Space Propagation of Instabilities in Zakharov Equations

In this paper we study an initial boundary value problem for Zakharov's equations, describing the space propagation of a laser beam entering in a plasma. We prove a strong instability result and prove that the mathematical problem is ill-posed in Sobolev spaces. We also show that it is well posed in spaces of analytic functions. Several consequences for the physical consistency of the model are discussed.Comment: 39

Whose problem? Disability narratives and available identities

In this article, the author demonstrates that contemporary cultural disability discourses offer few positive resources for people with impairments to draw upon in constructing positive personal and social identities. Examining the emergence of the Disability Arts Movement in Britain, consideration is given to alternative discourses developed by disabled people who have resisted the passive roles expected of them and developed a disability identity rooted in notions of power, respect and control. It is suggested that these alternative discourses provide an empowering rather than a disabling basis for community development and community arts practice and should be embraced by workers in these fields

A Hausdorff-Young theorem for rearrangement-invariant spaces

The classical Hausdorff-Young theorem is extended to the setting of rearrangement-invariant spaces. More precisely, if 1 <_ p <_ 2, p[-1] + q[-1] = 1, and if X is a rearrangement-invariant space on the circle T with indices equal to p[-1], it is shown that there is a rearrangement-invariant space X on the integers Z with indices equal to q[-1] such that the Fourier transform is a bounded linear operator from X into X. Conversely, for any rearrangement-invariant space Y on Z with indices equal to q[-1], 2 < q <__ oo, there is a rearrangement-invariant space Y on T with indices equal to p[-1] such that J is bounded from Y into Y. Analogous results for other groups are indicated and examples are discussed when X is L[p] or a Lorentz space L[pr]

Disability, the Organization of Work, and the Need for Change

[Excerpt] There is considerable historical and anthropological evidence that impairment is a human constant and that cultural responses to perceived abnormalities of the body and mind vary across time, culture and place. It is equally evident that throughout recorded history western society has systematically discriminated against or excluded various groups of people on the basis of perceived biological inferiority, and that this exclusion became systematic following the material and ideological changes associated with capitalist development. The combination of industrialisation, urbanisation, and associate ideologies including: liberal utilitarianism, Social Darwinism, and Eugenics, provided ‘scientific’ legitimacy to ancient myths, fears and prejudices, and the gradual but intensifying commodification of every day life. As a result \u27work\u27 became almost exclusively associated with wage labour and paid employment. This precipitated the development of an employment infrastructure geared to the needs of those deemed \u27capable\u27 of this type of activity. Hence, those considered incapable of work, and labelled \u27disabled\u27 were, apart from in, and immediately following, times of war, excluded from the workplace. This legacy remains with us today. Discrimination against disabled people is therefore institutionalised in the very fabric of western society; consequently, disabled people encounter a whole range of material, political and cultural barriers to meaningful mainstream employment and social participation

Drafting the Nineteen Propositions, January to July 1642

This article analyses the drafting of the document eventually printed as the Nineteen Propositions. Section two addresses certain issues regarding the methods and concepts employed in the subsequent analysis, focusing on consensus-building, constitutional leanings and the drafting of parliamentary declarations in early 1642. Section three examines the origins of the Nineteen Propositions in the draft Declaration of Ways and Means (January 1642) (hereafter cited as the Ways). Section four traces the emergence of the Declaration Concerning Grievances and Remedies (hereafter cited as the Grievances) from the Ways (January–February). Section five examines the junta's efforts to overcome the Lords' prevarication over passing the Grievances (February–May). Section six examines the emergence of the initial draft of the Nineteen Propositions from the Grievances (24–7 May). Section seven analyses the 28 May draft, while section eight explores the amendment of that draft (31 May and 1 June). Section nine examines parliament's abortive attempts to revise the Nineteen Propositions in light of His Majesty's Answer to the XIX Propositions (21 June–2 July). It is concluded that, contrary to the received view, the text of the Nineteen Propositions began to emerge in January rather than May 1642, and that the junta in the Commons rather than the Lords drove this process. The three appendices identify, respectively, the constitutional leanings of the relevant parliamentarians, the parts of the text of the Ways that were repeated in the Grievances, and dates on which the various parts of the final text of the Nineteen Propositions were written

Resource productivity management in the services sector

School of Managemen

Motzkin Intervals and Valid Hook Configurations

We define a new natural partial order on Motzkin paths that serves as an intermediate step between two previously-studied partial orders. We provide a bijection between valid hook configurations of $312$-avoiding permutations and intervals in these new posets. We also show that valid hook configurations of permutations avoiding $132$ (or equivalently, $231$) are counted by the same numbers that count intervals in the Motzkin-Tamari posets that Fang recently introduced, and we give an asymptotic formula for these numbers. We then proceed to enumerate valid hook configurations of permutations avoiding other collections of patterns. We also provide enumerative conjectures, one of which links valid hook configurations of $312$-avoiding permutations, intervals in the new posets we have defined, and certain closed lattice walks with small steps that are confined to a quarter plane.Comment: 22 pages, 8 figure