The Tate-Shafarevich group for elliptic curves with complex multiplication II

Let E be an elliptic curve over Q with complex multiplication. The aim of the present paper is to strengthen the theoretical and numerical results of \cite{CZS}. For each prime p, let t_{E/Q, p} denote the Z_p-corank of the p-primary subgroup of the Tate-Shafarevich group of E/Q. For each \epsilon 0, we prove that t_{E/Q, p} is bounded above by (1/2+\epsilon)p for all sufficiently large good ordinary primes p. We also do numerical calculations on one such E of rank 3, and 5 such E of rank 2, showing in all cases that t_{E/Q, p} = 0 for all good ordinary primes p < 30,000. In fact, we show that, with the possible exception of one good ordinary prime in this range for just one of the curves of rank 2, the p-primary subgroup of the Tate-Shafarevich group of the curve is zero (always supposing p is a good ordinary prime).Comment: 24 page

Time and frequency stability for the Crustal Dynamics Project

Very long base interferometry (VLBI) and laser ranging to artificial satellites and the Moon were used to determined vector baselines between stations with precisions of about one part in 10 to the 8th power. Deformations and strain accumulations in active earthquake regions were determined by making frequent measurements of baselines between many stations in active areas near plate boundaries

Nickel-cadmium cell life test

Over 6,9000 Low Earth Orbit cycles were accumulated at 30% Depth of Discharge on twelve INTELSAT-design nickel-hydrogen cells. Physical equipment and cells are described. Performance characteristics are seen to be uniform. Further testing is planned to seek a failure mode, and also to investigate the effects of a new additive for nickel-hydrogen cells. Initial results indicate improved performance at higher temperatures and diminished swelling of positive nickel plates

Worldwide time and frequency synchronization by planned VLBI networks

Accurate baseline determinations and clock synchronization results obtained from the Quasar Patrol observations at X band with the Goldstone-Haystack baseline are presented. In addition, data from stations at Greenbank, West Virginia, and Onsala, Sweden were used. It was estimated that clock accuracy was on the order of 16 cm

The GL_2 main conjecture for elliptic curves without complex multiplication

The main conjectures of Iwasawa theory provide the only general method known at present for studying the mysterious relationship between purely arithmetic problems and the special values of complex L-functions, typified by the conjecture of Birch and Swinnerton-Dyer and its generalizations. Our goal in the present paper is to develop algebraic techniques which enable us to formulate a precise version of such a main conjecture for motives over a large class of p-adic Lie extensions of number fields. The paper ends by formulating and briefly discussing the main conjecture for an elliptic curve E over the rationals Q over the field generated by the coordinates of its p-power division points, where p is a prime greater than 3 of good ordinary reduction for E.Comment: 39 page

Visual information transfer. Part 1: Assessment of specific information needs. Part 2: Parameters of appropriate instrument scanning behavior

The present study explored eye scan behavior as a function of level of subject training. Oculometric (eye scan) measures were recorded from each of ten subjects during training trials on a CRT based flight simulation task. The task developed for the study incorporated subtasks representative of specific activities performed by pilots, but which could be performed at asymptotic levels within relatively short periods of training. Changes in eye scan behavior were examined as initially untrained subjects developed skill in the task. Eye scan predictors of performance on the task were found. Examination of eye scan in proximity to selected task events revealed differences in the distribution of looks at the instruments as a function of level of training

Visual information transfer. 1: Assessment of specific information needs. 2: The effects of degraded motion feedback. 3: Parameters of appropriate instrument scanning behavior

Pilot and flight crew assessment of visually displayed information is examined as well as the effects of degraded and uncorrected motion feedback, and instrument scanning efficiency by the pilot. Computerized flight simulation and appropriate physiological measurements are used to collect data for standardization

Development of ride comfort criteria for mass transit systems

Two studies were conducted on the effects of simultaneous sinusoidal vibration in the vertical and lateral axes on ratings of discomfort in human subjects in a simulated passenger aircraft. In the first experiment each of 24 subjects experienced each of ten levels of vertical frequency in combination with each of ten levels of lateral frequency vibration and rated the discomfort produced on a nine-point, unipolar scale. In the second experiment 72 subjects experienced one of four levels of vertical frequency at each of four levels of vertical amplitude combined with 16 (or 4 x 4) lateral frequency and amplitude conditions. The results of these two studies strongly suggest that there are effects on discomfort that occur when subjects are vibrated in several axes at once that cannot be assessed with research using vibration in only one axis

The main conjecture

In his important papers [16], [17], Wiles proved in most cases the so-called main conjecture for the cyclotomic Zp-extension of any totally real base field F, for all odd primes p, and for all abelian characters of Gal(Q¯ /F) (we say most cases because his work only establishes the main conjecture up to µ-invariants for those abelian characters whose order is divisible by p). It would be technically too difficult for us in these introductory lectures to attempt to explain his proof in this generality. Instead, we have chosen the much more modest path of giving a sketch of his proof in the very special case that F = Q, and for all abelian characters of Q of p-power conductor. In fact, our account of Wiles’ proof in this case has been directly inspired by a series of lectures on this theme, which we attended, given by Chris Skinner in an instructional conference held at the Centre of Mathematical Sciences, Zhejiang University, Hangzhou, China, in August 2004