The Morse–Bott–Kirwan condition is local

The Morse–Bott–Kirwan condition is local

On the Local Equilibrium Condition

A physical system should be in a local equilibrium if it cannot be distinguished from a global equilibrium by “infinitesimally localized measurements”. This seems to be a natural characterization of local equilibrium, however the problem is to give a precise meaning to the qualitative phrase “infinitesimally localized measurements”. A solution is suggested in form of a Local Equilibrium Conditi...

Forming the Territorial Communities' Local Budgets in Ukraine Under Decentralization: Current Condition and Management Tasks

The budgetary capacity with the tax component as its key aspect is the basis for forming local budgets of a territorial community. The paper outlines the methods for diagnostics of the budgetary capacity of territorial communities by revenues aimed at providing a comprehensive quantitative and qualitative assessment of the status, strengths, and weaknesses of the economy of an administrative-te...

Condition numbers and local errors in the boundary element method

In this chapter we investigate local errors and condition numbers in the BEM. The results of these investigations are important in guiding adaptive meshing strategies and solvability of linear systems in BEM. We show that the local error for the BEM with constant or linear elements decreases quadratically with the boundary element mesh size. We also investigate better ways of treating boundary ...

Assessing illness behaviour: what condition is my condition in?

In a paper in this issue, Rief et al. [1] present a new scale for assessing illness behaviour. The Scale of the Assessment of Illness Behaviour (SAIB) comprises five dimensions: verification of diagnosis, expression of symptoms, medication reliance, illness consequences and bodily scanning. The initial validation of the scale has been completed through comparison of patients presenting with une...