Measurement of traffic noise shielding provided by buildings

This paper presents a comparison between some current prediction methods for traffic noise shielding provided by buildings and the actual measured attenuations in typical residential areas. Generally, it was found that the method developed by the Department of Environment in the UK gives a reasonably accurate prediction of attenuation by shielding in fairly simple situations. In more complex situations, and particularly where a receiving position is close to a significant shielding structure, such as building, the attenuation obtained is underpredicted by the DOE method, thus the design facade levels for the rear of a building are overpredicted; however, in some other situations, the DOE method overpredicts the attenuation obtained. The attenuations measured for individual noise events under nominally identical conditions are shown to have large variations in attenuation.     

Tamely Ramified Towers and Discriminant Bounds for Number Fields

The root discriminant of a number field of degree n is the nth root of the absolute value of its discriminant. Let R _2m be the minimal root discriminant for totally complex number fields of degree 2m, and put ₀ = lim inf _m R _2m . One knows that ₀ 4e 22.3, and, assuming the Generalized Riemann Hypothesis, ₀ 8e 44.7. It is of great interest to know if the latter bound is sharp. In 1978, Martinet constructed an infinite unramified tower of totally complex number fields with small constant root discriminant, demonstrating that ₀ < 92.4. For over twenty years, this estimate has not been improved. We introduce two new ideas for bounding asymptotically minimal root discriminants, namely, (1) we allow tame ramification in the tower, and (2) we allow the fields at the bottom of the tower to have large Galois closure. These new ideas allow us to obtain the better estimate ₀ < 83.9.     

Measurable cardinals and the cardinality of Lindelöf spaces

We obtain from the consistency of the existence of a measurable cardinal the consistency of “small” upper bounds on the cardinality of a large class of Lindelöf spaces whose singletons are Gδ sets.