Vekua theory for the Helmholtz operator

Vekua operators map harmonic functions defined on domain in \mathbb R2R2 to solutions of elliptic partial differential equations on the same domain and vice versa. In this paper, following the original work of I. Vekua (Ilja Vekua (1907–1977), Soviet-Georgian mathematician), we define Vekua operators in the case of the Helmholtz equation in a completely explicit fashion, in any space dimension N ≥ 2. We prove (i) that they actually transform harmonic functions and Helmholtz solutions into each other; (ii) that they are inverse to each other; and (iii) that they are continuous in any Sobolev norm in star-shaped Lipschitz domains. Finally, we define and compute the generalized harmonic polynomials as the Vekua transforms of harmonic polynomials. These results are instrumental in proving approximation estimates for solutions of the Helmholtz equation in spaces of circular, spherical, and plane waves.

Operator space structure of JC*-triples and TROs, I

We embark upon a systematic investigation of operator space structure of JC*-triples via a study of the TROs (ternary rings of operators) they generate. Our approach is to introduce and develop a variety of universal objects, including universal TROs, by which means we are able to describe all possible operator space structures of a JC*-triple. Via the concept of reversibility we obtain characterisations of universal TROs over a wide range of examples. We apply our results to obtain explicit descriptions of operator space structures of Cartan factors regardless of dimension

On the operator space structure of Hilbert spaces

Operator spaces of Hilbertian JC∗ -triples E are considered in the light of the universal ternary ring of operators (TRO) introduced in recent work. For these operator spaces, it is shown that their triple envelope (in the sense of Hamana) is the TRO they generate, that a complete isometry between any two of them is always the restriction of a TRO isomorphism and that distinct operator space structures on a fixed E are never completely isometric. In the infinite-dimensional cases, operator space structure is shown to be characterized by severe and definite restrictions upon finite-dimensional subspaces. Injective envelopes are explicitly computed.

Deviant disabilities: the exclusion of drug and alcohol addiction from the Equality Act 2010

The Equality Act 2010, in keeping with the Disability Discrimination Act 1995, excludes those identified as drug and alcohol ‘addicted’ from the scope of provisions prohibiting discrimination against disabled people. This article addresses the significance of, and justification for, this exclusion. It begins with a legislative background to the relevant limitation and subsequently examines its rationale according to prevailing legal, medical and sociological discourses. The article then considers the relevance of the discussion for disability rights. Although ‘addiction’, or the preferred term, ‘substance dependence’, is classified as a disability for international systems of disease classification, the relevance of substance dependence for discussion on disability rights, and of disability for discussion on substance dependence, has largely escaped critical comment.

Universally reversible JC*-triples and operator spaces

Abstract. We prove that the vast majority of JC∗-triples satisfy the condition of universal reversibility. Our characterisation is that a JC∗-triple is universally reversible if and only if it has no triple homomorphisms onto Hilbert spaces of dimension greater than two nor onto spin factors of dimension greater than four. We establish corresponding characterisations in the cases of JW∗-triples and of TROs (regarded as JC∗-triples). We show that the distinct natural operator space structures on a universally reversible JC∗-triple E are in bijective correspondence with a distinguished class of ideals in its universal TRO, identify the Shilov boundaries of these operator spaces and prove that E has a unique natural operator space structure precisely when E contains no ideal isometric to a nonabelian TRO. We deduce some decomposition and completely contractive properties of triple homomorphisms on TROs.

Competitive exclusion by Bacillus subtilis spores of Salmonella enterica serotype Enteritidis and Clostridium perfringens in young chickens

Cost effective control of avian diseases and food borne pathogens remains a high priority for all sectors of the poultry industry with cleansing and disinfection, vaccination and competitive exclusion approaches being used widely. Previous studies showed that Bacillus subtilis PY79(hr) was an effective competitive exclusion agent for use in poultry to control avian pathogenic Escherichia coli serotype O78:K80. Here we report experiments that were undertaken to test the efficacy of B. subtilis PY79(hr) in the control of Salmonella enterica serotype Enteritidis and Clostridium perfringens in young chickens. To do this, 1-day-old and 20-day-old specific pathogen free (SPF) chicks were dosed with a suspension of B. subtilis spores prior to challenge with S. Enteritidis (S1400) and C. perfringens, respectively. For both challenge models, a single oral inoculum of 1 x 10(9) spores given 24 h prior to challenge was sufficient to suppress colonisation and persistence of both S. Enteritidis and C perfringens. In particular, the faecal shedding of S. Enteritidis, as measured by a semi-quantitative cloacal swabbing technique, was reduced significantly for the 36 days duration of the experiment. B. subtilis persisted in the intestine although with decreasing numbers over the same period. These data add further evidence that B. subtilis spores may be effective agents in the control of avian diseases and food borne pathogens.

