Hattendorff Differential Equation for Multi-State Markov Insurance Models

We derive a Hattendorff differential equation and a recursion governing the evolution of continuous and discrete time evolution respectively of the variance of the loss at time t random variable given that the state at time t is j, for a multistate Markov insurance model (denoted by 2σt(j)). We also show using matrix notation that both models can be easily adapted for use in MATLAB for numerical computations.

Territorial Diagnosis of Ecotourism in Tunisian Mountain Protected Areas: Stakeholders, Positions and Power Relations

Since the 2000s, projects and studies have been multiplied for the development of ecotourism in Tunisian protected areas. Despite these efforts, the Tunisian case faces several failures. As part of this study, we aim to provide elements of reflection on a contractual scheme for a sustainable territorial development plan by ecotourism, around mountain protected areas in Tunisia. For this reason, we adopted the strategic prospective analysis revealing and analyzing the relationships between the different actors involved in ecotourism in the protected area. A Matrix of Alliances, Conflicts, Tactics and Objectives among MACTOR actors was developed in a participatory way to analyze the actors' strategies. After doing a triangular analysis which consists in to an inventory of the projects and studies about the protected area of Ichkeul and Cape Negro-Jbel Chitana, semi-structured interviews with personals from different sectors, we invited the actors met on the field or mentioned in the projects in a workshop organized in partnership with the General Directorate of Forests in Tunis in order to identify the different categories of actors and analyze the balance of power between them. This analysis is done through a matrix notation system. Eight categories of actors have been identified: international cooperation, resource managers, politic policy etc. Thanks to the matrix notation systems, we have been able in a participative way to classify these eight categories of actors into four types: dominant actors, relay actors, autonomous actors and dominated actors. Thus, the MACTOR method allowed us to identify actors who played a role in the development of ecotourism projects in Tunisia and to be able to diagnose their balance of power. This allowed showing the multidisciplinarity and complexity of the sector as well as the strong influence of certain actors such as international cooperation and public decision-makers. To conclude, the MACTOR analysis of the ecotourism actors in the protected area of Ichkeul and Cap Negro-Jbel Chitana enters into a methodology of prospective territorial analysis in this area to understand the points that caused the failure of several experiments.

On Advantages of the Kelvin Mapping in Finite Element Implementations of Deformation Processes

Classical continuum mechanical theories operate on three-dimensionalEuclidian space using scalar, vector, and tensor-valued quantities usuallyup to the order of four. For their numerical treatment, it is commonpractice to transform the relations into a matrix-vector format. Thistransformation is usually performed using the so-called Voigt mapping. Thismapping does not preserve tensor character leaving significant room forerror as stress and strain quantities follow from different mappings andthus have to be treated differently in certain mathematical operations.Despite its conceptual and notational difficulties having been pointed out,the Voigt mapping remains the foundation of most current finite elementprogrammes. An alternative is the so-called Kelvin mapping which hasrecently gained recognition in studies of theoretical mechanics. Thisarticle is concerned with benefits of the Kelvin mapping in numericalmodelling tools such as finite element software. The decisive difference tothe Voigt mapping is that Kelvin’s method preserves tensor character, andthus the numerical matrix notation directly corresponds to the originaltensor notation. Further benefits in numerical implementations are thattensor norms are calculated identically without distinguishing stress orstrain-type quantities and tensor equations can be directly transformedinto matrix equations without additional considerations. The onlyimplementational changes are related to a scalar factor in certain finiteelement matrices and hence, harvesting the mentioned benefits comes at verylittle cost.