Monotonically normal topological vector spaces are stratifiable

We prove that for any Hausdorff topological vector space E over the field R there exists A subset of E such that E is homeomorphic to a subset of A x R and A x R is homeomorphic to a subset of E. Using this fact we prove that E is monotonically normal if and only if E is stratifiable.

Orbital and strongly orbital spaces

We say that a (countably dimensional) topological vector space X is orbital if there is T∈L(X) and a vector x∈X such that X is the linear span of the orbit {Tnx:n=0,1,…}. We say that X is strongly orbital if, additionally, x can be chosen to be a hypercyclic vector for T. Of course, X can be orbital only if the algebraic dimension of X is finite or infinite countable. We characterize orbital and strongly orbital metrizable locally convex spaces. We also show that every countably dimensional metrizable locally convex space X does not have the invariant subset property. That is, there is T∈L(X) such that every non-zero x∈X is a hypercyclic vector for T. Finally, assuming the Continuum Hypothesis, we construct a complete strongly orbital locally convex space.

As a byproduct of our constructions, we determine the number of isomorphism classes in the set of dense countably dimensional subspaces of any given separable infinite dimensional Fréchet space X. For instance, in X=ℓ2×ω, there are exactly 3 pairwise non-isomorphic (as topological vector spaces) dense countably dimensional subspaces.

Hypercyclic and mixing operator semigroups

We describe a class of topological vector spaces admitting a mixing uniformly continuous operator group $\{T_t\}_{t\in\C^n}$ with holomorphic dependence on the parameter $t$. This result covers those existing in the literature. We also
describe a class of topological vector spaces admitting no supercyclic strongly continuous operator semigroups $\{T_t\}_{t\geq 0}$.

Comparing the orthogonal and homotopy functor calculi

Goodwillie’s homotopy functor calculus constructs a Taylor tower of approximations toF , often a functor from spaces to spaces. Weiss’s orthogonal calculus provides a Taylortower for functors from vector spaces to spaces. In particular, there is a Weiss towerassociated to the functor V ÞÑ FpSVq, where SVis the one-point compactification of V .In this paper, we give a comparison of these two towers and show that when F isanalytic the towers agree up to weak equivalence. We include two main applications, oneof which gives as a corollary the convergence of the Weiss Taylor tower of BO. We alsolift the homotopy level tower comparison to a commutative diagram of Quillen functors,relating model categories for Goodwillie calculus and model categories for the orthogonal calculus.

The preparation of highly ordered single layer ZSM-5 coating on prefabricated stainless steel microchannels

An elegant way to prepare catalytically active microreactors is by applying a coating of zeolite crystals onto a metal microchannel structure. In this study the hydrothermal formation of ZSM-5 zeolitic coatings on AISI 316 stainless steel plates with a microchannel structure has been investigated at different synthesis mixture compositions. The procedures of coating and thermal treatment have also been optimized. Obtaining a uniform thickness of the coating within 0.5 mm wide microchannels requires a careful control of various synthesis variables. The role of these factors and the problems in the synthesis of these zeolitic coatings are discussed. In general, the synthesis is most sensitive to the H2O/Si ratio as well as to the orientation of the plates with respect to the gravity vector. Ratios of H2O/Si=130 and Si/template=13 were found to be optimal for the formation of a zeolitic film with a thickness of one crystal at a temperature of 130 degreesC and a synthesis time of about 35 h. At such conditions, ZSM-5 crystals were formed with a typical size of 1.5 mu mx1.5 mu mx1.0 mum and a very narrow (within 0.2 mum) crystal size distribution. The prepared samples proved to be active in the selective catalytic reduction (SCR) of NO with ammonia. The activity tests have been carried out in a plate-type microreactor. The microreactor shows no mass transfer limitations and a larger SCR reaction rate is observed in comparison with pelletized Ce-ZSM-5 catalysts; (C) 2001 Elsevier Science B.V. All rights reserved.

Mixing operators on spaces with weak topology

We prove that a continuous linear operator T on a topological vector space X with weak topology is mixing if and only if the dual operator T' has no finite dimensional invariant subspaces. This result implies the characterization of hypercyclic operators on the space $\omega$ due to Herzog and Lemmert and implies the result of Bayart and Matheron, who proved that for any hypercyclic operator T on $\omega$, $T\oplus T$ is also hypercyclic.