### Table 7. Decomposing the Predicted Variation of Monthly Portfolio Returns by Economic Risk Variables, 1983:1 to 1995:9 (153 observations). Decile 1 (Q1) represents the returns on the decile of the smallest capitalization of firms on the NYSE, Amex and Nasdaq exchanges. The figures represent the proportions of the sample variances of the predicted returns using a multifactor asset pricing model conditional on a set of instrumental variables, which are allocated to different sources of predictable variation. Interaction effects reflect that the total predictable variation in the five economic risk variables is different than sum of the predictable variation due to each of the variables individually.

1998

"... In PAGE 15: ... D. Decomposing Predictable Variation by Economic Risk Variables In Table7 , we examine the extent to which each of the economic risk variables individually explains the predictable variation in asset returns. Not surprisingly, the market risk premium XVW explains a considerable amount of the predictable variation in the CRSP size portfolios (Q1-Q10).... ..."

Cited by 4

### Table 8. Decomposing the Predicted Variation of Monthly Portfolio Returns by Changes in Betas versus Changes in Prices of Beta Risks, 1983:1 to 1995:9 (153 observations). Decile 1 (Q1) represents the returns on the decile of the smallest capitalization of firms on the NYSE, Amex and Nasdaq exchanges. The figures represent the proportions of the sample variances of the predicted returns using a multifactor asset pricing model conditional on a set of instrumental variables, which are allocated to different sources of predictable variation. Interaction effects reflect that the total predictable variation in the five economic risk variables is different than sum of the predictable variation due to each of the variables individually.

1998

"... In PAGE 15: ... E. Decomposing Predictable Variation by Changes in Beta and the Price of Beta Risk Table8 presents the decomposition of predictable variation of asset returns by 1) changing betas or 2) changing prices of risk. The results indicate that the variation due to 3The property capitalization index used by Liu and Mei (1992) is not available on a monthly basis from the American Council of Life Insurance Companies in their publications.... ..."

Cited by 4

### Table 5: Sequences of I(10) AUGC folding into the same secondary structure are decomposed into mutationally connected components using single base exchanges and base pair sub- stitutions as variation operators.

2005

"... In PAGE 67: ... The fact, that the highest ranking structures of I(10) AUGC occur with almost the same frequency, is in agreement with the results obtained from large samples derived by folding random sequences of fixed chain length [7, 22, 73]. Table5 shows the decomposition of I(10) AUGC into Gl k components. The three largest structure components are connected networks.... ..."

### Table 8: Decomposing the Welfare Effects of Free Trade in Turkey The effect of income shares and consumption shares. Welfare effects are Hicksian Equivalent Variation as a percent of benchmark household income.

2003

"... In PAGE 2: ...able 7: Impact of Free Trade on Output by Sector ................................. -34- Table8 : Decomposing the Welfare Effects of Free Trade in Turkey .... In PAGE 13: ... An important step in that process is to determine if it is changes in factor prices or goods prices that is the source of the adverse impact on the poor. We use the data in Table8 for that purpose. If all households were identical in their income and expenditure patterns, then Hicksian equivalent variation as a percentage of benchmark income would be identical for all households.... In PAGE 13: ... The model would then essentially be equivalent to a single household model. We counterfactually impose identical consumption shares for all household and indentical factor endowment shares and present the results of that simulation in the three columns on the far right of Table8 . The result is that all households realize a welfare gain of 0.... ..."

Cited by 1

### Table 1: Sequences of I(9) AUGC folding into the same secondary structure Sk are decomposed into mutationally connected structure components Gl k using single base exchanges dh = 1 and base pair substitutions dc = 1 as variation operators.

2005

"... In PAGE 58: ... We call the connected components of Gk, Gl k, where Gk = uniontext l Gl k and Gl k is connected. Table1 shows the results of the decomposition of I(9) AUGC in Gl k components. Table 1: Sequences of I(9) AUGC folding into the same secondary structure Sk are decomposed into mutationally connected structure components Gl k using single base exchanges dh = 1 and base pair substitutions dc = 1 as variation operators.... ..."

### Table 1. Syntactic variation for Decl with the equivalent primitive form.

1999

"... In PAGE 6: ...3 Problem Introduction A Declare proof begins with the statement of a problem, introduced using some variant of the thm declaration. The example from the previous section uses the one shown in Table1 . This variant allows us to begin our proof in a conveniently decomposed form, i.... ..."

Cited by 7

### Table 4: Statistics of the decomposable problems.

"... In PAGE 13: ... We solve three real-life medium-scale block-angular linear programs: MARKAL, MACHINES and ENERGY-S. The statistics and the origin of these problems are given in Table4 in Section 5.2.... In PAGE 15: ... We repeated the same experiment for a set of real decomposable linear programs with the number of subproblems varying from 3 to 16. The statistics of these problems are collected in Table4 .... In PAGE 16: ... ENERGY-S is the energy planning problem developed at IIASA [24]. Table 5 reports the results of the solution of all problems from Table4 with two variants of ACCPM: the method with exact subgradients and the method with quot;-subgradients. For both variants of the decomposition, we report: the number of outer iterations, the number of inner iterations in ACCPM and the total number of IPM iterations required to reach the quot;-optimal... ..."

### Table 4: Statistics of the decomposable problems.

1997

"... In PAGE 13: ... We solve three real-life medium-scale block-angular linear programs: MARKAL, MACHINES and ENERGY-S. The statistics and the origin of these problems are given in Table4 in Section 5.2.... In PAGE 16: ... We repeated the same experiment for a set of real decomposable linear programs with the number of subproblems varying from 3 to 16. The statistics of these problems are collected in Table4 .... In PAGE 16: ... ENERGY-S is the energy planning problem developed at IIASA #5B24#5D. Table 5 reports the results of the solution of all problems from Table4 with twovariants of ACCPM: the method with exact subgradients and the method with quot;-subgradients. For both variants of the decomposition, we report: the number of outer iterations, the number of inner iterations in ACCPM and the total number of IPM iterations required to reach the quot;-optimal solutions in all p subproblems.... ..."

### Table I. A decomposable matrix

### Table 5: Decision Analysis Spreadsheet: Example 2

in Contents

2006

"... In PAGE 18: ... Table5 . Each subgroup is further decomposed one level further and weights are assigned.... In PAGE 18: ... The score for this variation differs slightly in that the final score for the subgroup is calculated by multiplying the total weighted score for each of the subcriteria by the total weighted value for the subgroup. In the example shown in Table5 , the subgroup weight is 20%, and the weighted value for System 1 is 18% (90% of 20%). The key to this variation is not to overly decompose the requirements.... ..."