In vivo characterization of Lactobacillus johnsonii FI9785 for use as a defined competitive exclusion agent against bacterial pathogens in poultry

Aims: To test the efficacy of Lactobacillus johnsonii FI9785 in reducing the colonization and shedding of Salmonella enterica serotype Enteritidis, Escherichia coli O78:K80 and Clostridium perfringens in poultry. Methods and Results: Specific pathogen-free chicks (1 day old) were dosed with a single oral inoculum of 1 x 10(9) CFU. Lactobacillus johnsonii FI9785 and 24 h later were challenged in separate experiments with S. Enteritidis (S1400, nal(r)) and E. coli O78:K80 (EC34195, nal(r)). There were no significant effects against S. Enteritidis whereas colonization of the small intestine by E. coli O78:K80 was reduced significantly. Both S. Enteritidis and E. coli colonized the caeca and colon to levels equivalent to control birds and there was no reduction in shedding as assessed by a semi-quantitative cloacal swabbing technique. Specific pathogen-free chicks (20 day old) were dosed with a single oral inoculum of 1 x 10(9) CFU L. johnsonii FI9785 and 24 h later were challenged with C. perfringens. A single oral dose of L. johnsonii FI9785 was sufficient to suppress all aspects of colonization and persistence of C. perfringens. Conclusions: Lactobacillus johnsonii FI9785 may be given to poultry for use as a competitive exclusion agent to control C. perfringens. Significance and Impact of the Study: Lactobacillus johnsonii FI9785 may be a valuable tool to control the endemic disease of necrotic enteritis, thereby reducing economic losses associated with reduced use of antimicrobials in the poultry industry.

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

Back to the margins in search of the core: "Foreign Land"'s geography of exclusion

The crisis of the national project in the early 1990s, caused by a short-lived but disastrous government, led Brazilian art cinema, for the first time, to look at itself as periphery and re-approach the old colonial center, Portugal. Terra estrangeira/Foreign Land (Walter Salles & Daniela Thomas, Brazil/Portugal, 1995), a film about Brazilian exiles in Portugal, is the best illustration of this perspective shift which provides a new sense of Brazil’s scale and position within a global context. Shot mainly on location in São Paulo, Lisbon and Cape Verde, it promotes the encounter of Lusophone peoples who find a common ground in their marginal situation. Rather than as a former empire, Portugal is defined by its situation at the edge of Europe and by beliefs such as Sebastianism, whose origins go back to the time when the country was dominated by Spain. As a result, notions of “core” or “center” are devolved to the realm of myth. The film’s carefully crafted dialogue combines Brazilian, Portuguese and Creole linguistic peculiarities into a common dialect of exclusion, while language puns trigger visual rhymes which refer back to the Cinema Novo (the Brazilian New Wave) repertoire and restage the imaginary of the discovery turned into unfulfilled utopia. The main characters also acquire historical resonances, as they are depicted as descendants of Iberian conquistadors turned into smugglers of precious stones in the present. Their activities define a circuit of international exchange which resonates with that of globalized cinema, a realm in which Foreign Land, made up of citations and homage to other cinemas, tries to retrieve a sense of belonging.

A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

Back to the margins in search of the core: foreign land's geography of exclusion

The crisis of the national project in the early 1990s, caused by a short-lived but disastrous government, led Brazilian art cinema, for the first time, to look at itself as periphery and re-approach the old colonial centre, Portugal. Terra estrangeira/Foreign Land (Walter Salles & Daniela Thomas, Brazil/Portugal, 1995), a film about Brazilian exiles in Portugal, is the best illustration of this perspective shift aimed at providing a new sense of Brazil’s scale and position within a global context. Shot mainly on location in São Paulo, Lisbon and Cape Verde, it promotes the encounter of Lusophone peoples who find a common ground in their marginal situation. Even Portugal is defined by its location at the edge of Europe and by beliefs such as Sebastianism, whose origins go back to the time when the country was dominated by Spain. As a result, notions of ‘core’ or ‘centre’ are devolved to the realm of myth. The film’s carefully crafted dialogues combine Brazilian, Portuguese and Creole linguistic peculiarities into a common dialect of exclusion, while language puns trigger visual rhymes which refer back to the Cinema Novo (the Brazilian New Wave) repertoire and restage the imaginary of the discovery turned into unfulfilled utopia. The main characters also acquire historical resonances, as they are depicted as descendants of Iberian conquistadors turned into smugglers of precious stones in the present. Their activities define a circuit of international exchange which resonates with that of globalized cinema, a realm in which Foreign Land, made up of citations and homage to other cinemas, tries to retrieve a sense of belonging.

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.