of fractional linear differential equations with Riemann-Liouville fractional derivatives is Hyers-Ulam stable. The results improve and extend some recent results.

14.
Orders of meromorphic mappings into Hopf and Inoue surfaces - Amemiya, Takushi
In a late paper of J. Noguchi and J. Winkelmann [7] (J. Math. Soc. Jpn., Vol. 64 No. 4 (2012), 1169-1180) they gave the first instance where Kähler or non-Kähler conditions of the image spaces make a difference in the value distribution theory. In this paper, we will investigate orders of meromorphic mappings into a Hopf surface which is more general than dealt with by Noguchi-Winkelmann, and an Inoue surface. They are non-Kähler surfaces and belong to VII_{0}-class. For a general Hopf surface S, we prove that there exists a differentiably non-degenerate holomorphic mapping f: C^{2} → S with order...

15.
Solvability of the initial value problem to a model system for water waves - Murakami, Yuuta; Iguchi, Tatsuo
We consider the initial value problem to a model system for water waves. The model system is the Euler-Lagrange equations for an approximate Lagrangian which is derived from Luke's Lagrangian for water waves by approximating the velocity potential in the Lagrangian. The model are nonlinear dispersive equations and the hypersurface
t = 0 is characteristic for the model equations. Therefore, the initial data have to be restricted in an infinite dimensional manifold in order to the existence of the solution. Under this necessary condition and a sign condition, which corresponds to a generalized Rayleigh-Taylor sign condition for water waves, on the...

16.
Sovereign and ribbon weak Hopf algebras - Zhang, Xiaohui; Zhao, Xiaofan; Wang, Shuanhong
In this paper, we study the Deligne's sovereign structure theorem on the finite dimensional weak Hopf algebras, and give a necessary and sufficient condition for a finite dimensional (co)quasitriangular weak Hopf algebra
H with bijective antipode to admit a (co)ribbon structure. As an application we discuss the ribbon structures over the Drinfeld doubles of some weak Hopf algebras to verify our theory.

17.
Universal inequalities for eigenvalues of a system of sub-elliptic equations on Heisenberg group - Du, Feng; Wu, Chuanxi; Li, Guanghan; Xia, Changyu
In this paper, we study the eigenvalue problem of a system of sub-elliptic equations on abounded domain in the Heisenberg group and obtain some universal inequalities. Moreover, for the lower order eigenvalues of this eigenvalue problem, we also give some universal inequalities.

18.
Minimaxness and finiteness properties of formal local cohomology modules - Rezaei, Shahram
Let
$\mathfrak{a}$ be an ideal of local ring (
R,
$\mathfrak{m}$ ) and
M a finitely generated
R-module and
n an integer. We prove some results concerning minimaxness and finiteness of formal local cohomology modules. We discuss the maximum and minimum integers such that
$\mathfrak{F}_\mathfrak{a}^i$ (
M) is minimax and also we obtain the maximum and minimum integers such that
$\mathfrak{F}_\mathfrak{a}^i$ (
M) is finitely gnerated.

19.
Monomorphisms in categories of log schemes - Mochizuki, Shinichi
In the present paper, we study
category-theoretic properties of
monomorphisms in categories of log schemes. This study allows one to give a
purely category-theoretic reconstruction of the
log scheme that gave rise to the category under consideration. We also obtain analogous results for categories of schemes of locally finite type over the ring of rational integers that are equipped with "
archimedean structures". Such reconstructions were discussed in two previous papers by the author, but these reconstructions contained some errors, which were pointed out to the author by C. Nakayama and Y. Hoshi. These errors revolve around certain elementary
combinatorial aspects of
fan decompositions of two-dimensional rational...

20.
On θ-congruent numbers on real quadratic number fields - Janfada, Ali S.; Salami, Sajad
Let
K =
Q (
$\sqrt{m}$ ) be a real quadratic number field, where
m > 1 is a squarefree integer. Suppose that 0 < θ < π has rational cosine, say cos(θ) =
s/r with 0 < |
s| <
r and gcd(
r,s) = 1. A positive integer
n is called a (
K,θ)-congruent number if there is a triangle, called the (
K,θ,
n)-triangles, with sides in
K having θ as an angle and
nα
_{θ} as area, where α
_{θ} =
$\sqrt{r^2-s^2}$ . Consider the (
K,θ)-congruent number elliptic curve
E
_{
n,θ
}:
y
^{2} =
x(
x + (
r +
s)
n) (
x − (
r −
s)
n) defined over
K. Denote the squarefree part of positive integer
t by sqf(
t). In this work, it is...