Method of Nicholson

According to the step-function method of Nicholson and Olmstead, the integral equation (A.24) can be transformed into the following approximate expression ... 

The more convenient CV diagnostic is the current ratio, irev/ifwd> which is unity when k /a is small (fast scan or slow reaction limit) and less than unity when k,./a is large enough to diminish the amount of B available for re-electroly-sis on the reverse sweep. The current ratio is measured conveniently by the empirical method of Nicholson [19], which requires only the measurement of the values ip(fwd), ip(rev), and ix (Fig- 23.14), where X designates the switching point. These quantities are then used in Equation 23.20 to obtain the current ratio ... 

The irreversibility of the reduction peak of 16 2+, combined with the appearance of a reversible peak corresponding to tetracoordinated copper, suggests that the reorganization of the rotaxane in its pentacoordinated form 16(S)+ (i.e., with the copper coordinated to terpy and to dpp units) to its tetracoordinated form (16 +, in which the copper is surrounded by two dpp units) occurs within the timescale of the cyclic voltammetry. Indeed, the cyclic voltammetry response located at -0.15 V becomes progressively reversible when increasing the potential sweep rate, as expected for an electrochemical process in which an electron transfer is followed by an irreversible chemical reaction (EC). Following the method of Nicholson and Shain, 9S the rate constant value, k, of the chemical reaction, i.e., the transformation of pentacoordinated Cu(i) into tetracoordinated Cu(i), was determined. A value of 17 s 1 was... 

Confirmation of the reaction mechanism is provided by kinetic data dependent upon the same pK for the N- l coordinated ruthenium(III) complex (see Figure 6) Owing to the instability of l-[(Ado)(NH3)3Ru(II)l and severe restrictions required of the oxidizing partner isomerization kinetic rates were derived from cyclic voltammetric data using the method of Nicholson and Shain " " after forming the N-1 coordinated Ru(II) complex at the electrode surface by electrolytic reduction of the N- 6 bound Ru(III) species. Since the specific rates estimated by this method were independent of concentration the rate law is taken to be first order in the complex. 

For 0.3 < a < 0.7 the AE values are nearly independent of a and depend only on Table 6.5.2, which provides data linking if/tolP m this range (14), is the basis for a widely used method (often called the method of Nicholson) for estimating in quasireversible... 

The task to measure quasi-reversible kinetic parameters is more common than the analysis of completely irreversible voltammograms. The method developed by Nicholson (5) for extraction of standard rate constants from quasi-reversible cyclic voltammograms (CVs) has been most frequently used (and misused) during the last four decades. The method of Nicholson became so popular because of its extreme simplicity. The only required experimental parameter is the difference of two peak potentials, Afip = F — 1, where F and F are the potentials of the anodic and cathodic peaks, respectively. Nicholson showed that A is a function of the single dimensionless kinetic parameter. 

Then, the computation of the cyclic voltammograms can be classically carried out, for example, by the method of Nicholson and Shain [173]. 

The Grank-Nicholson implicit method and the method of lines for numerical solution of these equations do not restrict the racial and axial increments as Eq. (P) does. They are more involved procedures, but the burden is placed on the computer in all cases. 

As initial distribution corresponds to the linear mode (2.11) of the given waveguide, the deviation of T z) with respeet to unity may he eonsidered as a measure of the error in this method. The results presented in Fig.2 allow one to analyze the accuracy of the method depending on the type of finite-difference scheme (Crank-Nicholson" or Douglas" schemes have been applied) and on the method of simulation of conditions at the interface between the core and the cladding for both (2D-FT) and 2D problems. 

The convolution integral in (1.19) and (1.20) can be solved by the method of numerical integration proposed by Nicholson and Olmstead [47], The time t is divided into m time increments t = md. It is assumed that within each time increment the function 1 can be replaced by the average value Ij ... 

So far, relatively little attention has been given to the variational method of solving diffusion problems. Nevertheless, it is a technique which may become of more interest as the nature of problems becomes more complex. Indeed, the variational method is the basis of the finite element method of numerical calculations and so is, in many ways, an equal alternative to the more familiar Crank—Nicholson approach [505a, 505b]. The author hopes that the comments made in this chapter will indicate how useful and versatile this approach can be. 

