Alternative method

So far, the methods discussed can be classified as standard. However, there are other techniques, some of which may even be applicable to a few nonlinear problems. For example, the problem 

Here the independent variable, x, is missing from the equation. By making the substitutions v = y and using the chain rule 

In engineering, prototype differential equations often occur as a result of some peculiarity of the system under investigation. Then the approach is to compare one s derived problem with a prototype, and extract and modify the pertinent result. For example, the problem 

The above equation is the confluent hypergeometric equation (the prototype) with linearly independent solutions tabulated in the literature [12] whereas Equation 3.76 resulted from a fluid flow problem with a parabolic velocity profile. 

Another example of a prototype equation that should be familiar to most chemical engineers is Bessel s differential equation of order n 

A large number of varied analytical procedures have been developed for the determination of alkaloids in tobacco. Only a few of these procedures have been described in detail. Other methods available for the analysis of alkaloids include near-infrared reflectance spectroscopy (NIRS) (McClure and Williamson 1986), lipophilic gel chromatography (Snook and Chortyk 1986), radioimmunoassay (Castro et al. 1979), mass spectrometry (Green et al. 1980), and pyrolysis-gas chromatography (Rosa 1979). 

There are a wide variety of methods available for the analysis of alkaloids in tobacco. Each method is associated with certain advantages and disadvantages, but fills a certain niche for tobacco scientists. If the percent total alkaloids determined as nicotine suffices, then steam distillation or autoanalyzer are appropriate methods. When secondary alkaloids need to be quantitatively determined, then one of the chromatographic methods is more appropriate. 

Acknowledgments. The authors gratefully acknowledge Drs. H.R. Burton and J.F. Chaplin for their critical review of the manuscript. We also thank Ms. J. Jwong for her preparation of the figures. 

Castro A, Monji N, Malkus H, Eisenhart W, McKennis H Jr, Bowman ER (1979) Automated radioimmunoassay of nicotine. Clin Chim Acta 95 473-481 Chaplin JF, Miner GS (1980) Production factors affecting chemical components of the tobacco leaf. Rec Adv Tob Sci 6 3-63 

Court WA (1986) High performance liquid chromatography of tobacco and tobacco smoke components. Rec Adv Tob Sci 12 143-184 Cundiff RH, Markunas PC (1955) Determination of nicotine, nornicotine, and total alkaloids in tobacco. Anal Chem 27 1650-1653 Cundiff RH, Markunas PC (1960) Modification of the extraction procedure for determination of alkaloids in tobacco. J Assoc Off Agric Chem 43 519-524 Cundiff RH, IVIarkunas PC (1964) Abbreviated techniques for determinations of alkaloids in tobacco using the extraction procedure. Tob Sci 8 136-137 Dawson RF (1945) An experimental analysis of alkaloid production in Nicotiana the origin of nornicotine. Am J Bot 32 416-423 

In an entirely different approach, Cioslowski has defined atomic charge based on the atomic polar tensor.This method makes no recourse to the nature of the atomic orbitals or the volume of an atom in a molecule. The method makes use of the dipole moment and the derivatives of the dipole moment, which are obtained from the wavefunction. 

The elements of the atomic polar tensor are defined by Eq. [50], where x, yi, and are the Cartesian coordinates of atom k. 

The total charge of a molecule Q is the sum of the atomic charges Q, and Q is the trace of the atomic polar tensor of rank one  

The electrostatic potential is a quantum mechanical observable that can be obtained directly from the wavefunction. Assuming an SCF wavefunction, the electrostatic potential V(r) is defined by Eq. [52], where Z, is the atomic charge of atom k centered at R.  

An alternative method for obtaining atomic charge is to fit this elearostatic potential to a series of point charges centered on the atomic nuclei. This monopole expansion VM(r) is given by Eq. [53]. 

The sequencing of the mouse genome and the widespread availability of transgenic fa-cihties makes it much easier today to generate gene-targeted mice than was possible some years ago. Nonetheless, the total 

The disadvantages of these methods are similar to all inhibitors and activators however the effect is quite likely only partial, and there may be unwanted side effects on other molecules. Consequently, in the future genetic alteration by targeted mutagenesis will be an indispensable tool for both in vivo and in vitro approaches to bio-pharmaceutical research. 

1 Inamdar, M.S. (2001) Functional genomics the old-fashioned way chemical mutagenesis in mice. BioBssays 23 116-120. 

2 Lund, A.H., Turner, G., Trubetskoy, A., Ver-hoeven, E., Wientjens, E., Hulsman, D., Russell, R., DePinho, R.A., Lenz, )., van Lohui-zen, M. (2002) Genome-wide retroviral inser-tional tagging of genes involved in cancer in Cdkn2a-deficient mice. Nat. Genet. 32 160-165. 

