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.
On α-solvable fundamental groups
We introduce a specific kind of equivalence relation ξn on a fuzzy hypergroup S such that the quotient S/ξn, the set of all equivalence classes, is an α-solvable group. This helps us to introduce the α-solvable fundamental relation ξ∗α. In particular, we obtain an equivalent condition with transitivity of ξα. Article Information Corresponding Author: F. Mohammadzadeh; Received: April 2021; Revised: May 2021; Accepted: June 2021; Paper type: Original.
Inhomogeneous Boundary Value Problems for Compressible Navier-Stokes Equations: Well-Posedness and Sensitivity Analysis
In this paper compressible, stationary Navier–Stokes equations are considered. A framework for analysis of such equations is established. In particular, the well-posedness for inhomogeneous boundary value problems of elliptic-hyperbolic type is shown. Analysis is performed for small perturbations of the so-called approximate solutions that take form (1.12). The approximate solutions are determined from Stokes problem (1.11). The small perturbations are given by solutions to (1.13). The uniqueness of solutions for problem (1.13) is proved, and, in addition, the differentiability of solutions with respect to the coefficients of differential operators is shown. The results on the well-posedness of nonlinear problems are interesting on their own and are used to obtain the shape differentiability of the drag functional for incompressible Navier–Stokes equations. The shape gradient of the drag functional is derived in the classical and useful for computations form; an appropriate adjoint state is introduced to ...