Multiplicity-free Hamiltonian group actions are the symplectic analogs of multiplicity-free representations, that is, representations in which each irreducible appears at most once. The most well-known examples are toric varieties. The purpose of this paper is to show that under certain assumptions multiplicity-free actions whose moment maps are transversal to a Cartan subalgebra are in one-to-...

2 Autonomous differential equations Lemma 1. If A ∈ B(R), then det(I + A+ o( )) = 1 + trA+ o( ) as → 0. Proof. Let λ1, . . . , λn be the eigenvalues of A, repeated according to algebraic multiplicity. For > 0, the eigenvalues of I + A + o( ) repeated according to algebraic multiplicity are 1 + λ1 + o( ), . . . , 1 + λn + o( ), as → 0. The determinant of a linear map R → R is the product of its ...

Abstract. Herzog, Huneke, and Srinivasan have conjectured that for any homogeneous k-algebra, the multiplicity is bounded above by a function of the maximal degrees of the syzygies and below by a function of the minimal degrees of the syzygies. The goal of this paper is to establish the multiplicity conjecture of Herzog, Huneke, and Srinivasan about the multiplicity of graded Cohen-Macaulay alg...

A result of Watanabe and Yoshida says that an unmixed local ring of positive characteristic is regular if and only if its Hilbert-Kunz multiplicity is one. We show that, for fixed p and d, there exist a number ǫ(d, p) > 0 such that any nonregular unmixed ring R its Hilbert-Kunz multiplicity is at least 1+ ǫ(d, p). We also show that local rings with sufficiently small Hilbert-Kunz multiplicity a...

Identical particle correlations at fixed multiplicity are considered in the presence of chaotic and coherent fields. The multiplicity distribution, one-particle momentum density and two-particle correlation function are obtained based on the diagrammatic representation for cumulants in semi-inclusive events. Our formulation is applied to the analysis of the experimental data on the multiplicity...

The energy and system size dependence of pseudorapidity (η) and multiplicity distributions of photons are measured in the region −2.3 ≤ η ≤ −3.7 for Cu + Cu collisions at √ sNN = 200 and 62.4 GeV. Photon multiplicity measurements at forward rapidity have been carried out using a Photon Multiplicity Detector (PMD) in the STAR experiment. Photons are found to follow longitudinal scaling for Cu + ...

Planning and learning in Partially Observable MDPs (POMDPs) are among the most challenging tasks in both the AI and Operation Research communities. Although solutions to these problems are intractable in general, there might be special cases, such as structured POMDPs, which can be solved efficiently. A natural and possibly efficient way to represent a POMDP is through the predictive state repr...

Going to college has long been assumed to liberalize students' religious beliefs. Using longitudinal data from the National Survey of Youth and Religion, we compare change in the content of religious beliefs of those who do and do not attend college. We find that, in general, college students are no more likely to develop liberal religious beliefs than nonstudents. In some cases, collegians act...