This can be compared to the fact that a conformally flat manifold of dimension n > 2 is locally conformal to a region of the sphere of the same dimension. In twistor theory, it is well-known that an even dimensional conformally flat manifold has an integrable twistor space ([7], [6], [1], [3]). It is interesting, as an analogy, that a Bochner-Kähler manifold has integrable twistor spaces define...

The nonlinear regression model yi = f}t(0u . . . . 0,„) + et with (e1, . . . , eN) ~ A (0, J)) a r , d with //,(.) twice continuously differentiable is considered. Under the assumption that the maximal curvature of the mean-values manifold {ii(0) :0eU}cR is bounded, an approximative probability density for the least squares estimates of (0U . . . , 6m) is proposed. This density depends on the f...

A mathematical model of a within-host viral infection is presented. A local stability analysis of the model is conducted in two ways. At first, the basic reproduction number of the system is calculated. It is shown that when the reproduction number falls below unity, the disease free equilibrium (DFE) is globally asymptotically stable, and when it exceeds unity, the DFE is unstable and there ex...

*Correspondence: [email protected] Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, P.R. China Abstract In this paper, the Hopf bifurcation control for a Lotka-Volterra predator-prey model with two delays is studied by using a hybrid control strategy. By analyzing the associated characteristic equation, its local stability and the exi...

We formulate and prove a local stable manifold theorem for stochastic differential equations (SDEs) that are driven by spatial Kunita-type semimartingales with stationary ergodic increments. Both Stratonovich and Itôtype equations are treated. Starting with the existence of a stochastic flow for a SDE, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of inva...

In this paper we prove a new geometric integrability theorem for almost complex manifolds. Let M be a connected, smooth 2m real dimensional manifold with an U(m) structure on its tangent bundle and ∇ be a compatible connection on it. Assume the complexified curvature of the connection has vanishing (0, 2) component. Then we claim that M can be given the structure of an m complex dimensional Käh...

In this paper we prove a new geometric integrability theorem for almost complex manifolds. Let M be a connected, oriented, smooth 2m real dimensional manifold with an U(m) structure on its tangent bundle. Moreover let ∇ be a compatible connection on it. Assume the complexified curvature of the connection has vanishing (0, 2) component. Then we claim that M can be given the structure of an m com...

Jerk systems with delayed feedback are considered. Firstly, by employing the polynomial theorem to analyze the distribution of the roots to the associated characteristic equation, the conditions of ensuring the existence of Hopf bifurcation are given. Secondly, the stability and direction of the Hopf bifurcation are determined by applying the normal form method and center manifold theorem. Fina...

We show the existence of a local stable manifold for a bidirectional discrete-time nondiffeomorphic nonlinear Hamiltonian dynamics. This is the case where zero is a closed loop eigenvalue and therefore the Hamiltonian matrix is not invertible. In addition, we show the eigenstructure and the symplectic properties of the mixed direction nonlinear Hamiltonian dynamics. We extend the Local Stable M...

The main purpose of the following article is to give a proof of Y. Kawa-mata's celebrated subadjunction theorem in the spirit of our previous work on Bergman kernels. We will use two main ingredients : an L 2 m –extension theorem of Ohsawa-Takegoshi type (which is also a new result) and a more complete version of our former results. §0 Introduction Let X be a projective manifold and let Θ be a ...