Spaces of orderings provide an abstract framework in which to study spaces of orderings of formally real fields. Spaces of orderings of finite chain length are well understood [9] [12]. The Isotropy Theorem [12] and the extension of the Isotropy Theorem given in [13] are the main tools for reducing questions to the finite case, and these are quite effective. At the same time, there are many que...

We introduce a new construction, the isotropy groupoid, to organize the orbit data for split Γ-spaces. We show that equivariant principal G-bundles over split Γ-CW complexes X can be effectively classified by means of representations of their isotropy groupoids. For instance, if the quotient complex A = Γ\X is a graph, with all edge stabilizers toral subgroups of Γ, we obtain a purely combinato...

We use a systematic construction method for invariant connections on homogeneous spaces to find the Einstein-SU (n)-Yang-Mills equations for Friedmann-Robertson-Walker and locally rotationally symmetric homogeneous cosmologies. These connections depend on the choice of a homomorphism from the isotropy group into the gauge group. We consider here the cases of the gauge group SU (n) and SO(n) whe...

In this paper, the equation of motion for an incompressible transversely isotropic fibre-reinforced elastic solid is derived in terms of a scalar function.   The general solution of the equation of motion is obtained, which satisfies the required radiation condition.  The appropriate traction free boundary conditions are also satisfied by the solution to obtain the required secular equation for...

The integration of topology optimization with lattice structures has shown great potential for the additive manufacturing (AM) lightweight superior mechanical properties and multifunctional characteristics. To further improve design manufacturability, structural efficiency, isotropy computational homogenization-based (HMTO) method was proposed to integrate plate–lattices exhibiting excellent el...

Deviations from statistical isotropy can be modeled in various ways, for instance, anisotropic cosmological models (Bianchi models), compact topologies and presence of primordial magnetic field. Signature of anisotropy manifests itself in CMB correlation patterns. Here we explore the symmetries of the correlation function and its implications on the observable measures constructed within the Bi...

A new global isotropy index (GII) is proposed to quantify the configuration independent isotropy of a robot's Jacobian or mass matrix. A new discrete global optimization algorithm is also proposed to optimize either the GII or some local measure without placing any conditions on the objective function. The algorithm is used to establish design guidelines and a globally optimal architecture for ...

We use a systematic construction method for invariant connections on homogeneous spaces to find the Einstein-SU (n)-Yang-Mills equations for Friedmann-Robertson-Walker and locally rotationally symmetric homogeneous cosmologies. These connections depend on the choice of a homomorphism from the isotropy group into the gauge group. We consider here the cases of the gauge group SU (n) and SO(n) whe...