Mohrの応力円,確率分布,線形計画法

抄録

It is pointed out that the same mathematical formalism obtains for (i) the well-known classical relation between the normal stress and the tangential (shearing) stress across an areal section of a continuum, which is represented in terms of the so-called Mohr's stress circle in elasticity theory (or the theory of strength of materials) , and for (ii) a less known relation between the mean and the standard deviation of a discrete probability distribution, and, moreover, that the well-established technique of linear programming is a best tool to handle that formalism for(i) and (ii)with. It is shown also that a number of traditionally noted, practically useful theorems on the location of eigenvalues of an Hermitian matrix by means of the Rayleigh quotient (and the norm of the residual vector) can be better understood intuitively and naturally within the same formalism. Throughout the present arguments, "probabilities" correspond to the squares of the absolute values of the orthogonal projections of a vector to the eigenspaces of an Hermitian operator. This fact may suggest some latent deeper connections between (i) and (ii).