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.

On supercyclicity of operators from a supercyclic semigroup

We show that for every supercyclic strongly continuous operator
semigroup $\{T_t\}_{t\geq 0}$ acting on a complex $\F$-space, every
$T_t$ with $t>0$ is supercyclic. Moreover, the set of supercyclic
vectors of $T_t$ does not depend on the choice of $t>0$.

Cyclic behaviour of Volterra composition operators

We determine the cyclic behaviour of Volterra composition operators, which are defined as $(V_\phif)(x) =\int_0^{\phi(x)}f(t) dt$, $f ? L^p[0, 1]$, 1\leq p <\infty$,
where $?$ is a measurable self-map of [0, 1]. The cyclic behaviour of $V_\phi$ is essentially determined by the behaviour of the inducing symbol $\phi$ at 0 and at 1. As a particular result, we provide new examples of quasinilpotent supercyclic operators, which extend and complement previous ones of Hector Salas.

Hypercyclic tuples of operators on $C^n$ and $R^n$

A tuple $(T_1,\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\dots,T_n$ is dense in $X$. This concept was introduced by N.~Feldman, who have raised 7 questions on hypercyclic tuples. We answer those 4 of them, which can be dealt with on the level of operators on finite dimensional spaces. In
particular, we prove that the minimal cardinality of a hypercyclic tuple of operators on $\C^n$ (respectively, on $\R^n$) is $n+1$ (respectively, $\frac n2+\frac{5+(-1)^n}{4}$), that there are non-diagonalizable tuples of operators on $\R^2$ which possess an orbit being neither dense nor nowhere dense and construct a hypercyclic 6-tuple of operators on $\C^3$ such that every operator commuting with each member of the tuple is non-cyclic.

Hidden costs of control: four repetitions and an extension

We report four repetitions of Falk and Kosfeld's (Am. Econ. Rev. 96(5):1611-1630, 2006) low and medium control treatments with 476 subjects. Each repetition employs a sample drawn from a standard subject pool of students and demographics vary across samples. We largely confirm the existence of hidden costs of control but, contrary to the original study, hidden costs of control are usually not substantial enough to significantly undermine the effectiveness of economic incentives. Our subjects were asked, at the end of the experimental session, to complete a questionnaire in which they had to state their work motivation in hypothetical scenarios. Our questionnaires are identical to the ones administered in Falk and Kosfeld's (Am. Econ. Rev. 96(5):1611-1630, 2006) questionnaire study. In contrast to the game play data, our questionnaire data are similar to those of the original questionnaire study. In an attempt to solve this puzzle, we report an extension with 228 subjects where performance-contingent earnings are absent i.e. both principals and agents are paid according to a flat participation fee. We observe that hidden costs significantly outweigh benefits of control under hypothetical incentives.

Hypercyclic operators on countably dimensional spaces

According to Grivaux, the group GL(X) of invertible linear operators on a separable infinite dimensional Banach space X acts transitively on the set s (X) of countable dense linearly independent subsets of X. As a consequence, each A? s (X) is an orbit of a hypercyclic operator on X. Furthermore, every countably dimensional normed space supports a hypercyclic operator. Recently Albanese extended this result to Fréchet spaces supporting a continuous norm. We show that for a separable infinite dimensional Fréchet space X, GL(X) acts transitively on s (X) if and only if X possesses a continuous norm. We also prove that every countably dimensional metrizable locally convex space supports a hypercyclic operator.

Surgical technique:Complex glaucoma case requiring molteno drainage tube extension

A 42-year-old man has been under long-term follow-up since he was a child for congenital glaucoma and buphthalmos in both eyes. His left eye best corrected visual acuity (BCVA) was counting fingers, due to end-stage glaucoma. He was on maximal medical therapy with an intraocular pressure (IOP) maintained at mid to low twenties. His right eye, the only seeing eye, had a BCVA of 6/9. This eye had undergone multiple glaucoma laser and surgical procedures, including an initial first Molteno drainage device inserted superonasally that failed in April 2003 due to fibrotic membrane over the tube opening. As a result, he subsequently had a second Molteno drainage device inserted inferotemporally. To further maximize his vision he had an uncomplicated cataract extraction and intraocular lens implant in December 2004, after which he developed postoperative cystoid macular edema and corneal endothelial failure. He underwent a penetrating keratoplasty in the right eye thereafter in March 2007. After approximately a year, the second Molteno device developed drainage tube retraction, which was managed surgically to maintain optimum IOP in the right eye. His right eye vision to date is maintained at 6/12. © 2011 Mustafa and Azuara-Blanco.

Completely bounded disjointness preserving operators between Fourier algebras

In this paper, we characterize surjective completely bounded disjointness preserving linear operators on Fourier algebras of locally compact amenable groups. We show that such operators are given by weighted homomorphisms induced by piecewise affine proper maps. © 2011 Elsevier Inc.

The structure of compact disjointness preserving operators on continuous functions

Let T be a compact disjointness preserving linear operator from C0(X) into C0(Y), where X and Y are locally compact Hausdorff spaces. We show that T can be represented as a norm convergent countable sum of disjoint rank one operators. More precisely, T = Snd ?hn for a (possibly finite) sequence {xn }n of distinct points in X and a norm null sequence {hn }n of mutually disjoint functions in C0(Y). Moreover, we develop a graph theoretic method to describe the spectrum of such an operator

NFA decomposition and multiprocessing architecture for parallel regular expression processing

This work presents a novel algorithm for decomposing NFA automata into one-state-active modules for parallel execution on Multiprocessor Systems on Chip (MP-SoC). Furthermore, performance related studies based on a 16-PE system for Snort, Bro and Linux-L7 regular expressions are presented. ©2009 IEEE.

Homologous size-extension of hybrid vanadate capsules – solid state structures, solution stability and surface deposition

The dimensions and cavity sizes of the molecular capsules with the general formula [V₁₀O₁₈L₄]¹⁰⁻ can be controlled modularly through the nature of the bifunctional, rigid organophosphonate ligands L¹ and L² (L¹ = bis(4-phosphonatophenyl)ethyne and L² = bis(4-phosphonatophenyl)butadiyne); the solution stability of the molecular entities as demonstrated by ESI-MS studies permits their assembly on the Au(111) surface on a sub-monolayer scale giving rise to a 2D supramolecular structure that is comparable to the packing arrangements of the capsules in the crystal structures.