Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events.In this paper we prove an inclusion-exclusion principle for IF-states based on a method which can also be used to prove Grzegorzewski's inclusion-exclusion principle for probabilities on IF-events.Finally, we give some applications of this principle by...

The equivalence principle, which states the local equivalence between acceleration and gravity, requires that a free falling observer must result in a co-moving local Minkowski space. On the other hand, covariance principle assumes any Gaussian system to be valid as a space-time coordinate system. Given the mathematical existence of the co-moving local Minkowski space along a time-like geodesic...

Understanding the transcriptional regulationnetworks that control the gene expression programs in a living cell is one of fundamental questions in molecular biology. Using single perturbations allows us to identify the key players in those networks. To better understand the structure, we can use double perturbations to measure genetic interactions between the components in the network. By syste...

With the advent of self-organizing systems such as ad hoc networks or ubiquitous computing, security protocols have to meet a new requirement for establishing trust among parties that have no a priori relationship like a shared naming structure or a common organization. Trust establishment in this context calls for a brand new paradigm with respect to classical scenarios whereby entities build ...

In the past few years, extensive improvements have been accomplished in reinforcing the structures through using shape memory alloys (SMAs). These materials absorb or dissipate energy through establishing a reversible hysteresis loop during a cyclic mechanical loading. This unique characteristic of the SMAs has made them appropriate for sensing, actuation, absorbing the impact energy, and vibra...

INTRODUCTION Current surgical training is still highly dependent on expensive operating room (OR) experience. Although there have been many attempts to transfer more training to the skills laboratory, little research is focused on which technical behaviors can lead to the highest profit when they are trained outside the OR. The Pareto principle states that in any population that contributes to ...