Spaces whose $n$th power is weakly infinite-dimensional but whose $(n+1)$th power is not

Whose voice? Whose choice? Whose power?

Coercion in psychiatry stems from the historic inequality between the psychiatrist and the person who is designated as the "patient," even though he/she may not have chosen this role, and may not see him/herself as needing psychiatric attention. The psychiatrist has the power to define an individual as mentally ill, and then to confine and treat the person based on that definition. The user/sur...

Characterization and axiomatization of all semigroups whose square is group

In this paper we give a characterization for all semigroups whose square is a group. Moreover, we axiomatize such semigroups and study some relations between the class of these semigroups and Grouplikes,introduced by the author. Also, we observe that this paper characterizes and axiomatizes a class of Homogroups (semigroups containing an ideal subgroup).  Finally, several equivalent conditions ...

Infinite Sets of Integers Whose Distinct Elements Do Not Sum to a Power

We first prove two results which both imply that for any sequence B of asymptotic density zero there exists an infinite sequence A such that the sum of any number of distinct elements of A does not belong to B. Then, for any ε > 0, we construct an infinite sequence of positive integers A = {a1 < a2 < a3 < . . . } satisfying an < K(ε)(1 + ε)n for each n ∈ N such that no sum of some distinct elem...

Whose difficulty is it?

Whose future is it?

Good morning. It is a great honour to deliver this talk to a research community of which I have been a member when we were not sure that it was a domain of its own. It has since then developed in an impressive manner, and today it offers all the signs of a maturing scientific community in a technical field: a yearly conference with growing attendance, some structuring paradigms, progress in mod...