The purpose of this text is to provide a simple explanation about the main features of TBSSurvival package for R language. In short, we give some examples on how to use the package.

This paper studies notions of scalar relations and crispness of relations.

Let X be a Banach space. Set, for x ∈ X and r ≥ 0 U(x, r) = {y ∈ X : ||x− y|| = r}. Given a nonempty, bounded set A ⊂ X, we set r(A, x) = sup{||x−a|| : a ∈ A} (x ∈ X) (radius of A with respect to x); r(A) = inf{r(A; x) : x ∈ X} (radius of A); δ(A) = sup{||a− b|| : a, b ∈ A} (diameter of A). Clearly, δ(A) ≤ 2r(A) always. Define, for A, the following properties: A is diametral: r(A, x) = δ(A) for...

Call a domain R an sQQR-domain if each simple overring of R, i.e., each ring of the form R[u] with u in the quotient field of R, is an intersection of localizations of R. We characterize Prüfer domains as integrally closed sQQR-domains. In the presence of certain finiteness conditions, we show that the sQQR-property is very strong; for instance, a Mori sQQR-domain must be a Dedekind domain. We ...

Now, the statement (i) follows from (S.1.3) by setting y = x. (ii) Since the vectors ci1 , . . . , ciK−1 are linearly independent in R , it follows that there exists a vector y such that det [ ci1 . . . ciK−1 y ] 6= 0. Hence, by (S.1.3), the (i1, . . . , iK−1)-th column of B(C) is nonzero. (iii) follows from (S.1.3) and the fact that det [ ci1 . . . ciK−1 y ] = 0 if and only if y ∈ span{ci1 , ....