The layered sodium cobalt oxide NaxCoO2 is studied by electron diffraction for a wide range of sodium contents, 0.15,x,0.75. An extensive series of ordered Na ion-Na vacancy superlattices is found beyond the simple hexagonal average structure. The most strongly developed superlattice is found for the composition Na0.5CoO2, which displays Co 3+/Co4+ charge ordering at low temperatures. The struc...

For C a set well-founded with respect to the partial ordering ” DQG IRU Q.x a predicate possibly with free variable x, the theorem of well-founded induction states that (∀x: x∈C: Q.x) is equivalent to (∀x: x∈C: (∀y: y∈C ∧ y<x: Q.y) ⇒ Q.x). Well-founded induction is very general. For example the so-called "principle of strong induction" is well-founded induction on the set of natural numbers wit...

Arrow’s celebrated theorem of social choice shows that the aggregation of individual preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individual preferences over that pair, unless the fundamental weak Pareto and nondictatorship principles are violated. In the standard model of division of commodities, we investigate how much information about...

Topological Dependency Grammar (TDG) is a new lexicalized formalism where word order phenomena arise from the interaction of a non-ordered syntax tree with a projective topological tree, both related by an emancipation mechanism. TDG proved capable of an elegant account of German word-order phenomena. We apply it now to the modelization of word-order variation in the Dutch verb cluster and furt...

In this paper, we introduce and study the GQL?-operations. We prove that class is a hyper of known QL?-operations. Similar to QL?-operations, GQL?-operations are not always fuzzy implications. On other hand, present necessary but sufficient condition leads generation GQL?-implication. Our completed by studying satisfaction or violation some basic properties implications, such as left neutrality...

Equality of opportunity is concerned with the level-the-playing-field principle: society should compensate individuals who suffer from bad circumstances but let the agents exercise their responsibility. This paper proposes a partial ordering based on the inequality-of-opportunity curve, a mechanism that gives preference to those who are worse in terms of opportunity. Moreover, it is provided a ...

*Correspondence: [email protected] Faculty of Mathematics and Informatics, Plovdiv University, Plovdiv, 4000, Bulgaria Abstract In this paper, we develop a unified theory for cone metric spaces over a solid vector space. As an application of the new theory, we present full statements of the iterated contraction principle and the Banach contraction principle in cone metric spaces over a sol...

There is a longstanding debate about how to appropriately model the combinability of affixes, especially English suffixes. One widely accepted principle is the notion of so-called selectional restrictions, i.e. grammatical requirements of particular affixes. For example, the suffix -ness can only combine with adjectival bases. Hay (2002) proposed a psycholinguistic approach to affix ordering no...

We write Z for the set of integers, and N = {1, 2, 3, . . . } for the set of natural numbers. I’ll use M 28 Aug the convention where natural numbers are assumed to be positive. I may also write Z>0 for N. We also use the notation Z≥0 = {0, 1, 2, . . . } for the set of non-negative integers. Well-ordering principle (WOP). Every non-empty subset of N contains a smallest element. Explicitly: if S ...

Sellers benefit on average from revealing information about their goods to buyers, but the incentive to exaggerate undermines the credibility of seller statements. When multiple goods are being auctioned, we show that revealing a complete or partial ordering of the different goods by value can be credible. Ordinal cheap talk of this form is not susceptible to exaggeration because it simultaneou...