Induction of the Field at Different Distances from the Permanent Magnet and Between Opposing Magnets. Testing of the Superposition Principle

The measurement data of the field induction at different distances from the permanent magnet Nd-Fe-B and between two equivalent magnets on distance are presented. It is shown that the obtained coordinate dependences are described by exponential function, but for a system of two magnets –only partially: up to the central area of the system and make 20-30% of the entire area between opposing magnets. Using the example of the coordinate dependence of induction for one of two identical magnets, it is shown that the use of the superposition principle makes it possible to obtain a coordinate dependence of induction between opposing magnets, which is equivalent to experimental one.

A New Generalized Inequality for Covariance in N Dimensions

Inspired by the work of Zhefei He and Mingjin Wang which was published in the Journal of Inequalities and Applications in 2015, this paper further generalizes some related results to the case of multidimensional random variables. The resulting inequality for covariance is then applied to different multidimensional statistical distributions (multiuniform, multinomial, and multinormal). Coordinate dependence of the inequality is also examined. The obtained formulas could be useful for making estimates in multivariate statistics.