Total order

Figure 5. Arrhenius-plot of three relaxation times involved in total ordering process. ( ) Xi, ( ) X2, atomic jump processes within domains (o) xj, change in domain size.

Cartoad tolerances shall not apply to orders less than a cartoad shipped from the mill. For any carload of pipe shipped from the mill to the final destination without transfer or removal from the car, the tolerance shall apply to each car. For any order consisting of more than a carload and shipped from the mill by rail, but not to the final destination in the rail cars loaded at the mill, the carload tolerances shall apply to the total order, but not to the individual carloads. 

Thus coefficients with an even total order I + m + n are real and coefficients with an odd total order I m + n are pure imaginary. In the following we consider only dipole hyperpolarizabilities. In this case the four operators A, B, C and D are cartesian components of the dipole operator and the odd dispersion coefficients vanish. 

From such reasoning it seems clear that scheme (22) provides an approximation of second total order in the negative norm. 

In an earlier series of experiments, Cullis and Ladbury examined the kinetics of the permanganate oxidation of hydrocarbons in acetic acid solution. Initial attack on toluene occurs at the methyl group and a total order of two was found. Electron-withdrawing agents reduced the rate of oxidation. However, the effects of added salts were complex and the authors believe that lower oxidation states of manganese are responsible for the oxidation. The oxidation of ethylbenzene produced acetophenone, the process being second-order with... 

Case II. The Orders with Respect to Each of the Constituents Are Different, but the Total Order (m + n) of Each Reaction Is the Same. 

Case III. The Total Order is Not the Same for Both Reactions. 

Note that the mean /i (8) has a proportional influence on the standard deviation of the total ordered amount. The tendency is intuitive The formula means that only a few large orders require more safety stock to cover random demand variations than many small orders. It is therefore a good idea to measure the mean and the variance of demands twice. First in the usual way as mean and variance of a sequence of, say weekly, figures and then by analyzing the orders of a historic period and applying Eq. (6.6). The comparison of the two results obtained often provides insight in the independence and the randomness of the historic demand. If the deviation of the two mean values and/or two variances is large then the demand can not be considered as a random sum. A reason could be, for example, that the demand... 

Figure 9.24 Many different total-ordered items.

What happens if you try to model a sorted list for something like project Tasks, which should not really be totally ordered based on must-precede The TotalOrdering properties would be imposed on Task, something that (1) is probably not what you intended, because it imposes a linear order on all tasks, and (2) could be inconsistent with the definitions of the must-precede operator itself. 

Banana is a Total Ordering with [< shorterThan], because... 

A thread is a totally ordered set of events, or a sequential trace of execution, that can run concurrently with other threads. A thread is conceptually orthogonal to an object,4 and its trace can involve the methods of many objects. Programming multithreaded systems is a tricky business, because you constantly must worry about the effects of concurrent activities specifically... 

You will probably find Time, Date, DateRange, and Duration to be useful types. In reality, we would write these as frameworks on any total-ordered type (T, Range(T), and Delta(T)). For more details, see www.catalysis.org. 

The Young operator Y in (1) antisymmetrizes with respect to permutations of sites in the same column in its tableau. The monomial yi, therefore, cannot be symmetrical with respect to any two sites in the same column, i.e., it cannot contain the same power of A for any two such sites. The powers of A for the sites in a given column, therefore, must all be different. The lowest possible choice consistent with this is that they be 0, 1, 2,. .., p, for a column of length /t. Thus, y can be chosen to be independent of A for sites in the first row of the tableau, and to contain A for sites in the second row, A2 for those in the third, etc. The total order is therefore... 

Determine the order with respect to A and B. Also find the total order of reaction and suggest rate law. 

Examples 21-25 are all for CO oxidation. A total order of one was reported for Example 23 the other four are first order in CO and zero order in oxygen. Evidently Step 1 or 6 for CO is a possibility in all cases, provided that the modifications discussed earlier are made where the log L values are too large. Kobal, Senegacnik, and Kobal (73) reported for Example 22 that their activation energy was anomalously large, since other values reported in the literature are in the 5-17 kcal mole range. If we arbitrarily change... 

A gas in which the pressure no longer depends on the temperature is said to be degenerate, an unfortunate term indeed, because the corresponding state borders on perfection. One might call it a state of perfect fullness, since no interstice is left vacant. Electrons occupy all possible energy states and total order prevails. Both the electrical conductivity and the fluidity also attain perfection. Objects made from this sublime form of matter are perfectly spherical. And yet, in quantum circles, this state of nature is obstinately referred to as degenerate ... 

What is the total order n of a given reaction What are the most common reaction orders in environmental organic chemistry Does the total order of a given reaction tell you anything about the reaction mechanism What is a pseudo-nth-order rate constant ... 

The concentration of each compound is raised to a power n, which is called the order of the reaction with respect to the considered reactant. The total order of the reaction is the sum of the orders for each reactant. 

We define a total ordering with vertex labels by the following rules. 

When N a is the over-all conversion rate per unit volume which depends on the concentration of the reactants according to Na = kanbm, then the total order of conversion is n + m, where n and m are the partial orders of conversion in the reactants A and B, respectively. In a continuous stirred tank reactor the concentration b is constant and the same throughout the reactor, and since we are only interested in the effect on the partial conversion order n we put /cbm = ku so that N a = ha in which a is the average concentration of A in the whole reactor. 

Note that the units of k depend on the total order of the reaction, not the way the total order is composed of the orders with respect to different reactants. 

---