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Hace 5 días · According to Einstein's theory of general relativity, particles of negligible mass travel along geodesics in the space-time. In flat space-time, far from a source of gravity, these geodesics correspond to straight lines; however, they may deviate from straight lines when the space-time is curved. The equation for the geodesic lines is
Hace 3 días · Curved spacetime. This article has developed the Dirac equation in flat spacetime according to special relativity. It is possible to formulate the Dirac equation in curved spacetime. The algebra of physical space. This article developed the Dirac equation using four-vectors and Schrödinger operators.
Hace 20 horas · A Riemannian metric makes it possible to define many geometric notions, including angles, lengths of curves, areas of surfaces, higher-dimensional analogues of area (volumes, etc.), extrinsic curvature of submanifolds, and the intrinsic curvature of the manifold itself.
Hace 4 días · Robust Control of Active Suspension. This example shows how to use Robust Control Toolbox™ to design a robust controller for an active suspension system. The example describes the quarter-car suspension model. Then, it computes an H ∞ controller for the nominal system using the hinfsyn command.
Hace 4 días · We reprove a result of Fiorenza–Kawai–Lê–Schwachhöfer, that closed orientable manifolds with a non-negative Ricci curvature metric and sufficiently large first Betti number are formal. Our method allows us to remove the orientability hypothesis; we further address some cases of non-closed manifolds.
Hace 2 días · The space-time curvature is a key concept in Albert Einstein's theory of relativity. What exactly is meant by the concept of space-time curvature, is not so easy to explain. We still try it.
Hace 2 días · Composition of Volumes. Spacious interiors, simple geometric shapes, and minimalism – these are the key features of contemporary houses. So, you will see circles, organic lines, curves, and smooth outlines instead of precise angles and rigid geometry in modern buildings.
