Power method

Two such new and possibly powerful methods are described in this paper. They allow for the detection of 1. extremely small ferromagnetic inclusions in the volume of a non ferromagnetic workpiece and 2. non ferromagnetic segregations in the volume of a non ferromagnetic workpiece. 

The standard Galerkin technique provides a flexible and powerful method for the solution of problems in areas such as solid mechanics and heat conduction where the model equations arc of elliptic or parabolic type. It can also be used to develop robust schemes for the solution of the governing equations of... 

If a sample solution is introduced into the center of the plasma, the constituent molecules are bombarded by the energetic atoms, ions, electrons, and even photons from the plasma itself. Under these vigorous conditions, sample molecules are both ionized and fragmented repeatedly until only their constituent elemental atoms or ions survive. The ions are drawn off into a mass analyzer for measurement of abundances and mJz values. Plasma torches provide a powerful method for introducing and ionizing a wide range of sample types into a mass spectrometer (inductively coupled plasma mass spectrometry, ICP/MS). 

Analysis of Surface Molecular Composition. Information about the molecular composition of the surface or interface may also be of interest. A variety of methods for elucidating the nature of the molecules that exist on a surface or within an interface exist. Techniques based on vibrational spectroscopy of molecules are the most common and include the electron-based method of high resolution electron energy loss spectroscopy (hreels), and the optical methods of ftir and Raman spectroscopy. These tools are tremendously powerful methods of analysis because not only does a molecule possess vibrational modes which are signatures of that molecule, but the energies of molecular vibrations are extremely sensitive to the chemical environment in which a molecule is found. Thus, these methods direcdy provide information about the chemistry of the surface or interface through the vibrations of molecules contained on the surface or within the interface. 

Solvent Extraction. The selective partitioning of metals by Hquid—Hquid solvent extraction is one of the most powerful methods of... 

The most powerful method for stmcture elucidation of steroid compounds during the classical period of steroid chemistry (- 1940 1950s) was ir-spectroscopy. As with the ultraviolet spectra, data collected on the infrared spectra of steroids are available in several books, spectmm atiases, and review articles (265,266). Unlike ultraviolet spectroscopy, even the least substituted steroid derivatives are relatively rich in characteristic absorption bands in infrared spectroscopy (264). 

Generally, the most powerful method for stmctural elucidation of steroids is nuclear magnetic resonance (nmr) spectroscopy. There are several classical reviews on the one-dimensional (1-D) proton H-nmr spectroscopy of steroids (267). C-nmr, a technique used to observe individual carbons, is used for stmcture elucidation of steroids. In addition, C-nmr is used for biosynthesis experiments with C-enriched precursors (268). The availability of higher magnetic field instmments coupled with the arrival of 1-D and two-dimensional (2-D) techniques such as DEPT, COSY, NOESY, 2-D J-resolved, HOHAHA, etc, have provided powerful new tools for the stmctural elucidation of complex natural products including steroids (269). 

TBDMSOSO2CF3, CH2CI2, 2,6-lutidine, 0-25°. This is one of the most powerful methods for introducing the TBDMS group. Other bases such as... 

We wish to solve the following problem how to model the force so that it implies the floating effect which prevents the particles from falling down to the bottom of the tube. The question itself already suggests the answer. The idea is based on the so-called virtual power method. An excellent review of this topic has been represented by G.A. Maugin. ... 

On the other hand this power is, on the basis of the ideal of the virtual power method, the same as the force multiplied by the velocity of the gas i i.e.,... 

The force /) , was obtained with the aid of the virtual power method by assuming that the floating power arises only from the force /) ,. This kind of approach has been used by Weber. ... 

This procedure constitutes an application of the steady-state approximation [also called the quasi-steady-state approximation, the Bodenstein approximation, or the stationary-state hypothesis]. It is a powerful method for the simplification of complicated rate equations, but because it is an approximation, it is not always valid. Sometimes the inapplicability of the steady-state approximation is easily detected for example, Eq. (3-143) predicts simple first-order behavior, and significant deviation from this behavior is evidence that the approximation cannot be applied. In more complex systems the validity of the steady-state approximation may be difficult to assess. Because it is an approximation in wide use, much critical attention has been directed to the steady-state hypothesis. 

A synthetically powerful method, an approach based on cycloaddition chemistry, allows one to assemble the pyridine ring in one step. Not only is this method efficient, atom economy, but also its convergency allows for the preparation for highly substituted systems in which one can, in principle, control all five positions on the pyridine ring. A versatile example of this methodology is the Boger reaction. It has been applied to the synthesis of a very diverse set of targets. 

