On the symmetric square. Unit elements

On group Elements Having Square Roots

On the Symmetric Square. Unstable Twisted Characters

We provide a purely local computa t ion of the (elliptic) twisted (by "transpose-inverse") character of the representat ion w = I (1) of PGL(3) over a p-adic field induced from the trivial representat ion of the maximal parabolic subgroup. This computa t ion is independent of the theory of the symmetr ic square lifting of [IV] of automorphic and admissible representat ions of SL(2) to PGL(3). I...

Triangular norms on the real unit square

T norms were introduced by Schweizer and Sklar see e g in the framework of probabilistic metric spaces and are based on a notion used by Menger in or der to extend the triangle inequality in the de nition of metric spaces towards probabilistic metric spaces They have been used extensively for de ning the in tersection of fuzzy sets and for modelling the logical and in fuzzy logic Continuous t n...

Groups of Negations on the Unit Square

The main results are about the groups of the negations on the unit square, which is considered as a bilattice. It is proven that all the automorphisms on it form a group; the set, containing the monotonic isomorphisms and the strict negations of the first (or the second or the third) kind, with the operator "composition," is a group G₂ (or G₃ or G₄, correspondingly). All these four kinds of map...

On Symmetric Square Values of Quadratic Polynomials

We prove that there does not exist a non-square quadratic polynomial with integer coefficients and an axis of symmetry which takes square values for N consecutive integers for N = 7 or N ≥ 9. At the opposite, if N ≤ 6 or N = 8 there are infinitely many.