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 VII₀-class. For a general Hopf surface S, we prove that there exists a differentiably non-degenerate holomorphic mapping f: C² → S with order at most one. For any Inoue surface S′, we prove that every non-constant meromorphic mapping f: Cⁿ → S′ is holomorphic and its order satisfies ρ_f ≥ 2.

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.

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.

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).

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.

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.

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.

To a link (obtained by closing a string link) we associate a certain diagram of groups. If two links are concordant, we show that there exists a certain type of isomorphism between the group diagrams.

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.

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.

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.

We describe a condition under which the claims in the paper cited above hold.

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 ordinary. We also prove that every projective smooth curve of genus two in characteristic three is hyperbolically ordinary. These two applications yield negative, partial positive answers to basic questions in the p-adic Teichmüller theory, respectively.

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.