Let $\Omega \subset \mathbb {R}^N$ ($N\geq 3$) be a $C^2$ bounded domain and $\Sigma \subset \partial \Omega$ be a $C^2$ compact submanifold without boundary, of dimension $k$, $0\leq k \leq N-1$. We assume that $\Sigma = \{0\}$ if $k = 0$ and $\Sigma =\partial \Omega$ if $k=N-1$. Let $d_{\Sigma }(x)=\mathrm {dist}\,(x,\Sigma )$ and $L_\mu = \Delta + \mu \,d_{\Sigma }^{-2}$, where $\mu \in {\mathbb {R}}$. We study boundary value problems ($P_\pm$) $-{L_\mu} u \pm |u|^{p-1}u = 0$ in $\Omega$ and $\mathrm {tr}_{\mu,\Sigma}(u)=\nu$ on $\partial \Omega$, where $p>1$, $\nu$ is a given measure on $\partial \Omega$ and $\mathrm {tr}_{\mu,\Sigma}(u)$ denotes the boundary trace of $u$ associated to $L_\mu$. Different critical exponents for the existence of a solution to ($P_\pm$) appear according to concentration of $\nu$. The solvability for problem ($P_+$) was proved in [3, 29] in subcritical ranges for $p$, namely for $p$ smaller than one of the critical exponents. In this paper, assuming the positivity of the first eigenvalue of $-L_\mu$, we provide conditions on $\nu$ expressed in terms of capacities for the existence of a (unique) solution to ($P_+$) in supercritical ranges for $p$, i.e. for $p$ equal or bigger than one of the critical exponents. We also establish various equivalent criteria for the existence of a solution to ($P_-$) under a smallness assumption on $\nu$.

This paper uses theories of small states (e.g. Katzenstein) and nationalism (e.g. Gellner) to explain why Denmark and Ireland responded to the 2008 financial crisis in different ways. In Denmark, a coordinated market economy with considerable corporatism and state intervention, the private sector shouldered much of the financial burden for rescuing the banking sector. In Ireland, a liberal market economy without much corporatism or state intervention, the state shouldered the burden. The difference stems in large part from the fact that Denmark had comparatively thick institutions and a strong sense of nationalism whereas Ireland did not. Lessons for the theories of small states and nationalism are explored.

This is a summary of the proceedings of the Conference on the Health Aspects of the Tsunami Disaster in Asia that was convened by the sunami World Health Organization in Phuket, Thailand from 04–06 May 2005. It contains reviews of the experiences of the health sector and early recovery fol following the Earthquake and Tsunami with emphasis onwhat was done well and what could have been done better and the lessons learned that can be incorporated into actions that will mitigate the damage created by future events. It outlines the national and international responses and recovery and the actions taken and not taken by the international community in support of the countries affected. Specific issuesaddressed include: (1) needs assessments; (2) coordi- coordination; (3) filling gaps in essential services, and (4) capacity building at the country level. Each of these aspects is analyzed as to its: (1) appropriateness; (2) adequacy; (3) effectiveness; (4) efficiency; and (5) connectedness.

Much of what occurred provided benefits to the stricen population, but there is substantial room for improvement through implementation of the lessons learned. These lessons must be converted into actions in order to mitigate the damagesustained and to enhance our responses to the damage from future

In this paper, we use the theorem of Burchnall and Shaundy to give the capacity of the spectrum $\sigma(A)$ of a periodic tridiagonal and symmetric matrix. A special family of Chebyshev polynomials of $\sigma(A)$ is also given. In addition, the inverse problem is considered: given a finite union $E$ of closed intervals, we study the conditions for a Jacobi matrix $A$ to exist satisfying $\sigma(A)=E$. We relate this question to Carathéodory theorems on conformal mappings.

AMS 2000 Mathematics subject classification: Primary 31B15; 30C20; 39A70

Coercive closed forms on L 2 -spaces are studied whose associated L 2 -semigroups are positivity preserving. Earlier work by other authors is extended by further developing the potential theory of such forms and completed by proving an analytic characterization of those of these forms which have a probabilistic counterpart, i.e., are associated with (special standard) Markov processes. Examples with finite and infinite dimensional state spaces are discussed.

We prove some new results on quasi-regular Dirichlet forms. These include results on perturbations of Dirichlet forms, change of speed measure, and tightness. The tightness implies the existence of an associated right continuous strong Markov process. We also discuss applications to a number of examples including cases with possibly degenerate (sub)-elliptic part, diffusions on loop spaces, and certain Fleming- Viot processes.