Related Methods

The oscillating jet method is not suitable for the study of liquid-air interfaces whose ages are in the range of tenths of a second, and an alternative method is based on the dependence of the shape of a falling column of liquid on its surface tension. Since the hydrostatic head, and hence the linear velocity, increases with h, the distance away from the nozzle, the cross-sectional area of the column must correspondingly decrease as a material balance requirement. The effect of surface tension is to oppose this shrinkage in cross section. The method is discussed in Refs. 110 and 111. A related method makes use of a falling sheet of liquid [112]. 

A closely-related method for detemiining free energy differences is characterized as themiodynamic integration. The configrirational free energy of an intemiediate state... 

As a sununary it may be of interest to point out why TREPR spectroscopy and related methods remain important in the EPR regime, even though pulsed EPR methods are becoming more and more widespread. (1) For the case of an inliomogeneously broadened EPR line the time resolution of TREPR compares favourably with pulsed teclmiques. 

The methods have in turn launched the new fields of nanoscience and nanoteclmology, in which the manipulation and characterization of nanometre-scale structures play a crucial role. STM and related methods have also been applied with considerable success in established areas, such as tribology [2], catalysis [3], cell biology [4] and protein chemistry [4], extending our knowledge of these fields into the nanometre world they have, in addition, become a mainstay of surface analytical laboratories, in the worlds of both academia and industry. 

The essential slow modes of a protein during a simulation accounting for most of its conformational variability can often be described by only a few principal components. Comparison of PGA with NMA for a 200 ps simulation of bovine pancreatic trypsic inhibitor showed that the variation in the first principal components was twice as high as expected from normal mode analy-si.s ([Hayward et al. 1994]). The so-called essential dynamics analysis method ([Amadei et al. 1993]) is a related method and will not be discussed here. 

Energy Minimisation and Related Methods for Exploring the Energy Surface... 

A central theme of carbohydrate chemistry today is the construction of oligosaccharides as they are found in glycoproteins (H. Paulsen, 1990). Three closely related methods have proven to be reliable in complex syntheses, namely the halide, imidate, and thioglycoside methods. 

In the pioneer work of Foster the correction due to film thinning had to be neglected, but with the coming of the BET and related methods for the evaluation of specific surface, it became possible to estimate the thickness of the adsorbed film on the walls. A number of procedures have been devised for the calculation of pore size distribution, in which the adsorption contribution is allowed for. All of them are necessarily somewhat tedious and require close attention to detail, and at some stage or another involve the assumption of a pore model. The model-less method of Brunauer and his colleagues represents an attempt to postpone the introduction of a model to a late stage in the calculations. 

Ioffe, B. V. Vitenberg, A. G. Head-Space Analysis and Related Methods in Gas Chromatography. Wiley-Interscience New York, 1982. 

A related method is the component synthesis method [17], which uses a so-called static condition to model the interactions between parts of a molecule whose corresponding diagonal blocks in the Hessian are first diagonalized. It has been combined with a residue clustering algorithm that provides a hierarchy of parts, which at the lowest level provides small enough matrices for efficient diagonalization [18]. It has been applied to double-helical DNA [17] and the protein crambin [18]. 

The present method for preparing aromatic dicarboxylic acids has been used to convert phthalic or isophthalic acid to tereph-thalic acid (90-95%) 2,2 -biphenyldicarboxylic acid to 4,4 -biphenyldicarboxylic acid 3,4-pyrroledicarboxylic acid to 2,5-pyr-roledicarboxylic acid and 2,3-pyridinedicarboxylic acid to 2,5-pyridinedicarboxylic acid. A closely related method for preparing aromatic dicarboxylic acids is the thermal disproportionation of the potassium salt of an aromatic monocarboxylic acid to an equimolar mixture of the corresponding aromatic hydrocarbon and the dipotassium salt of an aromatic dicarboxylic acid. The disproportionation method has been used to convert benzoic acid to terephthalic acid (90-95%) pyridine-carboxylic acids to 2,5-pyridinedicarboxylic acid (30-50%) 2-furoic acid to 2,5-furandicarboxylic acid 2-thiophenecar-boxylic acid to 2,5-thiophenedicarboxylic acid and 2-quinoline-carboxylic acid to 2,4-quinolinedicarboxylic acid. One or the other of these two methods is often the best way to make otherwise inaccessible aromatic dicarboxylic acids. The two methods were recently reviewed. ... 

