We study semi-linear elliptic free boundary problems in which the forcing term is discontinuous; i.e., a Poisson’s equation where the forcing term is the Heaviside function applied to the unknown minus a constant. This approach uses level sets to construct a monotonic sequence of iterates which converge to a class of solutions to the free boundary problem. The monotonicity of the construction b...

In this paper, a genetic algorithm is presented for an identical parallel-machine scheduling problem with family setup time that minimizes the total weighted flow time ( ). No set-up is necessary between jobs belonging to the same family. A set-up must be scheduled when switching from the processing of family i jobs to those of another family j, i  j, the duration of this set-up being the sequ...

We investigate a new algebraic structure which always gives rise to set-theoretic solution of the Yang-Baxter equation. Specifically, weak (left) brace is non-empty set $S$ endowed with two binary operations $+$ and $\circ$ such that both $(S,+)$ $(S, \circ)$ are inverse semigroups they hold \begin{align*} \circ \left(b+c\right) = a\circ b - +a\circ c \qquad \text{and} a^- + a, \end{align*} for...