the aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von neumann algebra on a hilbert space with a normal faithful semi-finite trace $tau$. the submajorization inequalities generalize some results due to zhang, furuichi and lin, etc..

We report that the submerged microbubbles are an efficient source of diffuse radiance and may contribute to a rapid transition to the diffuse asymptotic regime. In this asymptotic regime an average cosine is easily predictable and measurable.

By a space we shall mean a measurable space, i.e. an abstract set together with a <r-ring of subsets, called measurable sets, whose union is the whole space. The structure of a space will be the <r-ring of its measurable subsets. A measurable transformation from one space to another is a mapping such that the inverse image of every measurable set is measurable. Let X and F be spaces, F a set of...

Let an indirectly measurable variable Y be represented as a function of finite number of directly measurable variables X1, X2, ..., Xn. We introduce maximum absolute and relative inaccuracies of second order of Y – this idea is a continuation of our research of a new principle for representing the maximum inaccuracies of Y using the inaccuracies of X1, X2, ..., Xn. Using inaccuracies of second ...

In biological anthropology, bilateral asymmetry in living adult samples is a well-studied field. During the last decade, researchers have become more interested its developmental characteristics individuals of both and past populations. It still upper limb that gets attention, as handedness effects on bones via biomechanical loading an obvious easily measurable marker asymmetry. The majority po...