Compact operators without extended eigenvalues

A complex number lambda is called an extended eigenvalue of a bounded linear operator T on a Banach space B if there exists a non-zero bounded linear operator X acting on B such that XT = lambda TX. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set {1}.

Effects of Constraint Errors on Parallel Manipulators with Decoupled Motion

From perspective of structure synthesis, certain special geometric constraints, such as joint axes intersecting at one point or perpendicular to each other, are necessary in realizing the end-effector motion of kinematically decoupled parallel manipulators (PMs) along individual motion axes. These requirements are difficult to achieve in the actual system due to assembly errors and manufacturing tolerances. Those errors that violate the geometric constraint requirements are termed “constraint errors”. The constraint errors usually are more troublesome than other manipulator errors because the decoupled motion characteristics of the manipulator may no longer exist and the decoupled kinematic models will be rendered useless due to these constraint errors. Therefore, identification and prevention of these constraint errors in initial design and manufacturing stage are of great significance. In this article, three basic types of constraint errors are identified, and an approach to evaluate the effects of constraint errors on decoupling characteristics of PMs is proposed. This approach is illustrated by a 6-DOF PM with decoupled translation and rotation. The results show that the proposed evaluation method is effective to guide design and assembly.

'Last Vegas?'

This article, and the research out of which it springs, has a number of points of origin; it may also have more than one point of conclusion even as it argues that the current manifestation of Las Vegas could well be read as its last. This is not to say that Las Vegas will cease to create its new versions of itself; after all, this is one of the main sustaining factors of Las Vegas’ success in the last two decades as a new Strip on Las Vegas Boulevard has arisen from the demolitions and redesigns of the original Las Vegas Strip of the 1950s and 1960s. What is argued for here is a reading of Vegas as a terminal point within American culture and particularly within its visual realms. Las Vegas’ place within the dynamics of American visual and exhibition culture comes as the latest in a sequence which, since the nineteenth century, has included among its manifestations World’s Fairs, side shows, freak shows and travelling carnivals. America’s experiments in the visual domain have been updated in both the twentieth- and twenty-first centuries in a variety of spectacular forms and entertainment zones (Disneyland, EPCOT, the new Las Vegas). Vegas is the ultimate incarnation of a carnivalised display culture, the city’s casino Strip reclothed primarily as a theme park for digital camera-toting tourists than as a resort for dedicated gamblers. The possibility that the current incarnation of Las Vegas of late 2009 and 2010 will be the last Vegas hovers as a spectral remnant of the economic downturn and financial collapse of 2008, marked by the unfinished skeletons of projected new casino hotels on Las Vegas Boulevard and by a sudden reversal of fortune for the nation’s favourite gaming location.

Electronic Circuit Packages

This invention relates to electronic circuit packages designed to hold high frequency circuits operating particularly, but not exclusively, in the microwave, millimeter wave, and sub-millimeter wave bands. The invention provides a package incorporating a cavity in a material for containment of the circuits, wherein the package further incorporates at least one conductive surface mounted on an inner surface extending into the cavity, the conductivity thereof being adapted to be at least partially absorbent to electromagnetic radiation. The conductive surface according to the present invention will tend to attenuate electromagnetic radiation present within the cavity, and so help to prevent undesired coupling from one point to another within the cavity. The conductivity of the conductive material is preferably arranged to match the impedance of the radiation mode estimated or computed to be present within the cavity.

Time-Dependent Density Diagnostics of Solar Flare Plasmas Using SDO/EVE

Temporally resolved electron density measurements of solar flare plasmas are presented using data from the EUV Variability Experiment (EVE) on board the Solar Dynamics Observatory. The EVE spectral range contains emission lines formed between 104 and 107 K, including transitions from highly ionized iron (gsim10 MK). Using three density-sensitive Fe XXI ratios, peak electron densities of 1011.2-1012.1 cm–3 were found during four X-class flares. While previous measurements of densities at such high temperatures were made at only one point during a flaring event, EVE now allows the temporal evolution of these high-temperature densities to be determined at 10 s cadence. A comparison with GOES data revealed that the peak of the density time profiles for each line ratio correlated well with that of the emission measure time profile for each of the events studied.

