In this paper, we will give a brief survey on Nevanlinna theory of p-adic meromorphic functions and some of its applications. Also we will study p-adic meromorphic solutions of dierential equations, and show that some dierential equations have no admissible transcendental p-adic meromorphic solutions as in the complex-valued function cases.

In this paper we study the Hopf bifurcation for the Holling- Tanner model, a well-known predator-prey model in mathematical ecology. We show that for some parameter ranges, the Hopf bifurcation is subcritical and thus the system may have multiple limit cycles.

Let $M^n$ be a closed submanifold immersed into a real hyperbolic space form $\Bbb H^{n+p}$ of constant curvature $-1$. Denote by $R$ the normalized scalar curvature of $M^n$ and by $H$ the mean curvature of $M^n$. Suppose that $R$ is constant and bigger than or equal to $-1$. We first extend Cheng-Yau's technique to higher codimensional cases. Then, for $M^n$ with parallel normalized mean curvature vector field, we show that, if $H$ satisfies a certain inequality, then $M^n$ is totally umbilical or the equality part holds. We describe all $M^n$ whose $H$ satisfies this equality.

For a fixed positive integer $k$, the linear $k$-arboricity $\rm la_k(G)$ of a graph $G$ is the minimum number $\ell$ such that the edge set $E(G)$ can be partitioned into $\ell$ disjoint sets, each induces a subgraph whose components are paths of lengths at most $k$. This paper examines linear $k$-arboricity from an algorithmic point of view. In particular, we present a linear-time algorithm for determining whether a tree $T$ has $\rm la_2(T)\le m$. We also give a characterization for a tree $T$ with maximum degree $2m$ having $\rm la_2(T)=m$.

Reliability and efficiency are important criteria in the design of interconnection networks. Recently, the $w$-wide diameter $d_w(G)$, the $(w-1)$-fault diameter $D_w(G)$, and the $w$-Rabin number $r_w(G)$ have been used to measure network reliability and efficiency. In this paper, we study wide diameters for an important class of parallel networks---butterfly networks. The main result of this paper is to determine their wide diameters.

This paper studies the mathematical model that describes the deformation of a nonprismatic beam by its own weight. The nonprismatic beam is considered to be with circular or rectangular cross-section. We fix the density and hold an angle $\alpha$ at one end but free at the other end. The shape of the beam depends on the angle $\alpha$, the density and the length to that of flexural rigidity. We analyze the bifurcation phenomena for the vertical case, $\alpha = \pi$. Several numerical results are presented.

The purpose of this paper is to improve the previous results due to the author.

We establish two uniform convergence results for duality pairs consisting of vector-sequence spaces with some gliding humps property and the corresponding function-sequence spaces. These uniform convergence results imply some important facts.