Custom equation selection

Twelfth, click the OK button (shown as a framed button in Fig. 5.24). MATLAB will return to the main Fit Editor window as shown in Fig. 5.25a. Figure 5.25b shows the new look of the Curve Fitting Toolbox window where the user selects Custom Equation from the main category drop-down list and then enters the expression fory = f x a, b, c). 

After selecting what X, Y, and Z represent out of the list of vectors, choose Custom Equation from the drop-down list (see the framed drop-down list in Fig. 5.341. You will then be prompted to enter the function formula in the dedicated textbox (see Fig. 5.361. 

Compaction properties of each material were determined with a standardized test performed on a custom-built hydraulic compaction simulator using 8 mm (0.3150 in.) round flat-faced punches. A linear saw-tooth upper punch position profile was selected with a punch velocity of 300 mm/sec for both punch extension and retraction. The lower punch position was at a fixed position within the die during the compaction event. The powder weight loaded into the die for each compression was calculated from the equation below so as to form a cylindrical tablet having a thickness-to-diameter ratio of 0.30 at a theoretical SF of 1.0. These dimensions are typical of commercially elegant tablets. 

A cost equation may be written to include all the costs, which are expressed in terms of the capacity of the flow-scheme components. The selection of equipment sizes that minimize capital investment is (1) complicated by interrelations between pieces of equipment, (2) limited by the discontinuity in size of standard equipment, (3) fixed by the availability of idle or used equipment, and (4) restricted by the higher cost of custom-made equipment. Writing one equation for a complete plant is a complex task. It is more likely that it may be done for small sections of the plant which can be operated as interrelated trains. 

In manual work, method selection can be performed by manual inspection of the predicted chromatograms for resolution and run time, or according to the user-dehned automated rating process. The automated selection process can be customized on a similar basis as the selection process in method optimization software, with requirements based on targeted run time, resolution, or a combination of the two this suitability approach is described in equation (10-5) ... 

It is often desired to add a differential equation in COMSOL that is not available through one of their built-in application modes. For example, in our model, we wanted to add a custom PDF to calculate the redox potential drop through the biofilm via Ohm s law Equation 9.21. To achieve this, we use the generic PDE application mode. As in the built-in application modes, defining a custom PDE application mode consists of the application mode selection, boundary settings, and subdomain settings. However, in the generic PDE application mode, we must also define the PDE itself. For the coefficient form, which is used in this case, the PDE takes the form of ... 

Based on their need for reliability, the customers may request in the product specification that the system has a strictly defined high confidence level (e.g., 98 %). The predetermined level of confidence impacts the choice of product s components and selection between different available component grades, balancing cost with quality. The component grade selection is also dependent on how the system is designed, i.e., how many units of a specific component are used and if there is any component redundancy. Equations that are used to calculate the reliability factors are as follows ... 

Suppose that we would like to calculate the following volume-related properties of a pure substance (not necessarily an ideal gas)—the gas molar volume, liquid molar volume, isothermal compressibility factor (kappa, k), thermal expansion coefficient (alpha, a), and compressibility factor (Z)—while inputting both the pressure in atmosphere and temperature in Kelvin. The calculation is based on the van der Waals equation of state. Let us design a GUI that handles such a duty. Details on how to add controls to a blank GUI and how to customize them are shown in previous sections. However, more features are explored here that have not been covered before. Given that a database exists in the form of an Excel sheet, which lists the name of a substance, its chemical formula, its critical pressure, and its critical temperature, we would like the user to search for the substance of interest via a keyword that is based either on name or chemical formula. The search results shall be presented and the user will then decide on the substance of interest via selecting the corresponding... 

The model is formulated under the assumption that only one option may be selected per customer per plant for each period. Set Nj is introduced for each customer, which includes all the independent distributors that can supply customer j. Equation 5.1 summarizes the set of constraints that considers this assumption ... 

Another important assumption is that a customer may be distributed either from the company (i.e., a manufacturing plant or a DC) or from an independent distributor but not from both. Therefore, for each customer, options 3 and 4 may not be selected if option 1 or 2 is selected for a plant. This set of constraints is shown in Equations 5.2 and 5.3 ... 

Another important assumption is that, in all periods, only one distributor may be selected per customer. This is because the decision of moving a customer to an independent distributor is a strategic decision. This means that if a customer is to be given to an independent distributor, the customer will stay with that independent distributor for the entire time horizon and cannot be a direct customer of the company anymore or be moved to another distributor. To represent this, binary variable is introduced, where = 1 implies that customer j is supplied by distributor i. Equations 5.8 and 5.9 denote these constraints. 

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