Derivative substitution method

Derivative substitution method replace p = dy/dx if either y is not explicit or x is not explicit. 

Homogeneous function method replace v = y/x if the equation can be put into the homogeneous format 

as before, the dimensional ratio y/x appears throughout, which is a good indicator that the technique may work. 

Two classes of problems arise, which can be categorized by inspection Either y or X does not appear alone (is not explicit). In both cases, we start with the substitution p = dy/dx. 

The nonlinear Pendulum problem is a case where x is not explicit 

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Anilino vinyl derivatives of thiazolium (30, R = H) or acetanilido (30, R = C0CH3), as well as formyl methylene 30b (methods E-G), give asymmetrical dyes when condensed with a methyl reactive group of another species (Scheme 42). Mesosubstituted symmetrical or unsymmet-rical thiazolocyanines are obtainable via /S-alkylmercaptovinyl thiazolium derivatives (32) (methods H and I) (Scheme 43). a or /S carbon atoms of the trimethine chain can be substituted by acetyl when a dye is treated with acetic anhydride (method L). The hydrolysis of neocyanines lead to trimethine cyanine by fractional elimination of a composant chain (method K). 

The second extrathermodynamic method that we discuss here differs from Hansch analysis by the fact that it does not involve experimentally derived substitution constants (such as o, log P, MR, etc.). The method was originally developed by Free and Wilson [29] and has been simplified by Fujita and Ban [30]. The subject has been extensively reviewed by Martin [7] and by Kubinyi [8]. The method is also called the de novo approach, as it is derived from first principles rather than from empirical observations. The underlying idea of Free-Wilson analysis is that a particular substituent group at a specific substitution site on the molecule contributes a fixed amount to the biological activity (log 1/C). This can be formulated in the form of the linear relationship ... 

Fig. 4.16. The A dynamics method for alchemical transformations was developed by Guo and Brooks [57] for rapid screening of binding affinities. In this approach the parameter A is a dynamic variable. Techniques like ABF or metadynamics [34] can be used to accelerate this type of calculation. A dynamics was used by Guo [57] to study the binding of benzamidine to trypsin. One simulation is sufficient to gather data on several benzamidine derivatives. Substitutions were made at the para position C5 (H, NH2, CH3 and Cl). The hydrogen atoms are not shown for clarity...

Comparison of the relaxation spectra with those relating to the empirical functions [l]-[4] provided us with more insight into the inherent shortcomings of these functions. The analytical expressions for these spectra were derived from the Equations [l]-[4] by a substitution method involving complex algebra (1,... 

Preparation of cyclodextrin derivatives substitution at a secondary hydroxyl group of the cyclodextrin annulus. Murakami and cowor-kers described a new and convenient method for the regioselective tosylation of the 2-hydroxyl groups of alpha, beta, and gamma cyclodextrin by means of a cyclic tin intermediate. The method is based on the reaction of dibutyltin oxide with 1,2-diols to form five-membered dibutyl-stannylidene derivatives. Useful yields of the 2-6>-tosyl derivatives of the cyclodextrins were obtained. 

The parent compound (i), (7), is very difficult to prepare by the standard method from malonaldehyde and ethylenediamine [68JCS(B)1536], although it is one of the most stable, but can be prepared readily from imines of malonaldehyde and ethylenediamine under nonaqueous conditions (73S791). This is apparently because, despite its thermodynamic stability, it is hydrolyzed readily in aqueous solution. (Thus chromatographic separations, successful with many dihydrodiazepines, can result in progressive loss of material.) In contrast, derivatives substituted at positions 5 and 7 are hydrolyzed only very slowly, if at all, nucleophilic attack at these positions being sterically inhibited by the substituents. 

Carbon is, of course, unique in the number of hydrides it forms, but the elements in the proximity of carbon in the Periodic Table have a similar, if more restricted, propensity to form hydrides. Silicon, germanium, boron and phosphorus are obvious examples. For hydrides of these elements, and especially for their organic derivatives, the methods of substitutive nomenclature can be applied to obtain suitable names. 

