Operational Gaussian Schmidt-number witnesses

On the Number of False Witnesses for a Composite Number

If a is not a multiple of « and a"~ ' * 1 mod n, then n must be composite and a is called a "witness" for «. Let F(n) denote the number of "false witnesses" for n, that is, the number of a mod n with a"-1 s l mod «. Considered here is the normal and average size of F( « ) for « composite. Also considered is the situation for the more stringent Euler and strong pseudoprime tests.

Expected Number of Local Maxima of Some Gaussian Random Polnomials

Gaussian modeling and Schmidt modes of SPDS biphoton states

A double-Gaussian model and the Schmidt modes are found for the biphoton wave function characterizing spontaneous parametric down-conversion with the degenerate collinear phase-matching of the type I and with a pulsed pump. The obtained results are valid for all durations of the pump pulses, short, long and intermediately long.

On the Number of False Witnesses for a Composite Number1

When presented with a large number n which one would like to test for primality, one usually begins with a modicum of trial division . If n is not revealed as composite, the next step is often to perform the simple and cheap test of computing an-1 mod n for some pre-chosen number a > 1 with (a,n) = 1 . If this residue is not 1 , then n is definitely composite (by Fermat's little theorem) and we...

Scalar dissipation fronts in high-Schmidt number mixing.

Jörg Schumacher Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany Herwig Zilken Visualization Laboratory, Zentralinstitut für angewandte Mathematik, Forschungszentrum Jülich, D-52425 Jülich, Germany Bruno Eckhardt Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany Katepalli R. Sreenivasan International Centre for Theoretical Physics, 34014 Triest...