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

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

Exploratory investigation of sound pressure level in the wake of an oscillating airfoil in the vicinity of stall

Wind tunnel tests were performed on two oscillating two-dimensional lifting surfaces. The first of these models had an NACA 0012 airfoil section while the second simulated the classical flat plate. Both of these models had a mean angle of attack of 12 degrees while being oscillated in pitch about their midchord with a double amplitude of 6 degrees. Wake surveys of sound pressure level were made over a frequency range from 16 to 32 Hz and at various free stream velocities up to 100 ft/sec. The sound pressure level spectrum indicated significant peaks in sound intensity at the oscillation frequency and its first harmonic near the wake of both models. From a comparison of these data with that of a sound level meter, it is concluded that most of the sound intensity is contained within these peaks and no appreciable peaks occur at higher harmonics. It is concluded that within the wake the sound intensity is largely pseudosound while at one chord length outside the wake, it is largely true vortex sound. For both the airfoil and flat plate the peaks appear to be more strongly dependent upon the airspeed than on the oscillation frequency. Therefore reduced frequency does not appear to be a significant parameter in the generation of wake sound intensity

Dormancy and life span of saffron thistle seeds

RESEARCH in the Geraldton area has indicated that seeds of the saffron thistle (Carthamus lanatus) spread their germination over some seven years but most germinate in the first two years. Factors influencing the rate of germination and the survival of seeds are the depth of burial and the presence of termites in the soil

Control of soursob (Oxalis pres-caprae) in cereals

Trial 87NO107 Plant counts for soursob and Four O\u27clock will be more accurate when counts taken after the break of 1988 season to determine the bulb production from last season. Ally gave good control of doublegee. Isoproturon or mixtures with Isoproturon also gave good doublegee control. Logran & Glean were weak on doublegee

Readout of solid-state charge qubits using a single-electron pump

A major difficulty in realizing a solid-state quantum computer is the reliable measurement of the states of the quantum registers. In this paper, we propose an efficient readout scheme making use of the resonant tunneling of a ballistic electron produced by a single electron pump. We treat the measurement interaction in detail by modeling the full spatial configuration, and show that for pumped electrons with suitably chosen energy the transmission coefficient is very sensitive to the qubit state. We further show that by using a short sequence of pumping events, coupled with a simple feedback control procedure, the qubit can be measured with high accuracy.Comment: 5 pages, revtex4, 4 eps figures. v2: published versio

Counting rational points on smooth cyclic covers

A conjecture of Serre concerns the number of rational points of bounded height on a finite cover of projective space P^{n-1}. In this paper, we achieve Serre's conjecture in the special case of smooth cyclic covers of any degree when n is at least 10, and surpass it for covers of degree 3 or higher when n > 10. This is achieved by a new bound for the number of perfect r-th power values of a polynomial with nonsingular leading form, obtained via a combination of an r-th power sieve and the q-analogue of van der Corput's method