### Table 6: Generating Function Computation of Tn(x)

1998

"... In PAGE 6: ... By Taylor apos;s theorem, one can there- fore compute Tn(x) as Tn(x) = F (n)(0) n! : In Maple this is given as ChebyshevT:=proc(n,x) local F,z,Dn; F:=(1-x*z)/(1-2*x*z+z^2); Dn:=diff(F,z$n); RETURN(subs(z=0,Dn)/n!) end: Note that other than the determinant approach the generating functions approach in principle is capable to calculate the polynomial system iteratively. Table6 gives the timings for the calculation of a single Tn(x) with this approach. REDUCE brings each iterated derivative of F (z) to a rational normal representation which is quite expensive.... ..."

### Table 6: Generating Function Computation of Tn(x)

1997

"... In PAGE 7: ...Table6 gives the timings for the calculation of a single Tn(x) with this approach. MuPAD apos;s derivatives of F (z) are unnecessarily complicated (this defect starts already with n = 2) which makes their computation for high n inaccessible in reasonable time and space.... In PAGE 7: ... Remembering everything is a typical Maple feature which frequently causes problems. In the current situation this e ect can be avoided by clearing the memory ourselves with the implementation ChebyshevT:=proc(n,x) local j,F,z; readlib(forget); F:=((1-z^2)/(1-2*x*z+z^2)+1)/2; for j from 1 to n do F:=diff(F,z); forget(diff); od; RETURN(subs(z=0,F)/n!) end: which generates the right-most timings in Table6 : These are worse than the original ones for small n, but much better for large n, and still better than Mathematica apos;s. The generating functions approach is little better than the determinant approach in com- puter algebra systems without rational normal representation, but still is quite ine cient.... ..."

Cited by 2

### Table 1: Rationality Principles for Some Selection Functions

1998

"... In PAGE 3: ...Table 1: Rationality Principles for Some Selection Functions 3 CENTER OF MASS VS. MAXIMUM ENTROPY Table1 lists a number of results on which selection func- tions satisfy the rationality principles listed in the previous section. For the time being, we are only concerned with the first two lines in the table, which list (for the most part well known) results about maximum entropy and center of mass.... ..."

Cited by 3

### Table 1: Rationality Principles for Some Selection Functions

"... In PAGE 3: ...Table 1: Rationality Principles for Some Selection Functions 3 CENTER OF MASS VS. MAXIMUM ENTROPY Table1 lists a number of results on which selection func- tions satisfy the rationality principles listed in the previous section. For the time being, we are only concerned with the first two lines in the table, which list (for the most part well known) results about maximum entropy and center of mass.... ..."

### Table 1: Sizes of generated functions

2003

"... In PAGE 5: ... 4.5 Memory Usage Table1 and Table 2 show the sizes of the generated functions and variables for the system shown in Figure 5. Note that the system contains one port.... ..."

Cited by 33

### Table 1: Sizes of generated functions

2003

"... In PAGE 5: ... 4.5 Memory Usage Table1 and Table 2 show the sizes of the generated functions and variables for the system shown in Figure 5. Note that the system contains one port.... ..."

Cited by 33

### Table 5: Approximate dynamic programming results for the cases of Table 4. ~ J denotes the revenue generated by the approximate policy. For Cases 4 and 5 it is computationally intractable to obtain the optimal static and dynamic policies.

2000

"... In PAGE 24: ... The computation of optimal static and dynamic prices becomes computationally prohibitive as the state space grows, thus, we will resort to the approximation methods outlined in Sections 8 and 9. In Table5 we report approximate dynamic programming results for a number of problems including some large-scale ones. We have used the approach outlined in item 2 of Section 9.... In PAGE 25: ...19 35000 3500 2.06 Table 4: The input parameters for the results of Table5 . We considered two-class systems with demand functions of the form i(ui) = 0;i ?ui 1;i and r1 = 4, r2 = 1, 1 = 1, 2 = 2.... In PAGE 26: ...Figure 4: Approximate dynamic prices for Case 3 of Table5 . Figures (a) and (b) depict prices for classes one and two, respectively.... ..."

Cited by 81

### Table 5: Approximate dynamic programming results for the cases of Table 4. ~ J denotes the revenue generated by the approximate policy. For Cases 4 and 5 it is computationally intractable to obtain the optimal static and dynamic policies.

2000

"... In PAGE 24: ... The computation of optimal static and dynamic prices becomes computationally prohibitive as the state space grows, thus, we will resort to the approximation methods outlined in Sections 8 and 9. In Table5 we report approximate dynamic programming results for a number of problems including some large-scale ones. We have used the approach outlined in item 2 of Section 9.... In PAGE 25: ...19 35000 3500 2.06 Table 4: The input parameters for the results of Table5 . We considered two-class systems with demand functions of the form i(ui) = 0;i ?ui 1;i and r1 = 4, r2 = 1, 1 = 1, 2 = 2.... In PAGE 26: ...Figure 4: Approximate dynamic prices for Case 3 of Table5 . Figures (a) and (b) depict prices for classes one and two, respectively.... ..."

Cited by 81

### Table 4. System dynamic inconsistency diagnosis report.

"... In PAGE 10: ...2 Dynamic inconsistency diagnosis by BITs In case a dynamic inconsistency is detected, source and type of the inconsistency can be diagnosed and allocated based on the dynamic inconsistency detection report shown in the form of Table 3. An example diagnosis report for tracing the dynamic inconsistency is shown in Table4 . By this approach, detailed dynamic inconsistency can be allocated by the corresponding BITs at run-time.... In PAGE 11: ........ Subsystemk The diagnosis result shows the accurate sources and reasons of system dynamic inconsistency. Observing Table4 it can be found that one subsystem, two classes, five objects and seven functions have been allocated for a specific or hybrid dynamic inconsistency. 3.... ..."

### Table 1. Two Modes of Thinking. Comparison of the Experiential and Rational Systems Experiential System Rational System

"... In PAGE 4: ... (p. 710) Table1 , adapted from Epstein, compares these two systems. One of the characteristics of the experiential system is its affective basis.... ..."