Multiplication logic

As a first example, consider the case where a designer is not happy with the multiplication logic generated by a synthesis tool. This logic might have been generated from the following code. 

For instance, intersections between logical documents have to be avoided, at least if they are used for the same run of the integrator. It is not sufficient to simply define logical documents by selecting entire branches of the hierarchical database view of Comos PT, because a logical document can contain information from multiple branches in the tree and a tree branch can contain information that is relevant for multiple logical documents. Even for a specific document type, there are different storing policies. For instance, this is the case for the specialized flowsheet documents PFD and P ID. 

Time-Division Multiplexing Popular way to create multiple logical channels from one physical channel by using equally spaced cells. 

The CSD communicates with the outside world through physical links. A physical connection can support multiple logical paths within the meaning of the CSD. Each VL is protected by a safety coding. 

Figure 8-62 depicts a hypothetical distributed control system. A number of different unit configurations are illustrated. This system consists of many commonly used DCS components, including multiplexers (MUXs), single/multiple-loop controllers, programmable logic controllers (PLCs), and smart devices. A typical system includes the following elements as well ... 

Table 2.1-1 compares the ordinary algebra of continuous variables with the Boolean algebra of 1 s and Os. This table uses the symbols and -h for the operations of intersection (AND) and union (OR) which mathematicians represent by n and u respectively. The symbols and -f which are the symbols of multiplication and addition, are used because of the similarity of their use to AND and OR in logic. 

Figure 2.5-1 illustrates the fact that probabilities are not precisely known but may be represented by a "bell-like" distribution the amplitude of which expresses the degree of belief. The probability that a system will fail is calculated by combining component probabilities as unions (addition) and intersection (multiplication) according to the system logic. Instead of point values for these probabilities, distributions are used which results in a distributed probabilitv of system fadure. This section discusses several methods for combining distributions, namely 1) con olution, 2i moments method, 3) Taylor s series, 4) Monte Carlo, and 5) discrete probability distributions (DPD). 

The reason why we find it possible to construct, say, electronic calculators, and indeed why we can perform mental arilhinelie, cannot be found in mathematics or logic. The reason is that the laws of physics happen to permit the existence of physical models for the operations of arithmetic such as addition, subtraction and multiplication. If they did not, these familiar operations would be non-computablo functions. ... 

Learner becomes dissatisfied with his conception, cognitive conflict results Acquiring of the new conception, if it is logical, plausible and fruitful Replacement of the old conception, coexistence of multiple conceptions or restructuring of existing conceptions. 

Although pV2/2 represents kinetic energy per unit volume, pV2 is also the flux of momentum carried by the fluid along the conduit. The latter interpretation is more logical in Eq. (5-50), because rw is also a flux of momentum from the fluid to the tube wall. However, the conventional definition includes the (arbitrary) factor i. Other definitions of the pipe friction factor are in use that are some multiple of the Fanning friction factor. For example, the Darcy friction factor, which is equal to 4/, is used frequently by mechanical and civil engineers. Thus, it is important to know which definition is implied when data for friction factors are used. 

Joachim C, Martrou D, Rezeq M, Troadec C, Jie D, Chandrasekhar N, Gauthier S (2010) Multiple atomic-scale solid surface interconnects for atom circuits and molecule logic gates. J Phys Condens Matter 22 084025... 

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