Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

On the solvability of Hamilton's equations in Hilbert spaces

We construct a bounded function $H : l_2\times l_2 \to R$ with continuous Frechet derivative such that for any $q_0\in l_2$ the Cauchy problem $\dot p= - {\partial H\over\partial q}$, $\dot q={\partial H\over\partial p}$, $p(0) = 0$, q(0) = q_0$ has no solutions in any neighborhood of zero in R.

Three constructive examples of separable pre-Hilbert spaces nonisomorphic to their closed hyperplanes

An example of a sigma -compact infinite-dimensional pre-Hilbert space H is constructed such that any continuous linear operator T: H --> H is of the form T = lambdaI + F for some lambda is an element of R and for a finite-dimensional continuous linear operator F. A class of simple examples of pre-Hilbert spaces nonisomorphic to their closed hyperplanes is given. A sigma -compact pre-Hilbert space H isomorphic to H x R x R and nonisomorphic to H x R is also constructed.

An infinite-dimensional separable pre-Hilbert space non-homeomorphic to any of its closed hyperplanes

An example is constructed of an infinite-dimensional separable pre-Hilbert space non-homeomorphic to any of its closed hyperplanes.

The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

James Anderson's Political Economy--His Influence on Smith and Malthus

James Anderson's powerful critique of Adam Smith's position on the corn export bounty was published in 1777. It focuse d on Smith's proposition that the bounty could not lead to increased corn production because it could not increase corn's real price. Smit h's response to the critique is traced in later editions of Wealth of Nations. While Anderson's critique of Smith influenced Thomas Malthu s's writings from 1803 onwards, his theory of differential rent did n ot influence Malthus at this stage. An examination of the evolution o f Malthus's ideas on rent between 1803 and 1815, however, indicates t hat Malthus knew and used Anderson's work on rent.

Michel Foucault and Dorothy Smith in Case File Research: Strange Bedfellows or Complimentary Thinkers?

The aim of this article is to provide an exploration how the work of two theorists with notably different stances could be used effectively to enhance critical research methods in relation to the history of child welfare social work. The design and implementation of child welfare policies, practices and discourses could considerably benefit from a more historically well grounded scholarship that enables actors to connect their present concerns with the broader historical dynamics of social regulation. The article reports on how the work of Michel Foucault and Dorothy E. Smith might be considered in parallel as two different perspectives to the same scene in time and place. The differences and similarities in their approaches are explored with an emphasis on concepts most relevant to researching child welfare archives including discourse, text, the subject and power-knowledge. The article concludes with a commentary on further development to take forward this methodological analysis.

Analysing admittance of obstacles in evanescent waveguide using the Imaginary Smith Chart

We present a technique, using the Imaginary Smith Chart, for determining the admittance of obstacles introduced into evanescent waveguide. The admittance of an inductive iris, capacitive iris, capacitive post, variable width strip and length of evanescent waveuide are investigated. © 2012 IEEE.

Increased Bandwidth Evanescent Open-Ended Waveguide Antenna Design Using the Imaginary Smith Chart

We present a novel antenna matching technique that uses the Imaginary Smith Chart to permit wideband matching of an evanescent open-ended waveguide antenna using a dielectric sheet air-spaced from the aperture. The fabricated antenna design is demonstrated to have a measured bandwidth of 24%, from 2.13–2.7 GHz, for reflection coefficient $qquad{<} -!!10~{rm dB}$ , with 2.725 GHz waveguide cutoff. The antenna's maximum aperture dimension is ${< 0.5}lambda_{0}$ at the upper frequency in the bandwidth and so it is suitable for use in a wide angle scanning phased array

Prevalence, phenomenology, aetiology and predictors of challenging behaviour in Smith-Magenis syndrome

Background

The prevalence, phenomenology aetiology and correlates of four forms of challenging behaviour in 32 children and adults with Smith-Magenis syndrome (SMS) were investigated.

Methods

Cognitive assessments, questionnaires and semi-structured interviews were used to gather data on intellectual disability, verbal and physical aggression, destructive behaviour and self-injury and on characteristics known to be associated with aggression.

Results

Aggression in SMS was more prevalent (87%), but not more severe than aggression in contrast groups. Aggressive behaviour was more frequently associated with environmental contingencies (e.g. attention, escape and access to tangibles) than self-injury and destructive behaviours. Severity of challenging behaviours was associated with high impulsivity.

Conclusion

Aggression is seen in the majority of people with SMS. Results suggest that behavioural disinhibition and operant social reinforcement are associated with the manifestation of aggression.