When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...

the time-optimal trajectory for an airplane from some starting point to some final point is studied by many authors. here, we consider the extension of robot planer motion of dubins model in three dimensional spaces. in this model, the system has independent bounded control over both the altitude velocity and the turning rate of airplane movement in a non-obstacle space. here, in this paper a g...

Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...

In this paper, we give definitions of compatible mappings of type(I) and (II) in intuitionistic fuzzy metric space and obtain common fixed point theorem and example under the conditions of compatible mappings of type(I) and (II) in complete intuitionistic fuzzy metric space. Our research generalize, extend and improve the results given by many authors. : Common fixed point theorem, compatible m...

The purpose of this paper is to study the convergence problem of Mann and Ishikawa type iterative schemes of weakly contractive mapping in a complete convex metric space. We establish the results on invariant approximation for the mapping defined on a class of nonconvex sets in a convex metric space. Finally, we obtain the existence of common fixed points of two asymptotically nonexpansive mapp...

An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search. The binary search problem has a complexity of O(logN) for a list of N numbers while the sorting problem cannot be better than O(N) on any sequential computer f...

We describe a new proof of the complete integrability of the two related dynamical systems: the billiard inside the ellipsoid and the geodesic flow on the ellipsoid (in Euclidean, spherical or hyperbolic space). The proof is based on the construction of a metric on the ellipsoid whose nonparameterized geodesics coincide with those of the standard metric. This new metric is induced by the hyperb...

in this paper, we give some new definitions of m-fuzzy metric spaces and we prove a common fixed point theorem for six mappings under the condition of weakly compatible mappings in complete m-fuzzy metric spaces.

In the theory of generalized metric spaces, the notion of knetworks has played an important role. Every locally separable metric space or CW-complex, more generally, every space dominated by locally separable metric spaces has a star-countable k-network. Every LaSnev space, as well as, every space dominated by LaSnev spaces has a a-compact-finite knetwork. We recall that every space has a compa...

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.