Left ventricular (LV) systolic function is a major prognos-tic factor in cardiac disease 1–3 ; the serial reliable assessment of LV function is therefore essential. Since its development, echocardiography has played a major role in non-invasive evaluation. M mode echocardiography With the increasing sophistication of two dimensional echocardiography, it is notable that two groups with papers in...

Wang and Yeh proved that if P (x) is a polynomial with nonnegative and nondecreasing coefficients, then P (x + d) is unimodal for any d > 0. A mode of a unimodal polynomial f(x) = a0 + a1x + · · · + amx m is an index k such that ak is the maximum coefficient. Suppose that M∗(P, d) is the smallest mode of P (x + d), and M(P, d) the greatest mode. Wang and Yeh conjectured that if d2 > d1 > 0, the...

New energetic particle mode instabilities of fishbone type are predicted. The considered instabilities are driven by the circulating energetic ions. They can arise in plasmas of tokamaks and spherical tori with weak magnetic shear in the wide core region and strong shear at the periphery, provided that the central safety factor is close to the ratio m/n, where m and n are the poloidal mode numb...