Best Measure

When a problem involves two different measures, you choose one or the other measure to work with and convert the unchosen measure to the unit you want so that they re all the same. You may even decide to change measures when they re already all the same — just because you think that another measure may work better. 

A mile is much longer than an inch. In fact, there are 12 x 5,280 = 63,360 inches in 1 mile. If you re measuring how far it is from one side of the desk to another, you ll use inches. If you re measuring how far it is from your home to your workplace, you ll usually measure in miles. 

Two different measures are given 1 mile and 12 inches. You can work with inches, and change the 1 mile to 63,360 inches, or you can work with miles and write the 12 inches (1 foot) as mile. The choice here is between 

This looks pretty nasty, but a scientific calculator makes short work of the problem, and you get 

The height or rise of 0.009732 doesn t seem like much, but, remember, this is in miles. Multiply by 5,280 feet and you get over 51 feet. Whoa That s quite a rise  

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If the concentration of effective aromatic species does vary with acidity, as sometimes happens if the compound is substantially proto-nated, then the acidity-dependence of the rate will be less steep than usual, because the concentration of the active free base diminishes significantly with increasing acidity. This situation has been observed in certain cases ( 8.2). The fall in the concentration of the active species can be allowed for from a knowledge of its pK and the acidity function which, for the particular compound, gives the best measure of the acidity of the medium. Then the corrected acidity-dependence of the rate resembles that observed with compounds the concentration of which does not change significantly with acidity. The nitration of minor species is discussed later ( 8.2). 

The relevance of photonics technology is best measured by its omnipresence. Semiconductor lasers, for example, are found in compact disk players, CD-ROM drives, and bar code scaimers, as well as in data communication systems such as telephone systems. Compound semiconductor-based LEDs utilized in multicolor displays, automobile indicators, and most recendy in traffic lights represent an even bigger market, with approximately 1 biUion in aimual sales. The trend to faster and smaller systems with lower power requirements and lower loss has led toward the development of optical communication and computing systems and thus rapid technological advancement in photonics systems is expected for the future. In this section, compound semiconductor photonics technology is reviewed with a focus on three primary photonic devices LEDs, laser diodes, and detectors. Overviews of other important compound semiconductor-based photonic devices can be found in References 75—78. 

Sulfur [7704-34-9] S, a nonmetallic element, is the second element of Group 16 (VIA) of the Periodic Table, coming below oxygen and above selenium. In massive elemental form, sulfur is often referred to as brimstone. Sulfur is one of the most important taw materials of the chemical industry. It is of prime importance to the fertilizer industry (see Fertilizers) and its consumption is generally regarded as one of the best measures of a nation s industrial development and economic activity (see Sulfur compounds Sulfurremoval and recovery Sulfuric acid and sulfur trioxide). 

Minimum Fluidizing Velocity U,nj, the minimum fluidizing velocity, is frequently used in fluid-bed calculations and in quantifying one of the particle properties. This parameter is best measured in small-scale equipment at ambient conditions. The correlation by Wen audYu [A.l.Ch.E.j., 610-612 (1966)] given below can then be used to back calculate d. This gives a particle size that takes into account effects of size distribution and sphericity. The correlation can then be used to estimate U, at process conditions, if U,nj cannot be determined experimentally, use the expression below directly. 

Diffusion coefficients are best measured in the following way. A thin layer of a radioactive isotope of the diffusing atoms or molecules is plated onto the bulk material (for example, radioactive zinc onto copper). The temperature is raised to the diffusion... 

Tower Operations. The tower operator can quickly determine which type of flooding will tend to be the limiting one for a particular system. If a rigorous computer run is available for the anticipated or actual operation, the operator can quickly calculate the expected limiting column section. The operator can then provide DP cell recording for the entire column and limiting section(s). As mentioned previously, a DP cell is the best measure of internal traffic and flooding tendency. 

For the standby pump start test, which is an important test to ensure the pumps transfer without large pressure swings, a check should be made to see if the relief valves lift or the pressure falls to a pressure one half the difference between the standby pump start pressure and the compressor trip pressure. The transient pressure is best measured with a multipen chart recorder. The chart speed must be high enough to fully display the pressure variation. While not as good as the chart recorder, a simple shop-made test setup can be substituted. A spare switch is temporarily connected to the same location as the other switches. This switch is calibrated to close at the threshold acceptance pressure. The contacts are wired to a test light through a seal relay. The purpose of the relay is to maintain the cir-... 

The hardness and abrasion resistance of anodic coatings have never been easy properties to measure, but the development of a British Standard on hard anodising has made this essential. Film hardness is best measured by making microhardness indents on a cross-section of a film , but a minimum film thickness of 25 tm is required. For abrasion resistance measurements, a test based on a loaded abrasive wheel , which moves backwards and forwards over the film surface, has improved the sensitivity of such measurements. 

The direction of the burn is normal to the surface at every point that is in contact with the gas. Thus, zs is measured perpendicularly to the reaction front. It is best measured using a planar solid so that Aj is constant, but it can be inferred from short-term experiments on spherical particles or even from careful multiparticle experiments. 

