The existence of a random attractor for the stochastic FitzHugh-Nagumo system defined on an unbounded domain is established. The pullback asymptotic compactness of the stochastic system is proved by uniform estimates on solutions for large space and time variables. These estimates are obtained by a cut-off technique.

In this paper, we prove that the category of rack crossed modules (with a fixed codomain) is finitely complete. other words, construct product, pullback and equalizer objects in racks. We therefore unify group-theoretical analogy completeness property sense functor $\mathbf{Conj \colon Grp \to Rack} $.

We study Galerkin approximation of pullback attractors for a nonautonomous nonlocal parabolic equation. show that the $ n $th system has attractor in $-dimensional subspace Lebesgue space. then prove sequence is uniformly backward bounded and solutions converges on any set. Using these results, we establish upper semi-convergence towards original infinite-dimensional system.

We show that the category of coalgebras of a wide-pullback preserving endofunctor on a category of presheaves is itself a category of presheaves. This illustrates a connection between Jacobs’ temporal logic of coalgebras and Ghilardi and Meloni’s presheaf semantics for modal logic.

This article is the expanded version of a talk given at the conference: Algebraic geometry in East Asia 2008. In this notes, I intend to give a brief survey of results on the behavior of semi-stable bundles under the Frobenius pullback and direct images. Some results are new.

It is shown that a complex normal projective variety has non-positive Kodaira dimension if it admits a non-isomorphic quasi-polarized endomorphism. The geometric structure of the variety is described by methods of equivariant lifting and fibrations. Endomorphisms of the projective spaces are also discussed and some results on invariant subvarieties under the pullback of the endomorphism are obt...

It is shown that there is no continuous map from the quaternionic Grassmannian Grk,n(k ≥ 2, n ≥ k + 2) to the quaternionic projective space HP ∞ such that the pullback of the first Pontryagin class of the tautological bundle over HP is equal to the first Pontryagin class of the tautological bundle over Grk,n. In fact some more precise statement is proved.

Recently, Fourier domain OCT (FD-OCT) has been introduced for clinical use. This approach allows in vivo, high resolution (15 micron) imaging with very fast data acquisition, however, it requires brief flushing of the lumen during imaging. The reproducibility of such fast data acquisition under intracoronary flush application is poorly understood. To assess the inter-study variability of FDOCT ...