Kolmogorov


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Kolmogorov

(ˌkɒlmɒˈɡɔːrɒf)
n
(Biography) Andrei Nikolaevich (anˈdrjej nikaˈlajəvitʃ). (1903–87), Soviet mathematician, who made important contributions to the theoretical foundations of probability
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The analytical models mainly include the Avrami, Avrami-Ozawa, Kolmogorov and Schneider models, which are used to calculate the crystallinity evolution of polymers directly.
Then, the normality of the data was assessed by the Shapiro Wilk test (n = 50, p p[less than or equal to]0.05) and/or with the Kolmogorov Smirnov test (n>50, p[less than or equal to]0.05), but was observed the normality of the data through of the histogram.
Perihelia Reduction and Global Kolmogorov Tori in the Planetary Problem
The PDF can be obtained as a solution to the Kolmogorov forward equation (Fokker-Planck equation).
The proof of this theorem in [7] is nontrivial and uses the deep and powerful Kolmogorov Superposition Theorem which answered Hilbert's 13th Problem.
K-S test is based on the work of Kolmogorov (1933) and Smirnov (1948) and it was developed by Massey (1951).
Two common test methods used to test whether distributions are normal are Shapiro-Wilk method and Kolmogorov Smirnov (KS) method.
For the proof of Theorem 1.1, we make use of the Brownian expression of the radial part [R.sub.t] ((2.2) below) as in [4,7], together with a generalized version of Kolmogorov's test for the one dimensional Brownian motion ([9,10]).