On universal Banach spaces of density continuum

We consider the question whether there exists a Banach space X of density continuum such that every Banach space of density at most continuum isomorphically embeds into X (called a universal Banach space of density c). It is well known that a""(a)/c (0) is such a space if we assume the continuum hypothesis. Some additional set-theoretic assumption is indeed needed, as we prove in the main result of this paper that it is consistent with the usual axioms of set-theory that there is no universal Banach space of density c. Thus, the problem of the existence of a universal Banach space of density c is undecidable using the usual axioms of set-theory. We also prove that it is consistent that there are universal Banach spaces of density c, but a""(a)/c (0) is not among them. This relies on the proof of the consistency of the nonexistence of an isomorphic embedding of C([0, c]) into a""(a)/c (0).

Hypoellipticity in spaces of ultradistributions-Study of a model case

In this work we study C (a)-hypoellipticity in spaces of ultradistributions for analytic linear partial differential operators. Our main tool is a new a-priori inequality, which is stated in terms of the behaviour of holomorphic functions on appropriate wedges. In particular, for sum of squares operators satisfying Hormander's condition, we thus obtain a new method for studying analytic hypoellipticity for such a class. We also show how this method can be explicitly applied by studying a model operator, which is constructed as a perturbation of the so-called Baouendi-Goulaouic operator.

The Effect of Weight on the Perception of Political Candidates

Chris Christie recently visited the famous “Wailing Wall” in Jerusalem, Israel, during his first trip abroad as governor of New Jersey. The New York Post reported on his trip with the headline “The Whale at the Wall” (Campanile 2012). Given headlines like this, it is easy to see anecdotal evidence of the stigmatization that surrounds obesity within contemporary American society. What’s more important is that these social stigmas that Americans are faced with every day are not merely surface level jokes bantered about for a cheap laugh. They are often prejudices that permeate every aspect of human life. Whether it comes to finding a date, looking for a job, or trying to be taken serious by one’s peers, weight is always a topic of concern. In an effort to understand how far entrenched these biases are in society, this thesis studies the ramifications of obesity in politics. In this thesis, I attempt to understand to what extent, if any, obesity matters in regard to candidate appearance, voters' choices, and political behavior.