In this paper, we investigate the continuity of attractors in time-dependent phase spaces. (i) We establish two abstract criteria on upper semicontinuity and residual pullback D-attractor with respect to perturbations, an equivalence criterion between their equi-attraction, which generalize theory developed recently [27], [28] that (ii) propose notion D-exponential attractor, includes exponenti...

and Applied Analysis 3 Theorem 4 (see [21, 22]). Let X,Y be two Banach spaces satisfy the previous assumptions, and let {U(t, τ)} be amultivalued process onX andY, respectively. Assume that {U(t, τ)} is upper semicontinuous or weak upper semicontinuous on Y. If for fixed t ⩾ τ, τ ∈ R, U(t, τ) maps compact subsets of X into bounded subsets ofP(X), then U(t, τ) is norm-to-weak upper semicontinuou...

OBJECTIVE To observe the intracochlear behavior of a cochlear implant electrode insertion technique (called "pullback") in temporal bones. Study Design. Experimental. Settings. Tertiary referral center. METHOD The change of the intracochlear electrode position was investigated under various conditions of an electrode pullback (N = 54) in 9 radiologically, size-estimated temporal bones (TBs). ...

Introduction: Endovenous laser treatment (ELT) is a new treatment method for the reflux of the great saphenous vein. A successful ELT is dependent on the selection of optimum parameters required to achieve optimal vein damage while avoiding side effects including skin burns. The mathematical modeling of ELT can be used to understand the process of ELT. This study was conducted to examine the ef...

In this paper‎, ‎we give the notions of crossed polymodule and cat$^1$-polygroup‎ ‎as a generalization of Loday's definition‎. ‎Then‎, ‎we define the pullback cat$^1$-polygroup and we obtain some results in this respect‎. ‎Specially‎, ‎we prove that by a pullback cat$^1$-polygroup we can obtain a cat$^1$-group‎.

We develop a general compactification framework to facilitate analysis of nonlinear nonautonomous ODEs where terms decay asymptotically. The strategy is compactify the problem: phase space augmented with bounded but open dimension and then extended at one or both ends by gluing in flow-invariant subspaces that carry autonomous dynamics limit systems from infinity. derive weakest conditions poss...