Elimination procedure

To estimate the computational time required in a Gaussian elimination procedure we need to evaluate the number of arithmetic operations during the forward reduction and back substitution processes. Obviously multiplication and division take much longer time than addition and subtraction and hence the total time required for the latter operations, especially in large systems of equations, is relatively small and can be ignored. Let us consider a system of simultaneous algebraic equations, the representative calculation for forward reduction at stage is expressed as... 

HAZOP (Knowlton, 1989 Lees, 1980 CPQRA, 1989, pp. 419-422). HAZOP stands for hazard and operability studies. This is a set of formal hazard identification and elimination procedures designed to identify hazards to people, process plants, and the environment. The techniques aim to stimulate in a systematic way the imagination of designers and people who operate plants or eqmpment so they can identify potenti hazards. In effect, HAZOP studies make the assumption that a hazard or operating problem can arise when there is a deviation from the design or operating intention. Corrective actions can then be made before a real accident occurs. 

The Chugaev elimination is of synthetic value, because it proceeds without rearrangement of the carbon skeleton. Other non-thermolytic elimination procedures often lead to rearranged products, when applied to the same substrates. However applicability of the Chugaev reaction is limited if the elimination is possible in more than one direction, and if a /3-carbon has more than one hydrogen. Complex mixtures of isomeric olefins may then be obtained. For example the thermolysis of xanthate 12, derived from 3-hexanol yields 28% S-hex-3-ene 13, 13% Z-hex-3-ene 14, 29% -hex-2-ene 15 and 13% Z-hex-2-ene 16 ... 

The procedure for solving the relations between concentrations has been used in kinetic studies of complex catalytic reactions by many authors, among the first of them being Jungers and his co-workers 17-20), Weiss 21, 22), and others [see, e.g. 23-25a). In many papers this approach has been combined with the solution of time dependencies, at least for some of the single reactions. Also solved were some complicated cases [e.g. six-step consecutive reaction 26,26a) 3 and some improvements of this time-elimination procedure were set forth 27). The elimination of time is... 

The desulfiirisation of sultones results in the formation of an exocyclic alkene and can be achieved by an alkylation - elimination procedure <96TL 1841>. 

Equations (5)-(8) illustrate the use of this reverse salt elimination procedure. 

In SIMCA, we can determine the modelling power of the variables, i.e. we measure the importance of the variables in modelling the elass. Moreover, it is possible to determine the discriminating power, i.e. which variables are important to discriminate two classes. The variables with both low discriminating and modelling power are deleted. This is more a variable elimination procedure than a selection procedure we do not try to select the minimum number of features that will lead to the best classification (or prediction rate), but rather eliminate those that carry no information at all. 

Elimination Procedures. Chemical redox-induced elimination was performed on precursor thin films by exposure to bromine or iodine vapor or by immersion of films in hexane solutions of these halides. 

The classical treatment of diffuse SAXS (analysis and elimination) is restricted to isotropic scattering. Separation of its components is frequently impossible or resting on additional assumptions. Anyway, curves have to be manipulated one-by-one in a cumbersome procedure. Discussion of diffuse background can sometimes be avoided if investigations are resorting to time-resolved measurements and subsequent discussion of observed variations of SAXS pattern features. A background elimination procedure that does not require user intervention is based on spatial frequency filtering (cf. p. 140). 

Trost and coworkers have devised a stereocontrolled 1,3-diene synthesis employing a palladium-catalysed decarboxylative elimination procedure from allylic acetates carrying carboxylic acid functionality ji- to the acetate group (equation 18)48. This decarboxylative elimination strategy has been applied to the synthesis of an insect pheromone, codlemone48a and the ethyl ester of vitamin A carboxylic acid (Table 5)48b. 

For example, in the instance of 9-chloroacridine, the attachment of the halogen (leaving group) at a suitably electrophilic carbon site allows the occurrence of a replacement reaction, presumably occurring via an addition-elimination procedure for phosphorus attachment, followed by the common nucleophilic displacement (ester cleavage) of the Michaelis-Arbuzov process (Figure 6.1).4... 

