n-Expansively super-homogeneous and $(n,k)$-contractively sub-homogeneous fuzzy control functions and stability results with numerical examples

Numerical Computation of Homogeneous Slope Stability

To simplify the computational process of homogeneous slope stability, improve computational accuracy, and find multiple potential slip surfaces of a complex geometric slope, this study utilized the limit equilibrium method to derive expression equations of overall and partial factors of safety. This study transformed the solution of the minimum factor of safety (FOS) to solving of a constrained...

Integration and Homogeneous Functions

We show that integrating a (positively) homogeneous function f on a compact domain Ω ⊂ Rn reduces to integrating a related function on the boundary ∂Ω. The formula simplifies when the boundary ∂Ω is determined by homogeneous functions. Similar results are also presented for integration of exponentials and logarithms of homogeneous functions.

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

Convolution and Homogeneous Spaces

Homogeneous Principal Bundles and Stability

Let G/P be a rational homogeneous variety, where P is a parabolic subgroup of a simple and simply connected linear algebraic group G defined over an algebraically closed field of characteristic zero. A homogeneous principal bundle over G/P is semistable (respectively, polystable) if and only if it is equivariantly semistable (respectively, equivariantly polystable). A stable homogeneous princip...