3 Mikkers, H., Allen, )., Knipscheer, P., Ro-meijn, L, Hart, A., Vink, E., Berns, A., Ro-meyn, L. (2002) High-throughput retroviral tagging to identify components of specific signaling pathways in cancer. Nat. Genet. 32 153-159. 

For further reading, see Richards (1983), Kier (1971) and Purcell, Bass and Clayton (1973). 

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In many process-design calculations it is not necessary to fit the data to within the experimental uncertainty. Here, economics dictates that a minimum number of adjustable parameters be fitted to scarce data with the best accuracy possible. This compromise between "goodness of fit" and number of parameters requires some method of discriminating between models. One way is to compare the uncertainties in the calculated parameters. An alternative method consists of examination of the residuals for trends and excessive errors when plotted versus other system variables (Draper and Smith, 1966). A more useful quantity for comparison is obtained from the sum of the weighted squared residuals given by Equation (1). 

Eliminate extraneous materials for separation. The third option is to eliminate extraneous materials added to the process to carry out separation. The most obvious example would be addition of a solvent, either organic or aqueous. Also, acids or alkalis are sometimes used to precipitate other materials from solution. If these extraneous materials used for separation can be recycled with a high efficiency, there is not a major problem. Sometimes, however, they cannot. If this is the case, then waste is created by discharge of that material. To reduce this waste, alternative methods of separation are needed, such as use of evaporation instead of precipitation. 

Gas is produced to surface separators which are used to extract the heavier ends of the mixture (typically the components). The dry gas is then compressed and reinjected into the reservoir to maintain the pressure above the dew point. As the recycling progresses the reservoir composition becomes leaner (less heavy components), until eventually it is not economic to separate and compress the dry gas, at which point the reservoir pressure is blown down as for a wet gas reservoir. The sales profile for a recycling scheme consists of early sales of condensate liquids and delayed sale of gas. An alternative method of keeping the reservoir above the dew point but avoiding the deferred gas sales is by water injection. 

One way of calculating the IRR is to plot the NPV against discount rate, and to extrapolate/ interpolate to estimate the discount rate at which the NPV becomes zero, as in the Present Value Profile in Figure 13.16. The alternative method of calculating IRR is by... 

The suggested method is appropriately implemented at the practice. The cost and working hours of unit measurement of it is less than of any alternative method of destructive test and with respect to the authenticity inspection of Stress-Deformation the given method is inferior only to destructive testing. The method was successfully implemented while evaluation of service life of main pipe-lines sections and pressure vessels as well. Data of method and instrument are used as official data equally with ultrasonic, radiation, magnetic particles methods, adding them by the previously non available information about " fatigue " metalwork structure. 

Sample scan data is a good way to archive the results of an inspection. The inspection could be re-visited later to see how the eddy-current response has changed over time. Random audits of the quality of inspection detection could be monitored. The inspection could also be reviewed if new information becomes known, say from inspection conducted using alternate methods. 

A zero or near-zero contact angle is necessary otherwise results will be low. This was found to be the case with surfactant solutions where adsorption on the ring changed its wetting characteristics, and where liquid-liquid interfacial tensions were measured. In such cases a Teflon or polyethylene ring may be used [47]. When used to study monolayers, it may be necessary to know the increase in area at detachment, and some calculations of this are available [48]. Finally, an alternative method obtains y from the slope of the plot of W versus z, the elevation of the ring above the liquid surface [49]. 

The oscillating jet method is not suitable for the study of liquid-air interfaces whose ages are in the range of tenths of a second, and an alternative method is based on the dependence of the shape of a falling column of liquid on its surface tension. Since the hydrostatic head, and hence the linear velocity, increases with h, the distance away from the nozzle, the cross-sectional area of the column must correspondingly decrease as a material balance requirement. The effect of surface tension is to oppose this shrinkage in cross section. The method is discussed in Refs. 110 and 111. A related method makes use of a falling sheet of liquid [112]. 

An interesting alternative method for formulating f/(jt) was proposed in 1929 by de Boer and Zwikker [80], who suggested that the adsorption of nonpolar molecules be explained by assuming that the polar adsorbent surface induces dipoles in the first adsorbed layer and that these in turn induce dipoles in the next layer, and so on. As shown in Section VI-8, this approach leads to... 

Satellite transition MAS NMR provides an alternative method for detennining the interactions. The intensity envelope of the spimiing sidebands are dominated by site A2 (using the crystal structure nomenclature) which has the smallest Cq, resulting in the intensity for the transitions of this site being spread over the smallest... 

