We consider the space of weakly almost periodic functions on a transformation semigroup (S, X , ?) and show that if X is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of S on X, then every continuous function on X, vanishing at infinity is weakly almost periodic. We also use a number of diverse examples to show ...

This paper surveys some common state space models used in macroeconomics and finance and shows how to specify and estimate these models using the SsfPack algorithms implemented in the S-PLUS module S+FinMetrics. Examples include recursive regression models, time varying parameter models, exact autoregressive moving average models and calculation of the Beveridge-Nelson decomposition, unobserved...

Under the continuum hypothesis, there is a compact homogeneous strong S-space.

From left to right and from top bottom: 1. The Stephan's Quintet (interacting galaxies' group), 40 million 290 light-years away; 2. Cartwheel Galaxy, a merger of galaxies 144,300 across, 500 3. spectrum the exoplanet WASP-96b (1,150 away), showing evaporated water; 4. James Webb telescope in its clean room; 5. South Ring Nebula, 2,500 away (12 across); 6. Galactic cluster early universe SMACS 0...

Random bijective S-box generation methods are considered. An alternative S-box generation method by forming compositions of permutations from some fixed set is proposed. Experiments show that the rate of acceptable S-boxes for all the methods considered is essentially the same. The advantage of the composition method is an obvious parametrization, with the potentially large key space.