Phosphoethanolamine modification of lipid A in colistin-resistant variants of Acinetobacter baumannii mediated by the pmrAB two-component regulatory system

Colistin resistance is rare in Acinetobacter baumannii, and little is known about its mechanism. We investigated the role of PmrCAB in this trait, using (i) resistant and susceptible clinical strains, (ii) laboratory-selected mutants of the type strain ATCC 19606 and of the clinical isolate ABRIM, and (iii) a susceptible/resistant pair of isogenic clinical isolates, Ab15/133 and Ab15/132, isolated from the same patient. pmrAB sequences in all the colistin-susceptible isolates were identical to reference sequences, whereas resistant clinical isolates harbored one or two amino acid replacements variously located in PmrB. Single substitutions in PmrB were also found in resistant mutants of strains ATCC 19606 and ABRIM and in the resistant clinical isolate Ab15/132. No mutations in PmrA or PmrC were found. Reverse transcriptase (RT)-PCR identified increased expression of pmrA (4- to 13-fold), pmrB (2- to 7-fold), and pmrC (1- to 3-fold) in resistant versus susceptible organisms. Matrix-assisted laser desorption ionization-time of flight (MALDI-TOF) mass spectrometry showed the addition of phosphoethanolamine to the hepta-acylated form of lipid A in the resistant variants and in strain ATCC 19606 grown under low-Mg induction conditions. pmrB gene knockout mutants of the colistin-resistant ATCC 19606 derivative showed >100-fold increased susceptibility to colistin and 5-fold decreased expression of pmrC; they also lacked the addition of phosphoethanolamine to lipid A. We conclude that the development of a moderate level of colistin resistance in A. baumannii requires distinct genetic events, including (i) at least one point mutation in pmrB, (ii) upregulation of pmrAB, and (iii) expression of pmrC, which lead to addition of phosphoethanolamine to lipid A. Copyright © 2011, American Society for Microbiology. All Rights Reserved.

"...and they won land among the Picts by friendly treaty or the sword": How a re-examination of early historical sources and an analysis of early medieval settlement in north Co. Antrim confirms the validity of traditional accounts of Dál Riatic migration to Scotland from Ulster

Much recent scholarship has been critical of the concept of a Dál Riatic migration to, or colonisation of, Argyll. Scepticism of the accuracy of the early medieval accounts of this population movement, arguing that these are late amendments to early sources, coupled with an apparent lack of archaeological evidence for such a migration have led to its rejection. It is argued here, however, that this rejection has been based on too narrow a reading of historical sources and that there are several early accounts which, while differing in detail, agree on one point of substance, that the origin of Scottish Dál Riata lies in Ireland. Also, the use of archaeological evidence to suggest no migration to Argyll by the Dál Riata is flawed, misunderstanding the nature of early migrations and how they might be archaeologically identified, and it's proposed that there is actually quite a lot of evidence for migration to Argyll by the Dál Riata, in the form of settlement and artefactural evidence, but that it is to be found in Ireland through the mechanism of counterstream migration, rather than in Scotland.

