In this article, the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This will be referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and...

ABSTRACT. Inspired by the article of P. Grzegorzewski [The inclusion-exclusion principle for IF-events, Inform. Sci. 181 (2011), 536–546], who has worked two generalizations of the inclusion-exclusion principle for IF-events, a generalization of the inclusion-exclusion principle for mappings with values in semigroups is presented here. The main idea is in replacing the distributivity and idempo...

Bacteria and plants are able to form population waves in result of their consumer behaviour and propagation. A soliton-like interpenetration of colliding population waves was assumed but not proved earlier. Here we show how and why colliding population waves of trophically identical but fitness different species can interpenetrate through each other without delay. We have hypothesized and revea...

A short review is given of three experimental works on tests of the Pauli Exclusion Principle (PEP) in which the author has been involved during the last 10 years. In the first work a search for anomalous carbon atoms was done and a limit on the existence of such atoms was determined, C̃/C< 2.5×10. In the second work PEP was tested with the NEMO-2 detector and the limits on the violation of PEP ...

In this paper, we present improved techniques for computing and getting bounds on the cardinality of a union of sets using the inclusion-exclusion principle and Bonferroni inequalities. We organize the terms involved in the inclusionexclusion sum as a tree, showing that a set inclusion between a parent and its children yields a cancellation, where we may prune an entire subtree. Next, we provid...

The inclusion-exclusion principle is a well-known property of set cardinality and probability measures, that is instrumental to solve some problems such as the evaluation of systems reliability or of uncertainty over Boolean formulas. However, when using sets and probabilities conjointly, this principle no longer holds in general. It is therefore useful to know in which cases it is still valid....

The inclusion-exclusion principle is a well-known mathematical principle used to count the number of elements in the union of a collection of sets in terms of intersections of sub-collections. We present an algorithm for counting the number of solutions of a given k-SAT formula using the inclusion-exclusion principle. The key contribution of our work consists of a novel subsumption pruning tech...