The geometric interpretation for the preceding problem requires visualizing the objective function as the surface of a paraboloid in three-dimensional space, as shown in Figure 8.1. The projection of the intersection of the paraboloid and the plane representing the constraint onto the/(x2) = x2 plane is a parabola. We then find the minimum of the resulting parabola. The elimination procedure described earlier is tantamount to projecting the intersection locus onto the x2 axis. The intersection locus could also be projected onto the xx axis (by elimination of x2). Would you obtain the same result for x as before ... 

In the following a serial elimination procedure (Romagnoli and Stephanopoulos, 1981 Romagnoli, 1983) is described. This scheme isolates the sources of gross errors by a systematic treatment of the measurements. 

A data reconciliation procedure was applied to the subset of redundant equations. The results are displayed in Table 4. A global test for gross error detection was also applied and the x2 value was found to be equal to 17.58, indicating the presence of a gross error in the data set. Using the serial elimination procedure described in Chapter 7, a gross error was identified in the measurement of stream 26. The procedure for estimating the amount of bias was then applied and the amount of bias was found... 

Glycosyl cyanides have been thoroughly used as starting materials in the preparation of 1-formyl, and 1-cyano-glycals, mainly through base-induced elimination procedures (Scheme 10). 

Lee and Chau [66] have discussed the development and certification of a sediment reference material for total polychlorobiphenyls. Alford Stevens et al. [49] in an inter-laboratory study on the determination of polychlorobiphenyls in environmentally contaminated sediments showed the mean relative standard deviation of measured polychlorobiphenyl concentrations was 34%, despite efforts to eliminate procedural variations. Eganhouse and Gosset [67] have discussed the sources and magnitude of bias associated with the determination of polychlorobiphenyls in environmental sediments. Heilman [30] studied the adsorption and desorption of polychlorobiphenyl on sediments. 

Selenosulfonylation of olefins in the presence of boron trifluoride etherate produces chiefly or exclusively M products arising from a stereospecific anti addition, from which vinyl sulfones can be obtained by stereospecific oxidation-elimination with m-chloroper-benzoic acid134. When the reaction is carried out on conjugated dienes, with the exception of isoprene, M 1,2-addition products are generally formed selectively from which, through the above-reported oxidation-elimination procedure, 2-(phenylsulfonyl)-l,3-dienes may be prepared (equation 123)135. Interestingly, the selenosulfonylation of butadiene gives quantitatively the 1,4-adduct at room temperature, but selectively 1,2-adducts at 0°C. Furthermore, while the addition to cyclic 1,3-dienes, such as cyclohexadiene and cycloheptadiene, is completely anti stereospecific, the addition to 2,4-hexadienes is nonstereospecific and affords mixtures of erythro and threo isomers. For both (E,E)- and ( ,Z)-2,4-hexadienes, the threo isomer prevails if the reaction is carried out at room temperature. 

First priority is always elimination of sampling bias as generated by ISE (IDE, lEE, IWE, IPE). This principle reigns supreme for both 0-D and 1-D scenarios. If this imperative is not adhered to, sampling will be but an exercise in futility. All principal ISE-eliminating procedures for process sampling were delineated, and further literature was offered in abundance. 

Compound D was transformed into the exocyclic olefin E by a oxidation-elimination procedure. 

We have always aimed in CASVB for the simplest possible elimination procedure, bearing in mind that the number of variational prameters can be quite considerable in practical applications. 

The elimination procedure described below is merely offered as an alternative, which may be chosen when no mill is available for powdering KOH (indispensable in the phase--transfer method) or when no high-boiling petroleum ether is available. 

The successful synthesis of furanophane (27) by pyrolysis of the quaternary ammonium hydroxide (28) (60JA1428) has prompted the adaptation of this 1,6-Hofmann elimination procedure to the synthesis of numerous heterophanes (77CRV513,77H(7)81,78T1641). Fluoride anion-induced 1,6-elimination of (29) or (30) gives (27) or (31) and (32), respectively, in good yields (81JOC1043). 

The standard elimination procedure for mesylates was successfully applied to the synthesis of 2,6-diisopropyl-2//-thiopyran (281), prepared in 82% yield according to Eq. (13).285... 

---