On the solvability of second kind integral equations on the real line

This paper considers general second kind integral equations of the form(in operator form φ − kφ = ψ), where the functions k and ψ are assumed known, with ψ ∈ Y, the space of bounded continuous functions on R, and k such that the mapping s → k(s, · ), from R to L1(R), is bounded and continuous. The function φ ∈ Y is the solution to be determined. Conditions on a set W ⊂ BC(R, L1(R)) are obtained such that a generalised Fredholm alternative holds: If W satisfies these conditions and I − k is injective for all k ∈ W then I − k is also surjective for all k ∈ W and, moreover, the inverse operators (I − k) − 1 on Y are uniformly bounded for k ∈ W. The approximation of the kernel in the integral equation by a sequence (kn) converging in a weak sense to k is also considered and results on stability and convergence are obtained. These general theorems are used to establish results for two special classes of kernels: k(s, t) = κ(s − t)z(t) and k(s, t) = κ(s − t)λ(s − t, t), where κ ∈ L1(R), z ∈ L∞(R), and λ ∈ BC((R\{0}) × R). Kernels of both classes arise in problems of time harmonic wave scattering by unbounded surfaces. The general integral equation results are here applied to prove the existence of a solution for a boundary integral equation formulation of scattering by an infinite rough surface and to consider the stability and convergence of approximation of the rough surface problem by a sequence of diffraction grating problems of increasingly large period.

On the solvability of a class of second kind integral equations on unbounded domains

We consider integral equations of the form ψ(x) = φ(x) + ∫Ωk(x, y)z(y)ψ(y) dy(in operator form ψ = φ + Kzψ), where Ω is some subset ofRn(n ≥ 1). The functionsk,z, and φ are assumed known, withz ∈ L∞(Ω) and φ ∈ Y, the space of bounded continuous functions on Ω. The function ψ ∈ Yis to be determined. The class of domains Ω and kernelskconsidered includes the case Ω = Rnandk(x, y) = κ(x − y) with κ ∈ L1(Rn), in which case, ifzis the characteristic function of some setG, the integral equation is one of Wiener–Hopf type. The main theorems, proved using arguments derived from collectively compact operator theory, are conditions on a setW ⊂ L∞(Ω) which ensure that ifI − Kzis injective for allz ∈ WthenI − Kzis also surjective and, moreover, the inverse operators (I − Kz)−1onYare bounded uniformly inz. These general theorems are used to recover classical results on Wiener–Hopf integral operators of21and19, and generalisations of these results, and are applied to analyse the Lippmann–Schwinger integral equation.

Asymptotic behavior at infinity of solutions of multidimensional second kind integral equations

We consider second kind integral equations of the form x(s) - (abbreviated x - K x = y ), in which Ω is some unbounded subset of Rn. Let Xp denote the weighted space of functions x continuous on Ω and satisfying x (s) = O(|s|-p ),s → ∞We show that if the kernel k(s,t) decays like |s — t|-q as |s — t| → ∞ for some sufficiently large q (and some other mild conditions on k are satisfied), then K ∈ B(XP) (the set of bounded linear operators on Xp), for 0 ≤ p ≤ q. If also (I - K)-1 ∈ B(X0) then (I - K)-1 ∈ B(XP) for 0 < p < q, and (I- K)-1∈ B(Xq) if further conditions on k hold. Thus, if k(s, t) = O(|s — t|-q). |s — t| → ∞, and y(s)=O(|s|-p), s → ∞, the asymptotic behaviour of the solution x may be estimated as x (s) = O(|s|-r), |s| → ∞, r := min(p, q). The case when k(s,t) = к(s — t), so that the equation is of Wiener-Hopf type, receives especial attention. Conditions, in terms of the symbol of I — K, for I — K to be invertible or Fredholm on Xp are established for certain cases (Ω a half-space or cone). A boundary integral equation, which models three-dimensional acoustic propaga-tion above flat ground, absorbing apart from an infinite rigid strip, illustrates the practical application and sharpness of the above results. This integral equation mod-els, in particular, road traffic noise propagation along an infinite road surface sur-rounded by absorbing ground. We prove that the sound propagating along the rigid road surface eventually decays with distance at the same rate as sound propagating above the absorbing ground.

Approximate solution of second kind integral equations on infinite cylindrical surfaces

The paper considers second kind integral equations of the form $\phi (x) = g(x) + \int_S {k(x,y)} \phi (y)ds(y)$ (abbreviated $\phi = g + K\phi $), in which S is an infinite cylindrical surface of arbitrary smooth cross section. The “truncated equation” (abbreviated $\phi _a = E_a g + K_a \phi _a $), obtained by replacing S by $S_a $, a closed bounded surface of class $C^2 $, the boundary of a section of the interior of S of length $2a$, is also discussed. Conditions on k are obtained (in particular, implying that K commutes with the operation of translation in the direction of the cylinder axis) which ensure that $I - K$ is invertible, that $I - K_a $ is invertible and $(I - K_a )^{ - 1} $ is uniformly bounded for all sufficiently large a, and that $\phi _a $ converges to $\phi $ in an appropriate sense as $a \to \infty $. Uniform stability and convergence results for a piecewise constant boundary element collocation method for the truncated equations are also obtained. A boundary integral equation, which models three-dimensional acoustic scattering from an infinite rigid cylinder, illustrates the application of the above results to prove existence of solution (of the integral equation and the corresponding boundary value problem) and convergence of a particular collocation method.