Rapid, simple method for determining the porosity of mesoporous TiO2 films using a quartz crystal microbalance (QCM)

Two different mesoporous films of TiO2 were coated onto a QCM disc and fired at 450o C for 30 min. The first film was derived from a sol-gel paste that was popular in the early days of dye-sensitised solar cell, i.e. dssc, research, a TiO2(sg) film. The other was a commercial colloidal paste used to make examples of the current dssc cell; a TiO2(ds) film. A QCM was used to determine the mass of the TiO2 film deposited on each disc and the increase in the mass of the film when immersed in water/glycerol solutions with wt% values spanning the range 0-70%. The results of this work reveal that with both TiO2 mesoporous films the solution fills the film's pores and acts as a rigid mass, thereby allowing the porosity of each film to be calculated as: 59.1% and 71.6% for the TiO2(sg) and TiO2(ds) films, respectively. These results, coupled with surface area data, allowed the pore radii of the two films to be calculated as: 9.6 and 17.8 nm, respectively. This method is then simplified further, to just a few frequency measurements in water and only air to reveal the same porosity values. The value of the latter ‘one point’ method for making porosity measurements is discussed briefly.

Accountability for Forced Displacement in Democratic Republic of Congo and Uganda before the International Criminal Court

This article examines the challenges of investigating and prosecuting forced displacement in the Central African countries of Democratic Republic of Congo and Uganda, where higher loss of life was caused by forced displacement, than by any other. In the Democratic Republic of Congo, armed groups intentionally attacked civilian populations displacing them from their homes, to cut them off from food and medical supplies. In Northern Uganda, the government engaged in a forced displacement policy as part of its counter-insurgency against the Lord’s Resistance Army, driving the civilian population into “protected villages”, where at one point the weekly death toll was over 1,000 in these camps. This article critically evaluates how criminal responsibility can be established for forced displacement and alternative approaches to accountability through reparations.

Comparing the orthogonal and homotopy functor calculi

Goodwillie’s homotopy functor calculus constructs a Taylor tower of approximations toF , often a functor from spaces to spaces. Weiss’s orthogonal calculus provides a Taylortower for functors from vector spaces to spaces. In particular, there is a Weiss towerassociated to the functor V ÞÑ FpSVq, where SVis the one-point compactification of V .In this paper, we give a comparison of these two towers and show that when F isanalytic the towers agree up to weak equivalence. We include two main applications, oneof which gives as a corollary the convergence of the Weiss Taylor tower of BO. We alsolift the homotopy level tower comparison to a commutative diagram of Quillen functors,relating model categories for Goodwillie calculus and model categories for the orthogonal calculus.

An exactly solvable four transition point model

Heavy particle collisions, in particular low-energy ion-atom collisions, are amenable to semiclassical JWKB phase integral analysis in the complex plane of the internuclear separation. Analytic continuation in this plane requires due attention to the Stokes phenomenon which parametrizes the physical mechanisms of curve crossing, non-crossing, the hybrid Nikitin model, rotational coupling and predissociation. Complex transition points represent adiabatic degeneracies. In the case of two or more such points, the Stokes constants may only be completely determined by resort to the so-called comparison- equation method involving, in particular, parabolic cylinder functions or Whittaker functions and their strong-coupling asymptotics. In particular, the Nikitin model is a two transition-point one-double-pole problem in each half-plane corresponding to either ingoing or outgoing waves. When the four transition points are closely clustered, new techniques are required to determine Stokes constants. However, such investigations remain incomplete, A model problem is therefore solved exactly for scattering along a one-dimensional z-axis. The energy eigenvalue is b(2)-a(2) and the potential comprises -z(2)/2 (parabolic) and -a(2) + b(2)/2z(2) (centrifugal/centripetal) components. The square of the wavenumber has in the complex z-plane, four zeros each a transition point at z = +/-a +/- ib and has a double pole at z = 0. In cases (a) and (b), a and b are real and unitarity obtains. In case (a) the reflection and transition coefficients are parametrized by exponentials when a(2) + b(2) > 1/2. In case (b) they are parametrized by trigonometrics when a(2) + b(2) <1/2 and total reflection is achievable. In case (c) a and b are complex and in general unitarity is not achieved due to loss of flux to a continuum (O'Rourke and Crothers, 1992 Proc. R. Sec. 438 1). Nevertheless, case (c) coefficients reduce to (a) or (b) under appropriate limiting conditions. Setting z = ht, with h a real constant, an attempt is made to model a two-state collision problem modelled by a pair of coupled first-order impact parameter equations and an appropriate (T) over tilde-tau relation, where (T) over tilde is the Stueckelberg variable and tau is the reduced or scaled time. The attempt fails because (T) over tilde is an odd function of tau, which is unphysical in a real collision problem. However, it is pointed out that by applying the Kummer exponential model to each half-plane (O'Rourke and Crothers 1994 J. Phys. B: At. Mel. Opt. Phys. 27 2497) the current model is in effect extended to a collision problem with four transition points and a double pole in each half-plane. Moreover, the attempt in itself is not a complete failure since it is shown that the result is a perfect diabatic inelastic collision for a traceless Hamiltonian matrix, or at least when both diagonal elements are odd and the off-diagonal elements equal and even.

