Two-Thing

Then, two things (that are actually interdependent) happen (1) The field intensity F = 0, (2) There exists a unique gauge g(R) and, since F = 0, any apparent field in the Hamiltonian can be transformed away by introducing a new gauge. If, however, condition (1) does not hold, that is, the electronic Hilbert space is truncated, then F is in general not zero within the tmncated set. In this event, the fields A and F cannot be nullified by a new gauge and the resulting YM field is true and irremovable. 

When we report the result of a measurement a , there are two things a person reading the report wants to know the magnitude (size) of the measurement and the reliability of the measurement (its scatter ). If measuring errors are random, as they very frequently are, the magnitude is best expressed as the arithmetic mean p of N repeated tr ials xi... 

When 6 moles of the substrate analog PALA combine with the enzyme ACTase, two things happen at the same time. The enzyme T unfolds to a more active form R... 

So if one were to replace sec-butyl alcohol in the recipe above with an equimolar amount of safrole in the above reaction, Strike will wager that a positive bromination experience will occur. And all this using the very common 48% aq. HBr The oniy difference being that once the reaction mix had cooled, one should do either of two things (1) distill as described except the bromosafrole will be the last thing to come over (not the first), or (2) flood the reaction mix with water to bring the product out of solution after which it can be physically separated by decanting or sep funnel or some such shit. 

Rearrangements do not normally occur which can mean either of two things Either carbocations are not intermediates or if they are they are captured by a nucleophile faster than they rearrange We shall see m Section 6 16 that the first of these is believed to be the case... 

The simple and complex distillation operations just described all have two things in common (1) both rectifying and stripping sections are providea so that a separation can be achieved between two components that are adjacent in volatility and (2) the separation is effected only by the addition and removal of energy and not by the addition of any mass separating agent (MSA) such as in liquid-liquid extraction. 

In order to understand the origin of material properties like Young s modulus, we need to focus on materials at the atomic level. Two things are especially important in influencing the modulus ... 

The structure of a metal is defined by two things. The first is the constitution ... 

The precipitates can obstruct the dislocations directly. But their effectiveness is limited by two things dislocations can either cut through the precipitates, or they can bow around them (Fig. 10.8). 

At about 2,000 hours, one of two things ean happen to eause failure to a lip seal. Hither the frietional heat from the spinning shaft burns and eooks the rubber lip, or the rubber lip eats a groove into the shaft. How ean a soft elastomeile rubber lip eut a groove into a stainless steel shaft ... 

Here Iq is the thermal conductivity of the system, consisting of the porous solid and the reacting fluid inside the pores. This is the most uncertain value, while everything else is measurable. Two things must be remembered. First, data on thermal conductivity of catalysts are approximate. The solid fraction of the catalyst (1-0) always reduces the possibility for diflhision, while the solid can contribute to the thermal conductivity. Second, the outside temperature difference normal to the surface or Daiv, will become too high, much before the inside gradient can cause a problem. See Hutching and Carberry (19), Carberry (20). 

Interest Expense - Investment in equipment implies that one of two things must occur Either a company must pay for the project out of its own cash, or it must finance the cost by borrowing money from a bank, by issuing bonds, or by some other means. When a firm pays for a project out of its own cash reserves, the action is sometimes called an opportunity cost. If you must borrow the cash, there is an interest charge associated with using someone else s money. It is important to recognize that interest is a true expense and must be treated, like insurance expense. 

While writing this book, the authors felt too hot in the hotel meeting room. Three authors opened the digital thermostat, studied the complex set of buttons, and were unable to make the room any cooler. When we asked a hotel employee, he pointed to the almost invisible switches on the bottom edge of the thermostat and said, First, you should turn this switch to ON, and second, you should turn this switch to COOL. This incident reminded us of two things about inherent safety (Norman, 1988). 

To give this appropriate consideration you will need to do two things define the requirements the product/service has to meet and define how these requirements are to be verified. 

