Averages and moments associated to class numbers of imaginary quadratic fields

For any odd prime $\ell$, let $h_\ell(-d)$ denote the $\ell$-part of the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{-d})$. Nontrivial pointwise upper bounds are known only for $\ell =3$; nontrivial upper bounds for averages of $h_\ell(-d)$ have previously been known only for $\ell =3,5$. In this paper we prove nontrivial upper bounds for the average of $h_\ell(-d)$ for all primes $\ell \geq 7$, as well as nontrivial upper bounds for certain higher moments for all primes $\ell \geq 3$.Comment: 26 pages; minor edits to exposition and notation, to agree with published versio

Induction probe determines levels of liquid metals

Mutual-inductance probe accurately measures liquid levels in a variety of liquid metals at elevated temperatures. It can be used in pyrochemical processes for the recovery of spent reactor fuel

Simultaneous Integer Values of Pairs of Quadratic Forms

We prove that a pair of integral quadratic forms in 5 or more variables will simultaneously represent "almost all" pairs of integers that satisfy the necessary local conditions, provided that the forms satisfy a suitable nonsingularity condition. In particular such forms simultaneously attain prime values if the obvious local conditions hold. The proof uses the circle method, and in particular pioneers a two-dimensional version of a Kloosterman refinement.Comment: 63 page

Determination of tungsten resonance absorption integrals by activation

Determination of tungsten resonance absorption integrals by activatio

Two techniques enable sampling of filtered and unfiltered molten metals

Filtered samples of molten metals are obtained by filtering through a plug of porous material fitted in the end of a sample tube, and unfiltered samples are obtained by using a capillary-tube extension rod with a perforated bucket. With these methods there are no sampling errors or loss of liquid

Titanium-nitrogen reaction investigated for application to gettering systems

Titanium is one of several gettering materials available for removing nitrogen from inert gases. The reaction rate of titanium-metal sponge and nitrogen in argon-nitrogen mixtures was studied at 900 degrees C. The rate was found to depend upon the partial pressure of nitrogen in the gas phase. Mathematical relationships simulate titanium systems

Precipitation in a warming world: Assessing projected hydro-climate changes in California and other Mediterranean climate regions.

In most Mediterranean climate (MedClim) regions around the world, global climate models (GCMs) consistently project drier futures. In California, however, projections of changes in annual precipitation are inconsistent. Analysis of daily precipitation in 30 GCMs reveals patterns in projected hydrometeorology over each of the five MedClm regions globally and helps disentangle their causes. MedClim regions, except California, are expected to dry via decreased frequency of winter precipitation. Frequencies of extreme precipitation, however, are projected to increase over the two MedClim regions of the Northern Hemisphere where projected warming is strongest. The increase in heavy and extreme precipitation is particularly robust over California, where it is only partially offset by projected decreases in low-medium intensity precipitation. Over the Mediterranean Basin, however, losses from decreasing frequency of low-medium-intensity precipitation are projected to dominate gains from intensifying projected extreme precipitation. MedClim regions are projected to become more sub-tropical, i.e. made dryer via pole-ward expanding subtropical subsidence. California's more nuanced hydrological future reflects a precarious balance between the expanding subtropical high from the south and the south-eastward extending Aleutian low from the north-west. These dynamical mechanisms and thermodynamic moistening of the warming atmosphere result in increased horizontal water vapor transport, bolstering extreme precipitation events

Sound propagation over uneven ground and irregular topography

The development of theoretical, computational, and experimental techniques for predicting the effects of irregular topography on long range sound propagation in the atmosphere is discussed. Irregular topography here is understood to imply a ground surface that (1) is not idealizable as being perfectly flat or (2) that is not idealizable as having a constant specific acoustic impedance. The study focuses on circumstances where the propagation is similar to what might be expected for noise from low-altitude air vehicles flying over suburban or rural terrain, such that rays from the source arrive at angles close to grazing incidence