Without question, the most powerful method for cyclopropane formation by methylene transfer is the well-known Simmons-Smith reaction [6]. In 1958, Simmons and Smith reported that the action of a zinc-copper couple on diiodomethane generates a species that can transform a wide variety of alkenes into the corresponding cyclopropanes (Scheme 3.3) [7]. 

The 1,4-addition of an enolate anion 1 to an o ,/3-unsaturated carbonyl compound 2, to yield a 1,5-dicarbonyl compound 3, is a powerful method for the formation of carbon-carbon bonds, and is called the Michael reaction or Michael addition The 1,4-addition to an o ,/3-unsaturated carbonyl substrate is also called a conjugate addition. Various other 1,4-additions are known, and sometimes referred to as Michael-like additions. 

This multi-column swithching (GC-GC) technique has also been shown to be a powerful method for the separation of benzene and 1-methyl-cyclopentane in gasoline, as well as for the analysis of m-andp-xylenes in ethylbenzene. 

Our work demonstrates that EELS and in particular the combination of this technique with first principles electronic structure calculations are very powerful methods to study the bonding character in intermetallic alloys and study the alloying effects of ternary elements on the electronic structure. Our success in modelling spectra indicates the validity of our methodology of calculating spectra using the local density approximation and the single particle approach. 

Elucidating the stereochemistry of reaction at prochirality centers is a powerful method for studying detailed mechanisms in biochemical reactions. As just one example, the conversion of citrate to (ds)-aconitate in the citric acid cycle has been shown to occur with loss of a pro-R hydrogen, implying that the reaction takes place by an anti elimination mechanism. That is, the OH and H groups leave from opposite sides of the molecule. 

The Sn2 alkylation reaction between an enolate ion and an alkyl halide is a powerful method for making C-C bonds, thereby building up larger molecules from smaller precursors. We ll study the alkylation of many kinds of carbonyl compounds in Chapter 22. 

The cyclic /3-keto ester produced in a Dieckmann cyclization can be further alkylated and decarboxylated by a series of reactions analogous to those used in the acetoacetic ester synthesis (Section 22.7). For example, alkylation and subsequent decarboxylation of ethyl 2-oxocyclohexanecarboxylate yields a 2-alkylcvclohexanone. The overall sequence of (1) Dieckmann cyclization, (2) /3-keto ester alkylation, and (3) decarboxylation is a powerful method for preparing 2-substituted cyclohexanones and cyclopentanones. 

Schild analysis, this powerful method of quantifying the potency of a competitive antagonist was developed by Heinz Schild (Br. J. Pharmacol. 14,48-58, 1959 see Chapter 6.3). It is based on the principle that the antagonist-induced dextral displacement of a dose-response curve is due to its potency (K% value) and its concentration in the receptor compartment. Because the antagonism can be observed and the concentration of antagonist is known, the KB can be calculated. 

A powerful method of introducing a CF3 group into aromatics is the conversion of C02H with SF4. The use of SF4 with heterocyclics is not as widespread but it has been applied to imidazoles [81JFC(17)179], thiazoles, isothiazoles [91 JFC(55) 173], and furans (86BSF974). 

Fluoride ion-catalyzed polyfluoroalkylation is a powerful method for introducing RF groups into polyfluoroazaaromatics. Trichloro-1,2,3-triazine is such a reactive system that fluorination and polyfluoroalkylation... 

The theory introduced by Lennard-Jones and Devonshire13 17 for the study of liquids provides a powerful method for the quantitative evaluation of the partition function of a solute molecule within its cavity.51 Because the application of this method to the present problem has been described in detail,62 we shall restrict ourselves to its most essential features. 

It is only natural that computers present a powerful method for determining yield stress with the help of Eq. (3). A corresponding program of computations is based on such a selection of constants b, n, and m that provides a minimum deviation of the theoretical curve from experimental points. 

H. G. J. Moseley, Phil. Mag. [6], 26, 1024 (1913). The following remarkable quotation from this paper (p. 1030) supports Moseley as the founder of x-ray emission spectrography The prevalence of lines due to impurities suggests that this may prove a powerful method of chemical analysis. Its advantage over ordinary spectroscopic methods lies in the simplicity of the spectra and the impossibility of one substance masking the radiation from another. It may even lead to the discovery of missing elements, as it will be possible to predict the position of their characteristic lines. ... 

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