This paper deals with semihyperbolic semigroups which are generated by entire (possibly transcendental) functions. In particular, a criterion is given assuring that a given entire semigroup is semihyperbolic. Note that a semihyperbolic semigroup $G$ admits holomorphic scaling, that is to say, the branches of local inverses of functions $f \in G$ are of bounded degree and that the preimages shrink to zero in diameter.

In [17] the present authors investigated the stabilization of the weak solutions to space periodic problem for barotropic compressible Navier-Stokes equations. The main goal of this paper is to show the power of the method introduced in [17] by treating other boundary conditions. In fact, the only limitation of the method is potential external force and the validity of the Poincaré inequality for the velocity.

We prove some new relations between weak approximation and some rational equivalence relations (Brauer and R-equivalence) in algebraic groups over arithmetical fields. By using weak approximation and local-global approach, we compute completely the group of Brauer equivalence classes of connected linear algebraic groups over number fields, and also completely compute the group of R-equivalence classes of connected linear algebraic groups $G$, which either are defined over a totally imaginary number field, or contains no anisotropic almost simple factors of exceptional type ${}^{3,6}D_{4}$, nor $E_{6}$. We discuss some consequences derived from these, e.g., by giving some new criteria for weak approximation in algebraic groups over number fields, by indicating a new way to give examples of non stably rational algebraic groups over local fields and application to norm principle. Some related questions and relations with groups of Brauer and R-equivalence classes over arbitrary fields of characteristic 0 are also discussed.

Tachida (1991) proposed a discrete-time model of nearly neutral mutation in which the selection coefficient of a new mutant has a fixed normal distribution with mean 0. The usual diffusion approximation leads to a probability-measure-valued diffusion process, known as a Fleming-Viot process, with the unusual feature of an unbounded selection intensity function. Although the existence of such a diffusion has been proved by Overbeck et al. (1995) using Dirichlet forms, we can now characterize the process via the martingale problem. This leads to a limit theorem justifying the diffusion approximation, using a stronger than usual topology on the state space. Also established are existence, uniqueness, and reversibility of the stationary distribution of the Fleming-Viot process.

In this paper, based on a kind of Harnack estimate for the Calabi flow on surfaces, we show the longtime existence and convergence of solutions of 2-dimensional Calabi flow on surfaces $(\Sigma ,g_{0})$ of genus $h \geq 2$ with any arbitrary background metric $g_{0}$.

The main purpose of this paper is to give some invariance property of a homology cobordism invariant of plumbed homology 3-spheres under a kind of blowing up process for auxiliary 4-V-manifolds. By using this property, we prove a homology cobordism invariance of an integral lift of the Rohlin invariant constructed by W. Neumann [6] and L. Siebenmann [12] in the set of all homology 3-spheres bounding plumbed 4-V-manifolds with $b_{2}^{+} + b_{2}^{-} \leq 2$ which are obtained by blowing down of smooth spin 4-manifolds.