The Economics of Uniform Laws and Uniform Law Making

From Uniform Laws of Large Numbers to Uniform Ergodic Theorems

The purpose of these lectures is to present three different approaches with their own methods for establishing uniform laws of large numbers and uniform ergodic theorems for dynamical systems. The presentation follows the principle according to which the i.i.d. case is considered first in great detail, and then attempts are made to extend these results to the case of more general dependence str...

Wanted: Uniform Law Enforcement

Snell’s Law and Uniform Refraction

1.1. In vector form. Suppose Γ is a surface inR3 that separates two media I and II that are homogeneous and isotropic. Let v1 and v2 be the velocities of propagation of light in the media I and II respectively. The index of refraction of the medium I is by definition n1 = c/v1, where c is the velocity of propagation of light in the vacuum, and similarly n2 = c/v2. If a ray of light∗ having dire...

Determining the Hydro-acoustic Characteristics of the Ship Propeller in Uniform and Non-uniform Flow

This research has been carried out to determine the marine propeller hydro-acoustic characteristics by Reynolds-Averaged Navier-Stokes (RANS) solver in both uniform and non-uniform wake flow at different operating conditions Wake flow can cause changes in pressure fluctuation and gas effect on propeller noise spectrum. Noise is generated by the induced trailing vortex wake and induced pressure ...

Uniform connectedness and uniform local connectedness for lattice-valued uniform convergence spaces

We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...