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

An experiment in software reliability

The results of a software reliability experiment conducted in a controlled laboratory setting are reported. The experiment was undertaken to gather data on software failures and is one in a series of experiments being pursued by the Fault Tolerant Systems Branch of NASA Langley Research Center to find a means of credibly performing reliability evaluations of flight control software. The experiment tests a small sample of implementations of radar tracking software having ultra-reliability requirements and uses n-version programming for error detection, and repetitive run modeling for failure and fault rate estimation. The experiment results agree with those of Nagel and Skrivan in that the program error rates suggest an approximate log-linear pattern and the individual faults occurred with significantly different error rates. Additional analysis of the experimental data raises new questions concerning the phenomenon of interacting faults. This phenomenon may provide one explanation for software reliability decay

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

An empirical study of flight control software reliability

The results of a laboratory experiment in flight control software reliability are reported. The experiment tests a small sample of implementations of a pitch axis control law for a PA28 aircraft with over 14 million pitch commands with varying levels of additive input and feedback noise. The testing which uses the method of n-version programming for error detection surfaced four software faults in one implementation of the control law. The small number of detected faults precluded the conduct of the error burst analyses. The pitch axis problem provides data for use in constructing a model in the prediction of the reliability of software in systems with feedback. The study is undertaken to find means to perform reliability evaluations of flight control software

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

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

Preliminary evaluation of radar imagery of Yellowstone Park, Wyoming

Evaluation of radar imagery of Yellowstone Park, Wyomin

The Spatial Distribution Of OH And CN Radicals In The Coma Of Comet Encke

Multiple potential parent species have been proposed to explain CN abundances in comet comae, but the parent has not been definitively identified for all comets. This study examines the spatial distribution of CN radicals in the coma of comet Encke and determines the likelihood that CN is a photodissociative daughter of HCN in the coma. Comet Encke is the shortest orbital period (3.3 years) comet known and also has a low dust-to-gas ratio based on optical observations. Observations of CN were obtained from 2003 October 22 to 24, using the 2.7 m telescope at McDonald Observatory. To determine the parent of CN, the classical vectorial model was modified by using a cone shape in order to reproduce Encke's highly aspherical and asymmetric coma. To test the robustness of the modified model, the spatial distribution of OH was also modeled. This also allowed us to obtain CN/OH ratios in the coma. Overall, we find the CN/OH ratio to be 0.009 +/- 0.004. The results are consistent with HCN being the photodissociative parent of CN, but we cannot completely rule out other possible parents such as CH(3)CN and HC(3)N. We also found that the fan-like feature spans similar to 90 degrees, consistent with the results of Woodney et al..NASAOffice of the Vice President for Research and Economic Development at Mississippi State UniversityMcDonald Observator

The influence of composition, annealing treatment, and texture on the fracture toughness of Ti-5Al-2.5Sn plate at cryogenic temperatures

The plane strain fracture toughness K sub Ic and conventional tensile properties of two commercially produced one-inch thick Ti-5Al-2.5Sn plates were determined at cryogenic temperatures. One plate was extra-low interstitial (ELI) grade, the other normal interstitial. Portions of each plate were mill annealed at 1088 K (1500 F) followed by either air cooling or furnace cooling. The tensile properties, flow curves, and K sub Ic of these plates were determined at 295 K (room temperature), 77 K (liquid nitrogen temperature), and 20 K (liquid hydrogen temperature)