Affine metrics and its associated algebroid bundle are developed. Theses structures are applied to the general relativity and provide an structure for unification of gravity and electromagnetism. The final result is a field equation on the associated algebroid bundle that is similar to Einstein field equation but contain Einstein field equation and Maxwell equations simultaneously and contain a new equation that may have new results.
This paper is mainly intended to define a mathematical framework for unification of gravity and electromagnetism. The main idea is that affine concepts replace linear concepts in the context of general relativity. First, we introduce affine metrics on affine spaces,and then generalize semi-Riemannian manifolds to affine semi-Riemannian manifolds and investigate their associated connections and geodesics and curvatures. Then we apply these concepts to space-times in order to combine Maxwell's and Einstein's field equations into one equation.
Digital transformation and the adoption of technologies in the AEC-sector can lead to efficiency gains in facility management (FM). Digital twins, that is a living representative of the physical asset building, can facilitate real-time data gathering, data monitoring, data-based decision making and support predictive management. The purpose of this study is to analyse the gap between theory and practice regarding the application of digital twins for FM and to understand the benefits and challenges connected with its implementation during the use phase of a building. Despite the growing interest in this topic in academia, the concept of digital twins in connection with FM is rarely employed in practice in the AEC-industry. The findings obtained through a literature review and a set of semi-structured interviews with experts in the field, show that the main challenges for digital twins in FM relate to the organisational culture and that a robust framework for information management is a benefit for digital twins’ implementation. The adoption of digital twins in the built environment needs to be considered in the context of digital transformation. The study supports practitioners with the adoption of digital technologies for the built asset and suggests that future research should examine in further depth the challenges of implementing digital twins.
Yang-mills field equations describe new forces in the context of Lie groups and principle bundles. It is of interest to know if the new forces and gravitation can be described in the context of algebroids. This work was intended as an attempt to answer last question. The basic idea is to construct Einstein field equation in an algebroid bundle associated to space-time manifold. This equation contains Einstein and yang-mills field equations simultaneously. Also this equation yields a new equation that can have interesting experimental results.
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