Paranormal operator on a Hilbert space

In this thesis an extensive study is made of the set P of all paranormal operators in B(H), the set of all bounded endomorphisms on the complex Hilbert space H. T ϵ B(H) is paranormal if for each z contained in the resolvent set of T, d(z, σ(T))//(T-zI)^-1 = 1 where d(z, σ(T)) is the distance from z to σ(T), the spectrum of T. P contains the set N of normal operators and P contains the set of hyponormal operators. However, P is contained in L, the set of all T ϵ B(H) such that the convex hull of the spectrum of T is equal to the closure of the numerical range of T. Thus, N≤P≤L.

If the uniform operator (norm) topology is placed on B(H), then the relative topological properties of N, P, L can be discussed. In Section IV, it is shown that: 1) N P and L are arc-wise connected and closed, 2) N, P, and L are nowhere dense subsets of B(H) when dim H ≥ 2, 3) N = P when dimH ˂ ∞ , 4) N is a nowhere dense subset of P when dimH ˂ ∞ , 5) P is not a nowhere dense subset of L when dimH ˂ ∞ , and 6) it is not known if P is a nowhere dense subset of L when dimH ˂ ∞.

The spectral properties of paranormal operators are of current interest in the literature. Putnam [22, 23] has shown that certain points on the boundary of the spectrum of a paranormal operator are either normal eigenvalues or normal approximate eigenvalues. Stampfli [26] has shown that a hyponormal operator with countable spectrum is normal. However, in Theorem 3.3, it is shown that a paranormal operator T with countable spectrum can be written as the direct sum, N ⊕ A, of a normal operator N with σ(N) = σ(T) and of an operator A with σ(A) a subset of the derived set of σ(T). It is then shown that A need not be normal. If we restrict the countable spectrum of T ϵ P to lie on a C²-smooth rectifiable Jordan curve G_o, then T must be normal [see Theorem 3.5 and its Corollary]. If T is a scalar paranormal operator with countable spectrum, then in order to conclude that T is normal the condition of σ(T) ≤ G_o can be relaxed [see Theorem 3.6]. In Theorem 3.7 it is then shown that the above result is not true when T is not assumed to be scalar. It was then conjectured that if T ϵ P with σ(T) ≤ G_o, then T is normal. The proof of Theorem 3.5 relies heavily on the assumption that T has countable spectrum and cannot be generalized. However, the corollary to Theorem 3.9 states that if T ϵ P with σ(T) ≤ G_o, then T has a non-trivial lattice of invariant subspaces. After the completion of most of the work on this thesis, Stampfli [30, 31] published a proof that a paranormal operator T with σ(T) ≤ G_o is normal. His proof uses some rather deep results concerning numerical ranges whereas the proof of Theorem 3.5 uses relatively elementary methods.

Living on the hyphen: diaspora, identity and memory in Jamaica Kincaids Annie John / Lucy and Esmeralda Santiagos When I was Puerto Rican / Almost a woman

Esta dissertação tem por objetivo investigar o desenvolvimento de identidades de sujeitos diaspóricos em formas de narrativas nas quais a memória tem um papel crucial. As autobiografias e os memoirs têm despertado a curiosidade de muitas pessoas interessadas nos processos de construção de identidade de indivíduos que vivem em realidades singulares e nos relatos que dão sobre suas próprias vidas. Assim, o crescente interesse em diásporas e nos decorrentes deslocamentos fragmentários, provocados pelo distanciamento de raízes individuais e pelo contato com diferentes códigos culturais, poderiam legitimar as narrativas autobiográficas como maneiras estratégicas de sintetizar os nichos de identificação de autores e autoras que experimentaram uma ruptura diaspórica. Desta forma, ao analisar estes tipos de narrativas, deve-se estar atento às especificidades de algumas escritoras que passaram por processos diaspóricos e a como elas recorreram as suas memórias pessoais para, em termos literários, expressar suas subjetividades. Considerando todas essas idéias, tenciono usar Annie John e Lucy, de Jamaica Kincaid e When I Was Puero Rican e Almost a Woman, de Esmeralda Santiago como fontes de análise e amostras do desenvolvimento de identidades diaspóricas em narrativas autobiográficas

Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices

B.M. Brown, M. Marletta, S. Naboko, I. Wood: Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices, J. London Math. Soc., June 2008; 77: 700-718. The full text of this article will be made available in this repository in June 2009 Sponsorship: EPSRC,INTAS

On the positivity of the Jansen-He? operator for arbitrary mass

Iantchenko, A.; Jakuba?a-Amundsen, D.H., (2003) 'On the positivity of the Jansen-He? operator for arbitrary mass', Annales of the Institute Henri Poincar? 4 pp.1083-1099 RAE2008

‘It was almost like the opposite of what I needed’: a qualitative exploration of client experiences of unhelpful therapy

Background: The issue of unhelpful and harmful therapy outcome has received an increasing amount of attention within the research literature in recent years. However, little research exists on the client's perspective of what constitutes unhelpful therapy. Aim: The aim of this study was to explore clients’ experiences of unhelpful therapy. Method: Semi-structured interviews were carried out with ten therapists who, as clients, experienced unhelpful therapy. Interview transcripts were analysed using interpretative phenomenological analysis. Findings: Participants recounted therapy episodes characterised by an absence of negotiation, collaboration and care; pivotal moments when they knew that they would not return; and ongoing negative effects. Conclusions: The findings of this study have implications for training and strategies for supporting clients who have been harmed by therapy.

Securing Bulk Content Almost for Free

Content providers often consider the costs of security to be greater than the losses they might incur without it; many view "casual piracy" as their main concern. Our goal is to provide a low cost defense against such attacks while maintaining rigorous security guarantees. Our defense is integrated with and leverages fast forward error correcting codes, such as Tornado codes, which are widely used to facilitate reliable delivery of rich content. We tune one such family of codes - while preserving their original desirable properties - to guarantee that none of the original content can b e recovered whenever a key subset of encoded packets is missing. Ultimately we encrypt only these key codewords (only 4% of all transmissions), making the security overhead negligible.

A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.

Expression of liver-specific member of the 3β-hydroxysteroid dehydrogenase family, an isoform possessing an almost exclusive 3-ketosteroid reductase activity

We have recently characterized two types of rat 3β-hydroxysteroid dehydrogenase/Δ5-Δ4 isomerase (3β-HSD) isoenzymes expressed in adrenals and gonads. In addition, we have cloned a third type of cDNA encoding a predicted type III 3β-HSD protein specifically expressed in the male rat liver which shares 80% similarity with the two other isoenzymes. Transient expression in human HeLa cells of the cDNAs reveals that the type III 3β-HSD protein does not display oxidative activity for the classical substrates of 3β-HSD, in contrast to the type I 3β-HSD isoenzyme. However, in the presence of NADH, type III isoenzyme, in common with the type I isoform, converts 5α-androstane-3,17-dione (A-dione) and 5α-dihydrotestosterone (DHT) to the corresponding 3β-hydroxysteroids. In fact, the type I and the type III isoenzymes have the same affinity for DHT with K(m) values of 5.05 and 6.16 μM, respectively. When NADPH is used as cofactor, the affinity for DHT of the type III isoform becomes higher than that of the type I isoform with K(m) values of 0.12 and 1.18 μM, respectively. The type III isoform is thus a 3-ketoreductase using NADPH as preferred cofactor which is responsible for the conversion of 3-keto-saturated steroids such as DHT and A-dione into less active steroids.

Operator non-availability periods

In the scheduling literature, the notion of machine non availability periods is well known, for instance for maintenance. In our case of planning chemical experiments, we have special periods (the week-ends, holidays, vacations) where the chemists are not available. However, human intervention by the chemists is required to handle the starting and termination of the experiments. This gives rise to a new type of scheduling problems, namely problems of finding schedules that respect the operator non availability periods. These problems are analyzed on a single machine with the makespan as criterion. Properties are described and performance ratios are given for list scheduling and other polynomial-time algorithms.