A self-map, either single-valued or multi-valued, is multiply fixed if every map homotopic to it has at least two fixed points. Let p : X̃ → X be a finite covering space, of degree n, of a connected finite polyhedron, and let f : X → X be a map. We lift f to an n-valued map φp,f : X̃ ( X̃ and prove that it is multiply fixed if the Nielsen number of f is greater than or equal to two. We obtain a fo...

Let Q be a finite acyclic valued quiver. We define bialgebra structure and an integration map on the Hall algebra associated to morphism category of projective representations Q. As application, we recover surjective homomorphism defined in [12], which realizes principal coefficient quantum cluster $$\mathcal {A}\,_q(Q)$$ as sub-quotient morphisms. Moreover, also Caldero–Chapoton formula, well ...

In the classical Constraint Satisfaction Problem(CSP) two finite models are given and we are asked to find their homomorphism. In the Mixed-CSP problem, besides the models, a set of weighted pairs of elements of this two models is given and the task is to find a homomorphism that maximizes the weight of pairs consistent with the homomorphism, i.e. pairs for which homomorphism maps the first ele...

Roughness in modules have been investigated by B. Davvaz and M. Mahdavipour in 2006 [5]. The purpose of this paper is to introduce and discuss the concept of T -rough prime and primary submodules which is a generalization the lower and upper approximation submodules over a commutative ring. We define a set-valued homomorphism on a module and study some properties of it . We prove some results f...

The paper attempts a systematic study of homomorphisms of relational structures. Such structures are modeled as multialgebras (i.e., relation is represented as a set-valued function). The rst, main, result is that, under reasonable restrictions on the form of the deenition of homomorphism, there are exactly nine compositional homomorphisms of multialgebras. Then the comparison of the obtained c...

Introduction. By a lattice homorphism of a group G onto a group G' we mean a single-valued mapping of the lattice L(G) of subgroups of G onto the lattice L(G') of subgroups of G', which preserves all unions and intersections, that is, which is subject to the conditions 1. (U,S,)0 = U,(S¿), 2. (r\vSr) = Ç)ASd>), for every (finite or infinite) set of subgroups 5„ of G. We call proper any l...

In the classical Constraint Satisfaction Problem(CSP ) two finite models are given and we are asked to find their homomorphism. In the MinHom problem, besides the models, a set of weighted pairs of elements of this two models is given and the task is to find a homomorphism that maximizes the weight of pairs consistent with the homomorphism, i.e. pairs for which homomorphism maps the first eleme...

General logic programs with negation have the 3-valued minimal Herbrand models based on the Kripke’s fixpoint knowledge revision operator and on Clark’s completion. Based on these results we deifine a new algebra , (with the relational algebra embedded in it), and present an algorithmic transformation of logic programs into the system of tuple-variable equations which is a -coalgebra. The solut...

A Z-graded Lie bracket { , }P on the exterior algebra Ω(M) of differential forms, which is an extension of the Poisson bracket of functions on a Poisson manifold (M,P ), is found. This bracket is simultaneously graded skew-symmetric and satisfies the graded Jacobi identity. It is a kind of an ‘integral’ of the Koszul-Schouten bracket [ , ]P of differential forms in the sense that the exterior d...