Introduction The Muckle-Wells syndrome (MWS) is a rare inherited disease and belongs to the group of cryopyrin-associated periodic syndromes (CAPS). Recurrent fever attacks, myalgia, arthralgia, urticarial rash, headache, conjunctivitis, sensorineural deafness and a severe fatigue syndrome are the typical symptoms of MWS. Due to an unregulated production of IL1 a continuous formation of serum a...

We discuss the following general question and some of its extensions. Let (εk)k≥1 be a sequence taking its values in {0, 1}, which is not ultimately periodic. Define ξ := ∑ k≥1 εk/2 k and ξ′ := ∑ k≥1 εk/3 . Let P be a property valid for almost all real numbers. Is it true that at least one among ξ and ξ′ satisfies P ?

We define a class of languages of infinite words over infinite alphabets, and the corresponding automata. The automata used for recognition are a generalisation of deterministic Muller automata to the setting of nominal sets. Remarkably, the obtained languages are determined by their ultimately periodic fragments, as in the classical case. Closure under complement, union and intersection, and d...

Background The Muckle-Wells syndrome (MWS) is a rare inherited disease and belongs to the group of cryopyrin-associated periodic syndromes (CAPS). Recurrent fever attacks, myalgia, arthralgia, urticarial rash, headache, conjunctivitis, sensorineural deafness and a severe fatigue syndrome are the typical symptoms of MWS. Due to an unregulated production of IL1 a continuous formation of serum amy...

The class of 2-automatic paperfolding sequences corresponds to the class of ultimately periodic sequences of unfolding instructions. We rst show that a paper-folding sequence is automatic ii it is 2-automatic. Then we provide families of minimal nite-state automata, minimal uniform tag sequences and minimal substitutions describing automatic paperfolding sequences, as well as a family of algebr...

We consider a delayed Holling type II predator-prey system with birth pulse and impulsive harvesting on predator population at different moments. Firstly, we prove that all solutions of the investigated system are uniformly ultimately bounded. Secondly, the conditions of the globally attractive prey-extinction boundary periodic solution of the investigated system are obtained. Finally, the perm...

in the present paper the linear oscillator in r3 with z =constanthas been considered. the aim is to determine the necessary conditions forthe persistence of periodic solutions under discontinuous perturbations. a newapproach based on a computational method has been used. at the end weapply our method on an example.

We study ultimate periodicity properties related to overlaps between the suffixes of a left-infinite word [Formula: see text] and prefixes right-infinite text]. The main theorem states that set minimum lengths words such or is finite, where runs over positive integers are respectively suffix prefix length text], if only ultimately periodic form for some finite