Физическая математика

This work aimed at developing an alternative procedure to MANOVA test when there is problem of heteroscedasticity of dispersion matrices and compared the procedure with an existing multivariate test for vector of means. The alternative procedure was developed by adopting Satterthwaite’s approach of univariate test for unequal variances. The approach made use of approximate degree of freedom method in one way MANOVA when the dispersion matrices are not equal and unknown but positive definite. The new procedure was compared by using simulated data when it is Multivariate normal, Multivariate Gamma and real life data. The new procedure performed better in terms of power of the test and type I error rate when compared with Johanson procedure.

A change in approach in the theory of Relativistic Electromagnetic Fields, introduced by James Clerk Maxwell in 1865 and the theory of "Electric-Magnetic/Space-Time" conversions by Einstein-Lorentz-Minkovski in 1905 in the theory of Special Relativity (specially described by the Lorentz-Transformations) and the Theory of General Relativity (GTR) by Albert Einstein in 1915 has been presented in this article. What is known in Astrophysics has originally been based on the fundamental knowledge of the classical Electromagnetic theories of James Clerk Maxwell and the famous Theory of General Relativity by Albert Einstein. Electromagnetic radiation and in specific light has always been the carrier for this information. That is a fundamental problem. Because what do we really know about light? When James Maxwell published his famous set of 4 electromagnetic equations, the Maxwell equations, he did not built his theory on a logical fundament. His foundation was not logical at all. Why would a set of 4 electromagnetic equations which are correct at low frequencies describe a physical phenomenon like the propagation of light with a speed that at that time had never been measured before? Since then nobody ever doubted about the correctness of the theories of Maxwell. The success of his predictions made Maxwell famous. But fame is not a ground for fundamental science.

The present work analyses the Langevin formula and shows not the correctness of the basic assumptions of the output but more correct conclusion of similar formulas.