Temporal integration of equations possessing continuous symmetries (e.g. systems with translational invariance associated with traveling solutions and scale invariance associated with self-similar solutions) in a “co-evolving” frame (i.e. a frame which is co-traveling, co-collapsing or co-exploding with the evolving solution) leads to improved accuracy because of the smaller time derivative in ...

In this paper, we propose relative projective differential invariants (RPDIs) which are invariant to general projective transformations. By using RPDIs and the structural frame of integral invariant, projective weighted moment invariants (PIs) can be constructed very easily. It is first proved that a kind of projective invariants exists in terms of weighted integration of images, with relative ...

We give sufficient conditions for a group of homeomorphisms of a compact Hausdorff space to have an invariant probability measure. For a complex projective space CP we give a necessary condition for a subgroup of Aut(CP) to have an invariant probability measure. We discuss two approaches to Auslander’s conjecture.

A category is described to which the Cuntz semigroup belongs and as a functor into which it preserves inductive limits. 1. Recently, Toms in [26] used the refinement of the invariant K0 introduced by Cuntz almost thirty years ago in [4] to show that certain C*-algebras are not isomorphic. Anticipating the possible use of this invariant to establish isomorphism, we take the liberty of reporting ...

We show that, for both the conformal and projective groups, all the differential invariants of a generic surface in three-dimensional space can be written as combinations of the invariant derivatives of a single differential invariant. The proof is based on the equivariant method of moving frames.

In this paper, we introduce a new homological invariant called quasi-projective dimension, which is generalization of projective dimension. We discuss various properties Among other things, prove the following. (1) Over quotient regular local ring by sequence, every finitely generated module has finite (2) The Auslander--Buchsbaum formula and depth for modules dimension remain valid (3) Several...

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion that ensure that the restriction of invariant polynomials to subspaces is surjective. We apply our criterion to problems in Fourier analysis on projective/in...

Projectively invariant shape descriptors allow fast indexing into model libraries without the need for pose computation or camera calibration. This paper describes progress in building a model based vision system for plane objects that uses algebraic projective invari-ants. We give a brief account of these descriptors and then describe the recognition system, giving examples of the invariant te...

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion that ensure that the restriction of invariant polynomials to subspaces is surjective. We apply our criterion to problems in Fourier analysis on projective/in...