In this paper, we attempt to investigate the connection between various types of ideals (for examples $(m, n)$-ideal, bi-ideal, interior ideal, quasi ideal, prime ideal and maximal ideal) of an ordered semigroup $(S,cdot ,leq)$ and the correspond hyperideals of its EL-hyperstructure $(S,*)$ (if exists). Moreover, we construct the class of EL-$Gamma$-semihypergroup associated to a partially orde...

We give simple bounds for the exponential decay of a strongly continuous semigroup V (t) = exp(At) in a Hilbert space. The bounds are expressed by means of the solution X of the Ljapunov equation A X + XA = ?I and the quantity sup 0th kV (t)k for small h. Our main bound is attained on any normal semigroup and can therefore not be improved in general. Let V (t) be a strongly continuous semigroup...

Fix a non-square integer $$k\ne 0$$ . We show that the number of curves $$E_B:y^2=x^3+kB^2$$ containing an integral point, where B ranges over positive integers less than N, is bounded by $$\ll _k N(\log N)^{-\frac{1}{2}+\epsilon }$$ In particular, this implies $$B\le N$$ such $$-3kB^2$$ discriminant elliptic curve $$\mathbb {Q}$$ o(N). The proof involves discriminant-lowering procedure on bina...