Smooth and polyhedral approximation in Banach spaces

We show that norms on certain Banach spaces $X$ can be approximated uniformly, and with arbitrary precision, on bounded subsets of $X$ by $C^{\infty}$ smooth norms and polyhedral norms. In particular, we show that this holds for any equivalent norm on $c_0(\Gamma)$, where $\Gamma$ is an arbitrary set. We also give a necessary condition for the existence of a polyhedral norm on a weakly compactly generated Banach space, which extends a well-known result of Fonf.Comment: 12 page

Applied aerodynamics: Challenges and expectations

Aerospace is the leading positive contributor to this country's balance of trade, derived largely from the sale of U.S. commercial aircraft around the world. This powerfully favorable economic situation is being threatened in two ways: (1) the U.S. portion of the commercial transport market is decreasing, even though the worldwide market is projected to increase substantially; and (2) expenditures are decreasing for military aircraft, which often serve as proving grounds for advanced aircraft technology. To retain a major share of the world market for commercial aircraft and continue to provide military aircraft with unsurpassed performance, the U.S. aerospace industry faces many technological challenges. The field of applied aerodynamics is necessarily a major contributor to efforts aimed at meeting these technological challenges. A number of emerging research results that will provide new opportunities for applied aerodynamicists are discussed. Some of these have great potential for maintaining the high value of contributions from applied aerodynamics in the relatively near future. Over time, however, the value of these contributions will diminish greatly unless substantial investments continue to be made in basic and applied research efforts. The focus: to increase understanding of fluid dynamic phenomena, identify new aerodynamic concepts, and provide validated advanced technology for future aircraft

Extending the Coinvariant Theorems of Chevalley, Shephard--Todd, Mitchell and Springer

We extend in several directions invariant theory results of Chevalley, Shephard and Todd, Mitchell and Springer. Their results compare the group algebra for a finite reflection group with its coinvariant algebra, and compare a group representation with its module of relative coinvariants. Our extensions apply to arbitrary finite groups in any characteristic.Comment: The applications and Examples in section 4 have been extende

Probing the sheath electric field with a crystal lattice by using thermophoresis in dusty plasma

A two-dimensional dust crystal levitated in the sheath of a modified Gaseous Electronics Conference (GEC) reference cell is manipulated by heating or cooling the lower electrode. The dust charge is obtained by measuring global characteristics of the levitated crystal obtained from top-view pictures. From the force balance, the electric field in the sheath is reconstructed. From the Bohm criterion, we conclude that the dust crystal is levitated mainly above and just below the classical Bohm point

A Soccer Stadium for the Community of Phoenix

This project is a Major League Soccer stadium in Phoenix, AZ. It is built with the intention to provide both a place for sports entertainment and a landmark unique to a neighborhood of Pheonix. It incoporates local architectural practices, cultural references, and Olympic stadium design standards in order to create a site-specific architecture for sport