Fixed variable

The fixed variables used in the computer simulation are shown in Table 1 along with the kinetic rate constants for the polymerization reactions. 

Figure 7.4 Influence of nanorod shape on its optical extinction properties, as simulated using the discrete dipole approximation, (a) different aspect ratios, fixed volume, (b) fixed aspect ratio, variable volume, (c) aspect ratio and volume fixed, variable end cap geometry, (d) convexity of...

From the information-theoretical point of view, calibration corresponds to the coding of the input quantity into the output quantity and, vice versa, the evaluation process corresponds to decoding of output data. From the mathematical viewpoint, qin is the independent quantity in the calibration step and qout the dependent one. In the evaluation step, the situation is reverse qout is the independent, and qin the dependent quantity. From the statistical standpoint, qout is a random variable both in calibration and evaluation whereas qin is a fixed variable in the calibration step and a random variable in the evaluation step. This rather complicated situation has some consequences on which will be returned in Sect. 6.1.2. 

As mentioned above, the random character of the input and output variables are of importance with regard to the calibration model and its estimation by calculus of regression. Because of the different character of the analytical quantity x in the calibration step (no random variables but fixed variables which are selected deliberately) and in the evaluation step (random variables like the measured values), the closed loop of Fig. 6.1 does not correctly describe the situation. Instead of this, a linear progress as shown in Fig. 6.2 takes place. 

Figures 5 and 6 show the response surfaces plotted for Property A and Property B, respectively. Note that two variables are plotted at once, with the values of the other variables fixed at levels chosen by the experimenter. The contours in the graph represent constant levels of the response. Fortunately, the computer allows rapid replotting for various levels of the fixed variables, as well as changing the identities of the fixed and floating variables, so that the entire design space can be investigated.

Currently, a good LP solver running on a fast (> 500 mHz) PC with substantial memory, solves a small LP in less than a second, a medium-size LP in minutes to tens of minutes, and a large LP in an hour or so. These codes hardly ever fail, even if the LP is badly formulated or scaled. They include preprocessing procedures that detect and remove redundant constraints, fixed variables, variables that must be at bounds in any optimal solution, and so on. Preprocessors produce an equivalent LP, usually of reduced size. A postprocessor then determines values of any removed variables and Lagrange multipliers for removed constraints. Automatic scaling of variables and constraints is also an option. Armed with such tools, an analyst can solve virtually any LP that can be formulated. 

In essence, the durability of metal/adhesive joints is governed primarily by the combination of substrate, surface preparation, environmental exposure and choice of adhesive. As stated earlier, the choice of the two-part nitrile rubber modified epoxy system (Hughes Chem - PPG) was a fixed variable, meeting the requirement of initial joint strength and cure cycle and was not, at this time, examined as a reason for joint failure. Durability, as influenced by substrate, surface preparation, and environmental exposure were examined in this study using results obtained from accelerated exposure of single lap shear adhesive joints. 

Graphical method Assume the number of effects and calculate the fixed, variable, and total expenses for effect. 

For the unary diagram, we only had one component, so that composition was fixed. For the binary diagram, we have three intensive variables (temperature, pressure, and composition), so to make an x-y diagram, we must fix one of the variables. Pressure is normally selected as the fixed variable. Moreover, pressure is typically fixed at 1 atm. This allows us to plot the most commonly manipulated variables in a binary component system temperature and composition. 

Detector fixed, variable, programmable, or diode-array (DAD) UV-Vis detector Injector manual or automatic Pump Isocratic... 

For simplifying the notations, impedances in the following will be written without vertical bars and the subscript defining the fixed variable. 

Statistical mechanics was originally formulated to describe the properties of systems of identical particles such as atoms or small molecules. However, many materials of industrial and commercial importance do not fit neatly into this framework. For example, the particles in a colloidal suspension are never strictly identical to one another, but have a range of radii (and possibly surface charges, shapes, etc.). This dependence of the particle properties on one or more continuous parameters is known as polydispersity. One can regard a polydisperse fluid as a mixture of an infinite number of distinct particle species. If we label each species according to the value of its polydisperse attribute, a, the state of a polydisperse system entails specification of a density distribution p(a), rather than a finite number of density variables. It is usual to identify two distinct types of polydispersity variable and fixed. Variable polydispersity pertains to systems such as ionic micelles or oil-water emulsions, where the degree of polydispersity (as measured by the form of p(a)) can change under the influence of external factors. A more common situation is fixed polydispersity, appropriate for the description of systems such as colloidal dispersions, liquid crystals, and polymers. Here the form of p(cr) is determined by the synthesis of the fluid. 

The independent variable X is a fixed variable whose values can be observed without error ... 

To illustrate, let s assume we wish to fix the liquid rate leaving a particular stage, which is normally an unknown. If an unknown is going to be set, another fixed variable must be allowed to become an unknown, perhaps the duty on an exchanger. 

For some countries the cracking operation is based entirely on ethane and petrochemical operators enter take or pay contracts for ethane. Often there is a fixed-variable component in the contract linking ethane price to the prevailing price of crude oil. Obviously this limits the benefits to the operator in times of rising oil price with some or all of the benefit passed on to the ethane supplier. 

In order to give an informative account of the likely cost of carbon abatement of the various petrochemical operations, the carbon emissions have been estimated and a fixed variable relationship developed with carbon dioxide disposal cost as the variable. This cost can be either the cost of geo-sequestration facilities, the cost of purchasing emissions certificates or carbon tax. 

A typical world scale plant produces 850 kt/y (2,500 t/d) methanol and requires about 32 PJ/y of gas . Typical construction period is three years with a lifetime of 15 years. Recently, some plants have been constructed at double this capacity (5,000 t/d) and claim much reduced capital costs, which is detailed in the second column. However, although economy of scale applies, some of the reduction in capital claimed probably comes from importing oxygen into the complex to run an auto-thermal gasifier. The coal case produces about 1.4 million tonnes of methanol and is based on the optimum size of an entrained-bed gasifier and requires 45PJ (about 1.8 million tonnes) of black coal. The coal option produces by-products of sulphur, ash and electricity. The fixed variable relationship plotted in Figure 11.9. 

Coal based plants have a higher relative capital cost and the fixed variable curve is at a higher level than for gas based operations. However, coal is widely available at 0.5/GJ (c. 10/t) or less which reduces the production cost to below 200/t. 

The fixed variable relationship for the conversion of methanol into olefins using the statistics shown in Table 11.6 is shown in Figure 11.10. The analysis is based on a capital cost of for the methanol to olefin step of 300 million (2007). 

Where P, the unit production cost of the production of interest (ethylene say), is equal to the sum of the unit feedstock costs (F), the unit capital costs (C) and the unit non feedstock operating costs (O). This can he expressed as a fixed-variable equation with the fixed part of the equation representing the return on capital (the unit capital costs, C, independent of tax considerations) together with all the unit nonfeedstock operating costs (O). 

This leaves the feedstock as the only variable in the fixed-variable equation ... 

Once the fixed variable relationships are derived the equation can be used to estimate the production cost for any given feedstock price. By comparing the estimated production cost with traded prices for the product, the viability of a particular project can be determined. By considering alternative technologies at similar feedstock prices, alternative approaches can be critically compared. 

Fixed Variable Input Output Transfer Function... 

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