Analysis of the Solvability of Linear Vibration Models

In this article we consider a general linear vibration problem in variational form. Models for the vibration of systems of elastic bodies can be written in this form. We show how properties of the damping term determines the time differentiability of the solution and establish classes of permissible initial conditions. The proofs are based on a direct link between the variational form and an abstract differential equation.     

Positive Solutions for Semipositone ( p,n − p ) Right Focal Boundary Value Problems

We consider the ( p , n m p ) right focal boundary value problem: $${\matrix{{(- 1)^{n - p} u^{(n)} \! = \lambda \;f(t, u), } \hfill & \ {{\rm for }\ 0 \lt t \lt 1, } \hfill \cr \quad \quad \,{u^{(i)} (0) = 0, } \hfill & {0 \le i \le p - 1, } \hfill \cr \quad \quad \,{u^{(i)} (1) = 0, } \hfill & {p \le i \le n - 1, } \hfill \cr}} $$ where 1 h p h n m 1 is fixed and u > 0. Using a fixed point theorem for operators on a cone, we develop criteria for the existence of positive solutions of the boundary value problem for u on a suitable interval.     

Fixed point theorems for multivalued operators and application to discontinuous quasilinear BVP's

In this article, we prove an abstract fixed point theorem for increasing multivalued operators in ordered topological spaces, which provides an efficient tool to obtain qualitative results on the solution set of discontinuous quasilinear elliptic boundary value problems. In particular, we are able to show the existence of extremal solutions of such problems.     

Bayesian Inversion of Piecewise Affine Operators in a Gaussian Framework

Piecewise affine inverse problems form a general class of nonlinear inverse problems. In particular inverse problems obeying certain variational structures, such as Fermat's principle in travel time tomography, are of this type. In a piecewise affine inverse problem a parameter is to be reconstructed when its mapping through a piecewise affine operator is observed, possibly with errors. A piecewise affine operator is defined by partitioning the parameter space and assigning a specific affine operator to each part. A Bayesian approach with a Gaussian random field prior on the parameter space is used. Both problems with a discrete finite partition and a continuous partition of the parameter space are considered.

The main result is that the posterior distribution is decomposed into a mixture of truncated Gaussian distributions, and the expression for the mixing distribution is partially analytically tractable. The general framework has, to the authors' knowledge, not previously been published, although the result for the finite partition is generally known.

Inverse problems are currently of large interest in many fields. The Bayesian approach is popular and most often highly computer intensive. The posterior distribution is frequently concentrated close to high-dimensional nonlinear spaces, resulting in slow mixing for generic sampling algorithms. Inverse problems are, however, often highly structured. In order to develop efficient sampling algorithms for a problem at hand, the problem structure must be exploited.

The decomposition of the posterior distribution that is derived in the current work can be used to develop specialized sampling algorithms. The article contains examples of such sampling algorithms. The proposed algorithms are applicable also for problems with exact observations. This is a case for which generic sampling algorithms tend to fail.     

Two hyperfinite constructions of the brownian bridge

Infinitesimal Analysis is used to give two constructions of the brownian bridge process. In the first construction a hyperfinite tied down random walk is used and a brownian bridge is obtained via the standard part map. As a consequence it is shown that the brownian bridge is the weak limit of a sequence of normalized tied down random walks. The second construction is based on a hyperfinite uniform empirical process. This construction gives an almost trivial proof of Donsker's Invariance Principle for the uniform empirical process     

Random Homogenization of p-Laplacian with Obstacles in Perforated Domain

We study the homogenization of p-Laplacian with obstacles in perforated domain, where the holes are periodically distributed and have random size. And we assume that the p-capacity of each hole is stationary ergodic.     

Using the Viable System Model (VSM) to structure information processing complexity in disaster response

Earthquakes, hurricanes, flooding and terrorist attacks continue to threaten our society and, when the worst happens, lives depend on different agencies to manage the response. The literature shows that there is significant potential for operational research (OR) to aid disaster management and that, whilst some of this potential has been delivered, there is more that OR can contribute. In particular, OR can provide detailed support to analysing the complexity of information processing – an essential topic as failure could cause response agencies to act on low quality information or act too slowly – putting responders and victims at risk. However, there is a gap in methods for analysing information processing whilst delivering rapid response. This paper explores how OR can fill this gap through taking a Viable System Model (VSM) approach to analyse information processing. It contributes to the OR literature by showing how VSM can support the analysis of information processing as well as how the OR modelling technique can be further strengthened to facilitate the task.     

A problem structuring method for ecosystem-based management: The DPSIR modelling process

The purpose of this paper is to learn from Complex Adaptive Systems (CAS) theory to inform the development of Problem Structuring Methods (PSMs) both in general and in the specific context of marine management. The focus on marine management is important because it is concerned with a CAS (formed through the interconnection between natural systems, designed systems and social systems) which exemplifies their particularly ‘wicked’ nature. Recognition of this compels us to take seriously the need to develop tools for knowledge elicitation and structuring which meet the demands of CAS. In marine management, chief among those tools is the DPSIR (Drivers – Pressures – State Changes – Impacts – Responses) model and, although widely applied, the extent to which it is appropriate for dealing with the demands of a CAS is questionable. Such questioning is particularly pertinent in the context of the marine environment where there is a need to not only recognise a broad range of stakeholders (a question of boundary critique) but also to manage competing knowledge (economic, local and scientific) and value claims. Hence this paper emphasises how a CAS perspective might add impetus to the development of a critical perspective on DPSIR and PSM theory and practice to promote a more systemic view of decision-making and policy development.     

Towards a new framework for evaluating systemic problem structuring methods

Operational researchers and social scientists often make significant claims for the value of systemic problem structuring and other participative methods. However, when they present evidence to support these claims, it is usually based on single case studies of intervention. There have been very few attempts at evaluating across methods and across interventions undertaken by different people. This is because, in any local intervention, contextual factors, the skills of the researcher and the purposes being pursued by stakeholders affect the perceived success or failure of a method. The use of standard criteria for comparing methods is therefore made problematic by the need to consider what is unique in each intervention. So, is it possible to develop a single evaluation approach that can support both locally meaningful evaluations and longer-term comparisons between methods? This paper outlines a methodological framework for the evaluation of systemic problem structuring methods that seeks to do just this.