A Primer on the Tools and Concepts of Computable Economics

Computability theory came into being as a result of Hilbert's attempts to meet Brouwer's challenges, from an intuitionistc and constructive standpoint, to formalism as a foundation for mathematical practice. Viewed this way, constructive mathematics should be one vision of computability theory. However, there are fundamental differences between computability theory and constructive mathematics: the Church-Turing thesis is a disciplining criterion in the former and not in the latter; and classical logic - particularly, the law of the excluded middle - is not accepted in the latter but freely invoked in the former, especially in proving universal negative propositions. In Computable Economic an eclectic approach is adopted where the main criterion is numerical content for economic entities. In this sense both the computable and the constructive traditions are freely and indiscriminately invoked and utilised in the formalization of economic entities. Some of the mathematical methods and concepts of computable economics are surveyed in a pedagogical mode. The context is that of a digital economy embedded in an information society

Development of Boolean calculus and its applications

The development of Boolean calculus for its application to developing digital system design methodologies that would reduce system complexity, size, cost, speed, power requirements, etc., is discussed. Synthesis procedures for logic circuits are examined particularly asynchronous circuits using clock triggered flip flops

Integration of mathematics teaching with learning objects in classical and professional high school education

This article presents results of a research aimed at creating didactic material for the mathematics teaching-learning process in the high school and professional-technical education, which was developed within the period of a professional master's program. This research is the result of a cooperative work involving two study and research groups linked to both the respective master's program and institutions of integrated technical and high school education. All products were from masters' degree students and professors in the master’s degree program, who work in institutions of basic and professional education. Two products are highlighted: a "Repository of Learning Objects for Secondary and Professional Education (ROAMEP)" and a book (in press), which presents the productions and studies in the areas of mathematics and professional education. The Learning Objects (LOs) address most of the mathematics content in high school education and mathematics applications in professional technical courses. The LOs were created in the digital format, and some of them make the use of the dynamic geometry software whereas others involve activities without the use of digital technologies. In order to integrate mathematics education and professional education, the activities for technical courses address knowledge on technology including electricity, mechanics, and chemistry, involving questions of mathematical models and introduction to differential and integral calculus in addition to the knowledge required for secondary education

A model-free control strategy for an experimental greenhouse with an application to fault accommodation

Writing down mathematical models of agricultural greenhouses and regulating them via advanced controllers are challenging tasks since strong perturbations, like meteorological variations, have to be taken into account. This is why we are developing here a new model-free control approach and the corresponding intelligent controllers, where the need of a good model disappears. This setting, which has been introduced quite recently and is easy to implement, is already successful in many engineering domains. Tests on a concrete greenhouse and comparisons with Boolean controllers are reported. They not only demonstrate an excellent climate control, where the reference may be modified in a straightforward way, but also an efficient fault accommodation with respect to the actuators

Development of Boolean calculus and its application

Formal procedures for synthesis of asynchronous sequential system using commercially available edge-sensitive flip-flops are developed. Boolean differential is defined. The exact number of compatible integrals of a Boolean differential were calculated