Multi-fractal singular spectrum and Lipschitz regularity distribution were used to analyze the fractal parameters of abnormal flow, trying to identify the relationship between the changes of these parameters and the emergence of anomalies.

Use Lipschitz regularity to detect some aberrant phenomena;

Considering the interaction of practical gas, using the canonical distribution and statistical interpretation of gas pressure, this paper derives a pressure formula of practical gas directly.

We take them as examples for listing the microcanonical distribution,the canonical distribution and thegrand canonical distribution for illustrating the idea.

The initial microcanonical distribution is modified by using eleven different ionization thresholds of electrons in tht target.

We take them as examples for listing the microcanonical distribution,the canonical distribution and thegrand canonical distribution for illustrating the idea.

For C a bounded, injective with dense range, we define a C regularized smooth distribution group, and show the equivalence between an operator A generating a C regularized smooth distribution group of order k and ( iA) admitting a certain type of C regularized spectral distribution.

We take them as examples for listing the microcanonical distribution,the canonical distribution and thegrand canonical distribution for illustrating the idea.