The Obvious Approach

For generality, let y pco2 be the partial pressure of carbon dioxide and let x = t be the time. The equation is 

The value of y is known at some time x, and its value is sought at some future time x + delx. The obvious approach, which is called the direct Euler method, is to approximate the function by a straight line of slope yp(x,y(x)) and to calculate the new value of y from 

Program DGC01 implements this method of solution. Although the use of subroutines may appear unnecessarily elaborate in such a small program, I am introducing them now to facilitate future development of the program. 

OPEN RESULTS.PRN FOR OUTPUT AS 11 results to a file for plotting PRINT YEARS , PC02  

PRINT x, y PRINT 1, x, y FOR nx = 1 TO nstep GOSUB EQUATIONS GOSUB STEPPER G0SU8 PRINTER NEXT nx CLOSE 1 END 

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The obvious approach to answering this question is to remove an electron from this orbital and observe the effect on, for example, the metal-metal stretching frequency or metal-metal bond distance. Of course, removal of an electron from the delta bonding orbital creates a positive molecular ion for which determination of these properties may not be possible using normal techniques. In those cases where the ion is sufficiently stable that these properties can be measured, the meaning of the information may be clouded by changes in intermolecular interactions or other internal factors. 

My first attempt to calculate the time history of a geochemical system (Section 2.3) used the obvious approach (the direct Euler method) of evaluating the time derivatives and stepping forward. But it was not sue-... 

This class of carbohydrates has not been found in Nature. The absence of 5-OH group restricts the sugar to the furanose ring form. The first synthetic 5-deoxyhexose was the glucose analogue, 5-deoxy-D-. v/o-hexose (40), and the different methods reported have been reviewed by Overend.97 One of the obvious approaches was the reduction of compounds conveniently derivatized at C-5. For example, treatment of the 5-tolylsulfonyl derivative 38, with lithium aluminum hydride gave compound 39, which upon deprotection led to 40. 

The obvious approach to this problem would be to deposit from a SiH4 + PH3 mixture, in the hopes that a sufficient quantity of P dopant could be incorporated into the poly. Many attempts to do this have been unsuccessful. For example, depositions at 623°C and 100 mTorr were carried out with 30 seem of SiH4 and 0.75 seem of PH3.10 Without the PH3, deposition across a single wafer was very uniform (see Figure 14). Adding the small quantity of PH3 reduced the deposition rate at the wafer center by 20 1, and yielded a non-uniform film. 

Usually, the analytical chemist needs to determine the concentration of the ion of interest rather than its activity. The obvious approach to converting potentiometric measurements from activity to concentration is to make use of an empirical calibration curve, such as the one shown in Figure 5.3. Electrodes potentials of standard solutions are thus measured and plotted (on a semilog paper) versus the concentration. Since the ionic strength of the sample is seldom known, it is often useful to add a high concentration of an electrolyte to the standards and the sample to maintain approximately the same ionic strength (i.e., the same activity coefficient). The ionic strength adjustor is usually a buffer (since pH control is also desired for most ISEs). The empirical calibration plot thus yields results in terms of concentration. Theoretically,... 

To search for the average diameter(s) that would satisfy equation 18 in the intermediate particle size regime, a numerical approach was taken. The obvious approach is to calculate the right hand side of equation 18 for a variety of distributions and a... 

The obvious approach for chiral synthesis would be to find a chiral starting material, such as a natural amino acid, carbohydrates, carboxylic acids or terpene. The major source of these chiral starting materials sometimes called chirons is nature itself. The synthesis of a complex enantiopure chemical compound from a readily available enantiopure substance such as natural amino acids is known as chiral pool synthesis. For example, chiral lithium amides 1.39 that are used for several types of enantioselective asymmetric syntheses can be prepared in both enantiomeric forms starting from the corresponding optically active amino acids, and these are often available commercially. 

Since the fibre was hydrophobic the obvious approach was to use the water-insoluble disperse dyes, for which nylon proved to have an adequate affinity. Of all the classes of dye, they are the best for covering up yarn variations. In pale shades the wet-fastness is satisfactory. Not only, however, is it difficult to build up heavy shades, but also their wash-fastness leaves much to be desired. 

The very heavy shades such as blacks and navies cannot be dyed by conventional methods on polyester fibres, even with the help of carriers. Since the difficulty is the slow diffusion of the larger dyestuff molecules into the closely packed crystalline structure of the fibre, the obvious approach is to present simple molecules and cause them to combine to form a coloured pigment after they have entered. Brenthols and Naphthol AS products are not adsorbed by polyesters from aqueous solutions of their sodium salts. A limited measure of success was achieved by immersing the goods in a suspension of naphthoic acid anilide derivatives and then coupling with a diazotized base. The results were more successful, however, when coupling components with smaller molecules were used and a- and /3-naphthoIs, applied from suspension, were satisfactory but jS-hydroxynaphthoic acid proved to be the most suitable. 

Several methods are available for the assembly of tricarbonyl precursors the synthesis of chehdonic acid (4-pyrone-2,6-dicarboxylic acid) represents the obvious approach of bringing about two Claisen condensations, one on each side of a ketone carbonyl group. Chelidonic acid can be decarboxylated to produce... 

To the limited extent that mesoscale and smaller reactors are used for production, the obvious approach is to scale in parallel. More conventional scaleups, that is, increasing reactor dimensions, could be needed when the small reactor is used to find the perfect molecule by means of combinatorial chemistry. With possible exceptions where the ultimate in mixing and heat transfer is required, scaleups to conventional macroscale reactors should be possible. 

The basic idea was to change the method as little as possible at this late stage of the project in order to avoid introducing too many unknowns that could have an impact further downstream. Shifting to other activated propargyl alcohols as new reactants was the obvious approach thus, the corresponding tosylate, mesylate, and bezenesulfonate were tested. None was intrinsically... 

Since the discovery of the catalytic AD in 1987, there have been numerous attempts in the Sharpless group to render the old catalytic aminohydroxylation process asymmetric [7]. Until recently, the obvious approach of adding the AD s chiral ligands, but otherwise staying close to the original protocol [3] led to extremly slow catalyst turnover. The initial breakthrough [8] was not due to a sudden con-... 

One of the targets in the formation of 2D porous nanostructures is to define and control the size of the cavities. The obvious approach is to extend the distance between the carboxylic acid groups and the center of the molecule, for instance by a phenyl group. 1,3,5-Benzenetribenzoic acid (BTB) is a rigid molecule and self-assembles also at the liquid-solid interface into honeycomb-type networks (Fig. 21 A) [55]. The circular cavities have a diameter of about 2.8 nm. In case of TMA, the cavity diameter is about 1 nm only. 

It should be noted that the obvious approaches to the treatment of allergic diseases resulting from the availability of a peptide that inhibits IgE binding to cells illustrates the type of benefits obtainable from studies of functional sites on antibodies. 

Third, and already well recognised, is the problem of decay versus stabilisation of a molecule initially prepared in a highly excited state, either photochemically or by a chemical activation process. The solution to this problem requires more than a knowledge of just the smallest eigenvalue [81.V2], and the obvious approach is to use the separable approximation. 

As the obvious approach to open the epoxide in a base-catalyzed elimination gave only unsatisfactory results, it was decided to use a selenoxide elimination for the introduction of the double bond. As expected, however, straightforward sodium selenide substitution provided exclusively the useless Fiirst-Plattner product 54. 

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