On the spectrum of frequently hypercyclic operators

A bounded linear operator $T$ on a Banach space $X$ is called frequently hypercyclic if there exists $x\in X$ such that the lower density of the set $\{n\in\N:T^nx\in U\}$ is positive for any non-empty open subset $U$ of $X$. Bayart and Grivaux have raised a question whether there is a frequently hypercyclic operator on any separable infinite dimensional Banach space. We prove that the spectrum of a frequently hypercyclic operator has no isolated points. It follows that there are no frequently hypercyclic operators on all complex and on some real hereditarily indecomposable Banach spaces, which provides a negative answer to the above question.

Threshold In School – As Event And Place For The Autism Spectrum Disorder Pupil

As architects and designers we have a responsibility to provide an inclusive built environment. For the Autistic Spectrum Disorder (ASD) sufferer however, the built environment can be a frightening and confusing place, difficult to negotiate and tolerate. The challenge of integrating more fully into society is denied by an alienating built environment. This barrier can be magnified for ASD pupils in a poorly designed school, where their environment can further distance them from learning. Instead, if more at ease in their surroundings, in an ASD friendly environment, the ASD pupil stands a greater chance of doing better.

Whilst researchers have looked at the classroomenvironment, the transition of classroom to corridor andbeyond has so far been largely ignored. However, theneed for a well-considered threshold between class andcorridor needs to be considered. In this regard, threshold is much more than a doorway, but instead an event that demands a carefully considered place. The following paper firstly outlines why threshold as place andevent for the ASD pupil should be given consideration. It then goes onto highlight, through case studies in anIrish context, the opportunities for aiding the ASD pupil integrating in a mainstream school environment throughsensitive use of threshold. Finally it highlights inconclusion, some of the benefits for an enriched school environment for all pupils, if considering threshold as design generator.The objective is straightforward. By increasing awareness of the relationship between the ASD child and the built environment it will hopefully facilitate greater inclusion of the ASD pupil into mainstream education and society at large.

Far field subwavelength source resolution using Phase Conjugating Lens Assisted With Evanescent-to-Propagating Spectrum Conversion

The imaging properties of a phase conjugating lens operating in the far field zone of the imaged source and augmented with scatterers positioned in the source near field region are theoretically studied in this paper. The phase conjugating lens consists of a double sided 2D assembly of straight wire elements, individually interconnected through phase conjugation operators. The scattering elements are straight wire segments which are loaded with lumped impedance loads at their centers. We analytically and numerically analyze all stages of the imaging process; i) evanescent-to-propagating spectrum conversion; ii) focusing properties of infinite or finite sized phase conjugating lens; iii) source reconstruction upon propagating-to-evanescent spectrum conversion. We show that the resolution that can be achieved depends critically on the separation distance between the imaged source and scattering arrangement, as well as on the topology of the scatterers used. Imaged focal widths of up to one-seventh wavelength are demonstrated. The results obtained indicate the possibility of such an arrangement as a potential practical means for realising using conventional materials devices for fine feature extraction by electromagnetic lensing at distances remotely located from the source objects under investigation

On the Performance of Eigenvalue-Based Cooperative Spectrum Sensing for Cognitive Radio

In this paper, the distribution of the ratio of extreme eigenvalues of a complex Wishart matrix is studied in order to calculate the exact decision threshold as a function of the desired probability of false alarm for the maximum-minimum eigenvalue (MME) detector. In contrast to the asymptotic analysis reported in the literature, we consider a finite number of cooperative receivers and a finite number of samples and derive the exact decision threshold for the probability of false alarm. The proposed exact formulation is further reduced to the case of two receiver-based cooperative spectrum sensing. In addition, an approximate closed-form formula of the exact threshold is derived in terms of a desired probability of false alarm for a special case having equal number of receive antennas and signal samples. Finally, the derived analytical exact decision thresholds are verified with Monte-Carlo simulations. We show that the probability of detection performance using the proposed exact decision thresholds achieves significant performance gains compared to the performance of the asymptotic decision threshold.

High-velocity features: A ubiquitous property of Type Ia supernovae

Evidence of high-velocity features (HVFs) such as those seen in the near-maximum spectra of some Type Ia supernovae (SNe Ia; e. g., SN 2000cx) has been searched for in the available SN Ia spectra observed earlier than 1 week before B maximum. Recent observational efforts have doubled the number of SNe Ia with very early spectra. Remarkably, all SNe Ia with early data ( seven in our Research Training Network sample and 10 from other programs) show signs of such features, to a greater or lesser degree, in Ca II IR and some also in the Si II lambda 6355 line. HVFs may be interpreted as abundance or density enhancements. Abundance enhancements would imply an outer region dominated by Si and Ca. Density enhancements may result from the sweeping up of circumstellar material (CSM) by the highest velocity SN ejecta. In this scenario, the high incidence of HVFs suggests that a thick disk and/or a high-density companion wind surrounds the exploding white dwarf, as may be the case in single degenerate systems. Large-scale angular fluctuations in the radial density and abundance distribution may also be responsible: this could originate in the explosion and would suggest a deflagration as the more likely explosion mechanism. CSM interaction and surface fluctuations may coexist, possibly leaving different signatures on the spectrum. In some SNe, the HVFs are narrowly confined in velocity, suggesting the ejection of blobs of burned material.

Motor Skills in Children Aged 7–10 Years, Diagnosed with Autism Spectrum Disorder

This study used the Movement Assessment Battery for Children (M-ABC2) to assess the level of motor skill in children aged 7-10 years with autism (n=18) and compared their performance to two groups of age-matched typically developing children; a receptive vocabulary matched group (n=19) and a nonverbal IQ matched group (n=22). Although the results support previous work, as indicated by a significant general motor impairment in the group with autism, a sub-analysis of the M-ABC2 revealed that there were only 2 out of 8 subcomponent skills which showed universally significant specific deficits for the autism group; namely catching a ball and static balance. These results suggest that motor skill deficits associated with autism may not be pervasive but more apparent in activities demanding complex, interceptive actions or core balance ability.

School as ‘Micro-city’ for the Autism Spectrum Disorder (ASD) Pupil

As architects and designers we have a responsibility to provide an inclusive built environment. For the person with Autistic Spectrum Disorder (ASD) however, the built environment can be a frightening and confusing place, difficult to negotiate and tolerate. The challenge of integrating more fully into society is denied by both having difficulty in communication and in an alienating built environment. The following paper therefore firstly outlines the challenge when designing for those with ASD. It then illustrates, by critically examining the school as a 'micro-city' (Hertzberger 2008) that a voice can be given to those with ASD. It then goes onto highlight, through two case studies in an Irish context, some of the lessons that can be learnt from pupils with ASD that are applicable to the city beyond. Finally in conclusion it suggests some of the benefits for an enriched built environment for all, when listening to the pupil with ASD. The objective is twofold; firstly to gain a better understanding of the needs of those with ASD and secondly, to ascertain what can be learnt from those with ASD that can challenge our perception of not just school, but also of the city.