Interval arithmetic is based on the fact that for intervals on the real line, the element-wise product of two intervals is also an interval. This property is not always true: e.g., it is not true if we consider intervals on the set of integers instead of intervals on the set of real numbers. When is an element-wise product or a sum of two intervals always an interval? In this paper, we analyze ...

We define the notion of weakly ordered semigroups. For this class of semigroups, we compute the radical of the semigroup algebras. This generalizes some results on left regular bands and on 0Hecke algebras.

We prove that if M = (M,≤,+, . . .) is a weakly o-minimal non-valuational structure expanding an ordered group (M,≤,+), then its expansion by a family of ‘non-valuational’ unary predicates remains non-valuational. The paper is based on the author’s earlier work on strong cell decomposition for weakly o-minimal non-valuational expansions of ordered groups.

in a fuzzy metric space (x;m; *), where * is a continuous t-norm,a locally fuzzy contraction mapping is de ned. it is proved that any locally fuzzy contraction mapping is a global fuzzy contractive. also, if f satis es the locally fuzzy contractivity condition then it satis es the global fuzzy contrac-tivity condition.

In this paper, the concepts of minimal and maximal left hyperideals in ordered semihypergroups are introduced, and several related properties are investigated. Furthermore, we introduce the concepts of weakly prime, quasi-prime, quasi-semiprime and weakly quasiprime left hyperideals of an ordered semihypergroup, and establish the relationship among the four classes of left hyperideals. Moreover...

A dynamical system is called contractive if any two solutions approach one another at an exponential rate. More precisely, the dynamics contracts lines This property implies highly ordered asymptotic behavior including entrainment to time-varying periodic vector fields and, in particular, global stability for time-invariant fields. Contraction theory has found numerous applications systems and ...

Let the invariant probability measures for an orientation-reversing weakly expanding map of the interval [0, 1] be partially ordered by majorization. The minimal elements of the resulting poset are shown to be convex combinations of Dirac measures supported on two adjacent fixed points. A consequence is that if f : [0, 1] → R is strictly convex, then either its minimizing measure is unique and ...