Natural requirements

Equation (2.28), being statistical in nature, requires a large number of particles to be measured, especially if the spread of particle size is wide. The possibility of error from this source is stressed by Arnell and Henneberry who found that in a particular sample of finely ground quartz, two particles in a total of 335 had a diameter about twenty times the most probable diameter, and that if these were overlooked the calculated value of A would be nearly doubled. 

A closet member of this little group, revelation of whose i(>al nature requires metabolic transformation of an acetylenic linkage to an acetic acid moiety, is fl uretofen (14). The .ynthesis begins by Friedel-Crafts acylation of 2-fluorobi-phenyl (11) with acetic acid to give ketone 1. Heating with... 

Estimate acceptable air leakages resulting from leakage around static and rotary seals, valves, access ports, and other items of mechanical nature required for process operation from the following equations and the specific leak rates 0 indicated in Table 6-8, which is based on w < 10 lb/hr. 

We have not explained why two, but no more than two, electrons can occupy each orbital. This is not known and is accepted because the facts of nature require it. This assumption is called the Pauli Principle. 

However, in order to give an unambiguous answer to the question of how one is to calculate the probability of finding a Klein-Gordon particle at some point x at time t, we must first find a hermitian operator that can properly be called a position operator, and secondly find its eigenfunctions. It is somewhat easier to determine the latter since these should correspond to states wherein the particle is localized at a given point in space at a given time. Now the natural requirements to impose on localized states are ... 

In general mankind, since the improvement of cookery, eats twice as much as nature requires. 

All bioassays are comparative in nature, requiring parallel assay of a standard preparation against which the sample will be compared. Internationally accepted standard preparations of most biopharmaceuticals are available from organizations such as the World Health Organization (WHO) or the United States Pharmacopeia. 

The mischief of civilisation is the intensive life, which demands intensive stimulation. Human nature requires pleasure. Wholesome pleasures require leisure. We must choose between intoxication and the siesta. There are no cocaine fiends in Log rune. 

Despite its mathematical clarity this permutation nomenclature is of no practical value, due to its cumbersome nature, requiring a rather complicated procedure for generating the graphs with standard indices. 

Hereunto I may add, in conclusion, that one work is developed from another. First, our Matter should be carefully purified, then dissolved, destroyed, decomposed, and reduced to dust and ashes. Thereupon prepare from it a volatile spirit, which is white as snow, and another volatile spirit, which is red as blood. These two spirits contain a third, and are yet but one spirit. Now these are the three spirits which preserve and multiply life. Therefore unite them, give them the meat and drink that Nature requires, and keep them in a warm chamber until the perfect birth takes place. Then you will see and experience the virtue of the gift bestowed upon you by God and Nature. Know, also, that hitherto my lips have not revealed this secret to any one, and that God has endowed natural substances with greater powers than most men are ready to believe. Upon my mouth God has set a seal, that there might be scope for others after me to write about the wonderful things of Nature, which by the foolish are looked upon as unnatural. For they do not understand that all things... 

Industrial practice naturally requires the maximum use of the relatively expensive extractant, so that saturation of the extractant phase with reduction of the free ligand concentration to a minimum is the general rule. A model is thus needed to quantify the effect of a reduction in Dx as the concentration of the extracted species in the organic phase increases. 

Abdominal pain accompanied by rapid weight loss, vomiting and constipation, and which is unbearable in nature requires referral to exclude peptic ulcers, diverticular disease and carcinoma. 

Research in analytical chemistry is clearly an area where automation has a significant role to play. It is important that research data is fuUy validated and as accurate as possible. While it is not always possible to automate entire processes, the use of automated carousels to feed samples into a reaction system is an obvious area to improve the quality and rate of generation of data. It wiU also allow the researchers to quickly validate their proposed methodology on real-world samples and optimize the performance characteristics. This naturally requires a very close relationship between the researchers and the ultimate end-users of the analytical product. Given a good return for the investment, I am sure that the initial investment to automate the research activity will be justified and forthcoming. 

Figure 3-3b shows the profile. Note that the condition that C must be finite at r = 0 is a very important natural requirement. This requirement is also applied in many other problems, such as heat conduction and elastic equilibrium. 

Most components of an oil field process system rely on gravity separation. This can be the primary separation of oil, gas, and water or the further refinement of these products 1n an oil, water, or gas treater. The gravity separation process by Its very nature requires quiescence. Transmission of... 

The electron releasing or attracting substituents on the carbon-carbon double bond determines the balance of ionic nature required of the gegen ion of the catalysts to produce isotactic structure. 

Nature requires—as we have seen—that the complete wave function (space and spin) be antisymmetric. Consequently, for two electrons in one orbital tp, ... 

Other low-temperature studies have been motivated by the desire to characterize and understand processes occurring in unusual media. For example, the use of liquid ammonia [8-10] and liquid sulfur dioxide [11-13] naturally requires reduced temperatures unless high pressures are used, as is done for electrochemistry in supercritical fluids [14]. Frozen media are interesting systems in terms of mass transport phenomena and microstructural effects. Examples include glasses of acetonitrile and acetone [15], frozen dimethyl sulfoxide solutions [16,17], and the solid electrolyte HC104 5.5 H20 [18-20]. 

Many processes in nature require such a fine pH balance that they are dramatically upset by the shift that has occurred in the pH of rain. Thousands of lakes in the Adirondack region of upper New York State and in southeastern Canada have become so acidic that all fish life has disappeared. Massive tree die-offs have occurred throughout central and eastern Europe as acid rain has lowered the pH of the soil and leached nutrients from leaves. Countless marble statues have been slowly dissolved away as their calcium carbonate has been attacked by acid rain. 

Viruses and bacteria are the smallest biologically active identities discovered so far and, naturally, require nanodevices for their profiling. Analysis of viruses and bacteria on microchip devices are of particular interest for experiments with infectious material because of easy containment and disposal of samples. Thus, the use of NCE in routine analyses of viruses and bacteria is exceptionally attractive [171,172], These pathogens are detected based on their different migration times without the need for time consuming sample preparation [173,174]. 

Examination of tissues and excreta from humans or animals for exposure to carbamate pesticides, will almost never result in detection of the parent compound. Exposure assessment of this nature requires determination of metabolitic products, except in extreme situations such as acute poisoning. The most widely used indicator of exposure is probably the determination of urinary phenols (9). 

We have so far limited ourselves to a classical description, the natural requirement for which is the condition /, /" —> oo. In order that the description is valid for any angular momentum value, it is necessary to employ the quantum mechanical approach. We presume that the reader is acquainted with the density matrix (or the statistic operator) introduced into quantum mechanics for finding the mean values of the observables averaged over the particle ensemble. Under the conditions and symmetry of excitation considered here one must simply pass from the prob-... 

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