Some results on solvability of ordinary linear differential equations in locally convex spaces

Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x = Ax$, $x(0) = x_0$ with respect to functions $x: R\to E$. It is proved that if $E\in \Gamma$, then $E\times R^A$ is-an-element-of $\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to $\omega$, does not belong to $\Gamma$.

Is the pinning of ordinary dislocations in γ-TiAl intrinsic or extrinsic in nature? A combined atomistic and kinetic Monte Carlo approach

We address the question of the observed pinning of 1/2

Nonlinear perpendicular propagation of ordinary mode electromagnetic wave packets in pair plasmas and electron-positron-ion plasmas

The nonlinear amplitude modulation of electromagnetic waves propagating in pair plasmas, e.g., electron-positron or fullerene pair-ion plasmas, as well as three-component pair plasmas, e.g., electron-positron-ion plasmas or doped (dusty) fullerene pair-ion plasmas, assuming wave propagation in a direction perpendicular to the ambient magnetic field, obeying the ordinary (O-) mode dispersion characteristics. Adopting a multiple scales (reductive perturbation) technique, a nonlinear Schrodinger-type equation is shown to govern the modulated amplitude of the magnetic field (perturbation). The conditions for modulation instability are investigated, in terms of relevant parameters. It is shown that localized envelope modes (envelope solitons) occur, of the bright- (dark-) type envelope solitons, i.e., envelope pulses (holes, respectively), for frequencies below (above) an explicit threshold. Long wavelength waves with frequency near the effective pair plasma frequency are therefore unstable, and may evolve into bright solitons, while higher frequency (shorter wavelength) waves are stable, and may propagate as envelope holes.(c) 2007 American Institute of Physics.

Simplified theory of wideband spectra of liquid H2O and D2O (from 0 to 1000 cm(-1)) due to reorienting polar and vibrating H-bonded water molecules

A semi-phenomenological molecular model is presented, which is capable of describing with the use of analytical formulae, the wideband dielectric(1) and far-infrared spectra of ordinary and heavy water. In the model the vector of a dipole moment is presented as a sum of two components. The absolute value of the first one is constant; the second one changes harmonically with time. The key aspect of this work is consideration of FIR spectra due to the second component. In the context of the modified hybrid model presented in the work, reorientation of the dipoles in the rectangular potential well is considered, as a result of which the librational (near 700 cm (-1)) and translational (near 200 cm (-1)) absorption bands and the microwave Debye relaxation spectrum arise. It is shown that the time-dependent part of a dipole moment contributes most to the translational band, the relevant mechanism is taken to be stretching vibration of the H-bonded molecules. Previous linear-response molecular models were unsuccessful in describing this band (in heavy water) in terms of the complex dielectric permittivity. The spatial and time scales characteristic of water are estimated. (C) 2002 Elsevier Science B.V. All rights reserved.

Atomistic studies of interactions between the dominant lattice dislocations and γ/γ-lamellar boundaries in lamellar γ-TiAl

This paper reports on atomistic simulations of the interactions between the dominant lattice dislocations in ?-TiAl (<1 0 1] superdislocations) with all three kinds of ?/?-lamellar boundaries in polysynthetically twinned (PST) TiAl. The purpose of this study is to clarify the early stage of lamellar boundary controlled plastic deformation in PST TiAl. The interatomic interactions in our simulations are described by a bond order potential for L10-TiAl which provides a proper quantum mechanical description of the bonding. We are interested in the dislocation core geometries that the lattice produces in proximity to lamellar boundaries and the way in which these cores are affected by the elastic and atomistic effects of dislocation-lamellar boundary interaction. We study the way in which the interfaces affect the activation of ordinary dislocation and superdislocation slip inside the ?-lamellae and transfer of plastic deformation across lamellar boundaries. We find three new phenomena in the atomic-scale plasticity of PST TiAl, particularly due to elastic and atomic mismatch associated with the 60° and 120° ?/?-interfaces: (i) two new roles of the ?/?-interfaces, i.e. decomposition of superdislocations within 120° and 60° interfaces and subsequent detachment of a single ordinary dislocation and (ii) blocking of ordinary dislocations by 60° and 120° interfaces resulting in the emission of a twinning dislocation.

Same sex attraction, homophobic bullying and mental health of young people in Northern Ireland

This article reports on the relationship between same-sex attraction, experience of bullying in school and mental health measured using the 12-item version of the General Health Questionnaire (GHQ12). A random sample of 16 year olds, drawn from the Child Benefit Register, was invited to take part in the 2005 Young Life and Times survey, which is a postal survey carried out in Northern Ireland every year. Eight hundred and nineteen 16 year olds responded, which represented a return rate of 40%. The results of the survey showed that respondents who said they had been attracted to a person of the same sex at least once were significantly more likely to report experiences of school bullying. Same-sex-attracted 16 year olds were significantly less likely than those attracted to persons of the opposite sex only to say that their school provided real help to those who are being bullied. The 2005 Young Life and Times data also indicated that same-sex-attracted respondents were more than twice as likely as respondents who were only attracted to people of the opposite sex to have higher levels of psychiatric disorder. (Contains 5 tables.)

