The well known results on the inner limitations of classical mathematics (L6wenheim-Skolem Theorems, and G6del's Theorems) and the introduction of a host of new set-like concepts, indicate the presence of something which is beyond the grasp of Cantorian set theory. In different ways each limitation expresses a basic uncertainty in Mathematics. GOdel's Theorems essentially express the following:...

Compute the Chernoff bound on P [X ≥ a] where X is a random variable that satisfies the exponential law f X (x) = λe −λx u(x). Recall, from Equation 4.6-4 on page 214 in [3], that the Chernoff bound for a continuous random variable X is given by P [X ≥ a] ≤ argmin t>0 e −at θ X (t) , (1) where θ X (t) is the moment-generating function θ X (t) E[e tX ] = ∞ −∞ e tx f X (x)dx (2) as defined by Equ...

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,...

Article history: Received 16 April 2013 Available online 24 January 2014