Variant Method

The same general methodology ean also be applied to edit (for example) a deeoupled NMR speetnim into four subspeetra, for the CH, CH2, CH and C moieties separately. A eonnnon variant method ealled DEPT... 

The authors (Meyer et al., 1993) introduced a variant method derived from Kretsovalis and Mah (1987) that allows chemical reactions and splitters to be treated. It leads to a decrease in the size of the data reconciliation problem as well as a partitioning of the equations for unmeasured variable classification. 

Benzo[f]thiophene 710 is prepared by the dehydration of sulfoxide 709 with KOBu as a variant method of the Pummerer reaction. Irradiation of 710 affords 711 as a first example of Dewar benzo[dthiophene (Scheme 108) <1995TL3177>. Reaction of dinitrile 712 with thionyl chloride in the presence of EtsN yields thieno[3,4-dthio-phene 714 via Pummerer dehydration of the intermediate 713 <2000TL8843, 2002JOC2453>. 

Fast Reactions. Where reactions are essentially completed in times of seconds or much less, ingenious methods have been devised to give measurements of the rate. Such methods may involve static systems in which mixing is performed very rapidly. Also useful is excitation of the system by light for a specified period. A variant method involves a flow system in which reactants are rapidly mixed and flowed through a tube in which recording equipment can be employed to measure optical absorption, heat evolution (temperature), or electrical conductivity. The... 

The parameters that are measured run a wide gamut from the routine (current, potential or some electrical parameter) to the exotic (e.g., beam deflection due to refractive index changes). A hierarchical approach to discussing these variant methods has been described [52]. Thus, the methods in Table 2 fall under the categories of purely electrical (entries 1-3, 8 and 9), purely optical (entry titled photoluminescence spectroscopy and entries 12 and 13), electro-optic (electroluminescence spectroscopy) or opto-electric (entries 4-7). We can also distinguish between frequency-resolved (entries 3-7) and time-resolved (entries 10 and 14) measurements, although it must be noted that in many instances (e.g., entries 8 and 11) both steady-state and time-resolved approaches are feasible. 

Conventional PCR uses primers that are present in equal amounts, thereby ensuring that the majority of the products are double-stranded amplicons. A variant method uses different concentrations of the two primers to generate more of one strand than of the other (asymmetric PCR). For instance, the use of primer A at 0.5 jiM and primer B at 0.005 pM produces mostly single-stranded DNA extended off the more abundant primer. This is useful for sequencing purposes or making single-stranded probes. Yield of the product, however, may be low. With less extreme ratios (e.g., primer A at 0.5 pM and primer B at 0.2 pM), the yield is mostly preserved, with one strand produced in enough excess to make it more available for probe hybridization. 

The variant method described by the editor of the Nine Elixirs corresponds to the one found in the Liquid Pearl, 2.2a. 

It was inevitable that computers will be utilised to exploit the similarity of parts and this led to the Variant Method [4], it became the cornerstone of what is we now call Computer Aided Process Planning (CAPP). Variant Method exploits the similarity of parts as well as the similarity of processes. This similarity can be on the basis of individual process or it can be on the basis of group of processes. The main disadvantage of this procedure is that the quality of process design still depends to a considerable extent on the knowledge of the methods engineer. There are no inference mechanisms in the procedure to fine-tune the process design. This is often required because there are tolerances and various levels of stresses involved in the manufacture of parts and this requires experience to create a feasible process plan. 

The purpose of our researches is a study of variants for creation of an economic means for 3D tomographic inspection. For this purpose it is necessary to carry out the analysis of existing methods of 3D reconstruction, directed on solving problems of NDT a wide class of industrial products. 

The high accuracy of spatial and density resolution can be obtained by using exact methods. Thus it is necessary to apply of complete scanning geometry. The analysis of variants of scanning shows that the geometry sine on the cylinder is perspectiv enough by its characteristics. 

At first, it is statistical standard of the undefective section. Such standard is created, introducing certain lower threshold and using measured data. Under the classical variant of the shadow USD method it is measured fluctuations of accepted signal on the undefective product and installed in each of 512 direction its threshold in proportion to corresponding dispersions of US signal in all 128 sections. After introducting of threshold signal is transformed in the binary form. Thereby, adaptive threshold is one of the particularities of the offered USCT IT. 

The Woodward-Hoffmann method [52], which assumes conservation of orbital symmetry, is another variant of the same idea. In it, the emphasis is put on the symmetries of molecular orbitals. Longuet-Higgins and Abramson [53] noted the necessity of state-to-state correlation, rather than the orbital correlation, which is not rigorously justified (see also, [30,44]). However, the orbital symmetry conservation rules appear to be very useful for most themial reactions. 

But the methods have not really changed. The Verlet algorithm to solve Newton s equations, introduced by Verlet in 1967 [7], and it s variants are still the most popular algorithms today, possibly because they are time-reversible and symplectic, but surely because they are simple. The force field description was then, and still is, a combination of Lennard-Jones and Coulombic terms, with (mostly) harmonic bonds and periodic dihedrals. Modern extensions have added many more parameters but only modestly more reliability. The now almost universal use of constraints for bonds (and sometimes bond angles) was already introduced in 1977 [8]. That polarisability would be necessary was realized then [9], but it is still not routinely implemented today. Long-range interactions are still troublesome, but the methods that now become popular date back to Ewald in 1921 [10] and Hockney and Eastwood in 1981 [11]. 

The heightened appreciation of resonance problems, in particular, has been quite recent [63, 62], and contrasts the more systematic error associated with numerical stability that grows systematically with the discretization size. Ironically, resonance artifacts are worse in the modern impulse multiple-timestep methods, formulated to be symplectic and reversible the earlier extrapolative variants were abandoned due to energy drifts. 

For refined variants of this method in the context of many-particle systems, see [15, 12]. 

Unfortunately, discretization methods with large step sizes applied to such problems tend to miss this additional force term [3]. Furthermore, even if the implicit midpoint method is applied to a formulation in local coordinates, similar problems occur [3]. Since the midpoint scheme and its variants (6) and (7) are basically identical in local coordinates, the same problem can be expected for the energy conserving method (6). To demonstrate this, let us consider the following modified model problem [13] ... 

Ewald s formalism reduces the infinite lattice sum to a serial complexity of in the number of particles n, which has been reduced to n logn in more recent formulations. A review of variants on Ewald summation methods which includes a more complete derivation of the basic method is in [3]. 

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