COMMUTATIVE FUNDAMENTAL RELATION IN FUZZY HYPERSEMIGROUPS
We introduce and study the construction of commutative fundamental relation in fuzzy hypersemigroups and investigate its basic properties. We will determine some necessary and sufficient conditions so that this relation is transitive in fuzzy hypersemigroups. Also we show that this relation is transitive in every fuzzy hypergroup.
A NEW CHARACTERIZATION OF THE DERIVED HYPERGROUP VIA STRONGLY REGULAR EQUIVALENCES
ABSTRACT A new strongly regular equivalence is defined and a new characterization of the derived hypergroup of a hypergroup is determined.
Three-dimensional elasticity problems for the prismatic bar
A general solution is given to the three-dimensional linear elastic problem of a prismatic bar subjected to arbitrary tractions on its lateral surfaces, subject only to the restriction that they can be expanded as finite power series in the axial coordinate z. The solution is obtained by repeated differentiation of the tractions with respect to z, establishing a set of sub-problems . A recursive procedure is then developed for generating the solution to from that for . This procedure involves three steps: integration of the stress and displacement fields with respect to z, using an appropriate Papkovich–Neuber (P–N) representation; solution of two-dimensional in-plane and antiplane corrective problems for the tractions in that are independent of z; and expression of these corrective solutions in P–N form. The method is illustrated by an example.