Related papers: Evolution of Ehresmann's jet theory
Euler observers are a fundamental tool for the study of spacetime evolution. Cauchy surfaces are evolved through the use of hypersurface orthogonal fields and their relationship to coordinate observers, that enable the use of already…
Theory of Riemann Extensions of the spaces with constant affine connection for the studying of the properties of nonlinear the first order systems of differential equations is proposed. Quadratic planar system of equations and the Lorenz…
Though widely observed to be emanating out from a variety of galactic and extra-galactic sources, the underlying physical mechanism behind the formation of the cosmic jets and outflows are wrapped around by the veil of mystery till date.…
The Schmidt's subspace theory with moving targets, as a significant branch in this field, has been substantially developed in recent years. We continue the approach of the previous work, construct a weighted version of generalized Schmidt…
The space-time of modern physics is tailored on light. We rigorously construct the basic entities needed by kinematics: geometry of the physical space and time, using as tool electromagnetic waves, and particularly light-rays. After such a…
We generalize the H. Cartan's theory of holomorphic curves for a general open Riemann surface. Besides, a vanishing theorem for jet differentials and a Bloch's theorem for Riemann surfaces are obtained.
A continuously evolving geography requires a good understanding in networks. As such, this paper accounts for theories and applications of complex networks and their role both in geography in general, as well as in determining various…
The issue of the transformations of units is treated, mainly, in a geometrical context. It is shown that Weyl-integrable geometry is a consistent framework for the formulation of the gravitational laws since the basic law on which this…
Gravitation might make a preferred frame appear, and with it a clear space/time separation--the latter being, a priori, needed by quantum mechanics (QM) in curved space-time. Several models of gravitation with an ether are discussed: they…
A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the…
Robotic motion optimization often focuses on task-specific solutions, overlooking fundamental motion principles. Building on Riemannian geometry and the calculus of variations (often appearing as indirect methods of optimal control), we…
Einstein-aether theory is extended by allowing for spinning degrees of freedom of the aether. In addition to the acceleration, shear, expansion, and vorticity of the aether velocity field, a spin rotation describing the dynamics of a…
In a recent study [1] we have extended the opacity expansion approach to describe jet-medium interactions including medium motion effects in the context of heavy-ion collisions. We have computed color field of the in-medium sources,…
Broadening is a classic jet observable that probes the transverse momentum structure of jets. Traditionally, broadening has been measured with respect to the thrust axis, which is aligned along the (hemisphere) jet momentum to minimize the…
The theory of gamma-ray emission from e$^{\pm}$ jets and the implications for jet formation, dynamics and structure are reviewed. In particular, possible carriers of the jet's thrust on small scales, the transition from electromagnetic to…
We construct a space which is useful in order to study the entropy of meromorphic maps by using projective limits. We deduce a variational principle for meromorphic maps.
I begin by reviewing some recent work on the status of the geodesic principle in general relativity and the geometrized formulation of Newtonian gravitation. I then turn to the question of whether either of these theories might be said to…
At present we have only the very successful but phenomenological Einstein geometrical modelling of the spacetime phenomenon. This geometrical model provides a `container' for other theories, in particular the quantum field theories. Here we…
Recent developments in Seiberg-Witten theory and relations with Complex Geometry.
Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is…