The Ballad of Danny-The-Butcher

pages 110-11

A viability theory approach to a two-stage optimal control problem of technology adoption

A new technology adoption problem can be modelled as a two-stage control problem, in which model parameters ("technology") might be altered at some time. An optimal solution to utility maximisation for this class of problems needs to contain information on the time, at which the change will take place (0, finite or never), along with the optimal control strategies before and after the change. For the change, or switch, to occur the "new technology" value function needs to dominate the "old technology" value function, after the switch. We charaterise the value function using the fact that its hypograph is a viability kernel of an auxiliary problem and we study when the graphs can intersect. If they do not, the switch cannot occur at a positive time. Using this characterisation we analyse a technology adoption problem and showmodels, for which the switch will occur at time zero or never.technology adoption, value function, viability kernel, viscosity solutions

Numerical optimal control for HIV prevention with dynamic budget allocation

This paper is about numerical control of HIV propagation. The contribution of the paper is threefold: first, a novel model of HIV propagation is proposed; second, the methods from numerical optimal control are successfully applied to the developed model to compute optimal control profiles; finally, the computed results are applied to the real problem yielding important and practically relevant results.Comment: Submitted pape

Differential games and Zubov's method

To appear in SIAM Journal on Control and OptimizationInternational audienceIn this paper we provide generalizations of Zubov's equation to differential games without Isaacs' condition. We show that both generalizations of Zubov's equation (which we call min-max and max-min Zubov equation, respectively) possess unique viscosity solutions which characterize the respective controllability domains. As a consequence, we show that under the usual Isaacs condition the respective controllability domains as well as the local controllability assumptions coincide

Empowering hearts and minds through stories: fostering emotional intelligence and language development in young esl learners

This dissertation aims to explore the integration of Emotional Intelligence (EI) in English as a Foreign Language (EFL) classrooms for young learners in Infant Education. Specifically, it focuses on the use of storytelling as a resource to enhance both linguistic proficiency and emotional development. The final dissertation begins with a comprehensive theoretical review, examining the principles of Communicative Language Teaching (CLT), the significance of Emotional Intelligence, and the power of storytelling in Infant Education. A checklist for selecting suitable storybooks that address both EI and linguistic aspects is developed and implemented. Subsequently, a series of lesson plans are created based on these selected stories, following CLT and Task-Based Learning (TBL) principles. The dissertation also provides techniques for teachers to incorporate Emotional Intelligence in their EFL storytelling sessions, demonstrating that EI can be integrated even when the story's explicit focus is not on emotions and feelings. Moreover, an assessment tool is introduced to evaluate students' performance. The findings and the development of these materials conclude that the integration of emotional aspects can be achieved through both book selection and teaching techniques employed during storytelling sessions, emphasizing the role of teachers in promoting emotional and linguistic growth in young learners.<br /

HISTORICAL MONUMENTS AS TOURIST’S ATTRACTIONS IN EUROPE

A total of 187 people were surveyed regarding the choice of destinations, sources of information about holidays, the time spent visiting historic sites and the type of favorite monuments in Europe. Statistical correlations have been made between the various answers to questions and the results were expressed in graphs and tables. By statistical methods it was established which are the historical monuments that are preferred by the tourists when they go on holidays and if there is a correlation between them and the determining factor in choosing the holiday destinations. From the subjects interviewed, 54.6% preferred to visit medieval castles when they go on holidays, 57.8% used the Internet as a principal source of information when planning holidays, and 56.7% indicated that the main factor in the choice of destinations is the presence of the historical monuments in the area that will be visited.</p

Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions

We establish the stability under the formations of infimum and of convex combinations of subsolutions of convex Hamilton-Jacobi equations, some comparison and existence results for convex and coercive Hamilton-Jacobi equations with the Neumann type boundary condition as well as existence results for the Skorokhod problem. We define the Aubry-Mather set associated with the Neumann type boundary problem and establish some properties of the Aubry-Mather set including the existence results for the ``calibrated'' extremals for the corresponding action functional (or variational problem).Comment: 39 pages, 1 figur

A viability theory approach to a two-stage optimal control problem

A two-stage control problem is one, in which model parameters (“technology”) might be changed at some time. An optimal solution to utility maximisation for this class of problems needs to thus contain information on the time, at which the change will take place (0, finite or never) as well as the optimal control strategies before and after the change. For the change, or switch, to occur the “new technology” value function needs to dominate the “old technology” value function, after the switch. We charaterise the value function using the fact that its hypograph is a viability kernel of an auxiliary problem and study when the graphs can intersect and hence whether the switch can occur. Using this characterisation we analyse a technology switching problem