More recently, compounds bearing a second fluorine atom in position 6 (generally with ot configuration) have been developed (fluprednisolone). The introduction of this second fluorine atom can be performed by different pathways opening of 5,6-oxirane by HF, or electrophilic fluorination of dienol derivatives (cf. Figure 8.33, Chapter 8). " The fluorine in position 9 is introduced by means of the Fried method. These derivatives, substituted in both positions 6 and 9, are used in the treatment of asthma and allergy (fluocinolone, diflorasone, fluticasone cf. Chapter 8). 

The method of amidoalkylation was also suitable for the preparation of unsubstituted l,4-dihydro-3(2//)-isoquino inone (2) and derivatives substituted in position 1 by other than aryl substituents (80TL569 87T439). A number of Japanese patents deal with the synthesis of 2. A great variety of cyclization conditions in acidic media were studied in the reaction of... 

The second integration technique, known as the substitution method, derives from the inversion of the chain rule for differentiation described in Chapter 4. The objective here, once again, is to transform the integrand into a simpler or, preferably, a standard form. However, just like the integration by parts method, there is usually a choice of substitutions and although, in some cases, different substitutions yield different answers, these answers must only differ by a constant (remember that, for an indefinite integral, the answer is determined by inclusion of a constant). The substitution method is best illustrated using a worked problem. 

For benzenoid compounds, structures can be established by the historically important substitution method (Section 1-1F) or with the aid of correlations between spectroscopic properties and positions of substitution, as we indicated in Section 22-3. Also, it is often possible to identify the isomers by converting them to compounds of known structure. For example, trifluoromethylbenzene on nitration gives only one product, which has been shown to be the 3-nitro derivative by conversion to the known 3-nitrobenzoic acid by concentrated sulfuric acid ... 

Another conversion of 5,6-dihydro-4/f-l,3-oxazine derivatives into tetrahydro-l,3-oxazines treats the former with butyllithium in ether or tetrahydrofuran at -78°C.230 This method was applied to some 5,6-dihydro compounds that resisted borohydride such as /3-keto derivatives (substituted in position 2) of 5,6-dihydrooxazines.231... 

The production of anthraquinone dyes generally proceeds from a few key products generated by electrophilic substitution of unsubstituted anthraquinone or by synthesis of the nucleus. The major methods employed to prepare anthraquinone derivatives substituted in the a-position are sulfonation and nitration. Preparation of b-substituted anthraquinones and of quinizarin (1,4-dihydroxyan-thraquinone) generally is accomplished by synthesis of the nucleus starting from phthalic anhydride and a benzene derivative. 

During their work on the arylation of aromatic compounds by substitution, Fujiwara, et al. observed biaryl formation when aromatic compounds were placed in the presence of olefin-palladium complexes and silver nitrate.80 Developing this reaction as a method for biphenyl synthesis, these authors showed that the more stable the olefin-palladium complex was, the lower the yield. Ethylene dichloropalladium proved to be the best choice, when used with silver nitrate. However, the reaction required stoichiometric amounts of both catalysts (Scheme 10.47). Benzene derivatives substituted by electron-donating or -withdrawing groups reacted as well, but a mixture of regioisomers was produced, except for nitrobenzene, which only gave m,m -dinitrobiphenyl. 

Electrooxidative activation is just one of the tools with which synthetic organic chemists can effect the dearomatization of arenois and their ethers to give cyclohexa-2,4-dienone derivatives. Other methods are based on the utilization of oxidizing reagents that mediate the oxidative nucleophilic substitution of 2-substituted arenois in the presence of appropriate nucleophilic species. These reagents are for the most part all based on metals (Section 15.2.2) or halogens (Section 15.2.3). 

In contrast to the above Deveaux method, Mehta and Schulman [37] described that the native fluorescence of mefenamic, flufenamic and meclofenamic acids is more useful for determination of these drugs compared to the fluorescence of the derivatives-substituted acridones and benzoxazines of these drugs by treatment with H2S04 and HCHO, respectively. The determination of mefenamic acid at trace level by fluorescence spectrometry was also reported by Miller et al. [38]. 

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