Bost Nicholson(Ref 6) dissolve ca O.lg sample in 10ml acetone and add 3ml of 5% NaOH soln. No color is produced with MNB but a purplish -blue color is produced with m-DNB which becomes light purple on dilution with w and yel -brn on addn of HC1. Cruse Haul(Ref 7) describe a polarographic method of detng m-DNB. 

Consider laminar flow of a fluid over a flat plate. Use the Crank-Nicholson method of finite differencing to compute the two dimensionless velocity-component distributions within the boundary layer. 

Methods applying reverse differences in time are called implicit. Generally these implicit methods, as e.g. the Crank-Nicholson method, show high numerical stability. On the other side, there are explicit methods, and the methods of iterative solution algorithms. Besides the strong attenuation (numeric dispersion) there is another problem with the finite differences method, and that is the oscillation. 

Baskin, S.I., Petrovics, I., Kurche, J.S., Nicholson, J.D., Logue, B.A., Maliner, B.I., Rockwood, G.A. (2004). Insights on cyanide toxicity and methods of treatment. In Pharmacological Perspectives of Toxic Chemicals and their Antidotes... 

G. J. Dear, R. S. Plumb, B. C. Sweatman, J. Ayrton, J. C. Lindon, J. K. Nicholson, and I. M. Ismail, Mass directed peak selection, an efficient method of drug metabolite identification using directly coupled liquid chromatography-mass spectrometry-nuclear magnetic resonance spectroscopy, /. Chromatogr. B 748 (2000), 281-293. 

The method of zonation was applied to the energy and material conservation equations. Based on centered finite difTerence approximations, this method can transform three partial differential equations in radial distance and time to ordinary differential equations in time only. Following this, the ordinary differential equations were solved by using Crank-Nicholson algorithm. On the basis of this, the volumetric fluxes of those tar-phase and total volatile phase components were integrated with time by using in roved Euler method to evaluate overall pyrolysis product yields, and afterwards the gas yield can be deduced. 

ESI-MS is becoming a detection method of choice, which readily identifies the molecular composition of species separated by flowing mobile phases. For space limitations, the reviews by Stewart for separation and speciation,24 by Szpunar for metallo-biopolymers,25 by Shepherd on transition metal complexes,1,75 by Colton, D Agostino, and Traeger,76 and Henderson, Nicholson, and McCaffery77 for organometallic complexes are highly recommended. The subject of ESI-MS is also presented in Chapter 2.28. 

Nicholson, D.A., and Vaughn, H., General method of preparation of tetramethyl alkyl-1-hydroxy-1,1-diphosphonates, J. Org. Chem., 36, 3843. 1972. 

An unsophisticated numerical method is used here for simplicity. Various implicit and explicit methods of writing dilference equations and their limitations are discussed by Leon Lapidus in Digital Computation for Chemical Engineers, McGraw-Hill Book Company, New York, 1960. The Crank-Nicholson implicit method [G. Crank and P. Nicholson, Proc. Cambridge Phil. Soc., 43, 50 (1947)] is well suited for machine computation. 

Much has been said (see chapters by Tukey, Andrews, and Nicholson, this volume) concerning the Gaussian method of least squares (characterized repeatedly during discussion as the method of ill repute ) and possible modifications or replacements of it. Nevertheless, it is by far the most frequently used method for crystal structure refinement and will continue to be for some time to come. 

In this section, a model similar to that used by Cardoso and Luss (1969) is considered, with the exception that the assumption of solid isothermality is relaxed. A finite difference solution for the transient equations with symmetrical boundary conditions is presented using the Crank-Nicholson method (Lapidus, 1962). Another more efficient, method of solution is considered which is based on the orthogonal collocation technique first used by Villadsen and Stewart (1967), Finlayson (1972) and Villadsen and Michelsen (1978). Several assumptions for model reductions are investigated. 

In order to speed up the assignment of the urine and to find new signals or signals of a changed intensity, the group of Nicholson suggested methods of pattern recognition, such as principal component analysis [18]. 

Although not primarily concerned with activation analysis, the article by Nicholson (646) states that the characteristic of any analytical method is dynamic and that the determination of the sensitivity of the method of choice is a statistical problem. Heydorn (394,395,396) and Rakovic and Prochazkova (748) report specific instances of obtaining accuracy and correctness for activation analysis results. Jurs and Isenhour (438) and Smith (878) give a more general treatment of statistical techniques and their relationship to the sensitivity of activation analysis. 

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