SWAP circuit

Because the film growth rate depends so strongly on the electric field across it (equation 1.115), separation of the anodic and cathodic sites for metals in open circuit is of little consequence, provided film growth is the exclusive reaction. Thus if one site is anodic, and an adjacent site cathodic, film thickening on the anodic site itself causes the two sites to swap roles so that the film on the former cathodic site also thickens correspondingly. Thus the anodic and cathodic sites of the stably passive metal dance over the surface. If however, permanent separation of sites can occur, as for example, where the anodic site has restricted access to the cathodic component in the electrolyte (as in crevice), then breakdown of passivity and associated corrosion can follow. 

Figure 2.11 Sample fragment of a quantum circuit illustrating the effect of some typical quantum gates a SWAP operation between the upper and centre qubits is effected through three consecutive controlled-NOT ...

For Nell, this approach closely resembles the first of Marx s solutions in Capital, volume 2, to the problem of establishing where the money comes from to service the gap between the amount advanced by capitalists and the amount M they receive as income.2 As we saw in Chapter 3, Marx addresses this issue by positing that capitalists advance the amount M -M in addition to M. Under the Kalecki Principle, M —M is the amount of money cast into circulation by capitalists in order to realize profits. Ignoring for simplicity the role of capitalist consumption, this amount is required to purchase additional quantities of capital. Hence, capitalists advance the whole of M. On this view, theoretically, it is correct to speak of M becoming M, but in practice there is no initial sum of money, M, followed later by a larger sum, M there is only M (ibid. 207). In the single swap approach this advance of money is sufficient to fund total income in one run of the monetary circuit. 

The parallel assumption of the circuit approach is that the multiplier is also equal to 1, meaning that there are no income-expenditure spill-over effects between sectors, with the amount advanced having no multiplied impact upon income. The multiplier relationship in (4.23) can be presented as a general model in which the multiplier/velocity is a parameter that can vary in value. From this perspective, the Graziani and single swap models represent a particularly narrow case in which the value of this parameter is restricted to 1. 

It can be pointed out that Foley implicitly embraces a single swap approach to the circuit of money. He assumes that capitalists must advance as money capital the total value of output, which once sold earns the precise amount of revenue required to recover the outlay. This is seen most clearly in equation (5.1), where the money capital advance is equal to the total sales of all capital and consumption goods. In Chapter 4 we saw that this approach, associated with Seccareccia (1996), has been heavily criticized by Nell (2004) for overestimating the amount of money required to oil the circuit of money - a serious miscalculation since it is important to know the precise borrowing requirements placed on the financial system. 

Although it is traditional in Marxian frameworks for capitalists to initiate the circulation of money with an advance of constant and variable capital, our previous discussion, in Chapter 4, showed that there are a number of ways in which the circulation of money can be modelled. In the single swap approach all of income is advanced in the Franco-Italian circuit approach only the wage bill is advanced in Nell s mutual exchange approach only wages in the capital goods sector are advanced. Our contribution has been to suggest, under the Kalecki principle (first introduced in Chapter 3), that capitalists advance an amount of money sufficient to realize their profits. This model is predicated on the definition of investment as accumulation of constant and variable capital. 

If the geometry is fixed, the electrodes included, the R and the C wires may be swapped with no change in measured admittance (reciprocity). This is an important circuit quality test. The polarization impedance of C and the impedance of R should not infiuence the results, but if any of the electrodes are too small that electrode may be in the nonlinear region so that the reciprocity test fails. 

Inadvertent change in gas flow Breathing circuit misconnection Ventilator failure Ampule swap... 

If we swap R, and C, we yield the circuit in Figure 277, which can be considered a high-pass filter performing a differentiation function ... 

Servicing computer-based professional equipment typically involves isolating the problem to the board level and then replacing the defective PWB. Taken on a case-by-case basis, this approach seems efficient The inefficiency in the approach, however (which is readily apparent), is the investment required to keep a stock of spare boards on hand. Furthermore, because of the complex interrelation of circuits today, a PWB that appeared to be faulty may actually turn out to be perfect. The ideal solution is to troubleshoot down to the component level and replace the faulty device instead of swapping boards. In many cases, this approach requires sophisticated and expensive test equipment. In other cases, however, simple test instruments will do the job. 

The logic gate called SWAP is built from a circuit containing only cnot gates, as shown on Figure 3.3. The first CNOT is the controlled by the first qubit (CNOTa), and second one is controlled by the second qubit (CNOT ). 

After the application of these sequences the system wiU be in the state described by Equation (3.5.11). Therefore, a Swap logic gate must be applied, in order to exchange the sates of individual qubits, accomplishing the QFT. The quantum circuit describing the QFT, may be seen on Figure 3.6. 

Figure 3.6 Quantum circuit to implement the QFT (the SWAP operation at the end is not shown). Adapted with permission from [1].

For a three-qubit system the QFT operator can be easily implemented using the basic known logic gates H, S and T, apart from the SWAP. The quantum circuit which illustrates this implementation is shown on Figure 3.7. 

For coupled spins 1 /2, the temporal averaging method described above can be generalized to systems with larger number of spins. In these cases, it is necessary to combine 2" - 1 prepared states to create a pseudo-pure state in a system of n spins. The operations for preparing the individual states can be obtained based on CNOT and SWAP gates. For example, for three spins systems the quantum circuits of these operations are shown in Figure 4.9. 

Figure 4.9 Quantum circuit used to create pseudo-pure states in a three qubit system by temporal averaging using two-qubit CNOT and SWAP gates. The pseudo-pure state 000) is obtained after combining the results of the seven (add the identity operator) Uj operations. Adapted with permission from Reference [27] (Copyright 2007 American Physical Society).

The swapping of transmitters, preamps, and circuit wiring can isolate problems in the measurement circuit but does not rule out grounding or power problems or electrical interference. If a grounded wire inserted into a buffer solution shifts the reading, there is a ground path. This is best done in the field near the actual installation so that the effect of local ground potentials is included. 

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