Let (Mn, g), n ≥ 4, be a compact simply-connected Riemannian manifold with nonnegative isotropic curvature. Given 0 < l ≤ L, we prove that there exists ε = ε(l, L, n) satisfying the following: If the scalar curvature s of g satisfies l ≤ s ≤ L and the Einstein tensor satisfies |Ric − s n g| ≤ ε then M is diffeomorphic to a symmetric space of compact type. This is a smooth analogue of the result...

We show that two locally compact abelian groups Gx and G2 are isomorphic if there exists an algebra isomorphism T of L\Gλ) onto L\G2) with | | Γ | | < V2. This constant is best possible. The same result is proved for locally compact connected groups, but for the general locally compact group, the result is proved under the hypothesis | |T | |< 1.246. Similar results are given for the algebras C...

at present paper, we establish the existence of pullback $mathcal{d}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $l^2(mathbb{r}^n)times l^2(mathbb{r}^n)$. in order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{d}$-absorbing set, is pullback $widehat{d}_0$-asymptotically compact.

Extending the work of [7] on groups definable in compact complex manifolds and of [1] on strongly minimal groups definable in nonstandard compact complex manifolds, we classify all groups definable in nonstandard compact complex manifolds showing that if G is such a group then there are a linear algebraic group L, a definably compact group T , and definable exact sequence 1→ L → G → T → 1.