A number of alkyl-substituted cyclobutadienes have been prepared by related methods Increasing alkyl substitution enhances the stability of the compounds. The tetra-/-butyl derivative is stable up to at least 150°C but is very reactive toward oxygen. This reactivity reflects the high energy of the HOMO. The chemical behavior of the cyclobutadienes as a group is in excellent accord with that expected from the theoretical picture of the structure of these compounds. 

Despite several attractive features in this method of direct halogen introduction and the obvious applications in the synthesis of deoxy sugars, its uses have not been further exploited by other groups of workers. Some new related methods have become available which reportedly eliminate the difficulties previously encountered such as rearrangement, unreactivity due to steric hindrance, and phosphonate ester formation. The reaction is based on the observation (28) that triethylphosphine reacts with ethanol and carbon tetrachloride to give ethyl chloride, chloroform, and triethylphosphite. In a new adaptation (76, 77) of this... 

The nitrosation of amides may also be carried out with nitrosyl chloride.2 Related methods of deamination of aliphatic amines are the triazene3 and nitrous acid methods4... 

Conceptually related methods have been employed in the synthesis of a-substituted allylboron reagents 85 and 106. In the case of 8, a benzimidazoleoxy leaving group is introduced as part of the a-alkoxy-2-butenyllithium reagent. Fragmentation of the ate complex must be conducted at — 100 °C in order to avoid the isomerization of 8, which occurs readily if 8 is allowed to warm to — 78 °C for one hour before addition of an aldehyde5. 

Two closely related methods for the diastereoselective preparation of <5-oxo esters have been developed. The first method uses the chelated lithio enamine 2. These Michael donors are readily available from the tert-butyl ester of L-valine and jS-oxo esters. The Michael addition of this lithio enamine 2 to 2-(arylmethylene)propanedioates, followed by hydrolytic removal of the auxiliary, provides d-oxo esters with contiguous quaternary and tertiary carbon centers with high diastereoselectivity59 60. 

Three related methods based on the quasiisostatic method are used to measure permeability. The most commonly used technique allows the permeant gas or vapor to flow continuously through one chamber of the permeability cell. The gas or vapor permeates through the sample and is accumulated in the lower-concentration chamber. At predetermined time intervals, aliquots are withdrawn from the lower cell chamber for analysis. The total quantity of accumulated permeant is then determined and plotted as a function of time. The slope of the linear portion of the transmission-rate profile is related to the sample s permeability. 

The CRC-Elsevier materials selector , 2nd edition, N.A. Waterman, and M.E Ashby CRC Press (1996) ISBN 0412615509. (Now, also available on CD-ROM). Basic reference work. Three-volume compilation of data for all materials includes selection and design guide. The Materials Selector is the most comprehensive and up-to-date comparative information system on engineering materials and related methods of component manufacture. It contains information on the properties, performance and processability of metals, plastics, ceramics, composites, surface treatments and the characteristics and comparative economics of the manufacturing routes which convert these materials into engineering components and products. 

These issues are thought to account for much of the scatter apparent in literature values of t.3 16 PLP and related methods yield absolute values of kp directly (the methods used for extracting kp arc discussed in Section 4.5.2). These values may be combined with either kp kx or k k, to give k,. 

For very active transfer agents, the transfer agent-derived radical (T ) may partition between adding to monomer and reacting with the polymeric transfer agent (Pn 1) even at low conversions. The transfer constant measured according to the Mayo or related methods will appear to be dependent on the transfer agent concentration (and on the monomer conversion).40 2 A reverse transfer constant can be defined as follows (eq. 20) ... 

Other examples of esterification with trialkyloxonium salts have been reported.7,8 The present procedure offers the advantages that the reactive carboxylate ion is generated in sitv and that a low-boiling, nonaqueous solvent is employed, whereby the experimental procedure is considerably simplified. A related method has been reported which utilizes a hindered amine wdth dimethyl sulfate [Sulfuric acid, dimethyl csterj as the alkylating agent.9 The present procedure is carried out under somewhat milder conditions and avoids the use of highly toxic reagents. 

The net result of all these operations is that in place of the system Ax = h, the system CAx = Ch is obtained, where CA is an upper triangular matrix. Such a matrix is easfiy inverted (the inverse will be exhibited below), and the triangular system is even more easily solved. With this explanation of the gaussian method, the basic theory of this and related methods will now be developed. 

Before considering how to proceed to find the remaining roots, another, closely related method will be described. The method has several variants, but basically it is due to Wielandt. Suppose p0 is closer (in the complex plane) to some particular root A than to any other. Then, for a given initial v0, form the iterates vltv2, by solving the equations... 

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