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 ...

In this paper, we establish a Hopf bifurcation theorem for abstract Cauchy problems in which the linear operator is not densely defined and is not a Hille–Yosida operator. The theorem is proved using the center manifold theory for nondensely defined Cauchy problems associated with the integrated semigroup theory. As applications, the main theorem is used to obtain a known Hopf bifurcation resul...

We prove that under certain mild assumptions a Lie bialgebroid integrates to a Poisson groupoid. This includes, in particular, a new proof of the existence of local symplectic groupoids for any Poisson manifold, a theorem of Karasev and of Weinstein.

The discrete-time system has more complex and chaotic dynamical behaviors as compared to the continuous-time system. This paper extends a discrete Leslie–Gower predator-prey with Allee effect in predator’s population, whose dynamics are analyzed explored. We have determined equilibrium points studied their local stability properties. find that undergoes flip bifurcation Neimark–Sacker around in...

and Applied Analysis 3 the unstable manifold in U0 by using the method introduced in Zhu 9 . According to the invariance and symmetry of these manifolds, we can deduce that system 2.1 has the following form inU0: ẋ x ( λ ( , μ ) O 1 ) , ẏ y −λ , μ O 1 , u̇ v ( ω ( , μ ) O 1 ) u ( O x O ( y ) O u ) O ( xy ) , v̇ u −ω , μ O 1 ) − vO x Oy O v ) −Oxy, 3.1 where λ 0, μ λ, ω 0, μ ω,O 1 O x O y O u O v ...

1. Basic gradient estimate; different variations of the gradient estimates; 2. The theorem of Brascamp-Lieb, Barkey-Émery Riemannian geometry, relation of eigenvalue gap with respect to the first Neumann eigenvalue; the Friedlander-Solomayak theorem, 3. The definition of the Laplacian on L space, theorem of Sturm, 4. Theorem of Wang and its possible generalizations. 1 Gradient estimate of the f...

The center manifold is an invariant that plays a crucial role in the bifurcation analysis of dynamical systems. existence theorem assures local submanifold state space system around non-hyperbolic equilibrium point. Center theory essential reduction different scenarios to their normal forms. Our study focuses on predator-prey interactive with density-dependent growth predators subject contagiou...

We prove a direct analogue of the classical Duflo formula in the case of L∞algebras. We conjecture an analogous formula in the case of an arbitrary Q-manifold. When G is a compact connected Lie group, the Duflo theorem for the Q-manifold (ΠTG, dDR) is exactly the Duflo theorem for the Lie algebra g = LieG. The corresponding theorem for the Q-manifold (ΠTM,dDR), where M is an arbitrary smooth ma...

Theorem 1. Suppose (M; g) is a noncompact complete Riemannian manifold with Ric (n 1), we have 0 (n 1) =4. The estimate is sharp since the spectrum is the ray [(n 1) =4;+1) for the hyperbolic space H. For Kähler manifolds, this estimate can be improved. On a Kähler manifold (M; g) of complex dimension n, where g is the Riemannian metric, let ! = g (J ; ) be the Kähler form. In local holomorphic...