The acid-mediation hypothesis, that is, the hypothesis that acid produced by tumours, as a result of aerobic glycolysis, provides a mechanism for invasion, has so far been considered as a relatively closed system. The focus has mainly been on the dynamics of the tumour, normaltissue, acid and possibly some other bodily components, without considering the effect of an external intervention such ...

Let K be a number field and OK its ring of integers. Let E be an OK-module of rank N + 1 in P(E), the projective space representing lines in E. For all closed subvarieties X ⊆ P(E K) of dimension d let deg(X) be its degree with respect to the canonical line bundle O(1) of P(E K). If E is endowed with the structure of hermitian vector bundle over Spec(OK) we can define the Arakelov degree d̂eg ( ...

‎let $x=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the hankel matrix of size $2times n$ and let $g$ be a closed graph on the vertex set $[n].$ we study the binomial ideal $i_gsubset k[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $x$ which correspond to the edges of $g.$ we show that...

We recently introduced an extensional model of the pure λcalculus living in a cartesian closed category of sets and relations. In this paper, we provide sufficient conditions for categorical models living in arbitrary cpo-enriched cartesian closed categories to have H∗, the maximal consistent sensible λ-theory, as their equational theory. Finally, we prove that our relational model fulfils thes...