For gases, both permeation and diffusion data are best measured by permeation tests, many different types been described elsewhere. The same sheet membrane permeation test can quantify permeation coefficient Q, diffusion coefficient D, solubility coefficient s, and concentration c. The membrane, of known area and thickness, must be completely sealed to separate the high-pressure (initial) region from that containing the permeated gas it may need an open-grid support to withstand the pressure. The permeant must be suitably detected and quantified (e.g., by pressure or volume buildup, infrared (IR) spectroscopy, ultraviolet (UV), gas chromatography, etc.). 

Identification of sources of analytical bias in method development and method validation is another very important application of reference materials in geochemical laboratories. USGS applied simplex optimization in establishing the best measurement conditions when the ICP-AES method was introduced as a substitute for AAS in the rapid rock procedure for major oxide determinations (Leary et al. 1982). The optimized measurement parameters were then validated by analyzing a number of USGS rock reference samples for which reference values had been established first by classical analyses. Similar optimization of an ICP-AES procedure for a number of trace elements was validated by the analysis of U S G S manganese nodule P-i (Montaser et al. 1984). 

The initial velocity of reaction is defined by the slope of a linear plot of product (or substrate) concentration as a function of time (Chapter 2), and we have just discussed the importance of measuring enzymatic activity during this initial velocity phase of the reaction. The best measure of initial velocity is thus obtained by continuous measurement of product formation or substrate disappearance with time over a convenient portion of the intial velocity phase. However, continuous monitoring of assay signal is not always practical. Copeland (2000) has described three types of assay readouts for measuring reaction velocity continuous assays, discontinuous... 

Determination of the IC50 is a preliminary evaluation of the relative affinity of different compounds for a target enzyme. To evaluate affinity properly, however, one must first define the mechanism of inhibition of the target enzyme by each compound. The next step in the lead evaluation flowchart (Figure 5.1) is to determine if the inhibition caused by a compound is rapidly reversible, slowly reversible, or irreversible. This information will help the investigator understand whether or not the inhibition reaction can be treated as a reversible equilibrium, and thus decide on the best measure of true affinity for a particular compound. 

The properties of organic liquids relevant to their use as solvating agents have also been reviewed [76]. The ability of liquids to solvate a solute species depends mainly on their polarity and polarizability properties, ability to hydrogen bond, and cohesive electron density. These molecular properties are best measured by the Kamlet-Taft solvatochromic parameters, and the square of Hildebrand s solubility parameter. 

Laboratory tests for hypercoagulable states should be done only when the cause of the stroke cannot be determined based on the presence of well-known risk factors. Protein C, protein S, and antithrombin III are best measured in steady state rather than in the acute stage. Antiphospholipid antibodies are of higher yield but should be reserved for patients aged less than 50 years and those who have had multiple venous or arterial thrombotic events or livedo reticularis. 

Modem LP solvers can solve very large LPs very quickly and reliably on a PC or workstation. LP size is measured by several parameters (1) the number of variables n, (2) the number of constraints m, and (3) the number of nonzero entries nz in the constraint matrix A. The best measure is the number of nonzero elements nz because it directly determines the required storage and has a greater effect on computation time than n or m. For almost all LPs encountered in practice, nz is much less than mn, because each constraint involves only a few of the variables jc. The problem density 100(nz/mn) is usually less than 1%, and it almost always decreases as m and n increase. Problems with small densities are called sparse, and real world LPs are always sparse. Roughly speaking, a problem with under 1000 nonzeros is small, between 1000 and 50,000 is medium-size, and over 50,000 is large. A small problem probably has m and n in the hundreds, a medium-size problem in the low to mid thousands, and a large problem above 10,000. 

Minimum Fluidizing Velocity LO, the minimum fluidizing velocity, is frequently used in fluid-bed calculations and in quantifying one ol the particle properties. This parameter is best measured in small-scale equipment at ambient conditions. The correlation by Wen... 

As indicated, the specific refractive index increment is best measured by differential refractometry or interferometry. Experimental procedures as well as tabulated values of dn/ dc for many systems have been presented elsewhere40,63K The relevant wavelength and temperature are those used for LS. The value of X0 is invariably 436 or 546 nm, but with the advent of laser LS, values of dn/dc at other wavelengths are required. These can be estimated with good reliability using a Cauchy type of dispersion (dn/dc a 1/Xq). For example the values of dn dc for aqueous solutions of the bacterium T-ferrioxidans at 18 °C are 0.159, 0.141 and 0.125 ml/gm at X0 = 488, 633 and 1060 nm respectively64 ... 

The standard deviation is very sensitive to outliers if the data are skewed, not only the mean will be biased, but also s will be even more biased because squared deviations are used. In the case of normal or approximately normal distributions,, v is the best measure of spread because it is the most precise estimator for standard deviation is often uncritically used instead of robust measures for the spread. 

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