Runge-Kutta IMEX schemes for the Horizontally Explicit/Vertically Implicit (HEVI) solution of wave equations

Many operational weather forecasting centres use semi-implicit time-stepping schemes because of their good efficiency. However, as computers become ever more parallel, horizontally explicit solutions of the equations of atmospheric motion might become an attractive alternative due to the additional inter-processor communication of implicit methods. Implicit and explicit (IMEX) time-stepping schemes have long been combined in models of the atmosphere using semi-implicit, split-explicit or HEVI splitting. However, most studies of the accuracy and stability of IMEX schemes have been limited to the parabolic case of advection–diffusion equations. We demonstrate how a number of Runge–Kutta IMEX schemes can be used to solve hyperbolic wave equations either semi-implicitly or HEVI. A new form of HEVI splitting is proposed, UfPreb, which dramatically improves accuracy and stability of simulations of gravity waves in stratified flow. As a consequence it is found that there are HEVI schemes that do not lose accuracy in comparison to semi-implicit ones. The stability limits of a number of variations of trapezoidal implicit and some Runge–Kutta IMEX schemes are found and the schemes are tested on two vertical slice cases using the compressible Boussinesq equations split into various combinations of implicit and explicit terms. Some of the Runge–Kutta schemes are found to be beneficial over trapezoidal, especially since they damp high frequencies without dropping to first-order accuracy. We test schemes that are not formally accurate for stiff systems but in stiff limits (nearly incompressible) and find that they can perform well. The scheme ARK2(2,3,2) performs the best in the tests.

State practice, customary humanitarian law and civilian casualties of armed conflict

The article examines the customary international law credentials of the humanitarian law rules proposed by the International Committee of the Red Cross (ICR) in 2005. It relies on the BIICL/Chatham House analysis as a ‘constructive comment’ on the methodology of the ICRC study and the rules formed as a result of that methodology with respect to the dead and missing as an aid to determination of their customary law status. It shows that most of the rules studied have a customary international lawpedigree which conforms to the conclusions formed on the rules generally in the Wilmshurst and Breau study. However, the rules with respect to return of personal effects, recording location of graves and notification of relatives of access to gravesites do not seem to have even on a majoritarian/deductive approach enough volume of state practice to establish them as customary with respect to civilians.

On the dominance of roots of characteristic equations for neutral functional differential equations

We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations. A simple characteristic equation, arisen from the study of delay equations with small delay, is analyzed in greater detail. (C) 2009 Elsevier Inc. All rights reserved.

Rates of student-reported antisocial behavior, school suspensions, and arrests in Victoria, Australia and Washington State, United States

Background: Few methodologically rigorous international comparisons of student-reported antisocial behavior have been conducted. This paper examines whether there are differences in the frequency of both antisocial behavior and societal responses to antisocial behavior in Victoria, Australia and Washington State, United States. These 2 states were chosen due to their similarities on sociodemographic characteristics and their differences in policy frameworks around problem behavior including antisocial behavior and substance use.

Methods: State representative samples of students (N = 5769) in school grades 5, 7, and 9 in Victoria and Washington State completed a modified version of the Communities That Care self-report survey of behavior and societal responses to behavior. Chi-square analyses compared frequencies of antisocial behavior, school suspensions, and police arrests in the 2 states. Multivariate logistic regression analyses were conducted for each outcome measure to examine the effect of state, controlling for sample design, clustering of students within schools, age, socioeconomic status, and urbanicity.

Results: Few state differences in student-reported antisocial behavior were found, although frequencies varied across behavior type and grade level. Differences in societal responses were observed across grade levels with grade 5 Washington students reporting higher rates of school suspension. Older Washington students reported more arrests.

Conclusions: Rates of student antisocial behavior appear similar in these 2 states in Australia and the United States. However, youth in the United States relative to Australia may experience greater societal consequences for problem behavior. Further research is required to examine the impact of these consequences on subsequent behavior.

The rise and decline of Libya as a rogue state

From 1980 until 2006, the Great Socialist People’s Libyan Arab Jamahiriya (Libya) was considered by the United States as a “Rogue State&rdquo;. However, in May 2006, the U.S. Secretary of State, Condoleezza Rice, welcomed Libya back into the world community and declared that this erstwhile enemy had reformed. But has the American public registered this change in Libya’s status? Has this return to the fold influenced U.S. public opinion about Libya and its eccentric leader, Colonel Qaddafi? Or is it merely a case of new foes pushing old ones out of mind? What might some of America’s new “Rogue State&rdquo; enemies learn from Libya’s example? This paper explores the nexus between the tumultuous U.S.-Libyan relationship and the U.S. public, and analyses how and why perceptions of Libya have changed.

