We consider the question: can the isotropy representation of an irreducible pseudoRiemannian symmetric space be realized as a conformal holonomy group? Using recent results of Čap, Gover and Hammerl, we study the representations of SO(2, 1), PSU(2, 1) and PSp(2, 1) as isotropy groups of irreducible symmetric spaces of signature (3, 2), (4, 4) and (6, 8), respectively, describing the geometry in...

In the theory of transformation groups, it is important to know what kind of isotropy subgroups of G do occur at points of the space upon which the given group G acts. In this article, for a finite group G, we prove the Equivariant Bundle Subtraction Theorem (Theorem 2.2) which allows us to construct smooth G-manifolds with prescribed isotropy subgroups around the G-fixed point sets. In Theorem...

In industrial field, the need to ensure high levels of production enhancing working precision requires the development of ever more efficient robots. The behaviour of a serial or parallel manipulator can be investigated through its kinetostatic performances [1] such as repeatability, stiffness, maximum force or velocity. They all depend on the kinematics structure of the system, on its configur...

The dynamics of the subgrid-scale (SGS) stress and scalar flux in the convective atmospheric surface layer are studied using field measurements from the Advection Horizontal Array Turbulence Study (AHATS). We extend the array technique previously used to evaluate the SGS velocity and temperature to include measurements of the fluctuating pressure, enabling separation of the resolvableand subgri...

In both equivariant bifurcation theory [GSS, especially Chapter XIII] and physical theories of spontaneous symmetry breaking (for example, the Higgs-Landau theory [M]), there is the problem of determining the symmetries, stabilities and branching patterns for solutions of equations equivariant under a compact Lie group G. Very few general results and techniques are known for the analysis of thi...

To form regulated barriers between body compartments, epithelial cells polarize into apical and basolateral domains and assemble adherens junctions (AJs). Despite close links with polarity networks that generate single polarized domains, AJs distribute isotropically around the cell circumference for adhesion with all neighboring cells [1-3]. How AJs avoid the influence of polarity networks to m...

Representations from common pre-trained language models have been shown to suffer the degeneration problem, i.e., they occupy a narrow cone in latent space. This problem can be addressed by enforcing isotropy In analogy with variational autoencoders, we suggest applying token-level loss Transformer architecture and optimizing standard deviation of prior distribution function as model parameter ...

Recurrent curvature properties are considered on four-dimensional pseudo-Riemannian homogeneous manifolds with non-trivial isotropy, and also some geometric manifolds.

We present a new approach for developing more robust and error-oriented mesh adaptation methods. Specifically, assuming that a regular (in cell shape) and uniform (in cell size) computational mesh is used (as is commonly done in computation), we develop a criterion for mesh adaptation based on an error function whose definition is motivated by the analysis of function variation and local error ...

The local isotropy of turbulent plume flow in linearly stratified saltwater was examined by using the particle image velocimetry (PIV) technique. Linear stratification was produced in a 50×50×50 cm plexiglas tank by using the two-tank method. The plume was created by injecting dense fluid downward near the top of the stratified column. Images of seeding particles in the flow were recorded at 10...