System Boolean representation

The top events of a system to be investigated in FTA may also be identified through a PHA or may cortespond to a branch of an event tree or a system Boolean representation table (Wang et al. (1995)). The information produced from FMECA may be used in construction of fault trees. Detailed description of FTA and its applications can be found in various published documents such as (Andrews and Moss (2(X)2), Ang and Tang (1984), Halebsky (1989), Henley and Kumamoto (1992)). 

We first represent this text in a more lucid, graphic form (see Figure 3). The time sequence of the individual steps proceeds from top to bottom. The relation between concepts by the Boolean AND and OR operator is represented by a dot and a circle respectively, as is common in the TOSAR system (Topological representation of Synthetic and Analytical Relations of Concepts). ... 

Systems may be modeled using Boolean algebra with two-.state representation of component operability. Systems are not usually modeled as equations is not usually done because of preference by engineers for the more schematic methods that are presented in the next chapter. 

The Boolean equation for the probability of a chemical process system failure is R = A (B-i-C (D-rE (B-l-F G+C). Using Table 2.1-1, factor (he equation into a sum of products to get the mincut representation with each of the products representing an accident sequence. 

The basic element of a quantum computer is the quantum bit or qubit. It is the QC counterpart of the Boolean bit, a classical physical system with two well-defined states. A material realization of a qubit is a quantum two-level system, with energy eigenstates, 0) and 1), and an energy gap AE, which can be in any arbitrary superposition cp) = cos(d/2) 0) + exp(i0)sin(0/2) l).These pure superposition states can be visualized by using a Bloch sphere representation (see Figure 7.1). 

Before explaining the representation of systems by means of Boolean functions an important property of Boolean variables must be presented, that of idempotence or the idempotent operation... 

The system function assigns the value Zt = 1 or Zj = 0 to every value set of the state vector, according to whether the state has been assigned the system incident A, or AThe system function can be represented as a Boolean function as well as mathematically and depends on Z,. The mathematical form represents the logic structure of the system in formula. When the states of components are independent of each other, and if a suitable mathematical representation of ips is selected with Z, replaced by <7 the probability q, that in the overall system the incident A, respectively the state Zj= 1, occurs is... 

A novel approach to the nonlinear modeling of neural systems with point-process (spike) inputs and outputs has been recently proposed, whereby Boolean logical operators (OR, AND, NAND) are used in the context of a Volterra-like hierarchy of input lag combinations to express the binary output of the system/model (Marmarelis et al. 2009). This approach holds considerable promise in simplifying the input-output representation of neural models and facilitating the actual implementation of multichannel neural prostheses in the form of application-specific integrated circuits. 

The test part is a simple spinning top which was created in the EUCLID system by boolean operations applied on CSG primitives. The neutral file contains both the CSG tree and the polyhedron representation which corresponds to the EUCLID data structure. 

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