The gauge-invariant three-gluon vertex obtained from the pinch technique is characterized by thirteen nonzero form factors, which are given in complete generality for unbroken gauge theory at one loop. The results are given in d dimensions using both dimensional regularization and dimensional reduction, including the effects of massless gluons and arbitrary representations of massive gauge boso...

The Theory of Contexts is a type-theoretic axiomatization which has been recently proposed by some of the authors for giving a metalogical account of the fundamental notions of variable and context as they appear in Higher Order Abstract Syntax. In this paper, we prove that this theory is consistent by building a model based on functor categories. By means of a suitable notion of forcing, we pr...

We describe how a set-theoretic foundation for mathematics can be encoded in the new system Scunak. We then discuss an encoding of the construction of functions as functional relations in untyped set theory. Using the dependent type theory of Scunak, we can define object level application and lambda abstraction operators (in the spirit of higher-order abstract syntax) mediating between function...

Two lower bag domain constructions are introduced: the initial construction which gives free lower monoids, and the final construction which is defined explicitly in terms of second order functions. The latter is analyzed closely. For sober dcpo's, the elements of the final lower bag domains can be described concretely as bags. For continuous domains, initial and final lower bag domains coincid...

The objective of the present paper is twofold: first, to establish explicit conditions for the elicitation of consistent a priori and conditional probabilities for a set of events representing pieces of evidence and hypotheses. Furthermore, an algorithm is proposed which uses these consistent input probabilities to compute lower and upper bounds for higher order joint probabilities. Secondly, p...

In this work, we study the volume ratio of the projective tensor products `p ⊗π `q ⊗π `r with 1 ≤ p ≤ q ≤ r ≤ ∞. We obtain asymptotic formulas that are sharp in almost all cases. As a consequence of our estimates, these spaces allow for a nearly Euclidean decomposition of Kašin type whenever 1 ≤ p ≤ q ≤ r ≤ 2 or 1 ≤ p ≤ 2 ≤ r ≤ ∞ and q = 2. Also, from the Bourgain-Milman bound on the volume rat...