### Table 1 actually illustrates two phenomena. First, our theoretical formula (9.3) works

"... In PAGE 37: ...derivation of the Boltzmann free time formulas based solely on the Liouville equilibrium distribution for nite systems of hard balls. Lastly, a little numerical experiment reported below in Table1 shows that the above formulas are fairly accurate for hard disks at low densities. The rst column shows the value of the product tpar computed according to (9.... In PAGE 44: ...2661 (Boltz.) (Enskog) (Enskog) (Enskog) Table1 . Theoretical and experimental values of tpar .... ..."

### Table 3: Number of theoretical work articles

"... In PAGE 7: ...5 (15%) Other descriptive issues 5 (15%) Total 33 (100%) Table3 shows the number of articles categorised as theoretical works. The majority of them (16 articles, 59%) refers to market modelling issues, followed by 33% (9 articles) denoting to the study of convergence and equilibrium properties.... ..."

### Table 7.1. Theoretical criteria for female choice of males ___________________________________________________________________ I. All species, but especially those showing little or no male parental investment

1972

### Table 1. What can be known Relationship between

"... In PAGE 7: ... Table1 : Comparison of the epistemological positions implied by the 2 approaches The work is significant because there has been little previous work comparing epistemological commitments of alternative ISD methologies as they are played out in actual application. We will next use the data to compare the ontological and action theoretic commitments of the methodologies.... ..."

### Table 2. Experimental (Moore 1971) and theoretical (this work) energies of even Kr II states.

### Table 3: Theoretical operators used in performance evaluation.

"... In PAGE 4: ... When applied in practice to real images however, the difference in performance was not found to be significant. The functional forms of the operators derived can be found in Table3 . Plots of these functions are shown in Figure 2.... In PAGE 12: ... We then compared the performance of these operators against four of the operators derived in the theoretical work. The operators used are shown in Table3 . This gives four sets of operators, the relative performances of which is then tested on out-of-sample data, drawn from the same image ensembles used to produce the training data.... ..."

### Table 1 Summary of related works

2005

"... In PAGE 4: ... Singh and Dey proposed the design of a customized document- filtering scheme using rough-set theoretic approach [35]. Table1 summarizes the related works. 3.... ..."

### Table 1: Simulated and theoretical coverage probabilities for mean.

"... In PAGE 5: ...2 de ned by [?] (Section 3.7). The coverage errors of the intervals IP , ISH and IABC are of order n?1, while all the other inter- vals have coverage error of order n?2. The cover- age errors are given explicitly in Table1 , for four underlying distributions. These expressions allow a comparison of the various intervals in terms of asymptotic coverage error.... In PAGE 6: ... In the con dence interval context, the bootstrap iteration device of Hall [?] amounts to making an additive adjustment, estimated by the bootstrap, to the end-points of the con dence in- terval, while the method of Beran [?] amounts to making an additive adjustment, also estimated by bootstrapping, to the nominal coverage level of the bootstrap interval. It is the latter method that is demonstrated in Section 5 above and that is con- sidered in the example of Table1 . Analysis of the asymptotic coverage error of intervals produced by the two methods of calibration points strongly in favour of the procedure which adjusts the nominal coverage, a conclusion that is again valid in a wide range of problems.... In PAGE 6: ... Equally, however, consideration of some of the explicit error expressions we derive from a re ned analysis should alert us to the reality that much of the theory of bootstrap and related methods for con dence inter- val construction is founded on an asymptotic the- ory, derived from Edgeworth expansion techniques, which is of little value in predicting the actual lev- els of coverage error obtainable in practice. To il- lustrate this point, we include in Table1 results of a simulation by which we estimated the cover- age properties of the various intervals, using 1600 random samples of sizes n = 15 and 30 drawn from each of the four distributions. The intervals IP were each constructed using 1000 (outer level) bootstrap samples.... ..."

### Table 1. Comparison of previous work and the situation theoretic approach. (? denotes lack of information regarding a particular issue, or an incomplete characterization.)

1997

"... In PAGE 11: ... Our formal model of context di ers from these in being stated in the framework of situation theory (Devlin 1991). The comparison of previous works and the situation theoretic approach is summarized in Table1 , where the rst row categorizes the language of formalization. Since our work is essentially an application of Barwise apos;s ideas (Barwise 1986), no attempt is made in Table 1 to add an extra column corresponding to our approach.... In PAGE 11: ... The comparison of previous works and the situation theoretic approach is summarized in Table 1, where the rst row categorizes the language of formalization. Since our work is essentially an application of Barwise apos;s ideas (Barwise 1986), no attempt is made in Table1 to add an extra column corresponding to our approach.... ..."

Cited by 12

### Table 1. Simulation vs. theoretical results In Table 1, Age_Ph is the physiological age of metamers, M_S and V_S are the statistical mean and variance of simulation, while M_Th and V_Th are the corresponding theoretical value. Despite the small set size, there is little shift between the two results. This means simulation with stochastic structure is good approximation. With set size increase, the simulation result converges to the theoretical value.

Cited by 1