We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

biharmonic surfaces in euclidean space $mathbb{e}^3$ are firstly studied from a differential geometric point of view by bang-yen chen, who showed that the only biharmonic surfaces are minimal ones. a surface $x : m^2rightarrowmathbb{e}^{3}$ is called biharmonic if $delta^2x=0$, where $delta$ is the laplace operator of $m^2$. we study the $l_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...

In this paper we study the property of generic global rigidity for frameworks of graphs embedded in d-dimensional complex space and in a d-dimensional pseudo-Euclidean space (R with a metric of indefinite signature). We show that a graph is generically globally rigid in Euclidean space iff it is generically globally rigid in a complex or pseudo-Euclidean space. We also establish that global rig...

Biharmonic surfaces in Euclidean space $mathbb{E}^3$ are firstly studied from a differential geometric point of view by Bang-Yen Chen, who showed that the only biharmonic surfaces are minimal ones. A surface $x : M^2rightarrowmathbb{E}^{3}$ is called biharmonic if $Delta^2x=0$, where $Delta$ is the Laplace operator of $M^2$. We study the $L_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...

‎Einstein‎, ‎M"{o}bius‎, ‎and Proper Velocity gyrogroups are relativistic gyrogroups that appear as three different realizations of the proper Lorentz group in the real Minkowski space-time $bkR^{n,1}.$ Using the gyrolanguage we study their gyroharmonic analysis‎. ‎Although there is an algebraic gyroisomorphism between the three models we show that there are some differences between them‎. ‎Our...

This paper is concerned with a structural analysis of euclidean field theories on the euclidean sphere. In the first section we give proposal for axioms for a euclidean field theory on a sphere in terms of C*algebras. Then, in the second section, we investigate the short-distance behavior of euclidean field theory models on the sphere by making use of the concept of scaling algebras, which has ...