We address the problem of computing the fundamental group of a symplectic S1-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known results for compact manifolds equipped with a Hamiltonian S1-action. Several examples are presented to illustrate our main results.

We discuss BFV deformation quantization [5] in the special case of a linear Hamiltonian torus action. In particular, we show that the Koszul complex on the moment map of an effective linear Hamiltonian torus action is acyclic. We rephrase the nonpositivity condition of [2] for linear Hamiltonian torus actions. It follows that reduced spaces of such actions admit continuous star products.

We propose algorithms to get representatives and the images of the moment map of conormal bundles of GL(p,C)×GL(q,C)-orbits in the flag variety of GL(p+q,C), and GL(p+q,C)-orbits and Sp(p,C)×Sp(q,C)-orbits in the flag variety of Sp(p+ q,C) and their signed Young diagrams.

In this paper we represent harmonic moments in the language of transfinite functions, that is projective limits of polynomials in infinitely many variables. We obtain also an explicit formula for the Jacobian of a generalized harmonic moment map. Mathematics Subject Classification (2000). 13B35; 30E05; 47A57.

In this paper we study some properties of fibers of the invariant moment map for a Hamiltonian action of a reductive group on an affine symplectic variety. We prove that all fibers have equal dimension. Further, under some additional restrictions, we show that the quotients of fibers are irreducible normal schemes.

We have investigated the individual magnetic moments of Ni, Mn and Tb atoms in the intermetallic compound TbNi2Mn in the Laves phase (magnetic phase transition temperature TC ∼131 K) by X-ray magnetic circular dichroism (XMCD) studies at 300 K, 80 K and 20 K. Analyses of the experimental results reveal that Ni atoms at 20 K in an applied magnetic field of 1 T carry an intrinsic magnetic moment ...

We prove a Duistermaat-Heckman type formula in a suitable non-compact setting. We use this formula to evaluate explicitly the pushforward of the Liouville measure via the moment map of both an abelian and a non-abelian group action. As an application we obtain the classical analogues of well-known multiplicity formulas for the holomorphic discrete series representations.

2 Maximum a posteriori neural decoding 3 2.1 Gaussian approximations to the posterior p(~x|D) are tractable and useful . . 4 2.1.1 Moment-matching provides an alternative method for constructing the Gaussian approximation . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Numerical implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 MAP decoding examples: corre...

In this paper, a theoretical framework for Bayesian adaptive training of the parameters of discrete hidden Markov model (DHMM) and of semi-continuous HMM (SCHMM) with Gaussian mixture state observation densities is presented. In addition to formulating the forward-backward MAP (maximum a posterion’) and the segmental MAP algorithms for estimating the above HMM parameters, a computationally effi...

Associated to the Bergman kernels of a polarized toric \kahler manifold $(M, \omega, L, h)$ are sequences measures $\{\mu_k^z\}_{k=1}^{\infty}$ parametrized by points $z \in M$. For each $z$ in open orbit, we prove central limit theorem for $\mu_k^z$. The center mass $\mu_k^z$ is image under moment map; after re-centering at $0$ and dilating $\sqrt{k}$, re-normalized measure tends centered Gaus...