It is proven that the physical measure for the two-dimensional Yang-Mills theory is purely singular with respect to the kinematical Ashtekar-Lewandowski measure. For this, an explicit decomposition of the gauge orbit space into supports of these two measures is given. Finally, the results are extended to more general (e.g. confining) theories. Such a singularity implies, in particular, that the...

The rate of the beta decay of neutral kaons is calculated within the meson dominance approach taking into account the relation between the KKρ and ππρ coupling constants which follows from the vector meson dominance in electromagnetic interactions and isospin symmetry. The decay rate transforms into the following branching fraction summed over the charge states indicated: B(K L → Keν) = (2.53 ±...

We work throughout in the category Cmd of commutative monoids. In other words, all the monoids we meet are commutative, and consequently we say 'monoid' in place of the longer 'commutative monoid'. However, occasionally we will emphasize the commu-tativity. Almost every monoid A we meet will be written multiplicatively, that is we write xy for the compound of x, y ∈ A. In places we write someth...

1.1 Assumptions We will use the following assumptions throughout this paper, unless otherwise noted: 1. Risk Neutrality: Bidders are risk neutral and seek to maximize expected profits. 2. Quasi-linear Utility: Bidders utilities equal value minus payment. 3. IPV: Independent private values among bidders. 4. Common Knowledge: Everything except for individual private types (including valuation and...

This thesis examines theories of analysis, evaluation, and learning in policy development and applies them to a case study of developing legislation in Massachusetts to manage used motor oil from people who change their own oil. Policy-oriented learning is facilitated by open consensus building processes that build understanding of policy problems and solutions through discourse and argument. W...

In this paper, we prove the global risk optimality of the hedging strategy of contingent claim, which is explicitly (or called semi-explicitly) constructed for an incomplete financial market with external risk factors of non-Gaussian Ornstein-Uhlenbeck (NGOU) processes. Analytical and numerical examples are both presented to illustrate the effectiveness of our optimal strategy. Our study establ...

In building models of facial appearance, we adopt a statistical approach that learns the ways in which the shape and texture of the face vary across a range of images. We rely on obtaining a suitably large and representative training set of images of faces, each of which is annotated with a set of feature points that define correspondences across the set. The positions of the feature points als...

We construct a continuous state branching process with immigration (CBI) whose immigration depends on the CBI itself and we recover a continuous state branching process (CB). This provides a dual construction of the pruning at nodes of CB introduced by the authors in a previous paper [1]. This construction is a natural way to model neutral mutation. Using exponential formula, we compute the pro...

In this thesis, we study the behavior of bankrupt stocks. Bankrupt stock is a special case of the Hard-to-Borrow stocks. Besides the general nice feature of the Hard-to-borrow feedback for the buy-in demand, the bankrupt stocks could exclude the diffusive effects. This nice property would modify the Marco Avellaneda and Mike Lipkin’s jump-diffusion model for the Hard-to-Borrow stocks into the p...

The risk-neutral equilibrium bidding strategy for first-price auctions with independent private values is justified without assuming a well-defined Bayesian game. Bidders, aware of their own value, assume the private values to be linearly related. The latter, however, are independent and identically distributed, and this is only known by Nature. Allowing for arbitrary linear common value belief...