Bivariate Recursive Equations on Excess-of-loss Reinsurance

This paper investigates bivariate recursive equations on excess-of-loss reinsurance. For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and the number of claims belongs to R1 （a, b） family, bivariate recursive equations for the joint distribution of the cedent＇s aggregate claims and the reinsurer＇s aggregate claims are obtained.     

Freedom and trying: Understanding agent-causal exertions

In this paper, I argue that trying is the locus of freedom and moral responsibility. Thus, any plausible view of free and responsible action must accommodate and account for free tryings. I then consider a version of agent causation whereby the agent directly causes her tryings. On this view, the agent is afforded direct control over her efforts and there is no need to posit—as other agent-causal theorists do—an uncaused event. I discuss the potential advantages of this sort of view, and its challenges.     

Another independent self-dual basis for the trivial variety

We give a new independent self-dual 3-basis for the trivial variety with two binary operations. Received October 24, 2006; accepted in final form January 25, 2007.     

Ultra <Emphasis Type="Italic">LI</Emphasis>-ideals in lattice implication algebras and <Emphasis Type="Italic">MTL</Emphasis>-algebras

A mistake concerning the ultra LI-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an LI-ideal to be an ultra LI-ideal are given. Moreover, the notion of an LI-ideal is extended to MTL-algebras, the notions of a (prime, ultra, obstinate, Boolean) LI-ideal and an ILI-ideal of an MTL-algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in MTL-algebra: (1) prime proper LI-ideal and Boolean LI-ideal, (2) prime proper LI-ideal and ILI-ideal, (3) proper obstinate LI-ideal, (4) ultra LI-ideal. This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. Y605389) and K. C. Wong Magna Fund in Ningbo University.     

Multisplitting Iteration Schemes for Solving a Class of Nonlinear Complementarity Problems

We consider several synchronous and asynchronous multisplitting iteration schemes for solving aclass of nonlinear complementarity problems with the system matrix being an H-matrix.We establish theconvergence theorems for the schemes.The numerical experiments show that the schemes are efficient forsolving the class of nonlinear complementarity problems.     

Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier

Based on the matrix-analytic approach to fluid flows initiated by Ramaswami, we develop an efficient time dependent analysis for a general Markov modulated fluid flow model with a finite buffer and an arbitrary initial fluid level at time 0. We also apply this to an insurance risk model with a dividend barrier and a general Markovian arrival process of claims with possible dependencies in successive inter-claim intervals and in claim sizes. We demonstrate the implementability and accuracy of our algorithms through a set of numerical examples that could also serve as test cases for comparing other solution approaches.      

Mixing methodologies to enhance the implementation of healthcare operational research

Healthcare Operational Research (OR) has had limited success in achieving a sufficient level of stakeholder acceptance to lead to implementation of results. This research study is aimed at combining OR methodologies to achieve greater acceptance of results for organizational change. Patient flow delays in the Paediatric intensive care unit (PICU) at Children's Hospital of Wisconsin were identified using case studies. Patient flow was modelled using hard OR (simulation) using case study findings, with active stakeholder participation, and enhanced with outcomes research. Outcomes research allowed achieving greater clinical relevance of OR findings. Results from hard OR, particularly for politically sensitive issues, were persuasive but inadequate to result in change. Soft OR (cognitive mapping) was used to identify new issues and enhance results. Consequently, the planned PICU expansion was deferred, and resources focused on improving staffing strategies identified independently from both hard and soft OR. These findings suggest that: (1) Outcomes research can play a unique role to enhance results in healthcare OR. (2) After obtaining a holistic understanding of the system using hard and soft OR, stakeholders are willing to implement results from each independently, supporting the development of a common form of knowledge, which is consistent with Mixed-Mode Modelling. (3) Hard OR, enhanced with outcomes research, with active stakeholder participation, and combined with soft OR, results in greater acceptance and sustained organizational change.     

Acute Triangulations of Flat Mobius Strips

In this paper we investigate the acute triangulations of flat Mobius strips. We find out that we can always triangulate a flat Mobius strip with at most nine acute triangles, and sometimes (but not always) that many triangles are really needed.