The purpose of this paper is the study of direct limits in category of Krasner (m, n)-hyperrings. In this regards we introduce and study direct limit of a direct system in category (m, n)-hyperrings. Also, we consider fundamental relation , as the smallest equivalence relation on an (m, n)-hyperring R such that the quotient space is an (m, n)-ring, to introdu...

In this paper, we establish a lower bound on the number of inducing simple n-gons in grid-like arrangements of lines. We also show that the complexity associated with counting the number of inducing n-gons in an arrangement of collinear segments is #P-complete.

We investigate the complexity of membership problems for {∪,∩, ̄ , +,×}-circuits computing sets of integers. These problems are a natural modification of the membership problems for circuits computing sets of natural numbers studied by McKenzie and Wagner (2003). We show that there are several membership problems for which the complexity in the case of integers differs significantly from the ca...

For each prime p and each embedding σ of the multiplicative group of an algebraic closure of Fp as complex roots of unity, we construct a p-adic indecomposable representation πσ of the integral BC-system as additive endomorphisms of the big Witt ring of F̄p. The obtained representations are the p-adic analogues of the complex, extremal KMS∞ states of the BC-system. The role of the Riemann zeta f...

In normal activities such as walking, rn­ning, kneeling, climbing stairs and gettmg in and out of chairs the loa pu OI.the human knee joint can exceed five times the weight of the body. Nowadays large num­bers of people make ! urtrer d mands on the knee in participatmg 1_n sucli sport  as football, tennis and long distance runnng. It is no wonder that many people go mto their later years with o...

The problem of counting unlabelled subtrees of a tree (that is, subtrees that are distinct up to isomorphism) is #P-complete, and hence equivalent in computational difficulty to evaluating the permanent of a 0,1-matrix.

Implications of a formal context (G,M, I) have a minimal implication basis, called Duquenne-Guigues basis or stem base. It is shown that the problem of deciding whether a set of attributes is a premise of the stem base is in coNP and determining the size of the stem base is polynomially Turing equivalent to a #P-complete problem.

To compute the number of models of a 2-CF (conjunction of clauses with two literals at most), the well-known problem as #2-SAT, is a classical #P-complete problem. We show here an extensive class of instances of 2CF’s where to compute the number of models can be done