Let G be a compact Lie group, and let LG denote the corresponding loop group. Let (X,ω) be a weakly symplectic Banach manifold. Consider a Hamiltonian action of LG on (X,ω), and assume that the moment map μ : X −→ Lg∗ is proper. We consider the function |μ|2 : X −→ R, and use a version of Morse theory to show that the inclusion map j : μ(0) −→ X induces a surjection j∗ : H∗ G(X) −→ H∗ G(μ−1(0))...

We prove that for every proper Hamiltonian action of a Lie group G in finite dimensions the momentum map is locally G-open relative to its image (i.e. images of G-invariant open sets are open). As an application we deduce that in a Hamiltonian system with continuous Hamiltonian symmetries, extremal relative equilibria persist for every perturbation of the value of the momentum map, provided the...

In this paper we define invariants of Hamiltonian group actions for central regular values of the moment map. The key hypotheses are that the moment map is proper and that the ambient manifold is symplectically aspherical. The invariants are based on the symplectic vortex equations. Applications include an existence theorem for relative periodic orbits, a computation for circle actions on a com...

For C-algebras A1, A2 the map (I1, I2) → ker(qI1 ⊗ qI2) from Id′(A1) × Id ′(A2) into Id ′(A1 ⊗min A2) is a homeomorphism onto its image which is dense in the range. Here, for a C-algebra A, the space of all proper closed two sided ideals endowed with an adequate topology is denoted Id(A) and qI is the quotient map of A onto A/I. New proofs of the equivalence of the property (F) of Tomiyama for ...

Definition. A definable orientation of a definable manifold Y of dimension m is a map s which assigns to each point y ∈ Y a generator s(y) of the local definable homology group H m (Y, Y − y) and which is locally constant in the following sense: for each proper m-ball B of Y there is a class ζB ∈ H m (Y, Y − B) such that for each p ∈ B the natural homomorphism j p : H def m (Y, Y −B)→ H m (Y, Y...

In this paper we show how to embed the variable internal structure present in square implicit descriptions inside an (A, E, B) invariant subspace contained in the kernel of the output map. Thanks to this embedding, we make unobservable the variable internal structure, obtaining in this way a proper closed loop system with a controllable pre speciÞed structure. Copyright c ° 2002 IFAC.

Rectified images are needed for proper depth map estimation. In our solution, we used chessboard calibration pattern and corners extraction algorithms. First step was to capture independent sequences for each camera and find chessboard corners coordinates. Coordinates obtained from every sequence was averaged to eliminate noise influence. Then intrinsic matrices (I) and distortion parameters (D...

Modularity and rigor are two key elements for multi-agent technology. Hong Zhu’s multi-agent system (MAS) development method provides proper language facilities supporting modularity. To enhance this method with rigor advocates a DL method to map the specification of MAS into a DL TBox. Thus, we can use the existing DL reasoners and systems to verify and validate some system’s properties.

We explore the expressiveness of the BPMN workflow modelling language by applying it to MuCoMS, a paper submission system. This well known application domain is a suitable example for demonstrating how the flow objects that the standard provides map to real-world processes and how important a proper semantic foundation is for reasoning about workflow models.

Proof. The proof is by induction on dimX. The case dimX = 0 is clear. Let x ∈ X be a smooth H-fixed point and consider the blow up BxX with exceptional divisor E ∼= P. The H-action lifts to BxX and so we get an H-action on E which has a fixed point by (1.1). Since Y is proper, the induced rational map BxX → X 99K Y is defined outside a subset of codimension at least 2. Thus we get an H-equivari...