Yuan J-Y, Shao Z and Gao C 1991 Alternative method of imaging surface topologies of nonconducting bulk specimens by scanning tunnelling microscopy Phys. Rev. Lett. 67 863... 

An alternative method that can be used to characterize the topology of PES is the line integral technique developed by Baer [53,54], which uses properties of the non-adiabatic coupling between states to identify and locate different types of intersections. The method has been applied to study the complex PES topologies in a number of small molecules such as H3 [55,56] and C2H [57]. 

However, th ese alternative methods can be on ly applied to certain elements. For example, the projected CXDO/IXDOi may be used only for molecular system s with atom ic n iiin bers less than or ct nal to IS (Ari. Elements beyond IS are not available in the projected CXDO/IXD(f initial guess. 

Determination of Boiling-points. The following alternative methods are recommended, (a) Draw one drop of the liquid into a capillary tube so that the drop is about i cm. from one end. 

The use of selectively reduced integration to obtain accurate non-trivial solutions for incompressible flow problems by the continuous penalty method is not robust and failure may occur. An alternative method called the discrete penalty technique was therefore developed. In this technique separate discretizations for the equation of motion and the penalty relationship (3.6) are first obtained and then the pressure in the equation of motion is substituted using these discretized forms. Finite elements used in conjunction with the discrete penalty scheme must provide appropriate interpolation orders for velocity and pressure to satisfy the BB condition. This is in contrast to the continuous penalty method in which the satisfaction of the stability condition is achieved indirectly through... 

An alternative method for the complete removal of bromine consists in passing the hvdrogen bromide through a solution of phenol in dry carbon tetrachloride. 

An alternative method for ascertaining the end of the reaction, which does not involve the removal of the cover, is to conduct the exit gas through an empty wash bottle (to eict as a trap in case of sucking back ) and then collect a sample in a test-tube over water. If an inflammable gas (hydrogen) is absent, the reaction may be considered complete. Under no circumstances should the reaction be stopped until all the sodium has completely reacted too early arrest of the reaction may result in the product containing sodium hydride, which appears to be partially responsible for the explosive properties of the impure substance ... 

An alternative method for naming the size of the joint, which is sometimes used by manufacturers, consists in assigning a number to the joint diameter at the wide end, thus —... 

The experimental technique is similar to that given under Aromatic Amines, Section IV,100,2. The following alternative method may also be used. Mix together 0 -5-0 - 8 ml. of the polyhydroxy compound, 5 ml. of pyridine and 2 -5 ml. of redistilled benzoyl chloride in a 50 ml. flask. 

An alternative method of conducting the preparation consists in treating 100 g. of cycZohexanol with 250 ml. of concentrated hydrochloric acid, refluxing slowly whilst a stream of hydrogen chloride gas is passed into the mechanically stirred... 

An alternative method for isolating the n-butyl ether utilises the fact that n-butyl alcohol is soluble in saturated calcium chloride solution whilst n-butyl ether is slightly soluble. Cool the reaction mixture in ice and transfer to a separatory fimnel. Wash cautiously with 100 ml. of 2-5-3N sodium hydroxide solution the washings should be alkaline to litmus. Then wash with 30 ml. of water, followed by 30 ml. of saturated calcium chloride solution. Dry with 2-3 g. of anhydrous calcium chloride, filter and distil. Collect the di-n-butyl ether at 139-142°. The yield is 20 g. 

An alternative method of working up the distillate, which has its advantages when dealing with volatile ketones or when it is suspected that conversion into the ketone is incomplete, is to treat the combined ketones with sodium hydroxide pellets until the mixture is alkaline. Should solids separate, these may be dissolved by the addition of a little water. The ketone is then separated, dried over anhydrous potassium carbonate, and fractionated. 

Pimelic acid. This may be prepared from 1 5-peiitanediol or tetra-hydropyran, through the dibromide (Sections 111,35 and 111,37) and dinitrile exactly as described for Suberic Acid. An alternative method for the preparation of 1 5-dibromopentane, together with full details of the subsequent steps, is given in the following Section. 

An alternative method of separation consists in treating the dry residue several times with a warm mixture of benzene and ether. The residual solid (about 20 g.) is moderately pure succinic acid, m.p. 183-184°. Upon evaporating the benzene - ether extract, and recrystallising the residue from chloroform or from benzene, about 70 g. of glutaric acid, m.p. 95-96°, are obtained. 

An alternative method of determining the completion of the reaction is to weigh the flask cmd toluene, emd to stop the passage of chlorine when the increase in weight is 37 g. 

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