Common denominator

In spite of the diverse nature of alkaloid structures, two structural units, i.e. fused pyrrolidine and piperidine rings in different oxidation states, appear as rather common denominators. We therefore chose to give several examples for four types of synthetic reactions which have frequently been used in alkaloid total synthesis and which provide generally useful routes to polycyclic compounds with five- or six-membered rings containing one nitrogen atom. These are ... 

Leather Tanning and Textiles. Although chromium (VT) compounds are the most important commercially, the bulk of the appHcations in the textile and tanning industries depend on the abiUty of Cr(III) to form stable complexes with proteins, ceUulosic materials, dyestuffs, and various synthetic polymers. The chemistry is complex and not well understood in many cases, but a common denominator is the coordinating abiUty of chromium (ITT) (see LEATHER Textiles). 

Sometimes the expected consequences of an accident alone may provide you with sufficient information for decision-making purposes. Conventionally, the form of these estimates will be dictated by the purpose (concern) of the study (safety, economics, etc.). Absolute consequence estimates are best estimates of the impacts of an accident and, like frequency estimates, may have considerable uncertainty. Table 4 contains examples of typical consequence estimates obtained from QRA. These examples point to the difficulty in comparing various safety and economic results on a common basis—there is no common denominator. 

In addition, some common denominators probably apply across the board ... 

Note that in many companies levels of skill and knowledge may vary widely, even in the same facility. Since it s unrealistic to tailor training precisely to every level, a good rule of thumb is to aim for the lowest common denominator. 

Woodget, J. R., 1991. A common denominator linking glycogen metabolism, nuclear oncogenes, and development. Trends in Biochemical Sciences 16 177-181. 

Common Denominator for Use of K Factors in a System of Varying Sizes of Internal Dimensions... 

For a system of multiple components of valves, pipe, and fittings. Equation 2-25 can be used to establish a component size to which each separate resistance can be expressed as a common denominator, or common pipe size. Under these conditions, the corrected Rvalues are additive and can be used as one number in Equation 2-27. These types of corrections should be made to improve and more accurately represent the pressure drop calculations. 

Scope, 52 Basis, 52 Compressible Flow Vapors and Gases, 54 Factors of Safety for Design Basis, 56 Pipe, Fittings, and Valves, 56 Pipe, 56 Usual Industry Pipe Sizes and Classes Practice, 59 Total Line Pressure Drop, 64 Background Information, 64 Reynolds Number, R,. (Sometimes used Nr ), 67 Friction Factor, f, 68 Pipe—Relative Roughness, 68 Pressure Drop in Fittings, Valves, Connections Incompressible Fluid, 71 Common Denominator for Use of K Factors in a System of Varying Sizes of Internal Dimensions, 72 Validity of K Values,... 

To add fractions, transform each to a common denominator and add the numerators (b,y 0) ... 

Ultimately, all activities of an organization will be expressed in money, the common denominator within the accounts of the proprietor, be it a company, a partnership or a statutory organization. The accounting for these activities will be under the control of the finance department, which, in turn, will be controlled, through the financial director, by the board of directors. 

Fractions witii unlike denominators cannot be added until die denominators are changed to like numbers or numbers diat are die same The first step is to find the lowest common denominator, which is the lowest number divisible by (or diat can be divided by) all the denominators. 

The lowest number that can be divided by diese two denominators is 12 dierefore, 12 is die lowest common denominator. 

Divide the lowest common denominator (which in this example is 12) by each of Hie denominators in the fractions (in this example 3 and 4) ... 

When Hie denominators are not the same, for example, comparing 2/3 and 1/10, the lowest common denominator must first be determined. The same procedure is followed when adding fracfions with unlike denominators (see above). 

In Hie example above, 5/2 and 13/4 cannot be added because Hie denominators are not Hie same It will be necessary to find the lowest common denominator first. 

These techniques are known as linear free energy relations, LFER. Imagine that one has determined the rate constants, or the Gibbs free energies of activation, for a series of reactions. The reactions are all the same, save for (for example) a different substituent on each reactant. The substituent is not a direct participant in the reaction. In an LFER, the values of log k or AG are correlated with some characteristic of the substituent as manifested in another reaction series. If the correlation is successful, then the two series of reactions have a common denominator. This technique has proved to be a powerful one for systematizing reactivity. We shall see a number of such correlations. 

A common denominator of these models is the attempt to represent... 

The common denominator of all these CP-channel blockers (Fig. 2) is their acidic function (usually carboxylate), the secondary amine with a certain spacing to the acidic group, a nitro substitution at a certain distance from the carboxylate group, and the apolar groups such as the phenyl-propyl-residue. We have suggested that the interaction with the CP-channel requires all of these interaction sites, and that even the apolar moiety of the blocker molecule reacts with the channel protein rather than with the membrane lipid [70]. 

Reduction in temperature to above 0°C is the common denominator to all techniques for inhibiting warm ischaemic damage. However, hypothermia alone can only delay the onset of irreversible damage and not prevent it. Furthermore, cold can itself be damaging. Kidneys for transplantation are in clinical practice cooled to 0°-10°C either after they have been removed from... 

The visually most convenient choice of axes for this regression are the ones whose common denominator is so that projection of the 3-D regression line to the Th-free plane will give the detrital-corrected Th/ U and from which the... 

ThAJ age is calculated. Mathematically, however, the choice of ratios is unimportant, provided that there is a common-denominator isotope to all three axes, and the errors and error correlations for the data points are correctly calculated. Note that, unlike paired x-y isochrons, not only can the errors of the detrital-corrected Th/ U and be... 

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