Alasdair MacIntyre and the Hope for a Politics of Virtuous Interdependence

Rebellion, philosophic and political, impels the work of Alasdair MacIntyre. Neither of the left nor the right, he treads a borderline path between conservatism and radicalism in holding to a socialist Thomistic Aristotelianism underpinned by a deliberative ‘ethic of care’ that is implacably opposed to modernity and the advanced capitalist nation-state. The depth of this opposition arouses strong opinions in friend and foe alike. To some he is an eminently dispensable reactionary whose sole consistent feature is an inexplicable ‘hatred of liberal individualism’ (Lessnoff 1999: 4). To others he appears a revolutionary enunciating a departure capable of legitimating the activities of ordinary persons so ‘that previously isolated struggles might be transformed into a new class war of attrition’ (Knight 1996: 896). However, neither interpretation rings true. MacIntyre does develop a cogent critique of the present, but this critique points in directions towards which no politics could hope to move.

Dynamical instability in surface permeability characteristics of building sandstones in response to salt accumulation over time

This paper explores how the surface permeability of sandstone blocks changes over time in response to repeated salt weathering cycles. Surface permeability controls the amount of moisture and dissolved salt that can penetrate in and facilitate decay. Connected pores permit the movement of moisture (and hence soluble salts) into the stone interior, and where areas are more or less permeable soluble salts may migrate along preferred pathways at differential rates. Previous research has shown that salts can accumulate in the near-surface zone and lead to partial pore blocking which influences subsequent moisture ingress and causes rapid salt accumulation in the near-surface zone.

Two parallel salt weathering simulations were carried out on blocks of Peakmoor Sandstone of different volumes. Blocks were removed from simulations after 2, 5, 10, 20 and 60 cycles. Permeability measurements were taken for these blocks at a resolution of 20 mm, providing a grid of 100 permeability values for each surface. The geostatistical technique of ordinary kriging was applied to the data to produce a smoothed interpolation of permeability for these surfaces, and hence improve understanding of the evolution of permeability over time in response to repeated salt weathering cycles.

Results illustrate the different responses of the sandstone blocks of different volumes to repeated salt weathering cycles. In both cases, after an initial subtle decline in the permeability (reflecting pore blocking), the permeability starts to increase — reflected in a rise in mean, maximum and minimum values. However, between 10 and 20 cycles, there is a jump in the mean and range permeability of the group A block surfaces coinciding with the onset of meaningful debris release. After 60 cycles, the range of permeability in the group A block surface had increased markedly, suggesting the development of a secondary permeability. The concept of dynamic instability and divergent behaviour is applied at the scale of a single block surface, with initial small-scale differences across a surface having larger scale consequences as weathering progresses.

After cycle 10, group B blocks show a much smaller increase in mean permeability, and the range stays relatively steady — this may be explained by the capillary conditions set up by the smaller volume of the stone, allowing salts to migrate to the ‘back’ of the blocks and effectively relieving stress at the ‘front’ face.

Knowledge, innovation and emulation in the evolutionary thought of Bernard Mandeville

Of the early modern writers on the division of labour, Bernard Mandeville alone extended it to all aspects of human activity and emphasised its role in a cumulative process of evolution in which each generation modified and built on what had been achieved by earlier generations. This required exploration of the mechanisms through which new knowledge was developed as well as the means by which knowledge was transmitted between the generations. The present article examines Mandeville’s treatment of these mechanisms and explores their theoretical origins. It examines Mandeville’s understanding of the role of the division of labour in facilitating discovery and learning and the role of education and imitation in transmitting social knowledge. It shows that, for Mandeville, innovators were people of ordinary capacity who were alert to the opportunities and challenges of their environment. As a result of specialisation, they possessed tacit knowledge which was actualised in what they did rather than in theoretical propositions. Mandeville’s evolutionary thought influenced subsequent writers on political economy and evolutionary social thinkers. It may also have had some influence on Charles Darwin, though it is not, in itself, Darwinian. © The Author 2013. Published by Oxford University Press on behalf of the Cambridge Political Economy Society. All rights reserved.

Zooming In on the Progenitors of Superluminous Supernovae With the HST

We present Hubble Space Telescope (HST) rest-frame ultraviolet imaging of the host galaxies of 16 hydrogen-poor superluminous supernovae (SLSNe), including 11 events from the Pan-STARRS Medium Deep Survey. Taking advantage of the superb angular resolution of HST, we characterize the galaxies' morphological properties, sizes, and star formation rate (SFR) densities. We determine the supernova (SN) locations within the host galaxies through precise astrometric matching and measure physical and host-normalized offsets as well as the SN positions within the cumulative distribution of UV light pixel brightness. We find that the host galaxies of H-poor SLSNe are irregular, compact dwarf galaxies, with a median half-light radius of just 0.9 kpc. The UV-derived SFR densities are high ([Sigma(SFR)] similar or equal to 0.1M(circle dot) yr(-1) kpc(-1)), suggesting that SLSNe form in overdense environments. Their locations trace the UV light of their host galaxies, with a distribution intermediate between that of long-duration gamma-ray bursts (LGRBs; which are strongly clustered on the brightest regions of their hosts) and a uniform distribution (characteristic of normal core-collapse SNe), though cannot be statistically distinguished from either with the current sample size. Taken together, this strengthens the picture that SLSN progenitors require different conditions than those of ordinary core-collapse SNe to form and that they explode in broadly similar galaxies as do LGRBs. If the tendency for SLSNe to be less clustered on the brightest regions than are LGRBs is confirmed by a larger sample, this would indicate a different, potentially lower-mass progenitor for SLSNe than LRGBs.