It is an open question whether a non-trivial convex combination of triangular norms (resp. conorms) can be a triangular norm (resp. conorm). We investigate the analogous question for S-implications and R-implications.

An (n, q, r, s) book is a collection of r-subspaces in PG(n, q) called pages, which cover the whole projective space and intersect in a common s-subspace called the spine such that any point outside the spine is in exactly one page. An (n, q, r, s) book t-spread is a t-spread in PG(n, q) for which there exists an (n, q, r, s) book, such that the points of each page of this book and hence the po...

We develop the inverse scattering transform for the KdV equation with real singular initial data q (x) of the form q (x) = r′ (x) + r (x), where r ∈ Lloc, r|R+ = 0. As a consequence we show that the solution q (x, t) is a meromorphic function with no real poles for any t > 0.

The aim of the paper is to find efficient conditions for the unique solvability of the problem u′(t) = `(u)(t) + q(t), u(a) = h(u) + c, where ` : C([a, b];R) → L([a, b];R) and h : C([a, b];R) → R are linear bounded operators, q ∈ L([a, b];R), and c ∈ R.

An $(n, r)$-arc is a set of $n$ points of a projective plane such that some $r$, but no $r+1$ of them, are collinear. The maximum size of an $(n, r)$-arc in  $PG(2, q)$ is denoted by $m_r(2,q)$.  In this paper we present  a new $(184,12)$-arc in PG$(2,17),$  a new $(244,14)$-arc and a new $(267,15$)-arc in $PG(2,19).$

In this paper, first, we state an operator LR on ordered semihyperring R. We show that if φ:R⟶T is a monomorphism and K⊆R, then LT(φ(K))=φ(LR(K)). Afterward, hyperatom elements in semihyperrings are defined some results respect investigated. Denote by A(R) the set of all hyperatoms prove R finite |R|≥2, for any q∈R\{0}, there exists hq∈A*(R)=A(R)\{0} such hq≤q. Finally, study LR-graph give exam...