Transformation, direct

The function L[f t)] = g(s) is called the direct transform, and L [g. s)] =f t) is called the inverse transform. Both the direct and the inverse transforms are tabulated for many often-occurring functions. In general,... 

Just as there is only one direct transform F(s) for any f(t), there is only one inverse transform f(t) for any F(s) and inverse transforms are generally determined through use of tables. 

Diamino-substituted complexes of type 37 were first obtained by Fischer et al. [12] in two steps via the 1,2-addition-elimination product 34 from di-methylamine and 35 (Scheme 6). The (3-aminoallenylidene)chromium complexes 36, which can be prepared either from 33 [47,48] or directly from 35 [33], can also be transformed to l,3-bis(dialkylamino)-substituted complexes of type 37 (e.g., R2=z Pr) by treatment with dimethylamine in excellent yields [33]. Although the complex 37 is accessible by further reaction of the complex 34 with dimethylamine, and 34 itself stems from the reaction of 35 with dimethylamine, the direct transformation of 33 to 37 could not be achieved [12]. In spite of this, heterocyclic carbene complexes with two nitrogens were obtained by reactions of alkynylcarbene complexes 35 with hydrazine [49] and 1,3-diamines [50]. 

Direct transformation from 2,5-DSP to poly-2,5-DSP through 2,5-DSP oligomer in the crystal is shown in Scheme 1. This new reaction was named a four-centre-type photopolymerization. As well as being the first example of a topochemical reaction in a pure sense, the four-centre-type photopolymerization of 2,5-DSP crystals was the first example of photopolymerization via a step-growth mechanism. 

One main advantage of such a power source is the direct transformation of the chemical energy of methanol combustion into electrical energy. Hence, the reversible cell potential, can be calculated from the Gibbs energy change, AG, associated with the overall combustion reaction of methanol (1), by the equation ... 

While alkane metathesis is noteworthy, it affords lower homologues and especially methane, which cannot be used easily as a building block for basic chemicals. The reverse reaction, however, which would incorporate methane, would be much more valuable. Nonetheless, the free energy of this reaction is positive, and it is 8.2 kj/mol at 150 °C, which corresponds to an equihbrium conversion of 13%. On the other hand, thermodynamic calculation predicts that the conversion can be increased to 98% for a methane/propane ratio of 1250. The temperature and the contact time are also important parameters (kinetic), and optimal experimental conditions for a reaction carried in a continuous flow tubiflar reactor are as follows 300 mg of [(= SiO)2Ta - H], 1250/1 methane/propane mixture. Flow =1.5 mL/min, P = 50 bars and T = 250 °C [105]. After 1000 min, the steady state is reached, and 1.88 moles of ethane are produced per mole of propane consmned, which corresponds to a selectivity of 96% selectivity in the cross-metathesis reaction (Fig. 4). The overall reaction provides a route to the direct transformation of methane into more valuable hydrocarbon materials. 

It is thus obvious that the direct transformation of a simple alkene into an amine would be a more economic process, since it would suppress at least one step without formahon of co-products (atom efficiency) [Scheme 4-1, paths (c) and (d)]. 

Donovan and Pescatore described another fast-gradient approach with very short columns (20x4.6 mm internal diameter) packed with a porous polymer (known as ODP columns) [38]. This chromatographic support presents a high chemical stability and can be used at pH 2, 10 or 13 to analyze neutral analytes. This procedure allowed a relatively high flow rate (2mLmin ) and a gradient from 10 to 100% methanol in only 7 min. The mathematical treatment was simplified and based on the direct transformation of retention time to log P. For this purpose, two standards (toluene and triphenylene) were used to minimize retention time variations from run-to-run and instrument-to-instrument, and to facilitate the... 

Last, but not least, there is to be mentioned, that in some cases a direct transformation of dichlorophosphates (see section 3.4.) into difluorophosphates by fluorination with elementary fluorine (In(P02p2)3, F (P02F2)3 40)) or with arsenic trifluoride at elevated temperature is possible 41). ... 

J Naisbitt. Megatrends Ten New Directions Transforming Our Lives. New York Warner Books, Inc., 1982, p. 24. 

The synthesis of cycloheptatrienyl ketones 233 from benzene and a-diazoketones 232 proceeds in essentially quantitative yield the products were not isolated but directly transformed into benzyl ketones 234 through the action of trifluoroacetic acid 229 ... 

Aryl and vinyl nitriles have been prepared very efficiently from the corresponding bromides by palladium-catalyzed reactions under microwaves. This energy source has been employed for the conversion of these nitriles into aryl and vinyl tetrazoles by cycloaddition reactions with sodium azide (Scheme 9.66). The direct transformation of aryl halides to the aryl tetrazoles in a one pot procedure could be accomplished both in solution and on a solid support [115], The reactions were complete in a few minutes, a reaction time considerably shorter than those previously reported for the thermal reactions. The cydoadditions were performed with sodium azide and ammonium chloride in DMF and, although no explosion occurred in the development of this work, the authors point out the necessity of taking adequate precautions against this eventuality. 

This expression is a direct transformation of formula (5.124), where now c is arbitrary, such that c < xo < d. 

Chemiluminescence is defined as the production of light by chemical reactions. This light is cold , which means that it is not caused by vibrations of atoms and/or molecules involved in the reaction but by direct transformation of chemical into electronic energy. For earlier discussions of this problem, see 7 9h Recent approaches towards a general theory of chemiluminescence are based on the relatively simple electron-transfer reactions occurring in aromatic radical-ion chemiluminescence reactions 10> and on considerations of molecular orbital symmetry as applied to 1.2-dioxetane derivatives, which very probably play a key role in a large number of organic chemiluminescence reactions 11>. 

While this species certainly may be in solution, the relative importance of this intermediate or direct transformations upon the acetyl group in the production of hydrocarbons cannot be assessed at this point. 

To generate chiral nitrones (81) and (82) the direct transformation of chiral o -substituted cyanohydrins was used. Both of the approaches described in Reference 227 allow the production of nitrones in high yields and high optical purity in a one-pot synthesis (Schemes 2.28 and 2.29). 

The tendency of nitrones to react with radicals has been widely used in new synthetic routes to well-defined polymers with low polydispersity. The recent progress in controlled radical polymerization (CRP), mainly nitroxide-mediated polymerization (NMP) (695), is based on the direct transformation of nitrones to nitroxides and alkoxyamines in the polymerization medium (696, 697). In polymer chemistry, NMP has become popular as a method for preparing living polymers (698) under mild, chemoselective conditions with good control over both, the polydispersity and molecular weight. 

Recently, Nicolaou and coworkers have devised a novel, one-pot strategy for the direct transformation of acyclic olefinic esters to cyclic enol ethers [34]. Unlike the molybdenum alkylidene 1 (see Sect. 3.2), initial reaction between the Tebbe reagent 93 and an olefinic ester results in rapid carbonyl olefination to afford a diene intermediate. Subsequent heating initiates RCM to afford the desired cyclic product (Scheme 17). 

---