This article shows the controllability of nonlinear third-order dispersion inclusions with infinite delay. Sufficient conditions are obtained by using a fixed-point theorem for multivalued maps. Particularly, the compactness of the operator semigroups is not assumed in this article.

In this paper we obtain some versions of weak compactness James’ theorem, replacing bounded linear functionals by polynomials and symmetric multilinear forms. Mathematics Subject Classification (1991): 46B10, 46B50, 46G25

Given a convergence theorem in analysis, under very general conditions a model-theoretic compactness argument implies that there is a uniform bound on the rate of metastability. We illustrate with three examples from ergodic theory.

We show that the compactness of G-free k-colorability is equivalent to the Boolean prime ideal theorem for any graph G with more than two vertices and any k ≥ 2.

dL(Mo,M1) = inf[llogdil/l + Ilogdil/-II], f where I: Mo -+ MI is a homeomorphism and dil I is the dilatation of I given by dill = SUPXt#2 dist(f(x l ), l(x2))/ dist(x1 ,x2). If Mo and MI are not homeomorphic, define dL(Mo,M1) = +00. Gromov [20] proves the remarkable result that the space of compact Riemannian manifolds L(A,t5 ,D) of sectional curvature IKI :::; A, injectivity radius i M 2: t5 >...

In this paper, we consider the coupled Kirchhoff system in subcritical case and critical case. For case, first study least energy of limit by using Nehari manifold method exclude existence semi-trivial solutions. Then improve global compactness lemma to overcome loss compactness. Combining with linking theorem topological degree, construct a Palais-Smale sequence high level prove positive Moreo...

. The reason for including this chapter is to make the book as selfcontained as possible. It should in particular be accessible to physicists, who normally have no training in formal logic. We present the basics of classical propositional logic and non-monotonic logic. In fact, it is possible to provide the reader with all the logical equipment he needs in order to understand the logical invest...

In this paper, we consider a generalized Ricci flow and establish the higher derivatives estimates for compact manifolds. As an application, we prove the compactness theorem for this generalized Ricci flow.

We prove a smooth compactness theorem for the space of embedded selfshrinkers in R. Since self-shrinkers model singularities in mean curvature flow, this theorem can be thought of as a compactness result for the space of all singularities and it plays an important role in studying generic mean curvature flow. 0. Introduction A surface Σ ⊂ R is said to be a self-shrinker if it satisfies (0.1) H ...