The purpose of the requirements is to ensure that you have established the requirements you are obliged to meet before you commence work. This is one of the most important requirements of the standard. The majority of problems downstream can be traced either to a misunderstanding of customer requirements or insufficient attention being paid to the resources required to meet customer requirements. Get these two things right and you are halfway there to satisfying your customer needs and expectations. 

The standard does not in fact require follow-up audits but clearly if follow-up action is necessary to verify any corrective actions that have been taken, it should do two things verify that the agreed action has been taken and verify that the original nonconformity has been eliminated. Follow-up audits may be carried out immediately after the planned completion date of the corrective action or at some other agreed time. However, unless the audit is carried out relatively close to the agreed completion date, it will not be possible to ascertain if the action was timely. 

Formaldehyde also provides another excellent opportunity to compare the dipole moments computed via one-particle and Cl-Singles methods. In order to da so, r-null need to do two things ... 

The quality of a force field calculation depends on two things how appropriate is the mathematical form of the energy expression, and how accurate are the parameters. If elaborate forms for the individual interaction terms have been chosen, and a large number of experimental data is available for assigning the parameters, the results of a calculation may well be as good as those obtained from experiment, but at a fraction of the cost. This is the case for simple systems such as hydrocarbons. Even a force field with complicated functional forais for each of the energy contributions contains only a handful of parameters when carbon and hydrogen are the only atom types, and experimental data exist for hundreds of such compounds. The parameters can therefore... 

Here, as usual, the activity coefficient y takes into account two things ... 

We saw in the preceding chapter that the carbon-ha]ogen bond in an alkyl halide is polar and that the carbon atom is electron-poor. Thus, alkyl halides are electrophiles, and much of their chemistry involves polar reactions with nucleophiles and bases. Alkyl halides do one of two things when they react with a nucleophile/base, such as hydroxide ion either they undergo substitution of the X group by the nucleophile, or they undergo elimination of HX to yield an alkene. 

She said two things rapidly to the bartender I think I ll do white and What kind of Chardonnay She had her gold credit card down on the bar before the drink arrived. The tab was running. She looked at my unfinished drinks. 

The behavior of the strain softened material resembles the behavior of rubberlike polymers. For instance, the Poisson s ratio of an ideally plastic material is also close to 0.5 [94, 95], Proper understanding of crack propagation involves the microscopic level. Apparently, the load is transmitted by the molecular strands [97] from one crosslink to the next crosslink, exactly, as it is in rubberlike materials. However, two things are different in strain softened polymers as compared to rubberlike materials ... 

The difference between the SnI and Sn2 mechanisms is in the timing of the steps. In the SnI mechanism, first X leaves, then Y attacks. In the Sn2 case, the two things happen simultaneously. One could imagine a third possibility first the attack of Y, and then the removal of X. This is not possible at a saturated carbon, since it would mean more than eight electrons in the outer shell of carbon. However, this type of mechanism is possible and indeed occurs at other types of substrate (p. 424 Chapter 13). 

Re-orientation - What mnst 1 do 1 can do two things. Keep defects small, if I want to keep defects small 1 mnst start off with small particles. 

The above example shows that in designing difference schemes it is very desirable to reproduce the appropriate conservative law on a grid, The schemes with this property are said to be conservative. In subsequent sections the general method for constructing conservative schemes, which are convergent in the class of discontinuity coefficients, will be appreciated. Before we undertake the complete description of this method, it is worth noting two things. 

An accomplished architect once recommended a certain type of rubber tile for a laboratory floor because his data indicated its superior resistance to acids. He had not bothered to find out whether or not acid spills would be a problem in this case. They would not, in fact. Solvent spills, on the other hand, were quite likely to occur, and the recommended tile had poor solvent resistance. This example illustrates two things the importance of the laboratory operator s involvement with details that are sometimes overlooked even by experts, and the need to study each laboratory s requirements individually. 

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