This paper develops methods for designing a large class of locally dynamic isotropic modified symmetric Gough-Stewart parallel micromanipulators (MSGSPMs). First, by exploiting rotational symmetric geometry, the concept of dynamic isotropy is proposed and the dynamic isotropy matrix considering the mass geometry characteristics of the payload is constructed symbolically. Next, the singular valu...

An optimal designmethod for the Gough–Stewart platformmanipulators based on dynamic isotropy is proposed. First, a dynamic isotropy measure is derived from the analysis of the natural frequencies of a Stewart platform at a neutral pose using the inverse of the joint space mass matrix. Next, considering a specific Gough–Stewart platform (SGSP), it is found that, when the payload inertia matrix i...

A distribution of points that satisfies the property of local isotropy is not necessarily homogeneous: homogeneity is implied by the condition of local isotropy together with the assumption of analyticity or regularity. Here we show that the evidence of dipole saturation in galaxies (and clusters) catalogues, together with a monotone growth of the monopole, is an evidence of isotropy but not of...

The Bröcker–Prestel local-global principle characterizesweak isotropy of quadratic forms over a formally real field in terms of weak isotropy over the henselizations and isotropy over the real closures of that field. A hermitian analogue of this principle is presented for algebras of index at most two. An improved result is also presented for algebras with a decomposable involution, algebras of...

A connected Riemannian manifold (M,g) is said to be isotropy irreducible if for each point p ∈ M the isotropy group Hp, i.e. all isometries of g fixing p, acts irreducibly on TpM via its isotropy representation. This class of manifolds is of great interest since they have a number of geometric properties which follow immediately from the definition. By Schur’s lemma the metric g is unique up to...

Conventional lattice Boltzmann models only satisfy moment isotropy up to fourth order. In order to accurately describe important physical effects beyond the isothermal NavierStokes fluid regime, higher-order isotropy is required. In this paper, we present some basic results on moment isotropy and its relationship to the rotational symmetry of a generating discrete vector set. The analysis provi...

We examine statistical isotropy of large scale anisotropies of the Internal Linear Combination (ILC) map, based on three year WMAP data. Our study reveals no significant deviation from statistical isotropy on large angular scales of 3-year ILC map. Comparing statistical isotropy of 3-year ILC map and 1-year ILC map, we find a significant improvement in 3-year ILC map which can be due to the gai...

An orthogonal involution on a central simple algebra becoming isotropic over any splitting field of the algebra, becomes isotropic over a finite odd degree extension of the base field (provided that the characteristic of the base field is not 2). Our aim is a proof of the following result, generalizing the hyperbolicity statement of [5]: Theorem 1. Let F be a field of characteristic not 2, A a ...