Some probability distributions (e.g., Gaussian) are symmetric, some (e.g., lognormal) are non-symmetric (skewed). How can we gauge the skeweness? For symmetric distributions, the third central moment C3 def = E[(x − E(x))] is equal to 0; thus, this moment is used to characterize skewness. This moment is usually estimated, based on the observed (sample) values x1, . . . , xn, as C3 = 1 n · n ∑ i...

In the Minimal Supersymmetric Standard Model (MSSM), the process e+e− → g̃g̃ is mediated by quark/squark loops, dominantly of the third generation, where the mixing of leftand right-handed states can become large. Taking into account realistic beam polarization effects, photon and Z0-boson exchange, and current mass exclusion limits, we scan the MSSM parameter space for various e+e− center-of-mas...

We report third-order symmetry-adapted perturbation theory (SAPT) calculations for several dimers whose intermolecular interactions are dominated by induction. We demonstrate that the single-exchange approximation (SEA) employed to derive the third-order exchange-induction correction (E(exch-ind)((30))) fails to quench the attractive nature of the third-order induction (E(ind)((30))), leading t...

The singular point analysis of third order ordinary differential equations which are algebraic in y and y′ is presented. Some new third order ordinary differential equations that pass the Painlevé test as well as the known ones are found. Corresponding author. E-mail: [email protected]

Cryptography has been instrumental in reducing the involvement of overhead third parties in protocols. For example; a digital signature scheme assures a recipient that a judge who is not present at message transmission will nevertheless approve the validity of the signature. Similarly, in oo-line electronic cash the bank (which is oo-line during a purchase) is assured that if a user double spen...