Let E be an elliptic curve over Q, and for each prime p, let #E(Fp) be the number of rational points of E over the finite field Fp. Taking aE(p) = p+ 1−#E(Fp) to be the trace of Frobenius as usual, we recall the following important result of Hasse, which holds when E has good reduction at p: |aE(p)| ≤ 2 √ p. It follows that for each prime p, there is a unique angle θp ∈ [0, π] (which we call th...

20-gauge coaxial cutting needle. Clin Radiol. 2000;55: 281--7. 3. Geraghty PR, Kee ST, McFarlane G, Razavi MK, Sze DY, Dake MD. CT-guided transthoracic needle aspiration biopsy of pulmonary nodules: needle size and pneumothorax rate. Radiology. 2003;229:475--81. 4. Dennie CJ, Matzinger FR, Marriner JR, Maziak DE. Transthoracic needle biopsy of the lung: results of early discharge in 506 outpati...

Although phenol red, introduced by Rowntree and Geraghty (6) in 1912, has been widely used in man as an empirical renal function test, the excretion of this substance relative to its concentration in the plasma has been examined in only one instance. MacKay (1930) injected one gram intravenously and calculated the Addis excretory ratio in three successive periods when the plasma level was 5.80,...

The study of a variety of experimental renal lesions in the dog demonstrates that the phenolsulphonephthalein test of Rowntree and Geraghty is one of the most satisfactory and at the same time most delicate methods of estimating the functional activity of the kidney. The elimination of the test dye is decreased in so-called spontaneous nephritis and in experimental nephritis due to potassium ch...