1,720,992 research outputs found
A Generalization of Compensation Mechanism in Variable-Structure Systems
No full textThis paper introduces a mathematical mechanism generalizing the traditional one used in gauge field theories. The consequences of this generalization are explore
Electromagnetic-like generation of unified-gauge theories
No full textWe carry out a critical analysis of the Maxwell electromagnetic theory, with emphasis on ifs "geometrical" features and gauge-theoretical properties. This allows us to single out five fundamental principles, which are at the very foundation of electromagnetism and can be used to build up any (electromagnetic-like) unified-gauge theory Such principles are essentially based on the different order of commutators among covariant derivatives, and are connected in a natural way to the commutative diagrams of various orders, which relate the relevant operators involved in the electromagnetic theory. An application of this general procedure is given by considering general relativity, whose basic equations can also be derived from the five basic postulates. Moreover, the equations satisfied by the sources of the gauge field can be derived from a fundamental invariant by imposing that the continuity equation for the current be satisfied. Such an electromagnetic-like generation scheme permits us to obtain a family of unified-gauge theories, hierarchically arranged by increasing complexity
COMMUTATIVE DIAGRAMS AND TENSOR CALCULUS IN RIEMANN SPACES
No full textThe basic rules of tenser analysis in non-Euclidean spaces are derived by means of the formalism of commutative diagrams (widely used in many branches of mathematics, especially the theory of categories). We consider here as an example the case of general relativity (although this approach can be applied to gauge theories as well). The different dimensionality of the diagrams involved gives rise naturally to a hierarchy of the corresponding physical relations, starting from the simplest differential object-covariant derivative-to Bianchi identities and Einstein's equations. The commutative-diagram approach allows one to single out in a natural way three basic postulates, which can be applied to build up any gauge theory
Non-conservative gravitational equations
No full textWe propose a theory of gravity based on the interaction of the gauge field representing gravitation with a suitable vector ''substratum'' (physical vacuum). To build up the new theory, we exploit the formalism of the Symbolic Gauge Theory, an application to gauge theories of the General System Logic Theory, which results from the Fusion of three mathematical structures, the logical theory of systems, the categorial algebra and the Lie algebra. The coupling of gravity to the substratum implies the nonconservation of the energy-momentum tenser. The derivative coupling term is approximated to the first order, and a Schwarzschild-like solution of the corresponding nonconservative gravitational equations is obtained. It is shown that, in this approximation, the main effect of the new theory is to introduce an extra-mass term in the standard Schwarzschild metric. The application of such a result to perihelion shifts and light deflection yields results comparable to those obtained in General Relativity. Gravitational-wave solutions of the new equations are derived in the weak field approximation. It is shown that our nonconservative theory of gravity implies a cosmological model with a locally varying, non-zero cosmological ''constant''
A general system logical approach to task representation for intelligent robots
No full textGroningen, Oland
A general system logical theory and its applications to task description for intelligent robots
No full textBratislava, Slovacchi
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