By means of a kind of new idea, we redefine some kinds of fuzzy ideals in a ring and investigate some of their related properties. The concepts of strong prime (semiprime) generalized fuzzy (bi-, quasi-) ideals in rings are introduced. In particular, we discuss the relationships between strong prime (resp., semiprime) generalized fuzzy (bi-, quasi-) ideals and prime (resp. semiprime) generalize...

We introduce natural strategic games on graphs, which capture the idea of coordination in a local setting. We show that these games have an exact potential and have strong equilibria when the graph is a pseudoforest. We also exhibit some other classes of graphs for which a strong equilibrium exists. However, in general strong equilibria do not need to exist. Further, we study the (strong) price...

Let λ be א0 or a strong limit of cofinality א0. Suppose that 〈Gm, πm,n : m ≤ n < ω〉 and 〈Hm, π t m,n : m ≤ n < ω〉 are projective systems of groups of cardinality less than λ and suppose that for every n < ω there is a homorphism σ : Hn → Gn such that all the diagrams commute. If for every μ < λ there exists 〈fi ∈ Gω : i < μ〉 such that i 6= j =⇒ fif −1 j 6∈ σω(Hω) then there exists 〈fi ∈ Gω : i ...

We consider the damped and driven two-dimensional Euler equations in the plane with weak solutions having finite energy and enstrophy. We show that these (possibly non-unique) solutions satisfy the energy and enstrophy equality. It is shown that this system has a strong global and a strong trajectory attractor in the Sobolev space H. A similar result on the strong attraction holds in the spaces...

In the definition of the graph parameters μ(G) and ν(G), introduced by Colin de Verdière, and in the definition of the graph parameter ξ(G), introduced by Barioli, Fallat, and Hogben, a transversality condition is used, called the Strong Arnol’d Hypothesis. In this paper, we define the Strong Arnol’d Hypothesis for linear subspaces L ⊆ R with respect to a graph G = (V,E), with V = {1, 2, . . . ...

The debts’ clearing problem is about clearing all the debts in a group of n entities (eg. persons, companies) using a minimal number of money transaction operations. In a previous paper we conjectured the problem to be NP-complete. In this paper we prove that it is NP-hard in the strong sense and also NP-easy. We also show the same results for a restricted version of the problem.

Based on prime factorisation in number theory, a new but simple and efficient protection method for access control is proposed. This method has several advantages on performance over previous methods in the literature. Especially, a file I user can be added to or removed from the system without much effort. Excellence of this method is more pronounced for those systems where files are accessibl...

We investigate the instability of the Cauchy horizon caused by causality violation in the compact vacuum universe with the topology B × S × R, which Moncrief and Isenberg considered. We show that if the occurrence of curvature singularities are restricted to the boundary of causality violating region, the whole segments of the boundary become curvature singularities. This implies that the stron...

We investigate the theory IAo + Q, and strengthen [Bu86. Theorem 8.6] to the following: if NP 7 co-NP. then 1-completeness for witness comparison foumulas is not provable in bounded arithmetic.

We prove that a type-definable Lascar strong type has finite diameter. We answer also some other questions from [1] on Lascar strong types. We give some applications on subgroups of type-definable groups. In this paper T is a complete theory in language L and we work within a monster model C of T . For a0, a1 ∈ C let a0Θa1 iff 〈a0, a1〉 extends to an indiscernible sequence 〈an, n < ω〉. We define...