Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008)

This book is a collection of articles devoted to the theory of linear operators in Hilbert spaces and its applications. The subjects covered range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity; the stability of numerical methods is also discussed. Many of the articles deal with spectral problems for not necessarily selfadjoint operators. Some of the articles are surveys outlining the current state of the subject and presenting open problems.

Preparation and magnetic properties of La–Mn and La–Co doped barium hexaferrites prepared via an improved co-precipitation/molten salt method

LaMn and LaCo doped barium hexaferrites of formula Ba(1-x)LaxFe(12-x)MxO19 (M=Mn, Co) (x=0.05 to 0.40) were prepared with an improved co-precipitation/molten salt method. For the synthesis, aqueous solutions of the appropriate metal chlorides were prepared in the ratio required except that the initial mole ratio of Fe and dopants to Ba was chosen to be 11:1, and then mixed with excess Na2CO3. The solutions were then cooled, filtered off, dried, then mixed with KCl flux, and heated at 450 degrees C and for 2 h. The temperature was then raised to 950 degrees C and kept for 4 h, then cooled. This new synthesis method, which employs a lower temperature and shorter reaction time, gives products with improved crystallinity and purity while the saturation magnetization and coercivity values are comparable with those synthesized via the high temperature method.

Minimum jerk trajectory control for rehabilitation and haptic applications

Smooth trajectories are essential for safe interaction in between human and a haptic interface. Different methods and strategies have been introduced to create such smooth trajectories. This paper studies the creation of human-like movements in haptic interfaces, based on the study of human arm motion. These motions are intended to retrain the upper limb movements of patients that lose manipulation functions following stroke. We present a model that uses higher degree polynomials to define a trajectory and control the robot arm to achieve minimum jerk movements. It also studies different methods that can be driven from polynomials to create more realistic human-like movements for therapeutic purposes.

Gene-chip technology and its applications

Gene Chips are finding extensive use in animal and plant science. Generally microarrays are of two kind, cDNA or oligonucleotide. cDNA microarrays were developed at Stanford University, whereas oligonucleotide were developed by Affymetrix. The construction of cDNA or oligonucleotide on a glass slide helps to compare the gene expression level of treated and control samples by labeling mRNA with green (Cy3) and red (Cy5) dyes. The hybridized gene chip emit fluorescence whose intensity and colour can be measured. RNA labeling can be done directly or indirectly. Indirect method involves amino allyle modified dUTP instead of pre-labelled nucleotide. Hybridization of gene chip generally occurs in a minimum volume possible and to ensure the hetroduplex formation, a ten fold more DNA is spotted on slide than in the solutions. A confocal or semi confocal laser technologies coupled with CCD camera are used for image acquisition. For standardization, house keeping genes are used or cDNA are spotted in gene chip that are not present in treated or control samples. Moreover, statistical analysis (image analysis) and cluster analysis softwares have been developed by Stanford University. The gene-chip technology has many applications like expression analysis, gene expression signatures (molecular phenotypes) and promoter regulatory element co-expression.

ERP correlates of shared control mechanisms involved in saccade preparation and in covert attention

We investigated whether attention shifts and eye movement preparation are mediated by shared control mechanisms, as claimed by the premotor theory of attention. ERPs were recorded in three tasks where directional cues presented at the beginning of each trial instructed participants to direct their attention to the cued side without eye movements (Covert task), to prepare an eye movement in the cued direction without attention shifts (Saccade task) or both (Combined task). A peripheral visual Go/Nogo stimulus that was presented 800 ms after cue onset signalled whether responses had to be executed or withheld. Lateralised ERP components triggered during the cue–target interval, which are assumed to reflect preparatory control mechanisms that mediate attentional orienting, were very similar across tasks. They were also present in the Saccade task, which was designed to discourage any concomitant covert attention shifts. These results support the hypothesis that saccade preparation and attentional orienting are implemented by common control structures. There were however systematic differences in the impact of eye movement programming and covert attention on ERPs triggered in response to visual stimuli at cued versus uncued locations. It is concluded that, although the preparatory processes underlying saccade programming and covert attentional orienting may be based on common mechanisms, they nevertheless differ in their spatially specific effects on visual information processing.

Manual response preparation and saccade programming are linked to attention shifts: ERP evidence for covert attentional orienting and spatially specific modulations of visual processing

The premotor theory of attention claims that attentional shifts are triggered during response programming, regardless of which response modality is involved. To investigate this claim, event-related brain potentials (ERPs) were recorded while participants covertly prepared a left or right response, as indicated by a precue presented at the beginning of each trial. Cues signalled a left or right eye movement in the saccade task, and a left or right manual response in the manual task. The cued response had to be executed or withheld following the presentation of a Go/Nogo stimulus. Although there were systematic differences between ERPs triggered during covert manual and saccade preparation, lateralised ERP components sensitive to the direction of a cued response were very similar for both tasks, and also similar to the components previously found during cued shifts of endogenous spatial attention. This is consistent with the claim that the control of attention and of covert response preparation are closely linked. N1 components triggered by task-irrelevant visual probes presented during the covert response preparation interval were enhanced when these probes were presented close to cued response hand in the manual task, and at the saccade target location in the saccade task. This demonstrates that both manual and saccade preparation result in spatially specific modulations of visual processing, in line with the predictions of the premotor theory.

An unexpected photoadduct of N-carbomethoxymethylpyrrolidine with a chiral butenolide and benzophenone: X-ray structure and synthetic utility

The regio- and stereoselective photoinduced addition of N-carbomethoxymethylpyrrolidine to 5(S)-tert-butyldimethylsiloxymethyl-furan-2(5H)-one in the presence of benzophenone yields 3(R)-[N-(diphenylhydroxymethyl)carbo methoxymethylpyrrolidin-2′-yl]-4(S)-tert-butyldimethylsiloxymethyl)-butan-4-olides (epimeric at C-2′), and we report the X-ray structure of the major adduct together with its conversion into the 1-azabicyclo[4.3.0]-nonane ring system.

Preparation and magnetic properties of barium ferrites substituted with manganese, cobalt, and tin

Barium ferrites substituted by Mn–Sn, Co–Sn, and Mn–Co–Sn with general formulae BaFe12−2xMnxSnxO19 (x=0.2–1.0), BaFe12−2xCoxSnxO19 (x=0.2–0.8), and BaFe12−2xCox/2Mnx/2SnxO19 (x=0.1–0.6), respectively, have been prepared by a previously reported co-precipitation method. The efficiency of the method was refined by lowering the reaction temperature and shortening the required reaction time, due to which crystallinity improved and the value of saturated magnetization increased as well. Low coercivity temperature coefficients, which are adjustable by doping, were achieved by Mn–Sn and Mn–Co–Sn doping. Synthesis efficiency and the effect of doping are discussed taking into account accumulated data concerning the synthesis and crystal structure of ferrites.

Community engagement and social organization: introducing concepts, policy and practical applications

This chapter provides an introductory overview of how the term ‘community’ has been conceptualized in sociological literatures, noting that there remains considerable uncertainty with regard to the way in which communities could or should be defined. The chapter examines the salience of underlying concepts of social organization that can shape and influence the extent to which programmes of engagement are likely to be successful. Drawing on recent empirical work some of the key opportunities and challenges for local government in translating the concepts into practice are considered.