Related papers: Constant Speed Ramps
The concepts of relative velocity and acceleration, deviation velocity and acceleration and relative momentum of point particles in spaces (manifolds), the tangent bundle of which is equipped with a transport along paths, are introduced. If…
In this paper, we study an obstacle problem associated with the mean curvature flow with constant driving force. Our first main result concerns interior and boundary regularity of the solution. We then study in details the large time…
We consider scalar-tensor theory for describing varying speed of light in a spatially flat FRW space-time. We find some exact solutions in the metric and Palatini formalisms. Also we examine the dynamics of this theory by dynamical system…
Transformation rules for coordinates, velocities and accelerations in accelerated reference frames are derived. A generalized approach of the special relativity is taken for a basis. A 7-dimensional space including projections of velocity…
The classical problem of the brachistochrone asks for the curve down which a body sliding from rest and accelerated by gravity will slip (without friction) from one point to another in least time. In undergraduate courses on classical…
The purpose of this work is to introduce and characterize the Bounded Acceleration Shortest Path (BASP) problem, a generalization of the Shortest Path (SP) problem. This problem is associated to a graph: the nodes represent positions of a…
In this paper, acceleration of gradient methods for convex optimization problems with weak levels of convexity and smoothness is considered. Starting from the universal fast gradient method which was designed to be an optimal method for…
The paper provides results for the stabilization of a spatially uniform equilibrium profile for a scalar conservation law that arises in the study of traffic dynamics under variable speed limit control. Two different control problems are…
The relation among instantaneous, mean and average velocities in one-dimensional motion with constant acceleration is studied. It was shown that the instant velocity evaluated in the time $t_{p}=\left(t_2+t_1\right)/2$ is similar to the…
We consider f(R) modified gravity theories for describing varying speed of light in a spatially flat FRW model, and find some exact solutions. Also we examine the dynamics of this model by dynamical system method assuming a LambdaCDM…
By a curve in R^d we mean a continuous map gamma:I -> R^d, where I is a closed interval. We call a curve gamma in R^d at most k crossing if it intersects every hyperplane at most k times (counted with multiplicity). The at most d crossing…
We consider solutions with conformal symmetry of the static, spherically symmetric gravitational field equations in the vacuum in the brane world scenario. By assuming that the vector field generating the symmetry is non-static, the general…
We study convex entire graphs evolving with normal velocity equal to a positive power of the mean curvature. Under mild assumptions we prove longtime existence.
We study evolution of a closed embedded plane curve with the normal velocity depending on the curvature, the orientation and the position of the curve. We propose a new method of tangential redistribution of points by curvature adjusted…
Consider the circle $C$ of length 1 and a circular arc $A$ of length $\ell\in (0,1)$. It is shown that there exists $k=k(\ell) \in \mathbb{N}$, and a schedule for $k$ runners along the circle with $k$ constant but distinct positive speeds…
Inspired by Lelek's idea from [Disjoint mappings and the span of spaces, Fund. Math. 55 (1964), 199 -- 214], we introduce the novel notion of the span of graphs. Using this, we solve the problem of determining the \emph{maximal safety…
Although special relativity limits the actual velocity of a particle to $c$, the velocity of light, the observed velocity need not be the same as the actual velocity as the observer is only aware of the position of a particle at the time in…
We apply the variable speed of light into general relativity in order to solve the problems we met in the standard cosmology. We're surprised to find that, the results from the general relativity in cosmology are exactly the same as those…
We consider marginally trapped surfaces in a spherically symmetric spacetime evolving due to the presence of a perfect fluid in D-dimensions and look at the various definitions of the surface gravity for these marginally trapped surfaces.…
Aims. New or refined methods for determining instantaneous scalar and vector pattern speeds from a restricted domain are developed, for applications in N-body simulations or in galaxies. Methods. The general feature used throughout follows…