Display equations

Chapter 8 consists of the following in Sect. 8.2 the physical model of the process is described. The governing equations and conditions of the interface surface are considered in Sects. 8.3 and 8.4. In Sect. 8.5 we present the equations transformations. In Sect. 8.6 we display equations for the average parameters. The quasi-one-dimensional model is described in Sect. 8.7. Parameter distribution in characteristic zones of the heated capillary is considered in Sect. 8.8. The results of a parametrical study on flow in a heated capillary are presented in Sect. 8.9. 

Keep the default Linear Regression under the type tab and on the jOptions tab select Display equation on chart. This results in... 

Number displayed equations by using any consistent system of sequencing. 

Chapter 11 Numbers, Mathematics,and Units of Measure >- 221 > Do not use any closing punctuation on the line with displayed equations. 

When introducing a displayed equation, do not automatically use a colon in most cases a colon is incorrect because the equation finishes a phrase or sentence. 

Following a displayed equation that is part of a sentence, punctuate the text as if it were a continuation of a sentence including the equation but do not punctuate at the end of the equation. Note the absence of a comma at the end of the equation in the example. Punctuation that would normally be present at the end of an equation in text is absent but implicit at the end of a displayed equation. 

Molecular mechanics calculations have recently been used to assist in explaining the stereochemical course of several intramolecular cycloaddition reactions. - In one case, calculations were carried out to determine the relative energies of four diastereomeric products which could have been produced in the intramolecular azomethine cycloaddition reaction displayed (equation 23). A single product was isolated, though in only 25% yield, llie assumption was made that the calculated difrerences in product stability were reflected by similar, but smaller, energy difrerences in the transition states. 

Now choose the Options tab and check the boxes for Display Equation On Chart and Display R-squared Value On Chart then press OK. Excel displays the trendline on the chart as a heavy solid line and the equation (with the least squares coefficients) and Rp- value as a title on the chart. 

Now right-click on any data point and then click on Add Trendline. Under Type, select Linear. Under options, check Display equation on chart and Display / -squared value on chart. Then click on OK. The weight of the line can be adjusted... 

Step 2 Put the cursor on any data point and right click (on the Macintosh, use Ctrl-click). A menu appears choose Add trendline. The trendline is added as shown. Put the cursor on the trendline and right click. Choose Format trendline, then Options and click Display equation on chart also choose Display R-squared on chart. The result is Figure E.l notice that the equation in the figure agrees with Eq. (E.8). 

Also select Display equation on chart, then click OK. 

Use Trendline Polynomial Order 2, using the Option to Display Equation on Chart. 

Do not use any closing punctuation on the line with displayed equations. 

Following a displayed equation that is part of a sentence, punctuate the text as if it were a continuation of a sentence including the equation. 

Directories on Disc 3.0, 397—398 Discussion section in scientific papers, 21—22 Disk manuscripts, software choice, 281 Display equations... 

Display equation on chart Display R-squared value on chart OK... 

Numbers in parentheses refer to the equation number in which the symbol first appears or is first defined. When the first appearance of the symbol occurs within the text, rather than in a displayed equation, this is so indicated by giving the equation numbers lying on either side of that portion of the text. For example, (75)-(76) indicates that the first appearance of the symbol occurs somewhere between Eqs. (75) and (76),... 

Click on the "options" tab, and check the "Display Equation on Chart" box (and, if you want, the "Display R-squared value on Chart" box). Click OK. 

Tiendline dial< box, under Tiend/R tession type, select linear, as shown in Figure 14.15. Then dick on the Options tab of the Add Trendline dialog box and to on the Set inter cept= and the Display equation on chart, as shown in Figure 14.16. 

To find a polynomial that fits the data, first highlight the x-y data. Then go to the Excel tool bar and click on Layout Analysis Trendline More Trendline Options. Choose polynomial as type and in the menu select the desired order of the polynomial. (You can try different orders to find which has the best fit.) Make sure the boxes Display Equation on Chart and Set intercept = 0 are checked. Then click Close. 

Figure 43.25. The transient current (circles) in p-TajO after a potential step. The displayed equation is the exponential fit (full line) to the data. From this fit the shown proton density n and mobiUty /i could be extracted using Eqs (12) and (10).

We can try with exponential or polynomial types. We also enable Display Equation on chart and Display R-squared value on chart to show us the equations and the coefficient of variation. For the polynomial fitting, we can select the degree in this case, a third degree polynomial is selected. We see that we get better fitting with the polynomial than with the exponential one see Figure 3.10. 

Mathcad is a symbolic software tool for engineering applications. It has a what you see is what you get interface that allows the user to work in Mathcad more naturally. As an engineer or scientist, it is important to find solutions as well as be able to communicate the results. Mathcad s strengths, among others, include a readable format for displaying equations, built-in unit functionality, and the ability to deal with symbolic calculations. 

The addition reaction to pentane-2,3-dione 314 is remarkable, not only because of its superb levels of diastereo- and enantiocontrol, but also because of the high degree of regioselectivity it displays (Equation 29) [153, 154]. Thus, the reaction is observed to occur predominantly at the methyl ketone (98 2 selectivity). Another noteworthy aspect is the highly selective addition... 

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