In synchronous networks, protocols can achieve security guarantees that are not possible in an asynchronous world: i.e., they can simultaneously achieve input completeness (all honest parties’ inputs are included in the computation) and guaranteed termination (honest parties do not “hang” indefinitely). In practice truly synchronous networks rarely exist, but synchrony can be emulated if channe...

When programs communicate with other programs, exibil-ity is demanded. Programs do not necessarily have information about each other. When assigning types to these communications a certain amount of dynamic typing is unavoidable. But we do not want our entire language to become dynamically typed, and consequently an interface between the statically and dynamically typed parts of the program has...

In a pure functional language like Clean the values of the functional variables are constants; variables of functional programs do not change in time. Hence it seems that temporality has no meaning in functional programs. However, in certain cases (e.g. in interactive or distributed programs, or in ones that use IO) we would like to consider a series of values computed from each other as differ...

Suppose G is a finitely presented group that hyperbolic relative to P finite collection of proper subgroups G. Our main theorem states if the second cohomology H2(P,ZP) free abelian for each P?P, then H2(G,ZG) abelian. The problem reduces case when and members are 1-ended. In case, we prove “Cusped Space” this pair has semistable fundamental at ?. This provides starting point in our proof theor...

We show that if $R$ is a ring with an arbitrary idempotent $e$ such that $eRe$ and $(1-e)R(1-e)$ are both strongly nil-clean rings‎, ‎then $R/J(R)$ is nil-clean‎. ‎In particular‎, ‎under certain additional circumstances‎, ‎$R$ is also nil-clean‎. ‎These results somewhat improves on achievements due to Diesl in J‎. ‎Algebra (2013) and to Koc{s}an-Wang-Zhou in J‎. ‎Pure Appl‎. ‎Algebra (2016)‎. ‎...

We find zero-free regions in the complex plane at large |q| for the multivariate Tutte polynomial (also known in statistical mechanics as the Potts-model partition function) ZG(q,w) of a graph G with general complex edge weights w = {we}. This generalizes a result of Sokal [22] that applied only within the complex antiferromagnetic regime |1+we| ≤ 1. Our proof uses the polymer-gas representatio...

We find zero-free regions in the complex plane at large |q| for the multivariate Tutte polynomial (also known in statistical mechanics as the Potts-model partition function) ZG(q,w) of a graph G with general complex edge weights w = {we}. This generalizes a result of Sokal [22] that applied only within the complex antiferromagnetic regime |1+we| ≤ 1. Our proof uses the polymer-gas representatio...

Let G be a finite group. We show that the Bass Nil-groups NKn(RG), n ∈ Z, are generated from the p-subgroups of G by induction, certain twistings maps depending on elements in the centralizers of the psubgroups, and the Verschiebung homomorphisms. As a consequence, the groups NKn(RG) are generated by induction from elementary subgroups. For NK0(ZG) we get an improved estimate of the torsion exp...