Order meaning

First-order means that we consider nothing beyond that described here. In second-order , we would include the effects of mixing between ground and excited states brought about by the magnetic field. This is briefly discussed under second-order Zeeman effects later. 

The 1 means we are asking for information on the first of the four papers. The papers are listed in reverse chronological order, meaning paper 1 will be the latest of the four. Similarly, we can ask to see the information on any of the others. 

They were also typical when the regression model chosen was first order. Mean-level bandwidths greater than 20-30% are probably indicative that errors have been made in the analysis process that should not be tolerated. In this case techniques would be carefully scrutinized to find errors, outliers, or changing chromatographic conditions. These should be remedied and the analysis repeated whenever possible. Certain manipulation can be done to reduce the bandwidth values. For example, they would be... 

Notice that "stereoselectivity" means "order" and order means "negative entropy" which, in turn, means "rigidity", "lack of flexibility" or "absence of degrees of freedom". It is always easier to exert stereochemical control in rigid monocyclic or polycyclic systems than in the more flexible open-chain compounds (remember the limitations imposed by Corey s rule number 6 see 7.2.1). 

Term Order Mean deviation Mean deviation of zeroes... 

The refers to a nucleophilic substitution process where some nucleophile attacks an electrophile and substitutes for some part of the electrophile. The E refers to an elimination process where the nucleophile attacks an electrophile and causes the elimination of something. The 1 and 2 refer to the order of the reaction. A 1 (first order) means only one molecule determines the rate of the reaction, whereas a 2 (second order) means that a combination of two molecules determines the rate of the reaction. In many cases, two or more of these mechanisms are competing and more than one product may result. 

One way to rationalize and remember the rule is to think that "nature is lazy" and hence would like to accomplish a process with the least effort. Because ions and molecules in a liquid are more or less randomly distributed, one may guess that the phases with simple structure and with low degree of order (meaning ions and molecules do not have to be arranged in a specific way) tend to form more easily than the phases with complicated structure and high degree of order. This often means the formation of metastable phases such as opal. 

A full three factorial matrix on the 11 variables in the cure cycle shown in Figure 15.1 would mean 177,147 individual trials. A full two factorial design would still mean 2048 trials. Such a design, however, assumes that all interactions, even between all 11 variables, will be important. DOE provides an ordered means of combining variables to reduce the total number of trials. The assumption made is that high-order interactions (i.e., interactions of three or more variables) are rare and/or insignificant. There are several methods for combining variables by DOE. A detailed discussion of these methods is the subject of another book [9]. 

They are continuous at /c>0, but their derivatives with respect to k become infinite at ->0 (see Fig. 5). Thus p.m. is valid in this case only to the 0-th order (p.m. of the 0-th order means continuity of eigenvalues, see below). 

Altitude Response. Pressure response is an issue that needs to be addressed for every instrument deployed on an aircraft. First, it must be decided how chemical abundances are to be reported. If standard practice is followed and they are reported as mixing ratios, then it must be determined whether the instrument is fundamentally a mass- or a concentration-depen-dent sensor, because this definition determines the first-order means by which instrument response is converted to mixing ratios as a function of pressure. In this context, a mass-sensitive detector is a device with an output signal that is a function of the mass flow of analyte molecules a concentration-sensitive detector is one in which the response is proportional to the absolute concentration, that is, molecules per cubic centimeter. 

The reference state is the composition-weighted linear combination of pure A and B components. This approximation neglects vibrational entropy. Higher-order mean-field approximations to configurational entropy, known as the cluster-variation method, are known [5, 6]. 

The phase equilibria data for hydrates with inhibitors are presented below. As in previous results, data plots are provided for those systems which have been considered by more than one investigation, as a first order means of data evaluation. Individual investigators usually include plots of their data in the original reference. Unless otherwise indicated the mass concentration of the inhibitor in the aqueous phase is included in the column marked wt%, hydrocarbon/CC>2/H2S/N2 concentrations are mol% in vapor unless otherwise indicated. 

Let us now consider the problem from the standpoint of calcite precipitation kinetics. At saturation states encountered in most natural waters, the calcite reaction rate is controlled by surface reaction kinetics, not diffusion. In a relatively chemically pure system the rate of precipitation can be approximated by a third order reaction with respect to disequilibrium [( 2-l)3, see Chapter 2]. This high order means that the change in reaction rate is not simply proportional to the extent of disequilibrium. For example, if a water is initially in equilibrium with aragonite ( 2c=1.5) when it enters a rock body, and is close to equilibrium with respect to calcite ( 2C = 1.01), when it exits, the difference in precipitation rates between the two points will be over a factor of 100,000 The extent of cement or porosity formation across the length of the carbonate rock body will directly reflect these... 

The variable k represents the rate constant. Note the order of each reactant is 1. The reaction order, which describes the order of the entire reaction, can be determined by adding the order of each reactant. For instance, in this example each reactant is first order (meaning each has an understood exponent of 1). The reaction order is the sum of the exponents, or 1 + 1=2. This is a second-order reaction. Most reactions have an order of 0, 1, or 2, but some have fractional orders or larger numbers (though these are quite rare). The order of the reaction must be determined experimentally. Unlike equilibrium expressions, the exponents have nothing to do with the coefficients in the balanced equations. 

Second order means that two atoms or molecules have to collide so that the reaction will happen. Obviously, if the concentration of one or both of the reactants is low, the reaction will be slow. Thus, the rate of the reaction is proportional to the concentration of both reactants times each other, and the proportionality constant is the rate constant k. 

Second harmonic generation, described in this chapter, is an example of a second-order process. What does second-order mean in this context What are examples of a first-order (or linear) process ... 

What do the terms closely coupled and second order mean in terms of spin states ... 

When your subject is a physical object, you should select some orderly means of describing it from left to right, top to bottom, inside to outside, and so forth. For example, you might describe a sculpture as you walk around it from front to back. Below is a paragraph describing a cowboy in which the writer has ordered the details of his description in a head-to-feet pattern. 

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