The theory of locally convex cones, as developed in [3], deals with ordered cones that are not necessarily embeddable in vector spaces. A topological structure is introduced using order theoretical concepts. We will review some of the main concepts and globally refer to [3] for details and proofs. An ordered cone is a set endowed with an addition and a scalar multiplication for nonnegative real...

where Z denotes the set of integers. For positive integers A > 1, B > 1 we defineMn(A,B) to be the set of (a, b) with A ≤ |a| ≤ 2A, B ≤ |b| ≤ 2B such that f(t) is irreducible and Df is squarefree. It is reasonable to expect that for A, B tending to infinity, Mn(A,B) ∼ cnAB, for some positive constant cn. This is probably very difficult to prove. We will apply the abc conjecture to show that Mn(...

For all M,N∈P(U) such that M⊂N, we first introduced the definitions of (M,N)-uni-soft ideals and (M,N)-uni-soft interior ideals of an ordered semigroup and studied them. When M=∅ and N=U, we meet the ordinary soft ones. Then we proved that in regular and in intra-regular ordered semigroups the concept of (M,N)-uni-soft ideals and the (M,N)-uni-soft interior ideals coincide. Finally, we introduc...

Let L ∗ M denote the coproduct of the bounded distributive lattices L and M . At the 1981 Banff Conference on Ordered Sets, the following question was posed: What is the largest class L of finite distributive lattices such that, for every non-trivial Boolean lattice B and every L ∈ L, B ∗ L = B ∗ L′ implies L = L′? In this note, the problem is solved.

We show that the order complex of poset nonempty intervals, ordered by inclusion, is a Tchebyshev triangulation original poset. Besides studying properties this transformation, we dual type B permutohedron combinatorially equivalent to suspension intervals Boolean algebra (with minimum and maximum elements removed).

How much retirement income is needed in order to maintain one’s living standard at old age? As it is difficult to find a firm basis for an empirical treatment of this question, we employ a novel approach to assessing an adequate replacement rate vis-à-vis income in the pre-retirement period. We subject indications regarding satisfaction with current income as collected in the German Socio-Econo...

We show that no nontrivial principal ideal of the enumeration degrees is linearly ordered: In fact, below every nonzero enumeration degree one can embed every countable partial order. The result can be relativized above any total degree: If a,b are enumeration degrees, with a total, and a < b, then in the degree interval (a,b), one can embed every countable partial order.

Let $S$ be an ordered semigroup. A fuzzy subset of $S$ is anarbitrary mapping   from $S$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. In this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $S$ is introduced.Regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.Finally, two m...

Test score distributions of schools or demographic groups are often summarized by frequencies of students scoring in a small number of ordered proficiency categories. We show that heteroskedastic ordered probit (HETOP) models can be used to estimate means and standard deviations of multiple groups’ test score distributions from such data. Because the scale of HETOP estimates is indeterminate up...