We give mathematical reformulations of the cardinals p and t in terms of families of Borel functions. As an application we show that t is invariant under the addition of a single Cohen real.

We give a general recipe for explicitly constructing asymptotically optimal towers of modular curves such as {X0(l)}n>1. We illustrate the method by giving equations for eight towers with various geometric features. We conclude by observing that such towers are all of a specific recursive form and speculate that perhaps every tower of this form which attains the Drinfeld-Vlăduţ bound is modular...

design and construction of efficient and economic reinforced concrete (r.c.) hyperbolic cooling towers have driven the engineers toward the design of tall and thin-shell towers which have considerable high slenderness aspect ratio. consequently, the shell of r.c. cooling towers with relative high slenderness aspect ratio is extremely prone to buckling instability due to wind loading. to increas...

exergy analysis and response surface methodology (rsm) is applied to reduce the exergy loss and improve energy and exergy efficiency of acetic acid production plant. exergy analysis is run as a thermodynamic tool to assess exergy loss in reactor and towers of acetic acid production process. the process is simulated in aspen plus(v.8.4) simulator and the necessary thermodynamics data for calcula...

Abstract. Long-span suspended bridges rely upon networks of tensed cables that carry the weight deck. The are generally connected to a number vertical towers (pylons) transfer forces foundations as in case cable-stayed bridge. Their structural behaviour is highly influenced by pretension on account redundancy structure. Several methods have been proposed for determining cables, such Load-Balanc...

The structural condition of the cable-stayed towers anchorage on power transmission lines requires constant monitoring. Maintenance routines must be able to identify faulty anchor rods and substitute them avoid tower collapses delivery interruptions. Modern statistical diagnostic systems based machine learning generation several distinct rod sample signals trained, which is a time-consuming pro...

Walter D. Goldberger and Ira Z. Rothstein Dept. of Physics, Yale University, New Haven CT 06520, USA Dept. of Physics, Carnegie Mellon University, Pittsburgh PA 15213, USA Abstract In this essay we introduce a theoretical framework designed to describe black hole dynamics. The difficulties in understanding such dynamics stems from the proliferation of scales involved when one attempts to simult...