We present a systematic study of the dynamical scaling process leading to the establishment of the Kolmogorov-Zakharov (KZ) spectrum in weak three-wave turbulence. In the finite-capacity case, in which the transient spectrum reaches infinite frequency in finite time, the dynamical scaling exponent is anomalous in the sense that it cannot be determined from dimensional considerations. As a conse...

Smirnov domains with non-smooth boundaries do admit non-trivial functions of Smirnov class with real boundary values. We will show that the existance of functions in Smirnov classes with real boundary values is directly dependent on the boundary characteristics of a Smirnov domain. Mathematics Subject Classification (2000). 30H10, 30H15.

We prove the following conjecture of Narayana: there are no nontrivial dominance refinements of the Smirnov two-sample test if and only if the two sample sizes are relatively prime. We also count the number of natural significance levels of the Smirnov two-sample test in terms of the sample sizes and relate this to the Narayana conjecture. In particular, Smirnov tests with relatively prime samp...

We prove the following conjecture of Narayana: there are no nontrivial dominance reene-ments of the Smirnov two-sample test if and only if the two sample sizes are relatively prime. We also count the number of natural signiicance levels of the Smirnov two-sample test in terms of the sample sizes and relate this to the Narayana conjecture. In particular, Smirnov tests with relatively prime sampl...

Introduction: The Nagata-Smirnov Metrization theorem gives a full characterization of metrizable topological spaces. In other words, the theorem describes the necessary and sufficient conditions for a topology on a space to be defined using some metric. As a motivational example, consider the discrete topology on some space (every subset of the space is open). Though it might not be apparent to...

The use of the Kolmogorov-Smirnov (KS) statistic for testing hypotheses regarding activation in blood oxygenation level-dependent functional MRI data is critiqued on both theoretical and empirical grounds. Theoretically, it is argued that the KS test is formally unable to support inferences of interest to most neuro-imaging studies and has reduced sensitivity compared with parametric alternativ...