on the complex upper half-plane H, provably invariant under the linear fractional action of SL2(R), but it is oppressive to verify this directly. Worse, the goal is not merely to verify an expression presented as a deus ex machina, but, rather to systematically generate suitable expressions. An important part of this intention is understanding reasons for the existence of invariant operators, a...

The equivariant method of moving frames provides a systematic, algorithmic procedure for determining and analyzing the structure of algebras of differential invariants for both finite-dimensional Lie groups and infinite-dimensional Lie pseudo-groups. This paper surveys recent developments, including a few surprises and several open questions.

For two positive integers m and n, we let Pn be the open convex cone in R consisting of positive definite n × n real symmetric matrices and let R be the set of all m×n real matrices. In this article, we investigate differential operators on the non-reductive manifold Pn × R (m,n) that are invariant under the natural action of the semidirect product group GL(n,R)⋉R on the MinkowskiEuclid space P...

In this paper the notion of an M -th order invariant bilinear differential pairing is introduced and a formal definition is given. If the manifold has an AHS structure, then various first order pairings are constructed. This yields a classification of all first order invariant bilinear differential pairings on homogeneous spaces with an AHS structure except for certain totally degenerate cases....

The state of the art in the spectral theory of linear time-varying differential-algebraic equations (DAEs) is surveyed. To characterize the asymptotic behavior and the growth rate of solutions, basic spectral notions such as Lyapunovand Bohl exponents, and Sacker-Sell spectra are discussed. For DAEs in strangeness-free form, the results extend those for ordinary differential equations, but only...