We study algebraic properties of categories of Merotopic, Nearness, and Filter Algebras. We show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. The forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...

Let $K$ be a field of characteristic$p>0$, $K[[x]]$, the ring of formal power series over $ K$,$K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the fieldof rational functions over $K$. We shall give somecharacterizations of an algebraic function $fin K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $finL[[x]]$ is called differentially algebraic, if it satisfies...

In this paper we extend the notion of  degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and  introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. It would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. We give the main properties of the operations defined and prove som...

In this paper, let $L$ be a completeresiduated lattice, and let {bf Set} denote the category of setsand mappings, $LF$-{bf Pos} denote the category of $LF$-posets and$LF$-monotone mappings, and $LF$-{bf CSLat}$(sqcup)$, $LF$-{bfCSLat}$(sqcap)$ denote the category of $LF$-completelattices and $LF$-join-preserving mappings and the category of$LF$-complete lattices and $LF$-meet-preserving mapping...

Here a posteriori error estimate for the numerical solution of nonlinear Voltena- Hammerstein equations is given. We present an error upper bound for nonlinear Voltena-Hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of Brunner for these problems (the implicitly linear collocation method)...

This paper belongs to our series of works on algebraic geometry over arbitrary structures. In this one, there will be investigated seven equivalences (namely: geometric, universal quasi-equational, universal, elementary, and combinations thereof) in specific classes structures (equationally Noetherian, qω-compact, uω-compact, equational domains, co-domains, etc.). The main questions are the fol...

For regular strangeness-free linear differential-algebraic equations (DAEs) the definition of an adjoint DAE is straightforward. This definition can be formally extended to general linear DAEs. In this paper, we analyze the properties of the formal adjoints and their implications in solving linear-quadratic optimal control problems with DAE constraints.