It is shown that matroid theory may provide a natural mathematical framework for a duality symmetries not only for quantum Yang-Mills physics, but also for M-theory. Our discussion is focused in an action consisting purely of the Chern-Simons term, but in principle the main ideas can be applied beyond such an action. In our treatment the theorem due to Thistlethwaite, which gives a relationship between the Tutte polynomial for graphs and Jones polynomial for alternating knots and links, plays a central role. Before addressing this question we briefly mention some important aspects of matroid theory and we point out a connection between the Fano matroid and D=11 supergravity. Our approach also seems to be related to loop solutions of quantum gravity based in Ashtekar formalism.
By combining the concepts of graviton and matroid, we outline a new gravitational theory which we call gravitoid theory. The idea of this theory emerged as an attempt to link the mathematical structure of matroid theory with M theory. Our observations are essentially based on the formulation of matroid bundle due to MacPherson and Anderson–Davis. Also, by considering the oriented matroid theory, we add new observations about the link between the Fano matroid and D=11 supergravity which was discussed in some of our recent papers. In particular we find a connection between the affine matroid AG(3, 2) and the G2-symmetry of D=11 supergravity.
In the search for renewable energy sources, solar energy appears, among others, as a powerful alternative; mainly for those countries located at Earth's equatorial region. This is the case of a Fresnel device that uses solar radiation to warm-up the air; for instance, within saunas. Authors coined the term sustainable technological innovation to refer to a technological innovation in accordance to the principles of sustainability. The object of this research was comparing the sustainability of a Fresnel Lens Solar Concentration (FLSC) against the sustainability of other twelve alternatives to generate heat. This article assesses the sustainability of fourteen technological options for heat generation and transfer to saunas in the northwest region of Mexico where temperatures often reach above 45 C and where there is a greater potential for exploiting solar energy. Emergy accounting, economic analysis, and global warming potential are the three indicators considered in quantifying sustainability. Results show that infrared ceramic photovoltaic, infrared carbon photovoltaic and infrared metal photovoltaic are the most sustainable systems. The Fresnel device reached the fourth and tenth position, using electricity from photovoltaic and from grid respectively, among all fourteen assessed devices, respectively. Although Fresnel equipment does not release any global warming gases into the atmosphere, or even it demands low amount of nonrenewable resources, 1.40 and 4.47 E17 seJF/yr. it requires high economic investment, 20,800 and 79,600 USD/yr, for the implementation and operation phases, which decrease its sustainability performance compared to twelve other evaluated devices.
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