Interpretability into Lukasiewicz algebras
In this paper we give a characterization of all the interpretations of the varieties of bounded distributive lattices, De Morgan algebras and Lukasiewicz algebras of order m in the variety of Lukasiewicz algebras of order n. In the case of distributive lattices we give a structure theorem that is generalized to De Morgan algebras and to Lukasiewicz algebras of order m. In the last two cases we also give the number of such interpretations.
Resolution of Algebraic Systems of Equations in the Variety of Cyclic Post Algebras
There is a constructive method to define a structure of simple k-cyclic Post algebra of order p, L p,k , on a given finite field F(p k ), and conversely. There exists an interpretation ?1 of the variety $${\mathcal{V}(L_{p,k})}$$ generated by L p,k into the variety $${\mathcal{V}(F(p^k))}$$ generated by F(p k ) and an interpretation ?2 of $${\mathcal{V}(F(p^k))}$$ into $${\mathcal{V}(L_{p,k})}$$ such that ?2?1(B) = B for every $${B \in \mathcal{V}(L_{p,k})}$$ and ?1?2(R) = R for every $${R \in \mathcal{V}(F(p^k))}$$ . 
 
In this paper we show how we can solve an algebraic system of equations over an arbitrary cyclic Post algebra of order p, p prime, using the above interpretation, Grobner bases and algorithms programmed in Maple.
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 ...