Existence of multibreathers in one-dimensional Debye crystals

The existence of highly localized multisite oscillatory structures (discrete multibreathers) in a nonlinear Klein-Gordon chain which is characterized by an inverse dispersion law is proven and their linear stability is investigated. The results are applied in the description of vertical (transverse, off-plane) dust grain motion in dusty plasma crystals, by taking into account the lattice discreteness and the sheath electric and/or magnetic field nonlinearity. Explicit values from experimental plasma discharge experiments are considered. The possibility for the occurrence of multibreathers associated with vertical charged dust grain motion in strongly coupled dusty plasmas (dust crystals) is thus established. From a fundamental point of view, this study aims at providing a rigorous investigation of the existence of intrinsic localized modes in Debye crystals and/or dusty plasma crystals and, in fact, suggesting those lattices as model systems for the study of fundamental crystal properties.

Bimanual aiming and overt attention: one law for two hands

Reaching to interact with an object requires a compromise between the speed of the limb movement and the required end-point accuracy. The time it takes one hand to move to a target in a simple aiming task can be predicted reliably from Fitts' law, which states that movement time is a function of a combined measure of amplitude and accuracy constraints (the index of difficulty, ID). It has been assumed previously that Fitts' law is violated in bimanual aiming movements to targets of unequal ID. We present data from two experiments to show that this assumption is incorrect: if the attention demands of a bimanual aiming task are constant then the movements are well described by a Fitts' law relationship. Movement time therefore depends not only on ID but on other task conditions, which is a basic feature of Fitts' law. In a third experiment we show that eye movements are an important determinant of the attention demands in a bimanual aiming task. The results from the third experiment extend the findings of the first two experiments and show that bimanual aiming often relies on the strategic co-ordination of separate actions into a seamless behaviour. A number of the task specific strategies employed by the adult human nervous system were elucidated in the third experiment. The general strategic pattern observed in the hand trajectories was reflected by the pattern of eye movements recorded during the experiment. The results from all three experiments demonstrate that eye movements must be considered as an important constraint in bimanual aiming tasks.

Dynamics of nonlinearly coupled magnetic-field-aligned electromagnetic electron-cyclotron waves near the zero-group-dispersion point in magnetized plasmas

The nonlinear coupling between two magnetic-field-aligned electromagnetic electron-cyclotron (EMEC) waves in plasmas is considered. Evaluating the ponderomotive coupling between the EMEC waves and quasistationary plasma density perturbations, a pair of coupled nonlinear Schrodinger equations (CNLSEs) is obtained. The CNLSEs are then used to investigate the occurrence of modulational instability in magnetized plasmas. Waves in the vicinity of the zero-group-dispersion point are considered, so that the group dispersion terms may either bear the same or different signs. It is found that a stable EMEC wave can be destabilized due to its nonlinear interactions with an unstable one, while a pair of unstable EMEC waves yields an increased instability growth rate. Individually stable waves remain stable while interacting with one another. Stationary nonlinear solutions of the coupled equations are presented. The relevance of our investigation to nonlinear phenomena in space plasmas is discussed. (c) 2005 American Institute of Physics.