In recent publications Alain Connes [1] and John Barrett [2] proposed to change the KO-dimension of the internal space of the standard model in its noncommutative representation [3] from zero to six. This apparently minor modification allowed to resolve the fermion doubling problem [4], and the introduction of Majorana mass terms for the right-handed neutrino. The price which had to be paid was...

A non-trivial, transitive and reflexive binary relation on the set of lotteries satisfying independence that also satisfies any two of the following three axioms satisfies the third: completeness, Archimedean and mixture continuity (Dubra (2011)). This paper generalizes Dubra’s result in two ways: First, by replacing independence with a weaker betweenness axiom. Second, by replacing independenc...

A recently proposed axiom system for André’s central translation structures is improved upon. First, one of its axioms turns out to be dependent (derivable from the other axioms). Without this axiom, the axiom system is indeed independent. Second, whereas most of the original independence models were infinite, finite independence models are available. Moreover, the independence proof for one of...

1 The Axioms of Quantum Mechanics 1 1.1 The State Space Axiom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Unitary Evolution Axiom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 The Measurement Axiom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 The Composite System Axiom . . . . . . . . . . . . . . . . . . ...

The paper initially studies both the s-T3-separation and semi-T3-separation axiom of Khalimsky (K-for brevity) topological spaces. To do this work, first we investigate some properties semi-open semi-closed sets with respect to operations union or intersection further, a homeomorphism, semi-homeomorphism. Next, study various semi-topological K-topological spaces such as simple K-paths. Finally,...

In this paper, we introduce the concept of ordinary smooth topology on a set X by considering the gradation of openness of ordinary subsets of X . And we obtain the result [Corollary 2.13] : An ordinary smooth topology is fully determined its decomposition in classical topologies. Also we introduce the notion of ordinary smooth [resp. strong and weak] continuity and study some its properties. A...

We proceed with the study of net bundles over partially ordered sets (posets), defined as the analogues of ordinary fibre bundles. To this end, we analyze the connection between homotopy, net homology and net cohomology of a poset, providing versions of classical Hurewicz theorems. Focusing our attention to Hilbert net bundles, we define the K-theory of a poset and introduce functions over the ...

The Maschler–Owen consistent value for non-transferable utility games is axiomatized, by means of a marginality axiom. JEL Classification: C7, D7

Let f be a diffeomorphism of a closed C∞ manifold M . In this paper, we introduce the notion of the C1-stable specification property for a closed f -invariant set Λ of M , and we prove that f|Λ satisfies a C 1-stable specification property if and only if Λ is a hyperbolic elementary set. As a corollary, the C1-interior of the set of diffeomorphisms of M satisfying the specification property is ...

We show there is a residual set of non-Anosov C∞ Axiom A diffeomorphisms with the no cycles property whose elements have trivial centralizer. If M is a surface and 2 ≤ r ≤ ∞, then we will show there exists an open and dense set of of Cr Axiom A diffeomorphisms with the no cycles property whose elements have trivial centralizer. Additionally, we examine commuting diffeomorphisms preserving a com...