Let A be a closed subgroup of a connected, solvable Lie group G, such that the homogeneous space A\G is simply connected. As a special case of a theorem of C. T. C. Wall, it is known that every tessellation A\G/Γ of A\G is finitely covered by a compact homogeneous space G′/Γ′. We prove that the covering map can be taken to be very well behaved — a “crossed” affine map. This establishes a connec...

This paper provides a detailed discussion of the second covariant derivative of a map and its role in the Lie group projection operator approach (a direct method for solving continuous time optimal control problems). We begin by briefly describing the iterative geometric optimal control algorithm and summarize the general expressions involved. Particular emphasis is placed on the expressions re...

This paper presents an affine model for 3-D motion and shape recovery using two perspective views and their relative 2-D displacement field. The 2-D displacement vectors are estimated as parameters of a 2D affine model that generalizes standard block matching by allowing affine shape deformations of image blocks and affine intensity transformations. The matching block size is effectively found ...

In a previous paper [J. Combin. Theory Ser. A, 2019], the author constructed geometric crystal on variety Xk:=Gr(k,n)×C× which tropicalizes to affine structure rectangular tableaux with n−k rows. this sequel, we define and study R-matrix, birational map R:Xk1×Xk2→Xk2×Xk1 combinatorial R-matrix pairs of tableaux. We show that R is an isomorphism crystals, it satisfies Yang–Baxter relation. case ...

Let D be a bounded domain in C with ζ0 ∈ ∂D. We say that ζ0 is a substantial boundary point of D for the affine stretch x+ iy 7→ Kx+ iy, where K > 1, if for every neighbourhood U of ζ0 and for every component V of U ∩ D with ζ0 ∈ ∂V , the maximal dilatation of f is at least K for every quasiconformal map f of V such that f(x+ iy) = Kx+ iy for all x+ iy ∈ ∂V ∩ ∂D. We give here a criterion for a ...