Expanded new-products section goes on line

I. Expanded Methods Section

Partial Euler Products on the Critical Line

The initial version of the Birch and Swinnerton-Dyer conjecture concerned asymptotics for partial Euler products for an elliptic curve L-function at s = 1. Goldfeld later proved that these asymptotics imply the Riemann hypothesis for the L-function and that the constant in the asymptotics has an unexpected factor of √ 2. We extend Goldfeld’s theorem to an analysis of partial Euler products for ...

New untwist on diastole: what goes around comes back.

Diastolic dysfunction contributes significantly to the clinical syndrome of congestive heart failure in the settings of both preserved and impaired left ventricular (LV) systolic function.1,2 Over the past 20 years, the clinical diagnosis of diastolic dysfunction has been based largely on echocardiographic Doppler parameters of LV filling.3 The most important limitation of these parameters is t...

Forecasting Convective Downburst Potential Using GOES Sounder Derived Products

Page 5Pay attention to the “normal” landing path of an aircraft. In the case of a microburst, an aircraft will typically encounter a headwind that serves to slow and lift the nose of the aircraft above the normal landing path. A pilot may compensate for this condition by lowering the nose of the aircraft as it approaches the center of the downdraft core. Question: What problems may the pilot en...

Section 6.1 -inner Products and Norms

1. 〈x + z,y〉 = 〈x,y〉+ 〈z,y〉 2. 〈cx,y〉 = c〈x,y〉 3. 〈x,y〉 = 〈y,x〉, where the bar denotes complex conjugation. 4. 〈x,x〉 > 0 if x 6= 0 Note that if z is a complex number, then the statement “z ≥ 0” means that z is real and non-negative. Notice that if F = R, (3) is just 〈x,y〉 = 〈y,x〉. Definition. Let A ∈ Mm×n(F ). We define the conjugate transpose or adjoint of A to be the n ×m matrix A∗ such that ...