Stability of the global attractor under Markov-Wasserstein noise

We develop a "weak Wa\.zewski principle" for discrete and continuous time dynamical systems on metric spaces having a weaker topology to show that attractors can be continued in a weak sense. After showing that the Wasserstein space of a proper metric space is weakly proper we give a sufficient and necessary condition such that a continuous map (or semiflow) induces a continuous map (or semiflow) on the Wasserstein space. In particular, if these conditions hold then the global attractor, viewed as invariant measures, can be continued under Markov-type random perturbations which are sufficiently small w.r.t. the Wasserstein distance, e.g. any small bounded Markov-type noise and Gaussian noise with small variance will satisfy the assumption.Comment: 19 page

SEC Reporting Requirements for Publicly Traded Companies Should not be Expanded Despite Advancements in Information Technology

Advancements in information technology allow information to be collected and analyzed quickly within a corporation. As a result, technology also allows the quicker release of information to the Securities Exchange Commission (SEC)—much quicker than the Form 10-K and Form 10-Q releases that are currently required for publicly traded companies. Although publicly traded companies must also disclose certain significant events in Form 8-K, the reporting requirements for publicly traded companies are not nearly as expansive as they could be considering the easy access these companies have to their business information. Even with this in mind, the SEC is well into a reevaluation of Regulation S-K primarily because requirements have accreted over time to become not just burdensome to companies but also blinding to investors who are overwhelmed by the volume of disclosure thrown at them. This paper expounds on these arguments and posits additional arguments for why the SEC should not expand reporting requirements for publicly traded companies. Specifically, expanded requirements are associated with high compliance costs; market forces already induce higher-quality disclosures; the more information companies file with the SEC, the more advantages they give to their competitors; and both the liability concerns and the doctrinal issues already associated with the current requirements will be exacerbated with an expansion of the requirements

The Tennis Ball Problem

Stereoscopic vision is a well-established phenomenon: biological evolution showed its utility in ancient times. In this workshop, we have examined some subtleties and limitations in applying this old concept to an entirely new application: with modern technology, we attempt to track the position of an early segment of a flying object, and then extrapolate its later trajectory

Uniformly convex metric spaces

In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology called co-convex topology agrees with the usualy weak topology in Banach spaces. An example of a $CAT(0)$-spaces with weak topology which is not Hausdorff is given. This answers questions raised by Monod 2006, Kirk and Panyanak 2008 and Esp\'inola and Fern\'andez-Le\'on 2009. In the end existence and uniqueness of generalized barycenters is shown and a Banach-Saks property is proved.Comment: 23 page