Publishing dynamic state changes of resources through state aware WSDL

A common architecture in today's development of distributed systems is the service-oriented architecture (SOA) implemented using Web services. Until recently, it was difficult to build a SOA based grid/distributed system using Web services due to the inability to learn the state of services. The state of a Web service could only be accessed through specialized clients and/or services. Should the specialized client or service fail, the state can't be accessed. This paper shows the innovative resources via Web instances (RVWI) framework. RVWI grants to web services the ability to show the state of dynamic resources in their WSDL. This was achieved via software components called connectors which watch for any changes in a resource and updates the web service. The significance of this report is the support for resources which can change state between requests and the innovation is the improvement of state updates between the service and discovery services.

Still invisible : the myth of the woman-friendly state

Australian women faced the last two decades of the twentieth century, optimistic in their capacity to contribute positively to social change in the restructuring state. Encouraged by the relative euphoria of the late 1970s and early 1980s, women had a fleeting glimpse of the possibilities of woman-friendly legislation and feminist inspired government policy. What eventuated was the dismantling of supportive welfare structures, under the guise of economic rationalist state action, which undermined and eventually halted women’s economic and social advancement. This research project examines the impact of government policy on the welfare of Victorian women, through a feminist analysis of state and federal decision-making, framed in the context of case studies in the areas of employment, education and health. The promotion of ‘gender-neutral’ policy, by generally conservative bureaucracies, effectively exposes the mythical woman-friendly state. The implications do not auger well for Victorian women in the new millenium.

Policing, rule of law, state capacity and sustainable peace in Timor-Leste

This paper sets out to demonstrate the link between development, state capacity and peace, employing Timor-Leste as the case study. It employs the association between state capacity and development to illustrate where if state capacity is lacking or functions improperly there is likely to be a low level of state legitimacy. This in turn manifests as lack of respect for or failure of rule of law, developing as generalised lawlessness and anti-state activity and eventually manifesting as intra-state or civil conflict. In particular, policing is seen as a critical component in state legitimacy, being the 'front line' of the judicial system from which legitimacy ultimately derives. This issue is particularly critical in states emerging from traditional legal and judicial structures, but which have not yet articulated into 'rational-legal' structures. Ipso facto, key state institutions, such as the judicial system and police are required to function well, while these are alone not enough to guarantee peace, they are significant contributors to and guarantors of peace.

An analysis of potential barriers and enablers to regulating the television marketing of unhealthy foods to children at the state government level in Australia

Background In Australia there have been many calls for government action to halt the effects of unhealthy food marketing on children's health, yet implementation has not occurred. The attitudes of those involved in the policy-making process towards regulatory intervention governing unhealthy food marketing are not well understood. The objective of this research was to understand the perceptions of senior representatives from Australian state and territory governments, statutory authorities and non-government organisations regarding the feasibility of state-level government regulation of television marketing of unhealthy food to children in Australia.

Method Data from in-depth semi-structured interviews with senior representatives from state and territory government departments, statutory authorities and non-government organisations (n=22) were analysed to determine participants' views about regulation of television marketing of unhealthy food to children at the state government level. Data were analysed using content and thematic analyses.

Results Regulation of television marketing of unhealthy food to children was supported as a strategy for obesity prevention. Barriers to implementing regulation at the state level were: the perception that regulation of television advertising is a Commonwealth, not state/territory, responsibility; the power of the food industry and; the need for clear evidence that demonstrates the effectiveness of regulation. Evidence of community support for regulation was also cited as an important factor in determining feasibility.

Conclusions The regulation of unhealthy food marketing to children is perceived to be a feasible strategy for obesity prevention however barriers to implementation at the state level exist. Those involved in state-level policy making generally indicated a preference for Commonwealth-led regulation. This research suggests that implementation of regulation of the television marketing of unhealthy food to children should ideally occur under the direction of the Commonwealth government. However, given that regulation is technically feasible at the state level, in the absence of Commonwealth action, states/territories could act independently. The relevance of our findings is likely to extend beyond Australia as unhealthy food marketing to children is a global issue.

Does the burden of the experience sampling method undermine data quality in state based body image research?

Despite growing popularity of experience sampling methodology (ESM) for evaluations of state-based components of body image, there have been concerns that the frequent repeated measurement might encourage problematic responding resulting in low data quantity and/or quality. Using a sample of 105 women (mean age = 24.84), this study used multilevel modelling to investigate whether (a) there were changes in compliance or response variability across a 7-day period, and (b) whether such changes are explained by participant characteristics. Present findings suggest that demands of ESM protocol undermine quantity more so than quality of obtained data. Decline in procedural compliance across the testing period correlated with BMI and body shame, whereas reduced variability in state-based assessments did not adversely impact the strength of association between state body satisfaction ratings and other variables in the dataset. The authors make several recommendations for ensuring the quality of ESM-based data in future studies.

Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.