We consider nonnegatively curved 4-manifolds that admit effective isometric actions by nite groups and from that draw topological conclusions about the manifold. Our rst theorem shows that if the man-ifolds admits an isometric Zp Zp for p large enough that the manifold has Euler characteristic less than or equal to ve. Our second theorem requires no hypothesis on the structure of the group othe...

This paper addresses partly an open question raised in the Handbook of Mathematical economics about the orientability of the pseudo-equilibrium manifold in the basic two-period General Equilibrium with Incomplete markets (GEI) model. For a broad class of explicit asset structures, it is proved that the asset equilibrium space is an orientable manifold if S − J is even. This implies, under the s...

This paper considers the problem of the stabilization of affine nonlinear control systems. First, we assume that the systems under investigation are of the generalized Byrnes–Isidori normal form. A new way to approximate the center manifold is proposed, which can reduce the error degree of the center manifold approximation. A new matrix product, called the semi-tensor product, is introduced to ...

We derive an index theorem for the Dirac operator in the background of various topological excitations on an R × S geometry. The index theorem provides more refined data than the APS index for an instanton on R and reproduces it in decompactification limit. In the R limit, it reduces to the Callias index theorem. The index is expressed in terms of topological charge and the η-invariant associat...

N. Ó Murchadha** Physics Department University College Cork Cork, Ireland Fax: +353-21-276949, E-mail: [email protected] Abstract In this article we show that one can construct initial data for the Einstein equations which satisfy the vacuum constraints. This initial data is defined on a manifold with topology R with a regular center and is asymptotically flat. Further, this initial data will...

A delayed Lotka-Volterra two-species predator-prey system of population allelopathy with discrete delay is considered. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcations are demonstrated. Furthermore, the direction of Hopf bifurcation and the stabil...

The stability and bifurcation analysis for a delay differential equation of hepatitis B virus infection is investigated. We show the existence of nonnegative equilibria under some appropriated conditions. The existence of the Hopf bifurcation with delay τ at the endemic equilibria is established by analyzing the distribution of the characteristic values. The explicit formulae which determine th...

Abstract: In this paper, a delayed ratio-dependent eco-epidemiological model with Holling type III functional response and two time delays is investigated.By regarding the delay as the bifurcation parameter, local stability of each equilibrium is discussed at the endemic equilibrium. By analyzing the corresponding characteristic equations, the conditions for existence of Hopf bifurcation for th...

We derive an index theorem for the Dirac operator in the background of various topological excitations on an R × S geometry. The index theorem provides more refined data than the APS index for an instanton on R and reproduces it in decompactification limit. In the R limit, it reduces to the Callias index theorem. The index is expressed in terms of topological charge and the η-invariant associat...

In this work, we prove the existence of a center manifold for some partial functional differential equations, whose linear part is not necessarily densely defined but satisfies the Hille-Yosida condition. When the unstable space is reduced to zero, we also show the attractiveness of the center manifold. We prove that the flow on the center manifold is completely determined by an ordinary differ...