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 ...

Using Gröbner Basis, we introduce a general algorithm to determine the additive structure of a module, when we know about it using indirect information about its structure. We apply the algorithm to determine the additive structure of indecomposable modules over ZCp, where Cp is the cyclic group of order a prime number p, and the p−pullback {Z→ Zp ← Z} of Z⊕Z.

While decomposing graphs in simpler items greatly helps to design more efficient algorithms, some classes of graphs can not be handled using the classical techniques. We show here that a graph having enough symmetries can be factored into simpler blocks through a standard morphism and that the inverse process may be formalized as a pullback rewriting system.

Resumen We first study the existence and uniqueness of strong solutions of a three dimensional system of globally modified Navier-Stokes equations with delay in the locally Lipschitz case. The asymptotic behaviour of solutions, and the existence of pullback attractor are also analyzed.

If a normal quartic surface admits a singular point that is not a rational double point, then the surface is determined by the triplet (M,D,E) consisting of the minimal desingularization M , the pullback D of a general hyperplane section, and a non-zero effective anti-canonical divisor E of M . Geometric constructions of all the possible triplets (M,D,E) are given.