Inclusion-exclusion principle

For instance, if = 4, Xn = X12 +X123 -FX124 -FX1234. Equation (3) originates with the inclusion-exclusion principle for the probability of joint events ), because Ai2...m affects all systems states for which at least one component /( < / < ) is still operating before the multiple failure ... 

The network reliabUity is represented as a logical OR of all the paths acting in an active redundancy. A passive redundancy with imperfect switching would have been more realistic but more complicated to evaluate. There exist different techniques for computing Ax y(t) such as the inclusion-exclusion principle (Ru-bino, 1998) or the binary decision diagram (Rauzy, 1993) (Liudong, 2008). Here, the present paper takes into account the behavior of each sensor of WSN. For this reason, each boolean function of each monitored point... 

The geometric approach tries to calculate the volume of an arrangement of atom spheres exactly. The inclusion-exclusion principle can be appUed First, the volumes of all spheres are added, then each intersection of two spheres is subtracted, each intersection of three spheres is added, and so on. However, the calculation of... 

By expanding A2E, A E,..., A E, the expressions for the components of the cluster energy (and therefore interaction energy via Eq. [10] and [13]) can be simplified. In the following form, it is easier to see a connection between this many-body decomposition and the inclusion-exclusion principle (also known as the sieve principle) from combinatorial mathematics ... 

Figure 1 Inclusion-exclusion principle. For three objects, the formula is AUBUC = A-t-B- -C-AnB-AnC-BnC-l-An Bnc...

WilS72 Williamson, S. G. The combinatorial analysis of patterns and the principle of inclusion-exclusion. Discrete Math. 1... 

Inclusion of Pauli s exclusion principle leads to the standard methods of ab initio computational chemistry. Within these methods, molecular systems containing the same nuclei and the same number of electrons, but having a different total electronic spin, can roughly speaking be said to be different systems. Thus, matrix elements of the Hamiltonian between Slater determinants corresponding to different spin states will all be zero, and they will not interact or mix at all. The wavefunctions obtained will be pure spin states. ... 

The possibility of repair during accident situation is yet to be included into Probabilistic Safety Assessment (PSA). A PSA method Includes Event tree (ET) to generate accident scenario and Fault Tree (FT) used to quantify the probability of failure of the Safety Barrier (SB). In literature, there are some examples in which FT analysis has been done for systems with repair components. A FT analysis of phased mission systems has been performed with repairable and non-repairable components (Vaurio 2001). The other FT models with repairable basic events have been proposed based on renewal intensity principle and inclusion-exclusion methods (Yuge et al. 2012 Yuge et al. 2013). However, ET analysis of Initiating Events (IE) with repairable SB has not been dealt before. Therefore this paper proposes a scheme of PSA level-1 for systems with repairable components using a simplified combination of Repairable Event Tree (RET) and Repairable Fault Tree (RFT). 

Gordon Wood, perhaps the foremost student of the Revolutionary generation s republicanism, illumines the extent to which inclusions and exclusions based on whiteness did not contradict, but rather constituted, republican principles, though he himself is little concerned with race. Wood s gloss of popular republicanism contains several features that... 

Updates to SpinPro continue as new rotors and new techniques are developed or as inadequacies are found. New expert systems techniques, such as the ability to incorporate the principles of a problem domain, rather than just the experience of the expert, should give SpinPro the ability to design procedures for novel problems and to explain its reasoning. The updates insure that SpinPro will be a repository of knowledge about the current state of ultracentrifugation SpinPro s expertise should continue to improve. Furthermore, the expert remains gainfully employed as a final arbitrator on the inclusion or exclusion of any new knowledge. 

The allowance for polarization in the DH model obviates the need for separation of long-range and short-range attractive forces and for inclusion of additional repulsive interactions. Belief in the necessity to include some kind of covolume term stems from the confused analysis of Onsager (13), and is compounded by a misunderstanding of the standard state concept. Reference to a solvated standard state in which there are no interionic effects can in principle be made at any arbitrary concentration, and the only repulsive or exclusion term required is that described by the DH theory which puts limits on the ionic atmosphere size and hence on the lowering of electrical free energy. The present work therefore supports the view of Stokes (34) that the covolume term should not be included in the comparison of statistical-mechanical results with experimental ones. 

Educational inclusion and inclusive education are complex concepts that are difficult to define and are open to a range of understandings. These variations have developed out of different historical, geographical and theoretical contexts, although they clearly share certain principles based on notions of equity and social justice. Furthermore, inclusion is closely linked to other terms such as integration, special educational needs and exclusion which are also susceptible to differences of interpretations. Such differences inevitably affect the ways in which levels of inclusion in schools are assessed, as well as how the impact of inclusion on students learning is evaluated. 

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