for vectors x, y ∈ rn, it is said that x is left matrix majorizedby y if for some row stochastic matrix r; x = ry. the relationx ∼` y, is defined as follows: x ∼` y if and only if x is leftmatrix majorized by y and y is left matrix majorized by x. alinear operator t : rp → rn is said to be a linear preserver ofa given relation ≺ if x ≺ y on rp implies that t x ≺ ty onrn. the linear preservers o...

in this article, we characterize the involutiveness of the linear combination of the forma1a1 +a2a2 when a1, a2 are nonzero complex numbers, a1 is a quadratic or tripotent matrix,and a2 is arbitrary, under certain properties imposed on a1 and a2.

in this paper, at rst for a given set of real or complex numbers  with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which  is its spectrum. in continue we present some conditions for existence such nonnegative tridiagonal matrices.

The fuzziness and randomness are significant epistemic uncertainty within the qualitative categorization of two critical factors, frequency severity, which not fully considered in traditional risk matrix. This paper mainly proposes a cloud matrix method for assessment process safety considering expert elicitation. model is employed to provide mathematical expression linguistic variables by its ...

background: suicide is a problem worldwide and occupation is an important risk factor. in the last decade, 55 200 deaths in the us were attributed to occupational risk factors. objective: to determine if toxic metal exposure was associated with suicide risk among paducah gaseous diffusion plant (pgdp) workers. methods: we assembled a cohort of 6820 nuclear industry workers employed from 1952 to...