Recently an expansion of LΠ 1 2 logic with fixed points has been considered [23]. In the present work we study the algebraic semantics of this logic, namely μ LΠ algebras, from algebraic, model theoretic and computational standpoints. We provide a characterisation of free μ LΠ algebras as a family of particular functions from [0, 1]n to [0, 1]. We show that the first-order theory of linearly or...

This paper aims to give a clear and comprehensive view of the relations between the various classes of MV-algebras with product operations. The algebraic hyerarchy, from groups to algebras, can be transported by Γ-functors in order to provide the algebraic semantics for conservative extensions of Łukasiewicz logic. The MV-algebraic tensor product allows us to complete the picture with categoric...

Recently an expansion of LΠ 1 2 logic with fixed points has been considered [23]. In the present work we study the algebraic semantics of this logic, namely μ LΠ algebras, from algebraic, model theoretic and computational standpoints. We provide a characterisation of free μ LΠ algebras as a family of particular functions from [0, 1]n to [0, 1]. We show that the first-order theory of linearly or...

Recall that a subset of R is called semi-algebraic if it can be represented as a (finite) boolean combination of sets of the form {~ α ∈ R : p(~ α) = 0}, {~ α ∈ R : q(~ α) > 0} where p(~x), q(~x) are n-variable polynomials with real coefficients. A map from R to R is called semi-algebraic if its graph, considered as a subset of R, is so. The geometry of such sets and maps (“semi-algebraic geome...

In this section we will give an (extremely) brief Introduction to the concept of interior point methods • Logarithmic Barrier Method • Method of Centers We have previously seen methods that follow a path On the boundary of the feasible region (Simplex). As the name suggest, interior point methods instead Follow a path through the interior of the feasible region.

The dynamic simulation of the continuous catalytic reforming process is great significance to performance prediction and optimization entire process. In this study, a 34-lumped mechanism model described by differential algebra was established based on actual conditions in China, an efficient solution method simultaneous equations proposed. First, differential–algebraic basic principles kinetics...

Given a lattice polygon P with g interior points, we can associate to $$P$$ two moduli spaces: the space of algebraic curves that are non-degenerate respect and tropical genus Newton P. We completely classify possible dimensions such have in case. For non-hyperelliptic polygons, dimension must be between $$2g+1$$ take on any integer value this range, exceptions only cases 3, 4, 7. provide simil...

in this paper, we present the concepts of a fuzzy soft left (right) ideal and fuzzy soft interior ideal over an ordered semigroup s . some basic results of fuzzy soft left (right) ideals and fuzzy soft interior ideals are investigated and the supported examples are provided. different classes, regular, intra-regular, and simple ordered semigroups are   characterized by means of fuzzy sof...

In the first part of this article, we study feedback stabilization a parabolic coupled system by using localized interior controls. The is stabilizable with exponential decay $ -\omega<0 for any \omega>0 $. A stabilizing control found in form solving suitable algebraic Riccati equation. second part, conforming finite element method employed to approximate continuous dimensional discrete s...